Set-membership PHD filter

The paper proposes a novel Probability Hypothesis Density (PHD) filter for linear system in which initial state, process and measurement noises are only known to be bounded (they can vary on compact sets, e.g., polytopes). This means that no probabilistic assumption is imposed on the distributions of initial state and noises besides the knowledge of their supports. These are the same assumptions that are used in set-membership estimation. By exploiting a formulation of set-membership estimation in terms of set of probability measures, we derive the equations of the set-membership PHD filter, which consist in propagating in time compact sets that include with guarantee the targets' states. Numerical simulations show the effectiveness of the proposed approach and the comparison with a sequential Monte Carlo PHD filter which instead assumes that initial state and noises have uniform distributions.