Minimax Adaptive Estimation for Finite Sets of Linear Systems

TL;DR

This paper introduces a deterministic minimax-based estimation algorithm for finite sets of linear systems with uncertain parameters, which learns system dynamics and transitions to Kalman filtering once parameters are estimated.

Contribution

It proposes a novel minimax estimation method using constrained quadratic programming for finite set linear systems, bridging multiple-model estimation and Kalman filtering.

Findings

Estimator effectively learns system dynamics

Transitions to Kalman filter after parameter estimation

Provides a deterministic alternative to stochastic methods

Abstract

For linear time-invariant systems with uncertain parameters belonging to a finite set, we present a purely deterministic approach to multiple-model estimation and propose an algorithm based on the minimax criterion using constrained quadratic programming. The estimator tends to learn the dynamics of the system, and once the uncertain parameters have been sufficiently estimated, the estimator behaves like a standard Kalman filter.