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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 present a novel formulation of the PCRLB in which we initially determine a bound conditional on the sequence of measurements available. We then create an unconditional bound as a weighted average of these conditional PCRLBs. This new bound is proven to be less optimistic than the standard formulation of the PCRLB for cluttered environments recently developed [1, 2] and will therefore better predict optimal estimator performance. At each stage, the conditional PCRLB must evaluate the effect of the uncertain measurements, and we extend previous work [2] to show that the measurement origin uncertainty manifests itself as a single information reduction factor (IRF) that is dependent on the number of measurements available. We also present some useful approximations when the false alarm rate is low. Simulations then consider the problems of 1) determining the CRLB for the point of impact of a ballistic missile, and 2) determining the PCRLB for tracking a nearly constant-velocity (NCV) target in a high clutter environment. In each case, we compare the new bound with the standard approach, and as expected the new CRLB/PCRLB can be seen to be less optimistic. Moreover, in case 1) we compare the new CRLB with a heuristic bound specially constructed for this problem, and a maximum likelihood estimator (MLE). The new bound both compares favorably with the heuristic bound, and shows close agreement with the performance of the MLE. The new bound is therefore an accurate predictor of filter performance in this case. In example 2) we demonstrate some interesting features of the new theory. Of particular interest we determine both precisely when the new bound will be significantly greater than the standard bound and when the two bounds will be virtually identical. This is useful in determining when the new approach, with its greater computational burden, should be preferred to the established approach. We conclude that the novel PCRLB formulation introduced herein represents an exciting development in the determination of RMSE performance bounds in cluttered environments.

The development of a general framework for the systematic management of multiple sensors in target tracking in the presence of clutter is described. The basis of the technique is to quantify, and subsequently control, the accuracy of target state estimation. The posterior Cramer-Rao lower bound (PCRLB) provides the means of achieving this aim by enabling us to determine a bound on the performance of all unbiased estimators of the unknown target state. The general approach is then to use optimization techniques to control the measurement process in order to achieve accurate target state estimation. We are concerned primarily with the deployment and utilization of limited sensor resources. We also allow for measurement origin uncertainty, with sensor measurements either target-generated or false alarms. An example in which the aim is to track a submarine by deploying a series of constant false-alarm rate passive sanobuoys is presented. We show that by making some standard assumptions, the effect of the measurement origin uncertainty can be expressed as a state-dependent information reduction factor which can be calculated off-line. This enables the Fisher information matrix (FIM) to be calculated quickly, allowing Cramer-Rao bounds to be utilized for real-time, dynamic sensor management. The sensor management framework is shown to determine deployment strategies that enable the target to be accurately localized, and at the same time efficiently utilize the limited sensor resources.

Widemo and Owens presented a model that calculates the expected copulation rates of males on leks of a range of sizes. They claim that a negative relationship between lek size and male mating skew will result in low-ranking males having greater optimal lek sizes than higher ranking rivals. Widemo and Owens offered no proof of their claim, andtheir model assumes that the rank of a male does not change as lek size increases, whereas in reality, rank may change as more males arrive. We present a general model that allows rank to change as lek sizeincreases. We show that the crucial determinant of whether optimal lek size increases with male rank is whether relative competitive differences increase with lek size. Contrary to the claim of Widemo and Owens, the relationship between skew and lek size has no direct bearing on the optimal levels of aggregation of males of different rank. Weshow that a negative relationship between skew and lek size can exist even when high-ranking males have the greatest optimal lek sizes. [ABSTRACT FROM AUTHOR]