WSPR Tracking Validator Now Believes Testing Was Not Scientific

From “FALLACY: CHERRY PICKING DATA” by Alan Brooks, Jan 2019

In the last blog article, I explained in simple technical terms why WSPR data cannot be used to track aircraft over long distances, and certainly cannot be used to reconstruct the flight path of MH370. The article concluded:

At long distances and at low transmission powers, the received signals from hypothetical aircraft scatter are simply too weak by many orders of magnitude. What is claimed to be discernable “anomalies” in signal strength attributable to forward scatter by aircraft are within the expected deviations in signal strength for long distance skywave propagation involving refraction off the ionosphere. Although aircraft scatter could be detected if the aircraft were close to either the transmitter or receiver and if the transmitted power were sufficiently strong, the detection of the aircraft requires signal processing to separate the Doppler-shifted scattered signal from the much stronger direct signal, and this data is not available in the WSPR database.

Since publishing that article, even more evidence supporting these conclusions was presented by me and other contributors in 667 blog comments, which include analyses of experimental data of HF scatter off of aircraft, and statistical analyses of the WSPR-tracking claims. I considered writing a new blog article with the updated results, but reasoned that the informed already understood that WSPR-tracking was junk science, the uninformed wouldn’t appreciate the significance of the new results, and the WSPR proponents were too dug in to do anything but continue to double down on their flawed theory.

A question often asked is “How were aircraft successfully tracked in validation tests?” Those that have studied the tests respond that the tests were not scientifically rigorous, and the positive results simply reflect the biases of the WSPR proponents, i.e., the data were cherry-picked to support the claims that historical WSPR data could be used to track aircraft.

One of the participants in the validation tests was Mike Glynn, who was an airline captain for Qantas. Mike has commented on the blog that he now agrees that the validation tests he helped conduct were not scientific. I repeat his comment below in its entirety and without edits:

Having just read this thread it’s appropriate that I comment on a couple of things.

My involvement with RG goes back to learning that he was after an appropriate flight to test his method of detecting aircraft via WSPR. I was in possession of a candidate plan, which happened to be my final flight in Qantas, although I was not aware of that fact at the time.

The flight was a ferry of a 747 with an oil leak in the number 4 engine which could not be repaired in Johannesburg and had to be flown, empty, to Sydney.

I had experience in post-maintenance air-tests in the 747 and this was considered desirable by QF.

The flight was planned overhead Perth and Adelaide then direct to Sydney, and due to the unusual routing, I thought it may have been a suitable candidate for a test of WSPR.

The kick in the tail was that we only got as far as Perth due to the oil leak accelerating during the flight and we diverted to Perth and landed with the engine still running, with the oil quantity indication bouncing off zero, but still with sufficient oil pressure to keep the EICAS quiet.

So, I contacted RG and the test went ahead. The test was not a success. RG initially appeared to be tracking the aircraft till it crossed the African coast, although there was a cross-track error of 20NM or so. He eventually reported that the aircraft had landed in Melbourne.

This was obviously incorrect, but he had been making some wrong assumptions regarding the aircraft type, weight and tracking and so we decided on another test which was a flight plan of a QFA330 from Apia to Adelaide.

I supplied RG with the details of the flight including weight, type and time of departure. We had done a search of most flight-trackers and the flight was not on the sites we checked. Only after the analysis was complete did we find a site which had the flight recorded; however, I do not believe RG found and used this site.

An informational error on my part at the beginning of the plan meant RG turned the aircraft the shortest way towards Australia (to the Right) after take-off, however there is a procedure for departures on RWY 08 at APIA to turn left due to terrain. RG had stated that WSPR does not supply a direction of turns so I accepted the error at the start of the plan due to the incorrect turn.

After a couple of days RG informed me that the flight was tracking to Brisbane.

We were preparing to stop the test at that point but the following day he stated that the aircraft was tracking to Sydney and the following day he stated that the aircraft had flown to Adelaide from overhead Sydney and landed there.

This was correct; however, no documentation was given to me to substantiate how he had arrived at this conclusion.

Considering the process so far, I wanted to do another test and had another one, an A380 flight from Sydney to an Asian port, ready to go.

RG declined another test as he wanted to start on the MH370 analysis. I wasn’t happy with this, but it was his decision.

However, my opinion remains that the test process was not scientific.

When RG produced his MH370 analysis it made little sense to me as an airline pilot. The track to the north of Sumatra is very irregular and I found it difficult to reconcile it to anything an airliner would fly.

I had not heard of the “loiter” hypothesis either, so the holding pattern was new to me.

I asked RG whether he had considered the weather in the area in his analysis and he said he hadn’t. Despite comments made about the weather analysis on this thread, the results make sense to me as an airline pilot, particularly the diversion away from the thunderstorms off the south coast of Sumatra.

Recently, however, I have revisited the WSPR track analysis. My knowledge of the characteristics and limitations of WSPR is basic, and I simply don’t have the appropriate background to comment on that with any authority.

However, as a former RAAF pilot, I was trained in the principles of radio navigation and off-airways navigation. Andrew Banks arrived at my squadron just as I was leaving and was trained in the same techniques.

In my opinion, the methodology used in the construction of the WSPR track does not conform to any known principles of aircraft navigation that I am aware of.

It is arbitrary in the extreme and, I believe, constructed only to satisfy the constraints of the only solid data available, the BTO and BFO data.

I realise now that I should have looked at this earlier. and avoided looking as if the construction of this track makes any sense from an aviation POV.

Thats my error.

I will be explaining why I believe this in due course.

Thank you for your time and understanding.


Perhaps this is a positive step towards a more scientific discussion of the flaws in using historical WSPR data to track aircraft.

Posted in Aviation | 133 Comments »

WSPR Can’t Find MH370

Screenshot from WSPR software as developed by Joe Taylor (K1JT)

“I do not believe that historical data from the WSPR network can provide any information useful for aircraft tracking.”

Prof. Joe Taylor (K1JT), Nobel Prize in Physics, Inventor of WSPR

Despite many stories in the media repeating claims that historical WSPR data can be used to track MH370, there are many reasons why these claims are patently false. There is broad agreement among acknowledgeable researchers that have investigated these claims, and a handful of these researchers have documented their concerns. For instance, amateur radio enthusiast Hayden Haywood (VK7HH) has created a video explaining why, in simple terms, WSPR can’t track airplanes. MH370 investigator Steve Kent published a paper that formally treats skywave propagation and scatter off airplanes, and concludes there is insufficient signal strength (by many orders of magnitude) for WSPR to detect aircraft over long distances. In fact, even WSPR creator Joe Taylor (K1JT), who won a Nobel prize in physics for his research on pulsars and gravity, told fellow MH370 Independent Group (IG) member Mike Exner, “I do not believe that historical data from the WSPR network can provide any information useful for aircraft tracking.”

WSPR Background

WSPR (pronounced “whisper”) is an acronym for “Weak Signal Propagation Reporter”. Amateur radio stations implementing WSPR send and receive messages using low-power transmissions to test propagation paths on the Low Frequency (LF), Medium Frequency (MF), High Frequency (HF), and Very High Frequency (VHF) amateur radio bands. When a participating station successfully decodes the transmission transmitted by another participating station, it sends that information to a central database, and that information is available to the public for retrieval. For each 110-second contact between stations (“spots”), the available information includes station call signs, locations, transmitted power, and three parameters discriminated by the receiver: signal-to-noise ratio (S/N), frequency, and frequency drift. The proposed theory is that recorded deviations (“anomalies”) in the (S/N) and the frequency shifts/drifts are related to radio wave interactions with aircraft some thousands of kilometers distant from either amateur radio station.

The theory behind using bi-static radar (i.e., transmitter and receiver in different locations) for aircraft detection and tracking is well-known, and books (e.g., this) have been written on this subject. A special case is when an aircraft crosses the “baseline” between transmitter and receiver, resulting in a “forward scattered” signal caused by the diffraction around the silhouette (projected area) of the aircraft. The Forward Scatter Radar Cross Section (FSRCS) is typically much larger than the RCS that conventional mono-static radar uses to detect targets. It is this forward scattered signal that is of interest here in evaluating whether WSPR signals can be used to reconstruct the path of MH370.

In this article we apply the well-developed theory of bi-static radar to demonstrate that WSPR signals cannot be used to detect MH370 in the manner claimed in this paper. The relevant equations are presented in the Appendix, and the inputs and the calculational results for the test cases can be found in the accompanying table in the Appendix.

Detection of MH370 Before Radar Coverage Was Lost

We consider the claim that the WSPR data shows that MH370 was detected on the night of the disappearance at 17:16 UTC when it was still under radar coverage as it flew over the Gulf of Thailand towards waypoint IGARI, before the turnback, at FL350 (37,200 ft). At that time, a WSPR transmission from a station in Switzerland (HB9CZF) was received by an Australian station near Canberra (VK1CH) over a distance of 16,527 km on 14.097 MHz at a transmitted power of 1 W. The distance from the Swiss transmitter to the aircraft was 9,868 km and the distance from the aircraft to the receiver was 6,660 km, as depicted in this figure from the paper:

Although WSPR contacts greater than 16,000 km are rare, this spot shows they can indeed occur. Based on the distance between the stations, the transmission from Switzerland reached the Australian station via skywave propagation in which the radio waves were refracted off the ionosphere and reflected off the Earth’s surface (“hops”) about 5 times.

WSPR Signals Forward Scattered from an Aircraft Would be Undetectable at Long Distances

The column labeled “Case 1” from table in the Appendix shows the inputs and the calculational results for this scenario. Assuming that the propagation loss is the same as for free-space propagation, the expected strength of the direct signal at the receiver is -110 dBm, which is about the same value claimed in the paper when considering hops between the ionosphere and the Earth’s surface. This suggests that the refraction and reflection losses were either calculated to be very small, or were neglected.

At 14.097 MHz, the wavelength is 21.3 m, and the FSRCS for the B777-200ER for waves directly incident to the top or bottom is estimated to be 18,791 m2, or about 23 times the projected area. The forward scattered signal at the receiver is estimated to be -210 dBm, or about 100 dB (10 orders of magnitude) weaker than the direct signal. Can a signal of this strength be detected and decoded by the WSPR software?

Whether the signal could be detected by the radio and decoded by the software depends on the achievable noise level, as a minimum signal-to-noise ratio (S/N) of around -30 db is required by the WSPR software, where the noise level is referenced to a bandwidth of 2.5 kHz. I ran some simple experiments on my Flex 6400 amateur radio to measure the achievable noise level on the 20-meter band at my home in suburban Roanoke, Virginia. At 10:30 am on December 19, 2021, on a quiet part of the band, when connected to a horizontal resonant antenna, and after setting the bandwidth to 2.5 kHz, I measured a noise floor of -102 dBm. This largely consists of manmade and natural noise received at the antenna. To determine the sensitivity of the radio independent of the environmental noise, I disconnected the antenna and connected the radio to a resistive dummy load of 50 ohms. The noise level dropped to -105 dBm. By using the radio’s built-in pre-amplifier configured for its maximum gain of 32 dB, the noise level further dropped to -129 dBm. (Pre-amplification improves sensitivity but increases the distortion from strong signals, and so must be used judiciously.) Even though this noise level would be very difficult to achieve under real conditions, I used this noise level as the reference for calculating (S/N) values on 20 meters.

So, for the forward scattered signal strength of -210 dBm, the (S/N) would be (-210 – -129) = -81 dB. This is 51 dB weaker than WSPR requires (-30 dB), i.e., the forward scattered signal is 5 orders of magnitude too weak to be detected and decoded by WSPR! Considering the very favorable assumptions we made regarding propagation loss, incident angle, and noise floor, we can be quite confident that the WSPR signal originating in Switzerland at 17:16 UTC did not interact with MH370 in any way that was detectable in Australia, as was claimed.

WSPR Signals Forward Scattered by an Aircraft Would Be Masked by the Stronger Direct Signal

Assuming the skywave propagation loss was equal to the free-space propagation loss, the WSPR signals originating in Switzerland and forward scattered by MH370 over the Gulf of Thailand would be received in Australia with a strength of around -210 dBm. However, the direct radio waves that did not interact with the aircraft would be received with a strength of around -110 dBm. That means that the direct signal strength would be about (-110 – -210) = 100 db (10 orders of magnitude!) stronger than the scattered signal. Under these circumstances, the combined signal (direct plus forward scattered) would be absolutely indistinguishable from the direct signal, even if above the noise level (which it was not).

However, the equations presented in Appendix A predict that it IS possible for radio waves to forward scatter from an aircraft and be detected under the right conditions. For example, Joki et al. studied how broadcast TV transmissions at around 50 MHz may be passively used to detect, identify, and track airliners over a distance of hundreds of kilometers. Some of the factors that determine whether the aircraft could be detected include:

  • The projected area of the aircraft
  • Strength of the direct signal received, i.e., high power transmitters near the receiver increase the signal strength
  • The distance of the aircraft to the receiver, i.e., the proximity of the aircraft increases the strength of the forward scattered signal
  • The frequency of the transmission, higher frequencies increase the FSRCS and therefore the strength of the forward scattered signal
  • Frequency-based signal processing to separate the direct signal from the Doppler-shifted forward scattered signal

Recently, amateur radio operator Nils Schiffhauer (DK8OK) claims to have observed aircraft scatter by analyzing the signal from an AM broadcast of China Radio International (CRI), which operates on 17.530 MHz with a 250 kW carrier, and uses a beam antenna with a gain of 25 dBi towards Europe. Nils’ location is near Hannover Airport in Germany, some 7,600 km away from the CRI transmitter in Xianyang, China. The figure below depicts a “waterfall” plot showing aircraft scatter over a period of 3 hours. The Doppler-shifted signals from many aircraft are clearly visible in the lower sideband (LSB), some 5 to 20 Hz below the carrier frequency.

Waterfall plot of CRI broadcast on 17.530 MHz as received by Nils Shiffhauer DK8OK in Germany over a period of about 3 hours. Evidence of aircraft scatter can be clearly seen mostly in the lower side band (LSB).

After processing the data from a 1-hour measurement, Nils calculated that the carrier strength was -59.1 dBm, the average Doppler signal strength was -105.9 dBm, and the average noise level was -108 dBm.

I was curious if the forward scatter equations in Appendix A would produce calculational results consistent with Nils’ measurements. After using FlightRadar24 to observe flights passing near his residence, I estimated that planes landing on Hannover Airport’s Runway 27R would generally pass within a lateral distance of about 2 km and about 0.85 km (2800 ft) above his residence, which is a slant range of about 2.2 km . A good number of those airplanes were B737s, which I used to calculate the FSRCS. The inputs and the results from the calculations are shown in the column labeled “Case 2” from the table in Appendix.

We know the location, power, and antenna gain of the transmitter, and since we know the received strength of the carrier was -59 dBm, we can calculate the additional propagational loss of the skywave path due to refractions from the ionosphere and reflections from the Earth’s surface, which we estimate to be around -33 dB. The signal strength of the aircraft scatter is then calculated to be around -102 dBm, which is only 4 dB stronger than the measured value of -106 dBm. Considering that the value of FSRCS is assumed to be in the most favorable direction, the measured strength of the aircraft scatter is entirely consistent with the calculated value.

Nils concludes that since the signal from the aircraft scatter is 47 dB below the carrier, it would be impossible to look at the combined signal (which is all that is available in the WSPR database) and determine the contribution of the aircraft scatter. We strongly agree.

WSPR Signal Deviations are Not Related to Aircraft

Based on the extremely small signal generated by a hypothetical interaction with MH370 at 17:16 UTC, there can be little doubt that at that time, the WSPR database did not record a spot between Swiss and Australian stations consistent with forward scatter from the aircraft.

Yet it’s claimed that there was a detectable deviation in the recorded (S/N) values between the Swiss and Australian stations that is indicative of forward scatter from MH370. To evaluate this claim, Mike Exner and Bobby Ulich produced the following graph which shows the (S/N) for all WSPR contacts between the Swiss (HB9CZF) and Australian (VK1CH) stations over an time interval of around 16 hours. The particular (red) spot deemed as “anomalous” clearly shows no greater deviation from the trend than any other spot. What is claimed to be “anomalous” is within the scatter range of the other points. The dynamic characteristic of the ionosphere is all that is needed to explain these deviations.

To further demonstrate that there is nothing anomalous about the spot at 17:16 UTC, Mike and Bobby produced the following graphs which show that the reported values of frequency and frequency drift at 17:16 UTC are in no way anomalous to the other values recorded on that day for HB9CZF-VK1CH WSPR contacts.


This article attempts to lay out in simple technical terms why WSPR data cannot be used to track aircraft over long distances, and certainly cannot be used to reconstruct the flight path of MH370. At long distances and at low transmission powers, the received signals from hypothetical aircraft scatter are simply too weak by many orders of magnitude. What is claimed to be discernable “anomalies” in signal strength attributable to forward scatter by aircraft are within the expected deviations in signal strength for long distance skywave propagation involving refraction off the ionosphere. Although aircraft scatter could be detected if the aircraft were close to either the transmitter or receiver and if the transmitted power were sufficiently strong, the detection of the aircraft requires signal processing to separate the Doppler-shifted scattered signal from the much stronger direct signal, and this data is not available in the WSPR database.


This article benefited from many private communications with Mike Exner, Don Thompson, Bobby Ulich, Steve Kent, Nils Schiffhauer, John Moore, and Ed Anderson. I also acknowledge the many insightful blog comments from Mick Gilbert, Sid Bennett, and @George G.

Update on December 22, 2021

I asked Joe Taylor for a comment on the material covered in this article. Here was his response, shared with his permission:

As I’ve written several times before, it’s crazy to think that historical WSPR data could be used to track the course of ill-fated flight MH370. Or, for that matter, any other aircraft flight…

I don’t choose to waste my time arguing with pseudo-scientists who don’t understand what they are doing.

Appendix: Equations and Table of Results

where the variable definitions and the inputs and results for the two cases can be found in the table below:

Reference: Passive Radar Technology, Prof. Christopher Baker, University of Birmingham, NATO STO-EN-243-02.

Posted in Aviation | 668 Comments »

Italian Satellite May Have Detected MH370 Floating Debris

A source has disclosed that an Italian satellite that is part of the COSMO-SkyMed constellation detected three floating objects on March 21, 2014, near where MH370 is believed to have crashed in the Southern Indian Ocean on March 8, 2014. This information was never publicly released.

The three floating objects were detected at 34.9519°S, 91.6833°E; 34.5742°S, 91.8689°E; and 34.7469°S, 92.1725°E.

COSMO-SkyMed Satellite

The detections are significant because we know that a French satellite that is part of the Pleiades constellation detected what appears to be man-made floating debris on March 23, 2014, only 35 NM from where the Italian satellite had detected floating debris two days earlier. The French Military Intelligence Service shared four proximate images from Pleiades 1A with Geoscience Australia (GA) in March 2017, which then performed detailed analyses and determined that a cluster of nine objects that are probably man-made appear in one of the images near 34.5°S, 91.3°E. Australia’s Commonwealth Scientific and Industrial Research Organisation (CSIRO) then used this position information along with advanced ocean drift models to calculate the most likely point of impact (POI) to be 35.6°S, 92.8°E.

There is no definitive proof that either satellite detected floating debris from MH370. Our source also could not definitively state that there were no other floating objects detected near the 7th arc by these two satellites. However, the source believes that if there were other objects detected, they would have been shared with the MH370 search team.

The two satellites used different physical principles for detecting floating objects. The Pleiades satellite used optical sensors to capture images in multiple bands of color to achieve a pixel size of 0.5 m x 0.5 m. On the other hand, the COSMO-SkyMed satellites use Synthetic Aperture Radar (SAR) sensors to continuously scan the earth’s surface. Unfortunately, COSMO only obtained a wide-angle, low-resolution capture of the objects. On a subsequent satellite pass, attempts to capture the objects at high resolution were not successful.

Prior to 2014, researchers had already investigated using satellite SAR data to detect floating debris. For instance, in 2011, using SAR data from the crash of Air France 447 off the coast of Brazil in 2009, researchers presented a numerical method for processing the SAR data from COSMO-SkyMed to detect floating metallic objects. (HT Don Thompson.) Likely, those who have analyzed the COSMO data from March 2014 would know if the detected objects are metallic.

To determine if the objects detected by Pleiades and COSMO-SkyMed were from a common source, we used the results of a complex drift model (BRAN2015) developed by CSIRO and shared by oceanographer David Griffin. The results include the trajectories of 86,400 virtual drifters, representative of generic debris sitting flat on the surface. The virtual drifters start along the 7th arc on March 8, 2014, between latitudes 8°S and 44°S, and the trajectories are tracked for 1000 days. Our method was to find the two virtual drifters that best match the position and timing of the detections from the the two satellites. If those two virtual drifters started from nearby locations on March 8, likely the objects detected by the satellites came from a common source.

The results from the drift analysis are shown in the figure below. The yellow circles show the path of the virtual drifter that passed closest to the COSMO objects on March 21. The red circles show the path of the virtual drifter that passed closest to the Pleiades objects on March 23. These two virtual drifters start within 3.5 NM of each other on March 8, near to 35.4°S, 92.8°E. The proximity of the starting positions is consistent with a common source for the objects detected by the two satellites. That position is about 83 NM to the southwest of where a previous study estimated that MH370 crossed the 7th arc, and within the 140 NM radius recommended to search.

Floating objects detected by two satellites place MH370 impact near
35.4°S, 92.8°S. (Click on figure to enlarge)

In order to better estimate the likelihood that these objects were from MH370, we pose the following questions:

  1. Were there other detections of floating objects along the 7th arc by Pleiades, COSMO-SkyMed, or any other satellites?
  2. Were the COSMO-SkyMed detections on March 21 determined to be metallic objects?
  3. Exactly what areas along the 7th arc were surveilled by Pleiades, COSMO-SkyMed, or any other satellites?
  4. Will Airbus (the operator of the Pleiades satellites) provide the images for each color band so that independent researchers can analyze the raw data? (HT Bobby Ulich)
Posted in Aviation | 433 Comments »

FBI Investigation of MH370 Still Open

I recently submitted a FOIA request to the FBI for all documents related to MH370, which disappeared more than seven years ago. Yesterday, the FBI responded that the request was denied due to “a pending or prospective law enforcement proceeding”. This is identical to the response I received two years ago after I submitted a similar request. It implies the US intelligence community has relevant material that it will not release due to an open criminal investigation.

The FOIA request was one last attempt to obtain more information about MH370.

Independent investigators continue to use the data already in the public domain to guide future search efforts to find the debris field in the Southern Indian Ocean (SIO). Notably, Bobby Ulich continues to lead an effort that uses the timing and location of recovered debris, combined with CSIRO’s drift model results, to assess the most likely point of impact (POI), including uncertainty estimates of that position.

However, there exists other evidence not yet released that could aid researchers in localizing the POI:

  • All of the Malaysian military radar data.
  • Radar data from other sources, including the Singapore radar source operating in the vicinity of the Andaman Sea.
  • Existing subsea sonar data from Ocean Infinity to determine precisely what areas were searched and which areas have low quality or missing data due to steep terrain, sonar shadows, or equipment anomalies.
  • Any probative evidence discovered by the French judicial investigation.
  • Unpublished debris analysis, e.g., spoiler and vortex generator baseplate. (HT Mike Exner)
  • Boeing’s participation in detailed fuel calculations to confirm that our fuel models, which were used to help determine the southern-most limit of the POI, are accurate. Those models must include the effects of non-standard atmospheric temperatures and turning off the extraction of bleed air used to pressurize the cabin.
  • NTSB flight data and Inmarsat satellite data that were used by Australia’s DSTG to investigate the measurement error in recorded BTO and BFO values. (HT Don Thompson)

We are nearing the end of what is left to analyze that can realistically help us find the debris field in the SIO. Unless new data or insights are publicly released, there is not much more that the analysts can add to our understanding of the disappearance.

Posted in Aviation | 59 Comments »

Two New Reports on MH370 Debris Suggest a High Speed Final Descent

On the 7th anniversary of the disappearance of MH370, members of the MH370 Independent Group have released separate reports that analyze two wing parts that have been recovered from East Africa. The two parts represent the first and most recent pieces of MH370 that have been found. Both reports conclude that the flight likely ended in a high speed descent.

The first report, authored by Tom Kenyon, is the culmination of several years of work of structural analysis of the right flaperon that was recovered from Reunion Island in July 2015. After performing a Finite Element Analysis (FEA) on a numerical model of the flaperon and reviewing photographs of the damaged part, Tom believes that the damage on the part is not consistent with damage expected if the flaperon was attached to the wing as it impacted water. Rather, the damage to the two hinge attachments is consistent with high cycle fatigue from torsional flutter, which likely led to separation from the aircraft while still airborne. Based on Tom’s review of simulations of uncontrolled descents for the B777, he concludes the expected airspeeds are well beyond design limits that lead to flutter and structural failure.

Local police on Reunion Island examine flaperon in July 2015.

The second report, authored by Mike Exner and Don Thompson, analyzes a part that was recovered from Jeffreys Bay, South Africa, in August 2020. Based on an evaluation of features and markings, the authors positively identify the part as either spoiler #8 or spoiler #9 from the right wing from a Boeing 777, and by extension, almost certainly from MH370.

Spoiler with annotations for identified features.

The authors observe that the spoiler detached at structures that attach the spoiler to the rear spar of the right wing. The fracture along a chord line is consistent with bending of the spar along the span of the wing. At high airspeeds, wings dynamically flex due to flutter, and the dynamic aeroelastic loads that are induced will rapidly grow until the wing structurally fails.

A visualization of wing flutter can be seen in this video of a scaled model of a B747 in a wind tunnel.

The high speed descent theorized in both reports is consistent with the final BFO values recorded by the Inmarsat Ground Earth Station (GES) on March 8, 2014, at 00:19z. Those values suggest the plane was in a 0.7g downward acceleration. Without inputs from a skilled pilot, the aircraft would have impacted the ocean shortly after reaching this condition, which would mean the debris field on the seabed is relatively close to the 7th arc.

Posted in Aviation | 502 Comments »

Preliminary Accident Report Released for SJ182

Sriwijaya Air-NAM Air Boeing 737-524 WL PK-CLC (msn 27323) CGK (Michael B. Ing). Image: 929016.

Today, the Indonesian transportation authority KNKT released a Preliminary Report on Swriwijaya Air flight SJ182, a Boeing 737-500 that crashed after departing Jakarta on Jan 9, 2021. From the report:

On 9 January 2021, a Boeing 737-500 aircraft, registration PK-CLC, on a scheduled domestic flight, took off from Soekarno-Hatta International Airport, Jakarta, to Supadio International Airport (WIOO), Pontianak, at 0736 UTC (1436 LT).

The flight was cleared by Air Traffic Control (ATC) to depart on a Standard Instrument Departure (SID) ABASA 2D to Flight Level (FL) 290. After taking off from Runway 25R, the autopilot was engaged at altitude of 1,980 feet. The pilots subsequently requested a heading change to 075° to enable them to deviate from weather. ATC responded with clearance for heading 075° and the flight began a turn to the right. ATC then instructed the flight to stop climbing at 11,000 feet due to conflicting departure traffic from Runway 25L.

About 10,600 feet, the aircraft heading started turning to the left. About 10,900 feet, the autopilot disengaged, and the aircraft turned to the left and started its descent. At 14:40:37 LT, the radar target of the aircraft disappeared on the ATC radar screen. Thereafter, ATC attempted to obtain information of SJY182 aircraft by calling several times, activating and calling on the emergency frequency, and asking other pilots that were flying nearby. All efforts were unsuccessful to get a response from the SJY182 pilot.

About 1455 LT, the Air Traffic Services (ATS) provider reported the occurrence to the Indonesian Search and Rescue Agency (Badan Nasional Pencarian dan Pertolongan/BNPP), and at 1542 LT, declared the uncertainty phase (INCERFA) of SJY182. The distress phase of SJY182 (DETRESFA) was subsequently declared at 1643 LT.

At the time of issuing this preliminary report, the memory unit of the Cockpit Voice Recorder (CVR) has not been recovered and the search is continuing.

The Komite Nasional Keselamatan Transportasi (KNKT) acknowledged that the safety actions taken by the Directorate General of Civil Aviation (DGCA) and Sriwijaya Air were relevant to improve safety, however there are safety issues remain to be considered. Therefore, the KNKT issued safety recommendations to address the safety issues identified in this report.

This investigation involved the participation of the National Transportation Safety Board (NTSB) of the United States of America as the State of Design and the State of Manufacture, and the Transport Safety Investigation Bureau (TSIB) of Singapore as States providing assistance. Both agencies have appointed their accredited representatives to assist in this investigation in accordance with the provisions in ICAO Annex 13.

The investigation is ongoing. Should further safety issues emerge during the course of the investigation, KNKT will bring the issues to the attention of the relevant parties and issue safety recommendation(s) as required.

Notably, there are findings related to the behavior of the autothrottle, as the thrust to the left engine was reduced during the climb:

After the aircraft climbed past 8,150 feet, the thrust lever position of the left engine started reducing, while the thrust lever position of the right engine remained. The FDR data also recorded the left engine (N1) was decreasing whereas the right engine N1 remained.

The SJY182 pilot requested to the Terminal East (TE) controller for a heading change to 075° to avoid weather conditions and was approved. The TE controller predicted the heading change would make the SJY182 conflicted with another aircraft that was departing from Runway 25L to the same destination. Therefore, the TE controller instructed the SJY182 pilot to stop climbing at 11,000 feet.

The FDR data recorded that when the aircraft’s altitude was about 10,600 feet the aircraft began turning to the left. The thrust lever position of the left engine continued decreasing while the thrust lever position of the right engine remained.

At 14:39:54 LT, the TE controller instructed SJY182 to climb to an altitude of 13,000 feet, and the instruction was read back by an SJY182 pilot at 14:39:59 LT. This was the last known recorded radio transmission by the flight.

The highest aircraft altitude recorded in the FDR was about 10,900 feet, thereafter the aircraft started its descent. The AP system then disengaged with a recorded heading of 016°, the pitch angle was 4.5° nose up, and the aircraft continued to roll to the left to more than 45°. The thrust lever position of the left engine continued decreasing while the right engine thrust lever remained.

About 5 seconds after the aircraft started its descent, the FDR data recorded the autothrottle (A/T) system disengaged and the pitch angle was more than 10° nose down.

At 14:40:48 LT, the radar target of the aircraft disappeared on the TE controller radar screen. Thereafter, the TE controller attempted to obtain information of SJY182 aircraft by calling the flight several times, activating the emergency frequency and calling SJY182 on that frequency. The TE controller also asked other pilots that were flying nearby to attempt contact with the flight. All efforts were unsuccessful to get any response from the SJY182 pilot.

The data from the FDR indicates the start of the turn to the left coincided with a reduction in thrust from the left engine, which would cause a yaw-induced bank to the left, although that was likely moderated by the autopilot. After the autopilot disengaged, the left thrust continued to decrease, the plane rolled left to a bank angle of 45°, and the plane rapidly descended. The pilots were not able to recover from this upset attitude.

Comment: The preliminary report does not discuss what pilot inputs occurred after the turn to the left began, neither while the autopilot was engaged nor after it disengaged. Correct right rudder input would have helped control the aircraft; incorrect left rudder input would have exacerbated the problem.

Posted in Aviation | 254 Comments »

New Report Released for MH370 Search (Updated)

A Boeing 777 in Malaysia Airlines livery just after lifting off the runway


Independent researchers investigating the disappearance of MH370 today released a new technical report to guide the next search for the debris field on the floor of the Southern Indian Ocean (SIO). The report provides the scientific and mathematical foundation that was used to define the recommended search area that was disclosed last month. The authors of the report are Bobby Ulich, Richard Godfrey, Victor Iannello, and Andrew Banks.

The full report, including all appendices, is available for download. What follows is a brief summary of the important results.

The flight of MH370 was analyzed from takeoff to impact in the SIO using a comprehensive, fully integrated model. The model was developed using exhaustive data sets and technical documentation available from both public and confidential sources, and includes:

  • radar data collected by military and civilian installations in Malaysia
  • timing and frequency measurements collected by the Inmarsat satellite network
  • aircraft performance data for Boeing 777-200ERs
  • historical performance data for airframe 9M-MRO
  • navigation and speed modes for automated flight
  • drift analysis of debris that floated and was recovered in East Africa
  • aerial search results from March and April 2014
  • weather data along the flight path

A total of 2,300 possible flight paths were evaluated, and an overall probability metric was defined that incorporates the information from all the data sets. The highest probability flight path was identified as due south from waypoint BEDAX, which is about 185 km (100 NM) to the west of Banda Aceh, Sumatra, and an impact in the SIO near S34.2342° E93.7875°, which is 4380 km (2365 NM) from BEDAX.

The work included the development of an accurate fuel consumption model, and well as a statistical metric for the expected random noise inherent in the recorded satellite data. These improvements allowed the rejection of hypothetical flight paths that were previously believed to be possible.

Turnback Across Malaysia

After takeoff, the climb was normal, and the aircraft leveled at a cruise altitude of FL350 (35,000 ft standard altitude), tracking towards waypoint IGARI in the South China Sea. After flying by waypoint IGARI, the transponder was disabled as the aircraft turned towards waypoint BITOD. On passing the FIR boundary between Malaysia and Vietnam, the aircraft began turning back towards the Malay peninsula, and flew towards Kota Bharu airport, as shown in the figure below.

Flight path over Malaysia after turnback at IGARI

The civilian radar installation at Kota Bharu captured MH370 as it flew towards and then away from Kota Bharu. An analysis of this radar data shows that the aircraft climbed from FL350 to about FL385 (true altitude of 40,706 ft) and accelerated to near its maximum operating speed of Mach 0.87 as it passed to the north of Kota Bharu. It then flew across the Malay peninsula and towards Penang Island, where a civilian radar installation at Butterworth Airport captured the radar targets. As it passed to the south of Penang Island near Penang Airport, it slowed down to a speed closer to Mach 0.84, and turned to the northwest over the Malacca Strait.

Flight over the Malacca Strait and Around Sumatra

The flight over the Malacca Strait was captured by Malaysian military radar, as disclosed in a briefing to family members in Beijing in March 2014. After passing Penang Island, the aircraft proceeded on an exact course to waypoint VAMPI, and intercepted airway N571. The last radar target was captured at 18:22:12 about 10 NM after passing waypoint MEKAR on N571. The flight over the Malacca Strait, around Sumatra, and towards the South is shown in the figure below.

Flight path over the Malacca Strait and around Sumatra

In the report, it’s deduced that soon after the aircraft was beyond Malaysia radar coverage, MH370 began a “lateral offset” that would position the aircraft about 15 NM to the right of N571, possibly to ensure separation from other traffic. Once this offset was completed at around 18:29, a descent began, and when the altitude reached FL250 (well below the minimum altitude of FL275 for traffic on N571), the aircraft turned directly towards waypoint IGOGU on a westerly course.

On reaching IGOGU, it’s deduced that the aircraft continued its descent and turned due south, flying along the FIR boundary between Malaysia and India. It leveled at around FL100 (10,000 ft standard altitude), and continued south until reaching the FIR boundary of Indonesia. It then turned to the west, away from Indonesia, and flew along the FIR boundary.

It’s further deduced that the final course change was due south towards waypoint BEDAX. After passing BEDAX, a climb to FL390 began at around 19:24, ending at around 19:41. The aircraft continued on a due south course at LRC speed towards the South Pole until fuel exhaustion occurred in the SIO at around 00:17.

The authors observe that the trajectory last covered by Malaysian radar was to the northwest along N571. Only when beyond Malaysian radar coverage was a descent to a lower altitude initiated, which was followed by turns to the west and south. It’s hypothesized that the intention was to lead the searchers into believing the trajectory continued along N571 to the northwest, as the transit at low altitude would have been below the radar horizon of Indonesian and Thai radar installations. It is only because of the analysis of the satellite data first performed by Inmarsat that we know the flight path continued into the SIO. Very likely, the party responsible for the diversion was not aware that this data set was recorded and could be later used to deduce a path.

The entire flight path is summarized in the figure below.

The flight path from takeoff to impact in the SIO

Possible MH370 Sighting by Kate Tee

Kate Tee was on a sailboat on 7th March 2014 southeast of Great Nicobar Island and northwest of Sumatra. She reported seeing a large aircraft coming towards her from the north, flying at an unusually low altitude. At around the same time, she reported that the sailboat gybed accidentally. This gybe event and the track of the sailboat were recorded on the GPS system on board, and serves to define a position and an approximate timestamp for her sighting. In this time interval, the sailboat was close to waypoint NOPEK along the FIR boundary between Malaysia and India, which may help to explain her sighting.

The figure below depicts the path of MH370 at 18:55:57 and the GPS track from the sailing boat every five minutes from 18:25 to 19:25. The GPS track from the sailing boat and the deduced flight path of MH370 appear to align.

Possible MH370 sighting by sailor Kate Tee

Probability of Various Paths to the SIO

In order to rank the likelihood of various reconstructed paths to the SIO, the available data sets were compared to predictions from the mechanistic models, and the match between the measured data and the models were used to develop probabilities for each path. For each path, probabilities were calculated for four classes of measured data:

  • Measured satellite data compared with model predictions for navigation, weather, and data statistics
  • Observed fuel endurance with model predictions from fuel consumption models
  • Observed location and timing of recovered debris with predictions from drift models
  • Failure to find floating debris compared with the areas targeted by the aerial search

The overall (composite) probability for a path was calculated as the product of the of the probabilities of the four classes of data and then normalized to produce a probability density function (PDF) in which the cumulative probability across all latitudes is unity.

Each panel in the figure below shows the probabilities for each class of data, followed by the overall probability. If only considering the match to the measured satellite data presented in the first panel, the probability is highest for the path ending near 34.3°S latitude. However there are many other prominent peaks for paths ending along the 7th arc to the north and south of 34.3°S, so further discrimination is required using the other three data sets.

Probability of routes based on data sets

Peaks corresponding to end points to the south of 34.3°S are rejected because of low probabilities of matching the observed fuel endurance and the reports of the recovered debris in East Africa. On the other hand, end points to the north of 34.3°S are rejected because the impact would have produced a floating debris field that would have been detected by the aerial search with a high probability. What remains is a single prominent peak at 34.3°S, which represents a due south path from a position near waypoint BEDAX towards the South Pole.

Search Area Recommendation

The analysis presented above suggests that MH370’s flight path in its final hours followed E93.7875° longitude, corresponding to a great circle path between waypoint BEDAX and the South Pole. Using this result, the last estimated position (LEP) is S34.2342° E93.7875°. Although some of the subsea was previously searched in this vicinity, the terrain is challenging, and the debris field might have been not detected, or detected and misinterpreted. There is also the possibility that there was a controlled glide after fuel exhaustion, and an impact well beyond what was previously searched.

To define the search area near the LEP, three cases were considered, each with an associated search area. The highest priority search area, A1, of 6,719 NM2 (23,050 km2), assumes there were no pilot inputs after fuel exhaustion. The search area of next highest priority, A2, encompasses 6,300 NM2 (22,000 km2), and assumes there was a glide towards the south after fuel exhaustion. The lowest priority, A3, is the controlled glide in an arbitrary direction with an area of around 48,400 NM2 (166,000 km2). The three search areas are shown in the figure below.

Search area recommendation


A new report is now available that suggests that MH370’s flight path in its final hours followed E93.7875° longitude, corresponding to a great circle path between waypoint BEDAX and the South Pole. The report concludes that an impact near S34.2342° E93.7875° is most likely.

The technical details are included in the report so the analytical results can be evaluated, reviewed, and replicated by other investigators.

Three end-of-flight scenarios were considered, and a recommended search area for each scenario was defined and prioritized. As parts of the recommended search areas were already searched by GO Phoenix and Ocean Infinity, we recommend a thorough review of the existing sonar data, recognizing that the quality of the data in that vicinity varied due to challenging terrain.

As there are no ongoing MH370 search activities, the authors of the report believe the new technical results provide credible evidence that justifies a new search.

Update on March 9, 2020 – Civilian Radar Data

A newer version of the civilian radar data is now available as an Excel file. This data set represents the raw data from the Kota Bharu and Butterworth radar heads before the data was processed and stored by the radar network. This data set was used for the calculations in the report. Also included in the Excel file is the methodology for converting the raw data to latitude and longitude.

Update on March 12, 2020

The best estimate of the point of impact (BE POI) has been renamed the last estimated position (LEP), which is a more accurate description. The location is unchanged.

Update on January 7, 2021 – Links for CSIRO Drift Results

Some contributors are performing their own drift studies using the results from the CSIRO calculations. The following links can be used to download the results as MATLAB data files. The calculations were performed for floating particles that are considered “generic” and for floating particles that are hydrodynamically and aerodynamically similar to the flaperon.

Generic particles:

Flaperon particles:

Posted in Aviation | 2,442 Comments »

Search Recommendation for MH370’s Debris Field

[This is the web version of a paper written by me, Bobby Ulich, Richard Godfrey, and Andrew Banks. The PDF version is available here.]

1 Introduction

Presently, there is no active search to find MH370’s debris field on the seabed of the Southern Indian Ocean (SIO). The last search was conducted by Ocean Infinity, who consulted with official and independent researchers, and subsequently scanned the seabed along the 7th arc as far north as S25° latitude. Since then, independent researchers have continued to analyze the available data to understand what areas of seabed are the most likely, and why previous search efforts have been unsuccessful. The objective is to define a manageable area for conducting a new search of the seabed.

In a previous post [1], we presented an overview of Bobby Ulich’s research [2], aimed at more precisely locating the point of impact (POI) using statistical criteria that requires that random variables (such as the reading errors of the satellite data) are not correlated, i.e., are truly random. A subsequent post [3] describes the work of Richard Godfrey et al. [4] to analytically evaluate a large number of candidate flight paths using these and other criteria. The results of that work suggest that the final hours of the flight were due south in the Indian Ocean along E93.7875° longitude, which matches a great circle between the waypoint BEDAX (about 100 NM west of Banda Aceh, Sumatra) and the South Pole. The POI was estimated to lie close to the 7th arc around S34.4° latitude.

Work continues to evaluate candidate paths using an accurate integrated model that includes satellite data, radar data, flight dynamics, automated navigation, meteorological conditions, fuel consumption, drift models, and aerial search results. That exhaustive work is nearing completion, and documentation of the methods and the results is ongoing. Like the previous work [4], the ongoing work suggests that the final trajectory of MH370 was most likely along a due south path along E93.7875° longitude.

In the interest of providing information in a timely manner, we have chosen to recommend a search area based on this most likely path. A comprehensive paper which expands upon the methods and results presented in previous work [2,4], and provides further justification for the selected path, will be available in the near future.

2 Last Estimated Position (LEP)

Using the results of the analysis presented above, the last estimated position (LEP) is based on a final trajectory of a constant longitude of E93.7875°, which is consistent with the aircraft traveling due south from waypoint BEDAX towards the South Pole. The LEP is based on a location exactly on the 7th arc, and the uncertainty associated with the LEP helps define the limits of the recommended search area.

When the SDU logs onto the Inmarsat network, the SDU begins the log-on sequence by first transmitting a log-on request, which is followed some seconds later by transmitting a log-on acknowledge. For MH370, those were the final two transmissions, transmitted at 00:19:29 (BTO = 23,000 μs) and 00:19:37 (BTO = 49,660 μs), respectively. From past work [6,7], we also know that the BTO values for the log-on request and log-on acknowledge are “anomalous” in that the raw values are outliers that require a correction. Fortunately, the required corrections are repeatable, and can be determined by analyzing prior flights.

Using the Inmarsat transaction logs for MH371 and MH370 [8], the BTO log-on statistics from March 7, 2014, 00:51:00, to March 8, 2014, 16:00:00, were analyzed to determine what offsets might be applied to log-on requests and log-on acknowledges. There were 29 cases in which there was an R-channel burst just after the initial (R600) log-on request and subsequent (R1200) log-on acknowledge. Of those 29 cases, the number of packets in the burst was 3 for 20 bursts, 2 for 6 bursts, and 1 for 3 bursts. The average of each burst was used as the reference for the log-in request and log-on acknowledge. In 4 of the 29 cases, the correction for the log-on request was near zero, i.e., the BTO values were not anomalous, so only 25 cases were included for log-on request statistics.

For the log-on requests, the mean offset from the R-channel burst is 4,578 μs with a standard deviation of 94 μs. The maximum offset was 4,800 μs (+222 μs from the mean) and the minimum was 4,380 μs (-198 μs from the mean).

For the log-on acknowledge, we considered a correction of the form (a + N × W), where a is a constant, N is an integer, and W represents the delay per slot. We found that the standard deviation of the correction error (using the average of the R1200 burst as the reference) to be minimized for W = 7812.0 μs. That’s very close to the 7812.5 μs value suggested by the 128 Hz internal clock of the SDU. By forcing W=7812.5 μs, the mean error to the correction is 23 μs, and the standard deviation is 30 μs. The observed standard deviation is very close to the 29 μs that DSTG recommends to use for “normal” R1200 values [7]. The consistency of the standard deviation of the corrected anomalous values with the standard deviation of the values not requiring a correction is reassuring. The total correction to the BTO for log-on acknowledges is therefore (23 + N × 7812.5) μs.

Using these log-on corrections produces corrected BTO values at 00:19 equal to:

00:19:29: 23000 – 4578 = 18422 μs
00:19:37: 49660 – 23 – 4 × 7812.5 = 18387 μs

We combine these values to determine the BE value of BTO by using the inverse of the variance as weighting, yielding a BE value of BTO = 18,390 μs (σ = 29 μs). Using this BE value of BTO with the longitude of E93.7875° and an assumed geometric altitude of 20,000 ft results in a position of S34.2342° E93.7875° at 00:19:29, which we assign as the LEP.

3 Terrain Near the LEP

Figure 1 shows the subsea terrain in the vicinity of the LEP using data provided by Geosciences Australia [5]. Some of this area has already been searched by GO Phoenix (managed by the ATSB) using a towfish, and by Ocean Infinity (OI) using Seabed Constructor and its team of AUVs. However, as can be seen in Figure 1, some of the previously searched area has challenging terrain with steep slopes, and the debris field may have been either not detected due to terrain avoidance or shadows, or detected but not properly interpreted by reviewers. In particular, there is a steep slope that lies about 20 NM due south of the LEP that was not scanned by the towfish and appears to have been only partially scanned by the AUVs.

Figure 1. Terrain in the vicinity of the LEP

Figure 2 shows the ocean depth along a line of constant longitude in the vicinity of the LEP. The previously identified steep slope to the south of the LEP has a grade of about 30%. To the north, another slope has a grade of 44%. This slope was beyond the limits of the search boundaries of GO Phoenix, but was scanned by Seabed Constructor’s AUVs.

Figure 2. Ocean depth at constant longitude and +/- 46 km (+/- 25 NM) from the LEP

4 No Pilot Inputs after Fuel Exhaustion

In order to define the search area limits, we first consider no pilot inputs after fuel exhaustion. For this case, the search area limits are defined by the uncertainty of the LEP and the uncertainty of the uncontrolled flight path before impacting the ocean.

4.1 Uncertainty Due to BTO Noise

The uncertainty in the BTO produces a corresponding uncertainty in the position of the 7th arc. The calculated sensitivity of the arc position to the BTO is 0.104 NM/µs, i.e., a 1-µs increase in BTO pushes the 7th arc outward (southeast) by 0.104 NM. The 1-σ uncertainty of the arc position due to BTO noise is therefore 0.104 NM/µs × 29 µs = 3.0 NM.

4.2 Uncertainty Due to Altitude at 00:19:29

The LEP is based on an assumed altitude of 20,000 ft that is reached at 00:19:29, i.e., 1.5 to 2 minutes after fuel exhaustion. As the BTO represents the range between the aircraft and the satellite, the position of the 7th arc as projected on the surface of the earth depends on the altitude. As the aircraft would be between 0 and 40,000 ft at this time, we assign this altitude range as the 2-σ limits. The calculated sensitivity of the BTO to altitude is 12.8 µs/10,000 ft. The 1-σ uncertainty of the arc position due to altitude uncertainty is therefore 0.104 NM/µs × 12.8 µs = 1.33 NM.

4.3 Uncertainty of Turn Between Fuel Exhaustion and 00:19:29

Boeing conducted 10 simulations to determine the behavior of MH370 after fuel exhaustion with no pilot inputs [9] using a high-fidelity simulator for the 777-200ER aircraft. The trajectories for these simulations are shown in Figure 3. For each simulation, the autopilot was automatically disengaged after fuel exhaustion, and the aircraft turned slightly either to the right or to the left depending on a number of factors, including the electrical configuration, the initial conditions of the flight parameters, and the meteorological conditions. Within the 2-minute interval between fuel exhaustion and the log-on request at 00:19:29, the slight turn shifted the location that the aircraft crossed the 7th arc relative to where it would have crossed the 7th arc if the autopilot had remained engaged and the course was maintained. For the 10 cases, the lateral shift along the arc varied between 1.1 and 8.8 NM. As we don’t know how well the 10 cases represented the actual conditions, we conservatively assign a 1-σ uncertainty of 8.8 NM along the 7th arc due to the slight turn between fuel exhaustion and crossing the 7th arc.

4.4 Uncertainty of Trajectory Between 00:19:29 and the POI

In all 10 of the Boeing simulations, the aircraft banked after the autopilot was disengaged following fuel exhaustion. The magnitude and direction of the bank that develops is the net effect of a many factors, including thrust asymmetry, rudder inputs from the Thrust Asymmetry Compensation (TAC), rudder trim input, lateral weight imbalance, aerodynamic asymmetry, and turbulence, any of which increases the bank angle. On the other hand, the tendency to bank is opposed by the dihedral effect of the wings and the low center-of-mass. For all the simulations, the POI was within 32 NM from the 7th arc crossing at 00:19:29, as shown in Figure 3.

Figure 3. Calculated end-of-flight trajectories from the Boeing simulations [9]

In some of those simulations, the bank was shallow, and phugoids lasting many minutes developed. In only 5 of the simulations did the rate of descent exceed 15,000 fpm while also experiencing a downward acceleration exceeding 0.67 g, which are the values of descent rate and downward acceleration derived from the two final values of the BFO. For these cases, the POI occurred between 4.7 and 7.9 NM from the point where the descent rate first exceeded 15,000 fpm. Other simulations of a banked descent after fuel exhaustion [10] suggest that an uncontrolled Boeing 777 would travel an additional distance of about 5 NM after a downward acceleration of 0.67 g and a rate of descent of 15,000 fpm simultaneously occur.

None of the Boeing simulations predict that the aircraft was in a steep descent as the 7th arc was crossed, so there is an unexplained discrepancy between the Boeing simulations and the descent rates derived from the final BFO values. In light of this discrepancy, we choose to not limit the distance traveled after crossing the 7th arc by only considering the distance traveled after the steep descent. Instead, we assign a 2-σ value of 32 NM for the distance traveled after crossing the 7th arc, based on the farthest distance that was observed in all 10 simulations, irrespective of the magnitude and timing of the descent rates.

4.5 Uncertainty Due to Navigation Error

There are two autopilot modes that could result in a trajectory that nominally follows a great circle between BEDAX and the South Pole. After passing BEDAX, if the autopilot remained in LNAV and the active waypoint was the South Pole (entered as 99SP, S90EXXXXX, or S90WXXXXX), the aircraft would fly along the longitude E93.7875° within the accuracy of the GPS-derived navigation. In this case, the expected navigational error would be much smaller than other sources of error, and can be safely ignored.

The other possibility is that after passing BEDAX, the autopilot was configured to fly along a constant true track (CTT) of 180°. Selecting this mode would require manually changing the heading reference switch from NORM to TRUE, as directions on maps, procedures, and in ATC communications are normally referenced to magnetic north, except in polar regions.

Unlike LNAV mode in which the cross-track error of the target path is continuously calculated and minimized, errors in track (which may be positive or negative) in CTT mode produce error in the due south path that may accumulate without correction. We assume here that that course is nominally 180° True, with a 1-σ uncertainty of 0.1 deg (0.001745 rad). As the distance between BEDAX and the 7th arc along the line of constant longitude is around 2365 NM, the cross-track error has a mean value of zero and a 1-s uncertainty of 4.1 NM. However, since the path crosses the 7th arc at an angle of 46 deg, the 1-σ uncertainty in position along the 7th arc is increased to 5.9 NM.

4.6 Search Area Based on No Pilot Inputs

Assuming there were no pilot inputs after 19:41, the uncertainties in the POI are summarized in Table 1. The 1-σ uncertainty along the 7th arc is 19.2 NM, and 16.3 NM normal to the 7th arc.

Table 1. Summary of POI Uncertainties Assuming No Pilot Inputs

To achieve a confidence level of 98% requires searching an area defined by ±2.3-σ limits, with the LEP at its center. Based on this, the recommended area is 91 NM × 74 NM, and the total area is 6,719 NM2, or 23,050 km2. This area is depicted as A1 in Figure 4.

Figure 4. Search recommendation, showing areas A1, A2, and A3

5 Controlled Glide Due South

We next consider the case in which there was a controlled glide after fuel exhaustion, which would extend the search area beyond the search area based on no pilot inputs. For a Boeing 777 gliding at an optimum speed, a glide ratio of about 20:1 can be achieved. This corresponds to a descent angle of 2.86°, and a continuous reduction in altitude of 1000 ft for every 3.29 NM traversed. Assuming an initial altitude of 42,400 ft (based on a standard altitude of 40,000 ft), the impact could be as far as 140 NM from the point of fuel exhaustion (ignoring the headwind at some altitudes, which would reduce the ground distance of the glide). If the glide started at a lower altitude, or if non-optimum airspeed was flown, the glide distance would be less. The uncertainty associated with the glide distance is much larger than other uncertainties, so we assume that with a glide, the POI might have been as far as 140 NM from the LEP, and use that as the southern limit.

The width of the search area as defined by a controlled glide is more difficult to estimate. If an experienced pilot wished to continue the flight path on a due-south course, that could be accomplished quite precisely. For example, if the autopilot mode was CTT before the fuel exhaustion, then a constant (true) track of 180 deg could be maintained using the indicated track shown in the navigation display. On the other hand, if the autopilot mode was LNAV before fuel exhaustion, then the cross-track error could be minimized by following the “magenta” line defined by the BEDAX-South Pole leg. In either case, the search area width could be limited to less than 10 NM to either side of the projected flight path.

Because we cannot be sure that there was an attempt to precisely follow a due south path, we assign a generous width to this part of the search area, centered on the due south path. A width of +/- 33 NM results in an additional search area of 6,300 NM2 (22,000 km2), and produces an area in similar size to A1. It is depicted as A2 in Figure 4.

6 Controlled Glide in an Arbitrary Direction

If there was a controlled glide that did not continue along the path flown prior to fuel exhaustion, it is nearly impossible to predict the direction. For instance, a path to the west would shield the pilot’s eyes from the rising sun to the east. A path to the northeast would extend the glide due to the tailwind. A path to the west would create more distance to the Australian shoreline. A path towards the northwest would be towards Mecca. Any of these directions is less likely than a continuation of the due south path, but it becomes nearly impossible to prioritize among these or other directions. Instead, we define area A3 as the circle with a radius of 140 NM, excluding the areas already included in A1 and A2. The area is roughly 48,400 NM2 (166,000 km2), and is depicted as A3 in Figure 4.

7 Conclusions

Recent analyses suggest that MH370’s flight path in its final hours followed E93.7875° longitude, corresponding to a great circle path between waypoint BEDAX and the South Pole. Using this result, the last estimated position (LEP) is S34.2342° E93.7875°. Although some of the subsea was previously searched in this vicinity, the terrain is challenging, and the debris field might have been not detected, or detected and misinterpreted. There is also the possibility that there was a controlled glide after fuel exhaustion, and an impact well beyond what was previously searched.

To define the search area near the LEP, three cases were considered, each with an associated search area. The highest priority search area of 6,719 NM2 (23,050 km2) assumes there were no pilot inputs after fuel exhaustion. The search area of next highest priority encompasses 6,300 NM2 (22,000 km2), and assumes there was a glide towards the south after fuel exhaustion. The lowest priority is the controlled glide in an arbitrary direction with an area of around 48,400 NM2 (166,000 km2).

8 References

[1] Iannello, “A New Methodology to Determine MH370’s Path”, May 31, 2019,

[2] Ulich, Technical Note presented in [1].

[3] Iannello, “A Comprehensive Survey of Possible MH370 Paths”, June 30, 2019,, excerpted from [4].

[4] Godfrey, Ulich, Iannello, “Blowin’ In The Wind: Scanning the Southern Indian Ocean for MH370”, June 24, 2019,

[5] “MH370 Data Release”, Geosciences Australia,

[6] Ashton, Shuster-Bruce, College, Dickinson, “The Search for MH370”, The Journal of Navigation, Vol 68 (1), January 2015.

[7] Davey, Gordon, Holland, Rutten, Williams, “Bayesian Methods in the Search for MH370”, Defense, Science, and Technology Group, Australia, November 30, 2015.

[8] Iannello, “The Unredacted Satellite Data for MH370”, June 12, 2017,

[9] Iannello, “End-of-Flight Simulations of MH370”, August 2018,

[10] Iannello, “MH370 End-of-Flight with Banked Descent and No Pilot”, June 4, 2017,

Update on March 12, 2020

The best estimate of the point of impact (BE POI) has been renamed the last estimated position (LEP), which is a more accurate description. The location is unchanged.

Posted in Aviation | 534 Comments »

A Comprehensive Survey of Possible MH370 Paths

This is the second in a series of articles that is dedicated to defining a new area for the underwater search of MH370. In the previous article, we presented Bobby Ulich’s overview of a new statistical criteria that supplements the criteria that many investigators have used in the past for evaluating candidate flight paths. In the present article, we present an overview of an exhaustive study principally undertaken by Richard Godfrey, with contributions by Bobby Ulich and me, to examine flight paths with the assumption that after 19:41, the flight was automated and with no pilot inputs. The results indicate that a flight crossing the 7th arc near 34.4S latitude merits a deeper investigation, which will be the subject of the next (third) paper.

What follows are excerpts from “Blowin’ in the Wind”, by Richard Godfrey et al. For more details, please consult the full paper.


Following on from Richard Godfrey’s earlier paper entitled “How to play Russian Roulette and Win” published on 13th February 2019, which covered the first part of the flight and diversion of MH370 into the Straits of Malacca, Richard was contacted by Bobby Ulich, who asked the question “where do we go from here?” Richard Godfrey, Bobby Ulich and Victor Iannello came up with the idea to scan the Southern Indian Ocean (SIO) for possible flight paths of MH370 using a degree of precision that we believe has not been previously applied, and to use certain statistical checks on the presence or absence of correlations in the data. Each of us had independently developed a MH370 flight model using the Boeing 777-200ER aircraft performance data, Rolls Royce Trent 892 fuel range and endurance data, Inmarsat satellite data and the GDAS weather data. The goal was to find all possible MH370 flight routes that fit the data within appropriate tolerances. Additionally, the data would be checked using a set of correlations.


Our assumptions about the automated flight after 19:41 are that there are 7 parameters that determine a possible MH370 flight path:

  1. Start Time
  2. Start Latitude
  3. Start Longitude
  4. Flight Level
  5. Lateral Navigation Method
  6. Initial Bearing
  7. Speed Control Mode

If you draw an arbitrary line of latitude between the area of the last known point and the SIO, MH370 must have crossed this line at a certain time, longitude, flight level and initial bearing using a particular lateral navigation method and speed control mode.

Having fixed the start latitude, the start time and start longitude can be varied for any given flight level, lateral navigation mode, initial bearing and speed control mode, and the fit to the aircraft performance data, satellite data and weather data ascertained. The flight model used in the wide area scan was developed by Richard Godfrey. First the altitude and air pressure at the selected flight level is determined. The GDAS weather data provides the actual surface air pressure and surface air temperature for a given position and time by interpolation. The air pressure for a given flight level is calculated based on the ISA standard surface pressure of 1013.25 hPa and standard surface temperature of 15.0°C. The geometric altitude for a given flight level is then approximated using the actual surface pressure and actual surface temperature. The altitude is used in the satellite data calculations, assuming the flight level is maintained between 19:41:03 UTC and 00:11:00 UTC. Similarly, the GDAS weather data is interpolated for the exact latitude, longitude and time to find the Outside Air Temperature (OAT) and wind at the given flight level.

The scan method for each Lateral Navigation Method (LNAV, CTT, CTH, CMT and CMH) and for each Speed Control Mode (Constant Mach and Long Range Cruise) requires stepping through each possible Initial Bearing (initially from 155°T to 195°T) in steps of 1°T. In Constant Mach (CM) the value was set initially at 0.85 and decremented in steps of 0.01 Mach.

[Note: LNAV = Lateral navigation (following waypoints connected by geodesics); CTT = Constant true track; CTH = Constant true heading; CMT = Constant magnetic track; CMH = Constant magnetic heading]

Once the Initial Bearing and (if relevant) the Mach has been set, the Start Time or Start Latitude is adjusted to minimise the RMS BTO Residual (BTOR) across the 5 satellite handshake points between 19:41:03 UTC and 00:11:00 UTC. The BTOR is the difference between the predicted BTO and the observed BTO. Then the Start Longitude is varied to minimise the RMS BTOR. Finally the Flight Level is adjusted in steps of 1 (standard altitude steps of 100 feet) to minimise the RMS BTOR. A full report is then produced for each scan. (The definition of GSE is found later in the paper, and the significance of the correlation coefficients is based on the work of Bobby Ulich and will be presented in a future paper.)

A number of MH370 candidate flight paths have been found over the years by various analysts resulting in Regions of Interest (ROIs) that have either already been searched or have been proposed for a further search. The table below lists some of the ROIs. The table includes some new ROIs which have been found as a result of the current systematic search. Some of the ROIs can be readily dismissed as the standard deviation BTO residual (<47 μs), standard deviation BFO residual (<4.3 Hz) or the calculated PDA (<1.5%) is too high.

Possible MH370 flight paths resulting in a candidate Region of Interest (ROI)

Systematic initial bearings from 155°T to 195°T in steps of 1°T were analysed, plus some exotic cases in steps of 0.1°T. All navigation methods were covered: LNAV, CTT, CTH, CMT and CMH, all speed modes: Constant Mach 0.80 to 0.85, LRC 0.7047 to 0.8408, MRC, ECON CI52 and all flight levels: from FL290 to FL430. The fuel endurance was allowed to vary around 00:17:30 UTC and the resulting PDA was noted. The PDA was allowed to vary from the nominal 1.5% and the possibility that the bleed air was shut off for part or all of the time was considered.

In total 1,372 flight paths have been analysed, of which 828 flight paths since the start of this systematic study on 17th February 2019. Start latitudes from 16.0°N to 4.3°S have been covered and the start longitudes were unconstrained. Start times from 18:41:00 UTC to 19:32:00 UTC, but the final major turn had to be completed before the 2nd Arc at 19:41:03 UTC was reached.


A more detailed analysis reveals 3 candidate ROIs for further investigation: ROI 1 – LNAV180 CM 0.84 FL403, ROI 2 – LNAV 170 LRC FL350 and ROI3 – CTH170 LRC FL290.

From a pilot’s point of view, a LNAV path on a bearing of 180°T would require setting a final waypoint as the South Pole. This flight path passes close to waypoint BEDAX. The overall fuel endurance and range fits and for a Main Engine Fuel Exhaustion (MEFE) at 00:17:30 UTC, a PDA of 1.37% is calculated (the nominal PDA is 1.5%). The RMS GSE is 2.49, which fits the expected range between 1.0 and 3.0 knots. This flight path ends at 00:19:37 UTC at around 34.5°S near the 7th Arc. This area was originally searched by Go Phoenix but all possible sightings were reexamined and discounted. The search area was widened in later search by Ocean Infinity, but again nothing was found.

An LNAV path on an initial bearing of 170°T starts close to Car Nicobar Airport (VOCX) and passes close to Cocos Island before ending at 00:19:37 UTC at around 28.9°S near the 7th Arc. The overall fuel endurance and range fits and for a MEFE at 00:17:30 UTC, with a calculated PDA of 1.17%. Notably, the Mean BFOR for this flight path is low at -6.87 Hz and is out of the expected range. The area around 28.9°S was searched by Ocean Infinity, but nothing was found.

The CTH path on an initial bearing of 170°T is unlikely as the fuel endurance and range does not fit well. The RMS BTOR is high at 79.6 μs and individual BTOR values are out of normal range. It is also unlikely that a pilot would switch to a True Heading mode. Normal operation is Magnetic Track and this mode is only used for short flight paths, such as during an approach or deviating to avoid bad weather. Switching from Magnetic to True compass mode is only normally done in the region of the north or south poles.

Candidate ROIs for further investigation. (Click on image to enlarge.)


All possible MH370 end points of flight routes in any navigation mode and any speed mode have already been searched, within at least ± 25 NM of the 7th Arc (partially ± 40 NM). This means that MH370 has either been missed in a previous search or recovered from a steep descent of around 15,000 fpm and glided out to an end point outside the previously searched area.

There is only one Region of Interest, where we recommended a further analysis and search at around 34.4 °S near the 7th Arc, following a flight route from close to waypoint BEDAX using the LNAV lateral navigation mode with an ultimate waypoint of the South Pole on a track of 180°T due south, in Long Range Cruise speed mode and at a flight level between FL390 and FL403.

This Region of Interest will be analysed in more depth in the next paper in this series.

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A New Methodology to Determine MH370’s Path

Ocean Infinity associates review sonar data

The community of independent researchers is divided about where a new underwater search should be conducted. In this light, Bobby Ulich, PhD, has been quietly developing new statistical criteria that supplement the criteria that many of us have used in the past. The objective of this research is to define a new search area that is of manageable size and has a reasonable chance of success. Bobby has been working closely with Richard Godfrey to identify candidate paths, and with me to a lesser extent. At this point, the most promising candidate is a path of constant longitude, i.e., following a constant track of due south, aligned with waypoint BEDAX, and crossing the 7th arc near 34.3S latitude. This path, which was identified as a candidate path some years ago, could have been easily programmed into the flight computers with the waypoints BEDAX and the South Pole (e.g., by entering the waypoint S90E000). Work continues to evaluate this and other paths.

The note below from Bobby gives an overview of the new methodology, and is provided here to elicit comments from contributors of the blog.

Note from Bobby Ulich, PhD

There are two pieces of available MH370 information that have not yet been fully utilized in predicting the southern route and the most likely impact latitude near the 7th Arc.  Neither one was included in the DSTG Bayesian analysis.

The first item is the inclusion of a detailed and accurate fuel flow model.  All DSTG analyses effectively ignored fuel consumption as a route discriminator by assuming “infinite fuel”.   I and several others subsequently developed fuel flow models and compared them with Boeing tables, prior 9M-MRO flights, and the MH370 flight plan in order to validate the predictions.  My model fuel flows are consistent with these comparisons, nearly always within +/- 1 %.  As I understand it, Boeing did some range and endurance calculations and found that it was possible, at some combination of altitude and speed, for 9M-MRO to have reached a wide stretch of the 7th Arc, totally excluding only the region beyond circa 39S.  However, the DSTG analyses did not factor in fuel consumption for each route they examined, so it is unknown whether or not that route was actually flyable with the available fuel.  This is an important consideration, especially considering the fact that over a large portion of the SIO region of interest, the high-altitude air temperatures on the night in question varied by as much as 12 C with respect to ISA over an altitude range of only about 5,000 feet.  Thus, small altitude changes had major effects on TAS and on fuel flow. 

In my route fitter, one can either predict the main engines fuel exhaustion (MEFE) time using the known average cruise PDA for the engines, or hold the MEFE time at 00:17:30 (per ATSB) by adjusting the assumed PDA.  I generally do the latter because that gives the correct weight as a function of time, which affects the commanded airspeed.  It is also important to allow for the possibility that bleed air was turned off after diversion, reducing fuel flow by several percent.  So, in fact the effective PDA which would give the correct endurance is potentially a range of values between 1.5% (the known value with bleed air on) and about -0.8% (the equivalent of bleed air off for the entire flight after diversion).  Best-fit PDAs higher than +1.5% and lower than -0.8% are increasingly less likely.

Inmarsat and DSTG have provided some analyses of the BTO and BFO reading errors based on prior flights.  Generally speaking, up to now, the statistics associated with those reading errors are the mean and the standard deviation.  In many cases the RMS statistic has also been used as a convenience when performing route model fits to the satellite data, but the fundamental statistics are the mean and standard deviation of the BTO/BFO reading errors.  In the case of the BFOs, we cannot know that the mean reading error (effectively the BFO bias term) did not change as a result of the in-flight power cycle ending circa 18:24.  Therefore, we really only have three of these four statistics available for route fitting – the BTO residual mean, the BTO residual standard deviation, and the BFO residual standard deviation.

Regarding the standard deviation of the BFO reading errors, there has been much discussion in the past regarding the seemingly inconsistent criteria used by Inmarsat and by DSTG.  I have been modeling the BFO reading errors comprising (1) random electronic noise, (2) non-ergodic and non-stationary OCXO drift, (3) trigonometric quantization errors in the AES Doppler compensation code that give the appearance of being quasi-random for readings widely spaced in time, and (4) vertical speed errors of roughly 40 fpm or higher from the nominal vertical speed profile (caused primarily by turbulence).  I have developed a simple statistical model for the BFO reading noise, and this model gives results which are consistent with both sets of criteria.  This new BFO reading noise model is what I use in my current route fitter.

The second item of previously unused information is also significant in discriminating against incorrect routes.  That item is the fact that the BTO and BFO reading errors are uncorrelated with themselves and with each other, and, in effect, with most route-fitting parameters (with possibly one exception).  Note that it is the reading errors which are uncorrelated, not the actual expected values for BTO/BFO.  The degree of correlation of pairs of parameters is quantified using the Pearson correlation coefficient, and these values may be used as additional statistical metrics of the goodness of fit for the True Route.  The one exception that could have occurred is for the BFO reading errors, which could change linearly with time due to OCXO drift.  So, we must use that one correlation case (BFO residuals with respect to time) cautiously, knowing that it is possible such a drift might have occurred, although we do not see obvious cases of large linear drifts in previous flights.  It seems possible that a very cold cycling of the OCXO might produce a shift in the bias frequency, but it is not apparent that such a cycling would be more likely to produce greater linear drift of the bias frequency well after warm-up.  Small drifts of several Hz during a single flight are seen on prior flights, and it would not be surprising if they occurred in MH370 after 19:41.

We can substantially increase the number of statistical metrics that must be satisfied by a fit using the True Route by adding numerous correlation coefficients to the previously used means and standard deviations of the BTO and BFO residuals.  Using more metrics (~10-12 total) provides greater selectivity in route fitting and better discrimination against incorrect routes.

A requirement for effectively utilizing these additional correlation metrics is the development of a method which allows us to obtain best-fit BTO/BFO residuals which behave statistically the same as the BTO/BFO reading errors.  Those two parameters, the best-fit residuals and the reading errors, are generally not the same quantity.  They are the same only when the model used to predict the aircraft location in 4-D (with 7 assumed route parameters) is perfect.  No 4-D aircraft prediction model is perfect, especially in light of the expected errors in the GDAS temperature and wind data (which must be interpolated in 4-D for calculations along the route).  At best, there will be small (a few NM) systematic errors in the model predicted position at the handshake times.  The along-track and cross-track components of the position errors are systematic and must be allowed for in order to compare the expected BTO/BFO reading errors with the best-fit BTO/BFO residuals.  If this is not done, then accurate correspondence with statistical metrics is impossible.  In other words, just getting a fit consistent with the expected mean and standard deviation is not very discriminating because it ignores the even larger number of statistical metrics which the True Route must also satisfy.  The question is, how can we remove the systematic errors in the handshake location predictions of the flight model (using GDAS data) so that the best-fit residuals are essentially just the reading errors?

I have found that this is indeed possible if the systematic prediction errors are small.  Basically, the procedure is to fit lat/lon positions at the handshake times.  I use only the five handshake points from 19:41-00:11. These data can be well-fitted with a single set of seven route parameters with no maneuvers, and this eliminates the need to make any assumptions about the FMT except that it occurred prior to 19:41. The MH370 data recorded by Inmarsat between 19:41 and 00:11 UTC on 7-8 March 2014 is entirely consistent with a path during that period, while southbound and heading into the Southern Indian Ocean, without major maneuvers such as turns or holds or major speed changes. With the assumption of a preset route during this period using the auto-pilot, solutions may be found consistent with the BTO and BFO data, comprising 5 sets of BTOs and BFOs at 5 known handshake times. The 23:14 phone call BFOs are not used because there is no independent determination of that channel’s frequency bias (offset).

Once I have the five fitted locations, I compare them to the model-predicted locations to generate a set of five along-track position errors and five cross-track position errors.  Then I find the ground speed errors for each route leg that produce the along-track position errors.  I also find the lateral navigation errors that would produce the cross-track position errors.  Note that the cross-track position errors do not occur for LNAV (great circle) routes, but only for constant track and constant heading routes.  The ground speed errors are caused by airspeed errors and by GDAS along-track wind errors.  The airspeed errors are small (probably 1 kt or less) and are caused primarily by errors in the GDAS temperature data. The along-track wind error is probably at least several kts at any given location and time.  However, we only need the average wind error for each ~1-hour long leg along the route, and these leg average errors will generally be smaller.  I estimate that the overall along-track ground speed error using my model is about 1-2 kts.  That means that we must constrain the fit so that the difference between the model-predicted location and the best-fit location (in the along-track direction) is equivalent to a maximum ground speed error less than about 1-2 kts.  I also expect the ground speed errors to vary smoothly with time and location.  So, I put constraints on the GSEs in terms of peak value and smoothness during the route fitting process. 

For the constant track and constant heading navigation modes, the cross-track position errors are caused by a combination of cross-track GDAS wind errors and FMC lateral navigation bearing errors.  The lateral navigation errors are largely undocumented publicly, but I expect them to be a small fraction of a degree for the constant track modes. The lateral navigation errors in the constant heading modes are caused primarily by errors in the predicted cross-track winds, and they will be larger than the lateral navigation errors in the constant track modes.  In LNAV there are no cross-track position errors.

One benefit of this route fitting method is that it requires a very good, but not a perfect model.  It must predict the locations, based on the 7 route parameters and the GDAS 4-D wind and temperature data, with an accuracy of about 5-10 NM.  This is a significantly larger region than the location uncertainty (in one dimension) due to BTO reading noise.  Still, one can estimate the true locations with the full precision of the satellite data following the route fitting method described above, using the statistical metrics to separate the truly random portion of the residuals from the systematic, non-random model/GDAS errors.  When the synthesized locations are the True Route, the best-fit residuals will behave statistically identically with the BTO/BFO reading errors.

It is also possible to compute a single figure of merit for a given fit based on the 10-12 metrics described above.  I use Fisher’s chi-squared combination calculation that finds a single percentile value that is most consistent with the percentile values for each of the independent statistics being combined.  The percentile values represent the percentage of random trials which are no better than this fit result, assuming the null hypothesis.  In the MH370 case the null hypothesis is the same for each statistic – that the fitted route is the True Route.  The alternative hypothesis is that the route is not True for at least one of the statistics.  The expected value of all individual and combined percentiles is 50%; that is, half of the random trials will fit better, and half will fit worse.  We can use no other assumption than the route is True, because we have no idea what the values of the metrics should be when the route is not True.  We only know their expected values (and their standard deviations) for the case when the route is True. Thus, we expect the True Route will have an expected Fisher combined percentile value of 50% (with a standard deviation of 29%).  Non-True (i.e., incorrect) routes will have Fisher percentile values significantly less than 50%.  This is how incorrect routes are discriminated.  The route fitter objective function maximizes the Fisher percentile, so each trial is trying to match the expected values of the statistics for the True Route.

Two related activities have been carried out to validate the percentile calculations.  First, a simulated processor was coded which generated random BTO and BFO reading errors.  Then all the individual statistics and their percentile values were computed.  Finally, the combined Fisher percentile was computed.  Using 100,000 trials, the actual percentile values were found to be within 1% of their nominal values for all the individual and combined statistics.  In order to achieve this result, the statistics were segregated into four classes, each with is own Z statistic and probability density function.  The second validation experiment involved injecting random BTO and BFO reading errors into the route fitter program itself and verifying the correct combined percentiles were obtained.

It will be appreciated that this statistical fitting method, with a dozen or so metrics and with synthesized handshake locations, involves considerable computational time, so it is not ideal for identifying Regions of Interest (ROI).  The previous generation of route fitters using just BTO/BFO metrics is much more efficient for evaluating the very large number of combinations of route parameters in order to identify all ROI, which may then be refined and evaluated using the statistical fitting method for assessment and comparison.

So far, after a lengthy systematic search, we have identified quite a few ROI, and these are being evaluated with the new statistical method.  I have already demonstrated that one route in particular (LNAV at 180 degrees true bearing through BEDAX at LRC and at FL390, ending near 34.3S) is fully consistent with the True Route using the statistical method.  At the present time, numerous other ROI are being evaluated and compared. Preliminary results to date show them to be inferior fits, but this work is not yet completed.

The goal of this work was to develop a means to better discriminate among routes by using additional metrics, including PDA and numerous correlation coefficients, and to compensate for systematic errors in model-predicted locations so that the best-fit residuals may be directly compared with the known BTO/BFO reading errors.  Our initial results are promising.  It may actually be possible to demonstrate that there is only one route solution which is fully consistent with the satellite data.  More complete and detailed information will be provided once our assessments are finished.

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