An Estimation Algorithm for Stochastic Linear Hybrid Systems with Continuous-State-Dependent Mode Transitions

We propose an estimation algorithm for stochastic linear hybrid systems with continuous-state-dependent mode transitions. We utilize Gaussian mixture approximations to overcome the exponentially growing complexity of the estimation problem. Furthermore, when computing the mode transition probabilities, we need to solve a multivariate integral that arises due to the continuous-state-dependent mode transition property. By Gaussian approximations, we simplify the integral and propose two methods for computing it: a Monte Carlo (MC) integration method for a general class of mode transition probability functions; and an analytical method for a special class of mode transition probability functions that can be expressed in terms of Gaussian probability density functions. We analyze the convergence and probabilistic error bound of the MC integration and demonstrate the performance of the proposed algorithm with an aircraft tracking example