New Approximation Techniques in Nonlinear Filtering
Thursday 25 October 2007, 1300-1400
Richard Vinter, Imperial College London
One of the most important areas of application of nonlinear filtering is to Bayesian target tracking: that is, estimating the position of a target from noisy sensor measurements. In this area, linear Gaussian models are commonly used to describe motion of the target and sensor platform. The estimation problem is typically non-linear because of the nature of the measurement process which, depending on the precise nature of the application, provides noisy information about angle-to-line-of-sight (or bearing), range or range rate, all of which quantities are nonlinear functions of target position.
Traditional approaches to target tracking are based on the application of the Kalman filter to a linearization of the underlying equations about current estimates (the extended Kalman filter approach). However, the Kalman filter breaks down (fails to provide convergent estimates) when applied to many challenging tracking problems involving, perhaps, multiple sensor platforms or degenerate configurations where the measurements provide very little information about some aspects of target motion. This accounts for the great interest in recent years in particle filters; according to this approach the conditional density, on which estimates of target position are based, is approximated by a discrete distribution obtained by carrying out on-line Monte Carlo tests. The ability of particle filters to provide useful estimates for difficult tracking problems where extended Kalman filters are inadequate is now well documented. Their main disadvantage however is the large computation requirements of such tracking algorithms. The question therefore arises whether tracking algorithms can be devised which achieve the accuracy of particle filters for difficult tracking problems but whose computational demands are comparable to those of Kalman filters. We show that, if we focus on specific classes of tracking problems, 'bearings only' tracking or 'range only' tracking for example, this goal is achievable. The filters however need to be tailored to the geometric structures of the measurement process concerned. We examine the performance of new filters, devised at Imperial College according to these principles, in collaboration with Martin Clark. We illustrate their benefits in a range of challenging scenarios where particle filters are computationally expensive, and where the extended Kalman filter fails altogether.