Analysis of Methods Used to Reconstruct the Flight Path of Malaysia Airlines Flight 370

1. Introduction. In the early hours of March 8, 2014, a Malaysia Airlines Boe-ing 777 disappeared en route from Kuala Lumpur to Beijing with 239 people on board [14]. At the time of writing this article there has been no confirmation of any debris from the aircraft and no survivors have been found. 1 If the crash site is not discovered, this tragedy may become one of the great aviation mysteries. The disappearance of MH370 is all the more mysterious in the age of highly accurate global navigation and communications systems. During flight, commercial aircraft use satellite communications links to exchange information with ground stations via the Aircraft Communications Addressing and Reporting System (ACARS) [7]. Although most of the functionality of ACARS was disabled early in the flight, for six hours after the last radar contact the aircraft and ground station exchanged a series of short messages, which we will refer to as pings. These messages were relayed to a ground station in Perth, Australia, by the Inmarsat 3-F1 satellite which was in a geosynchronous orbit over the equator at longitude 64.5 • E. A team of engineers at the British satellite company Inmarsat discovered that for each ping, ACARS recorded three pieces of data: the ping time, the Burst Timing Offset (BTO), and the Burst Frequency Offset (BFO). The BFO, which is discussed in Section 3 below, is a quantity that is related to the Doppler shift due to the motion of the aircraft relative to the satellite. The BTO is a time delay measured at the ground station which the satellite engineers used to accurately determine the distance between the aircraft and the satellite at each ping time [2]. As we see in Figure 1.1, the set of all points on a sphere (the earth) that are at a fixed distance from a given point (the satellite) forms a circle. Therefore, factoring in the speed and fuel constraints of the aircraft, the satellite engineers determined that at each ping time the aircraft was located somewhere on a segment of a circle, which we call a ping arc. Each such circle is characterized by a ping arc angle, which is the angle between the aircraft and the satellite, as measured from the center of the earth (see Figure 1.1). Consequently, they were able to deduce that at the last ping time, the aircraft was located somewhere on a ping …