Computationally efficient PCRLB for tracking in cluttered environments: measurement existence conditioning approach

Abstract

In this paper, we consider the problem of calculating the posterior Cramer-Rao lower bound (PCRLB) for tracking in cluttered domains in which there can be both missed detections and false alarms. We introduce a novel approach, whereby we condition on the 'existence sequence', which is a sequence of zeros and ones depending on whether at least one measurement exists at each sampling time. An existing Riccati-like recursion then provides a PCRLB conditional on each existence sequence, and an unconditional PCRLB is calculated as a weighted average of these conditional bounds. This new approach is referred to as 'measurement existence sequence conditioning' (MESC). The MESC approach is compared with both the information reduction factor (IRF) approach and measurement sequence conditioning (MSC) approach. It is proved that the MESC approach provides a less optimistic bound than the IRF approach. This is a desirable property, as it shows that the MESC bound is more realistic than the IRF bound. It is also shown that the MESC bound provides a more optimistic bound than the MSC approach. Although this is undesirable, in the simulations differences between the MESC and MSC bounds are very small (typically less than 5%). This suggests that the key reason for the over-optimism of the IRF bound is the fact that it does not take into account the effect of missed detections. Although the MESC approach treats cases with one or more detection differently to the MSC approach, the similarity between these two bounds suggests that discriminating between such cases is of less importance. However, the greatest value of the new MESC approach is that the bound can be enumerated precisely, without the need for inefficient and computationally expensive sampling. In case studies, we show that the MESC bound can be calculated 10-100 times more quickly than the MSC bound. It is concluded that the novel MESC formulation introduced herein represents an exciting development in the determination of the PCRLB in cluttered environments.