Reduced Mode-Tree Expansion Rates in Jump Markov Estimators

Abstract

In jump Markov linear systems, estimators usually consider possible mode changes at each measurement occasion. This paper shows that mode-tree expansion in jump Markov estimators can be done at rates lower than the measurement rate, with great savings in computations. In fact, even gains in performance can be made by choosing the right mode expansion rate. The paper shows the results from Monte Carlo simulations of a simple two-mode Markov system. The estimators used are the pruned optimal Bayesian estimator and the generalized pseudo Bayesian of order 2. The estimators are run with mode-tree expansions at the measurement rate as well as with reduced rates. The results show considerable savings in computations and optimum RMSE performance for a mode-tree expansion rate 2-4 times the highest mean transition rate of the modes. A tractable approximation of the CRLB for jump Markov linear systems is also introduced as a performance reference for the cases tested.