A CPHD approximation based on a discrete-Gamma cardinality model

The Cardinalized Probability Hypothesis Density (CPHD) filter has become one of the most acclaimed algorithms for multi-target Bayesian filtering due to its ability to accurately estimate the number of objects and the object states in tracking scenarios affected by clutter. The CPHD filter generalizes the Probabilistic Hypothesis Density (PHD) filter by jointly propa- gating the first-order multi-target moment (intensity function) along with the entire probability distribution on the number of targets (cardinality distribution). In general, the CPHD recursion is computationally intractable, however successful approxima- tions have been devised with reported computational complexity dominated by O(m³) operations per filtering iteration, where m is the number of measurements. Room for improvement was originally acknowledged by Mahler, who conceived the idea of approximating the cardinality distribution by two-parameter distributions. In this paper, we further explore this idea to provide an efficient approximation of the CPHD filter where the cardinality distribution is modeled as a discretized Gamma distribution. Experiments show that the resulting filter is less computationally complex than the standard implementation of the CPHD filter but shows similar cardinality accuracy and variance.