The IGMARP Data Fusion Algorithm

The IGMARP Data Fusion Algorithm Andrew R. Runnalls University of Kent Computing Laboratory Technical Report 05-07 IGMARP (Iterative Gaussian Mixture Approximation of the Reduced-Dimension Posterior) is a data fusion algorithm for handling non-linear measurements, particularly ambiguous measurements (i.e. measurements for which the likelihood function may be multimodal), in conjunction with a linear or linearisable system model. It is particularly well suited to system models of high dimensionality, and applications where it is desired to interoperate with existing approaches using a Kalman Filter or multi-hypothesis Kalman Filter. The algorithm was developed under sponsorship from QinetiQ Ltd over the period 2001-5 as a means of integrating data from terrain-referenced navigation systems into a multiway integrated navigation solution also comprising an inertial navigation system (INS) and GPS. An example of a terrain-referenced navigation system is terrain-contour navigation (TCN), in which an air vehicle uses a radio altimeter or similar sensor to take measurements of the height above sea level of the terrain being overflown. The paper describes the mathematical foundations of the algorithm, and illustrates its application to an integrated TCN/INS system. Sec. 2 introduces the motivating application, TCN. Sec. 3 reviews the measurement update equations for the multi-hypothesis Kalman filter (MHKF), which represent an application of Bayes' Theorem to the case in which the prior distribution is a Gaussian mixture, and the likelihood function also has the form of a (slightly generalised) Gaussian mixture. Sec. 4 then discusses how the likelihood function can be computed for TCN, and gives the flavour of the resulting functions, which are by no means of a Gaussian mixture form; this motivates Sec. 5, which discusses how the MHKF approach can be adapted to handle more general likelihood functions, and introduces the key theorems on which the IGMARP method depends. Then Sec. 6 describes the algorithm itself, and Sec. 7 illustrates the results of applying the algorithm to TCN/INS flight data. Finally Sec. 8 discusses conclusions and possible further work.