Framework for state and unknown input estimation of linear time-varying systems

TL;DR

This paper introduces an extended Double-Model Adaptive Estimation method for state and unknown input estimation in linear time-varying systems, overcoming traditional existence condition limitations.

Contribution

It extends the Double-Model Adaptive Estimation approach to estimate states and unknown inputs without the need for the existence condition.

Findings

The proposed method successfully estimates states and unknown inputs.

Numerical examples show improved performance over existing methods.

The approach works for systems where traditional conditions are not met.

Abstract

The design of unknown-input decoupled observers and filters requires the assumption of an existence condition in the literature. This paper addresses an unknown input filtering problem where the existence condition is not satisfied. Instead of designing a traditional unknown input decoupled filter, a Double-Model Adaptive Estimation approach is extended to solve the unknown input filtering problem. It is proved that the state and the unknown inputs can be estimated and decoupled using the extended Double-Model Adaptive Estimation approach without satisfying the existence condition. Numerical examples are presented in which the performance of the proposed approach is compared to methods from literature.