Seminars
Finance seminar: 1pm Thursday 25th November, MS457 (Research Collection).
New Gaussian Mixture Techniques For Filtering and Smoothing Of Discrete-Time Gauss-Markov Jump Markov Systems, W. P. Malcolm, National ICT Australia, Research School of Information Sciences and Engineeering, The Australian National University, Canberra, Australia. NB: This seminar is joint work with:
  • Prof. Robert J. Elliott Haskayne School of Business, University of Calgary
  • Prof. Francois Dufour Universite Bordeaux, France

Abstract:

In this seminar we extend the new state and mode estimation algorithms computed by Professors Robert J Elliott and Francois Dufour. The algorithm developed by Elliott and Dufour is distinct from extant methods, such as the so called Interacting Multiple Model algorithm (IMM) and Sequential Monte Carlo methods, in that it is precise; that is, their algorithm is based upon well defined approximations of the "exact" hybrid filter.

To compute our smoothing algorithm, we exploit a duality between forwards and backwards (dual) dynamics. The natural framework to exploit this duality is the method of reference probability, whereby one chooses to work under a new, or 'reference' probability measure. Under this new measure, both the state process and the observation process are independently and identically distributed with Gaussian statistics, however, the Markov chain, whose state value fully determines the system dynamics, remains unchanged. A closed form expression is given for the smoothed estimate of state. An interesting feature of our smoother is it provides a new degree of freedom, that is, the product decomposition of the smoother density is approximated by mutually independent Gaussian mixtures. This means the chosen accuracy of 'the past', (influencing the smoother density), is independent of the chosen accuracy of 'the future', influencing the smoother density. To fix the memory requirements of our smoother we extend ideas based upon the so called K-best paths problem and the Viterbi algorithm.

Since our smoothing algorithm depends upon its corresponding filter, we start by giving a review of the jump Markov system filter developed by Elliott and Dufour. This filter has been shown to significantly outperform the IMM in conventional object tracking scenarios and the more challenging bearings only maneuvering target tracking problem. Applications of the work presented are immediate in Defence Science, for example, tracking, IMMJPDA, and the so called third party targeting problem including maneuver scenarios, such as those arising in Network Centric Warfare. Further, the algorithm we present does not suffer any of the technical difficulties arising in particle filter tracking methods, such as the so called degeneracy problem, or the inclusion of a stationary mode for a maneuvering target.