A bank of maximum a posteriori estimators for single-sensor range-only target tracking

In this paper, we study estimation consistency of single-sensor target tracking using range-only measurements. We show analytically that the cost function minimized by the iterated extended Kalman filter (IEKF) has up to three local minima, which can potentially result in inconsistency or even divergence. To address this issue, we instead propose a bank of maximum a posteriori (MAP) estimators to determine the target state-space trajectory. In particular, we use the local minima of the IEKF cost function at each time step as highly accurate initial hypotheses to start a bank of iterative nonlinear optimizations. Moreover, we employ pruning and marginalization to control computational complexity. Extensive Monte Carlo simulations show that the proposed algorithm significantly outperforms the IEKF, the unscented Kalman filter (UKF), the bank of IEKFs, the particle filter (PF), and the standard MAP, both in terms of accuracy and convergence speed.