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Multitarget filtering using a multitarget first-order moment statistic

The theoretically optimal approach to multitarget detection, tracking, and identification is a suitable generalization of the recursive Bayes nonlinear filter. This approach will never be of practical interest without the development of drastic but principled approximation strategies. In single- target problems, the computationally fastest approximate filtering approach is the constant-gain Kalman filter. This filter propagates a first-order statistical moment of the single-target system (the posterior expectation) in the place of the posterior distribution. This paper describes an analogous strategy: propagation of a first-order statistical moment of the multitarget system. This moment, the probability hypothesis density (PHD), is the density function on single-target state space that is uniquely defined by the following property: its integral in any region of states space is the expected number of targets in that region. We describe recursive Bayes filter equations for the PHD that account for multiple sensors, missed detections and false alarms, and appearance and disappearance of targets.