A performance bound for manoeuvring target tracking using best-fitting Gaussian distributions

In this paper, we consider the problem of calculating the Posterior Cramer-Rao Lower Bound (PCRLB) in the case of tracking a manoeuvring target. In a recent article [11 the authors calculated the PCRLB conditional on the manoeuvre sequence and then determined the bound as a weighted average, giving,an unconditional PCRLB (referred to herein as the Enumer-PCRLB). However, we argue that this approach can produce an optimistic lower bound because the sequence of manoeuvres is implicitly assumed known. Indeed, in simulations we show that in tracking a target that can switch between a nearly constant-velocity (NCV) model and a coordinated turn (CT) model, the Enumer-PCRLB can be lower than the PCRLB in the case of tracking a target whose motion is governed purely by the NCV model. Motivated by this, in this paper we develop a general approach to calculating the manoeuvring target PCRLB based on utilizing best-fitting Gaussian distributions. The basis of the technique is, at each stage, to approximate the multi-modal prior target probability density function using a best-fitting Gaussian distribution. We present a recursive formula for calculating the mean and covariance of this Gaussian distribution, and demonstrate how the covariance increases as a result of the potential manoeuvres. We are then able to calculate the PCRLB using a standard Riccati-like recursion. Returning to our previous example, we show that this best-fitting Gaussian approach gives a bound that shows the correct qualitative behavior, namely that the bound is greater when the target can manoeuvre. Moreover, for simulated scenarios taken from [11, we show that the best-fitting Gaussian PCRLB is both greater than the existing bound (the Enumer-PCRLB) and more consistent with the performance of the variable structure interacting multiple model (VS-IMM) tracker utilized therein.