Convergence Results for the Gaussian Mixture Implementation of the Extended-Target PHD Filter and Its Extended Kalman Filtering Approximation

The convergence of the Gaussian mixture extended-target probability hypothesis density GMEPHD filter and its extended Kalman EK filtering approximation in mildly nonlinear condition, namely, the EK-GM-EPHD filter, is studied here. This paper proves that both the GM-EPHD filter and the EK-GM-EPHD filter converge uniformly to the true EPHD filter. The significance of this paper is in theory to present the convergence results of the GM-EPHD and EK-GM-EPHD filters and the conditions under which the two filters satisfy uniform convergence.