The Cardinalized Probability Hypothesis Density Filter for Linear Gaussian Multi-Target Models

The probability hypothesis density (PHD) recursion propagates the posterior intensity of the random finite set of targets in time. The cardinalized PHD (CPHD) recursion is a generalization of the PHD recursion, which jointly propagates the posterior intensity and the posterior cardinality distribution. The incorporation of cardinality information naturally improves the accuracy and stability of state estimates. In general, the CPHD recursions are computationally intractable. This paper proposes a closed-form solution to the CPHD recursions under linear Gaussian assumptions on the target dynamics and birth process. Based on this solution, an effective multi-target tracking algorithm is developed. Extensions to non-linear models are also given using linearization and unscented transform techniques. The proposed CPHD implementations not only sidestep the need to perform data association found in traditional methods, but also dramatically improve the accuracy of individual state estimates as well as the variance of the estimated number of targets when compared to the standard PHD filter.