A thorough study of the stability of PHD filters

Mahler´s PHD (Probability Hypothesis Density) filter provides a solution to multi-target tracking problems by jointly estimating the number of targets and their states through recursively propagating the state intensity function. However, the estimates of the intensity function and the number of targets comprise of an irreducible likelihood density term and they will therefore rely on particular likelihood calculation functions. Theoretical studies and simulations suggest that the likelihood function including measurement noise or number of sensor have an obvious impact on the estimation result. More importantly, this impact is unstable and uncertain. This instability applies to both the Sequential Monte Carlo implementation and Gaussian mixtures implementation of PHD filters.