Recursive state estimation for a set-membership description of uncertainty

TLDR

The paper addresses state estimation for linear dynamic systems with unknown disturbances and observation errors confined to bounded sets. The authors formulate the estimation problem under energy and instantaneous boundedness constraints, deriving ellipsoidal bounds for the state set and relating filtering, prediction, and smoothing to optimal control theory. They show that the admissible state set is an ellipsoid with computable center and weighting matrix, and that the resulting estimators, analogous to stochastic minimum‑variance filters, outperform existing set‑membership recursive estimation methods.

Abstract

This paper is concerned with the problem of estimating the state of a linear dynamic system using noise-corrupted observations, when input disturbances and observation errors are unknown except for the fact that they belong to given bounded sets. The cases of both energy constraints and individual instantaneous constraints for the uncertain quantities are considereal. In the former case, the set of possible system states compatible with the observations received is shown to be an ellipsoid, and equations for its center and weighting matrix are given, while in the latter case, equations describing a bounding ellipsoid to the set of possible states are derived. All three problems of filtering, prediction, and smoothing are examined by relating them to standard tracking problems of optimal control theory. The resulting estimators are similar in structure and comparable in simplicity to the corresponding stochastic linear minimum-variance estimators, and it is shown that they provide distinct advantages over existing schemes for recursive estimation with a set-membership description of uncertainty.