| A performance bound for manoeuvring target tracking using best-fitting gaussian distributions (2005) | |||||||
Abstract | |||||||
| 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 (Bessell et al., 2003) 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 utilising 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 behaviour, namely that the bound is greater when the target can manoeuvre. Moreover, for simulated scenarios taken from Bessell et al. (2003), 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 utilised therein. | |||||||
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