Quantifying the Estimation Error for a Constant-Gain Tracker

We present a new method of calculating approximate probabilistic bounds for the state estimation error of a constant-gain Kalman filter in nonlinear multivariate systems. A critical part of the method is an analysis of the convergence in distribution and the mean-square error of the algorithm. Based on such analysis, a surrogate error process is constructed to mimic the dynamics of the unknown tracking error. We analyze the distance between the true filtering error and the surrogate process and show that it can be bounded under some circumstances. The surrogate process provides a means of computing probabilistic bounds and confidence regions for the tracking error.