Robust Multiple Model Filtering with Uncertain Transition Models
Luca F. Bertuccelli · AIAA Guidance, Navigation, and Control Conference and Exhibit · 2008
The goal of multiple model estimation is to estimate the state and covariance of a hybrid system. In this paper, we are concerned about stochastic hybrid estimation, where common applications include Air Traffic Control (ATC) and UAV multi-target tracking problems. The basic modeling assumption is that the system switches between individual dynamic models according to a probabilistic process modeled with a known Markov Chain. Unfortunately, uncertainty in the parameters of this Markov Chain can degrade estimator performance by generating a covariance mismatch from the true covariance. A main concern of this paper is the issue of covariance underestimation in which the estimator is overly confident about the state estimate, as it can ultimately lead to increased estimation errors and tracking inefficiencies. We therefore introduce a new filter formulation that tackles the specific problem of estimator overconfidence and find the largest covariance matrix admissible given a Bayesian prior on the uncertain Markov Chain parameters. At each step of the filter, the uncertain Markov Chain is propagated by using Monte Carlo sampling, and a small quadratic program is solved that maximizes the trace of the robust covariance matrix within an admissible set. Our simulations show improved estimator performance over techniques that do not account for this uncertainty in the context of two tracking problems.