Generalized Iterated Kalman Filter and its Performance Evaluation

In this paper, we present a generalized iterated Kalman filter (GIKF) algorithm for state estimation of a nonlinear stochastic discrete-time system with state-dependent multiplicative observation noise. The GIKF algorithm adopts the Newton-Raphson iterative optimization steps to yield an approximate maximum a posteriori estimate of the states. The mean-square estimation error (MSE) and the Cramér-Rao lower bound (CRLB) of the state estimates are also derived. In particular, the local convergence of MSE of GIKF is rigorously established. It is also proved that the GIKF yields a smaller MSE than those of the generalized extended Kalman filter and the traditional extended Kalman filter. The performance advantages and convergence of GIKF are demonstrated using Monte Carlo simulations on a target tracking application in a range measuring sensor network.