Stability of the modified probabilistic data association filter: Lyapunov function based analysis

The probabilistic data association filter (PDAF) is known to provide better tracking performance than the standard Kalman filter in a cluttered environment. In this paper, the stability of the modified PDAF of Fortmann et al. (1985), in the presence of uncertainties with regard to the origin of a measurement, is investigated. The modified Riccati equation derived by approximating two random terms with their expectations is used to prove the stability of the modified PDAF. A new Lyapunov function based approach, which is different from the quantitative evaluation of Li and Bar-Shalom (1991), is pursued. With the assumption that the system and observation noises are bounded, specific tracking error bounds are established.