Approximate EKF-based multiple model filters: a case study

Abstract

In target tracking, the track filter is an important element. It is also quite important that it is implemented efficiently. This is even better seen if one thinks of it that a filter is running for each data association hypothesis and in a real multi target tracking application the number of hypotheses, that need to be updated every scan, may easily be in the order of thousands. A standard 'single model' building block for a track filter is the (Extended) Kalman Filter (EKF). Multiple model filters, such as the popular and widely used Interacting Multiple Model filter (IMM) or the recently developed Multiple Model Multiple Hypothesis filter (M3H), are based on banks of EKF's that run in parallel and interact according to an underlying Markov transition modeling assumption. It is well known that, in case of a single model filter, the standard Kalman Filter gains and covariances can be calculated off line, when the process noise covariance and the measurement noise covariance are known. Unfortunately, this does not hold for the two types of multiple model filters, mentioned before. The main reason for this is that these multiple model filters interact. In this paper we investigate several methods to (partially) do the calculations off line and thus use less computations, while at the same time aiming at a minimal loss of performance. We will compare such an approximate IMM or M3H filter with the full on line IMM or M3H filter, both in terms of computational load and performance.