Estimation for Uncertain Linear Systems with Jump Parameters.

摘要

The problem of state estimation for a class of linear discrete-time dynamical systems with unknown time-varying parameters is investigated. Attention is focused mainly on systems with unknown noise statistics. Two different approaches to modelling and estimation under time-varying uncertainties are investigated. In one of the approaches, a finite state Markov chain model is used for the jump parameters which can take values only from a finite set with transitions from one value to another determined by a Markov transition probability matrix. The transition matrix may or may not be known; if unknown, it is assumed to belong to a finite set. A Bayes optimal solution is obtained in a recursive form and several suboptimal algorithms are discussed to alleviate the large storage and computation requirements of the optimal estimator. The asymptotic behavior of the optimal solution for the case of unknown transition probabilities is analyzed. In the second approach, multiple bounds on the unknown parameter values and its time derivatives are assumed to be available. A detection-estimation approach is proposed for state estimation and its asymptotic behavior is analyzed. The main objective of the proposed approach is to reduce the pessimism of the standard minimax estimator for large observation records and large uncertainties, while retaining its desirable small-sample properties.