Discrete-time minmax filtering subject to a norm-constrained state estimate

Abstract

This paper considers discrete-time minmax filtering when the state estimate, or part of the state estimate, is subjected to a norm constraint. Derivation and use of minmax filters are motivated by the desire to estimate systems’ states in a more robust manner. There are various methods for enforcing constraints on the state estimate using the Kalman filter, however, enforcing constraints on the state estimate in the minmax framework has been less explored. This paper presents the derivation of a minmax filter for a discrete-time system with a full or partial equality norm constraint on the state estimate. This is accomplished by modifying the minmax filter’s optimization problem using Lagrange multipliers to enforce the constraint on the state estimates.