Aerospace and Electronic Systems Magazine April 2017 - 57

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of possible aircraft paths from 18:01 until 00:19. To account for
distance traveled from 00:19 until the crash, they used a probability distribution developed by the ATSB. The motion model for the
aircraft employed a random sequence of deliberate maneuvers followed by periods of cruising in which the speed and direction are
almost constant. This was felt to model the behavior of a commercial aircraft, which typically operates by maintaining a constant
speed through the air, altitude, and heading. The speed and heading
variations of the aircraft during cruise periods are modeled by the
use of an Ornstein Uhlenbeck process. The periods between maneuvers were given an exponential distribution, and the choice of
speed and heading resulting from the maneuver was governed by
an additional probability distribution. A number of possible flight
models were used based on expert information provided by Boeing
and other members of the Flight Path Reconstruction group. The
modeling of the actual flight path over ground is done carefully
and in great detail accounting for effects such as wind speed and
direction during flight.
This motion model was initiated from a prior distribution obtained from applying a Kalman filter to the radar data to compute
a probability distribution on position and velocity at 18:01. The
speed through the air was taken to be uniformly distributed between Mach 0.73 and Mach 0.84; the altitude was assumed to
be uniformly distributed between 25,000 and 43,000 ft. Using
these assumptions the authors produced a large number of sample
paths (particles) for the aircraft. The large number of particles is
necessitated by the well-known fact that the number of particles
required for an accurate representation of a probability density
increases exponentially as the number of dimensions increases
[2]. In contrast to the usual resampling approach applied to particle filters to maintain a fixed number of particles, the authors
used a branching mechanism to repeatedly construct full paths.
The method resampled each particle separately by branching a
new set of particles from each parent. This leads to an exponential growth in the number of paths, which was balanced by pruning low likelihood paths. Since the authors were not dealing with
a real-time filtering problem, they could look ahead and apply the
likelihood functions corresponding to the measurements obtained
from satellite messages and failed phone calls to compute the
likelihood of a path and remove those with low likelihood. This
branching method was employed to guarantee a rich set of paths
from which to estimate the aircraft's likely paths and final crash
location.
The authors developed detailed measurement models, adjusted
for biases, and carefully estimated measurement errors in producing the likelihood functions for the BTO and BFO measurements
obtained from the satellite messages and for the BFO information contained in the unanswered phone calls. The statistics of the
measurement errors were tested against known flight paths for the
same or similar aircraft. The particle filter methodology was used
to predict the landing location for a number of comparable flights
for which the flight path is known. Some of these were flights the
MH370 aircraft made before the crash. They down-sampled the
message information from these flights to approximate the information in the satellite messages obtained for the MH370 flight and
computed a distribution of landing positions using their particle
APRIL 2017

filter methodology and models. They compared the actual containment statistics for the aircraft landing place to those predicted by
the filter and concluded that the filter was a bit conservative in the
sense of predicting larger containment areas than were observed.
They concluded that this was an appropriate and reasonable bias
for the search area predictions.
The final step was to apply the likelihood functions from the
satellite and missed phone call messages to their particle filter to
obtain a distribution of aircraft locations at 00:19. To the location
of each particle at 00:19, they applied the distribution of distances
and headings traveled to the time of crash supplied by the ATSB
to obtain the prior distribution on the location of the crash. This
distribution, shown in Figure 10.10 of the book, formed the basis
for the underwater area being searched by the Australians in the
hope of finding the wreckage of MH370. The authors do not say
what the containment probability is for this search region, but the
Australian Deputy Prime Minister was quoted [3] as saying that
the region contains 97% of the probability in the distribution. As
of the time this review was written, the search had not found the
wreckage. An ATSB analysis report [4] published on December
20, 2016 suggested an area of 25,000 square kilometers just north
of the present search area as a high likelihood area for the location
of the wreckage given the failure of the present search. However,
The Associated Press reported [8] Australian Transport Minister
Darren Chester as suggesting that an extension of the hunt ... was
unlikely, noting that the report "does not give a specific location of
the missing aircraft."

COMMENTS
The authors deserve high praise for doing a careful, diligent, and
analytically sound job of producing this prior probability distribution. The care with which the measurement models were developed and tested is exceptional as well as the modeling of the possible aircraft flight paths. It is impressive that the ATSB provided
the time and funding to perform these analyses. The book is well
written and a pleasure to read. The analytic details and the models
used are presented clearly and in detail. The use of a branching
process to develop the sample paths is an important and useful innovation for this type of search planning.
The book uses a new and improved method of incorporating
debris information into a search object location distribution. In the
past, as for example in the AF447 search [5], the information from
floating debris recovered after an aircraft crash or boat sinking was
incorporated into the search object location distribution by reverse
drift. This is not a correct method. In chapter 11, the book uses the
location and time of the finding of the flaperon from the MH370
on Reunion Island and an empirical drift model to compute a likelihood function for the crash location of the aircraft. They applied
this likelihood function to update the prior in the standard Bayesian
fashion. However the high likelihood regions of this function are
in very low probability areas of the prior, so the resulting posterior
differed only slightly from the prior. The use of this type of likelihood function for incorporating debris information was suggested
in [6]. The authors are the first to apply it to a search. This should
become standard practice in the future.

IEEE A&E SYSTEMS MAGAZINE

Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine April 2017