Quantifying the Bias Dynamics in a Mode-Based Kalman Filter for Stochastic Hybrid Systems

Many estimation algorithms proposed for stochastic hybrid systems (SHS) typically involve a bank of (mode-based) Kalman filter used to estimate the continuous states. The accuracy of discrete state knowledge has a significant impact on the error performance of the mode-based Kalman filter. In this paper, we quantify this relationship between the mode estimation quality and continuous state estimation in terms of the bias dynamics of the mode-based Kalman filter. We also derive sufficient conditions for statistical convergence of the bias dynamics and illustrate the stable region in which the mode-based Kalman filter has high tolerance to mode estimation error. The fundamental theoretical results are validated via simulation of an SHS. The analysis presented in this work is important for many practical applications such as quantifying the impact of network topology error in a smart grid.