Objective functions for bayesian control-theoretic sensor management, 1: multitarget first-moment approximation

Multisensor-multitarget sensor management is, ultimately, a problem in optimal nonlinear controitheory for multi-object stochastic systems. This paper is the first of a series concerned with formulating a foundational but computationally viable basis for control-theoretic sensor management based on an intuitively sensible Bayesian paradigm. Single-sensor, single-target control requires a core objective function (typically, a Mahalanobis distance) that determines the degree to which the sensor Field of View (FoV) overlaps the predicted target track. We address the problem of defining Bayesian control-theoretic objective functions for multisensor-multitarget problems. In future papers we will analyze a range of such functions, based on a number of optimization and computational-simplification strategies. In this paper we concentrate on one particular computational approach: multitarget filtering using firstorder multitarget moment approximation ("PHD filter"). We show that the PHD filter can be generalized to include state-dependent probability of detection. The PHD filter is then used as the prediction step of a control process, the objective of which is to maximize the expected RMS number of targets.