Performance Analysis of Hybrid Estimation Algorithms

In this paper, we analyze the performance of estimation algorithms for discrete-time stochastic linear hybrid systems. The problem of being able to estimate both the discrete and continuous states of a hybrid system given only the continuous output sequence is a difficult one, and while algorithms [1], [2] exist for this purpose, little has been proved on the limitations of these algorithms, or even the dependence of their performance on system parameters. We find necessary conditions to guarantee the convergence of these hybrid estimation algorithms. We also derive expressions to determine bounds on the discrete mode detection delay. These conditions also provide a method to predict a priori which transitions in a hybrid system are relatively easy to detect, as a function of the system parameters. Finally, we validate our conditions and predictions using first a simple yet illustrative 1-D example, and then a more complex aircraft tracking example.