On the effective action and the Cramér-Rao bound for multi-target tracking parameters

The inverse of the Fisher information, known as the Cramér-Rae bound, provides a bound on the estimator of a parameter and is fundamental for statistical analysis. It provides a minimum achievable variance or covariance for a parameter for a univariate or vector-valued parameter. However, multi-target systems often have parameters that are described by functions and the variance and covariance for point processes are themselves functions with spatial variates. Consequently, the usual formulation of the Cramér-Rae bound in these contexts is not applicable for providing a bound for the covariance of a point process. In this article we consider commonly used multi-target tracking models and determine Cramér-Rae lower bounds on the variance for different parameters, including the detection probabilities, the false alarm intensity, and the intensity of the process. This provides the first application of the Cramér-Ran bound for point processes for the analysis of practical algorithms.