Error Analysis on the Initial State Reconstruction Problem

TL;DR

This paper introduces a real-time method for estimating the initial state of linear dynamical systems with noisy observations, providing error covariance and stability guarantees for the estimator.

Contribution

It presents a novel real-time estimation technique with stability analysis and conditions for asymptotic stability in linear systems.

Findings

Estimator error is Lyapunov stable at each step

Error covariance matrix is known in real time

Conditions for asymptotic stability are established

Abstract

In this paper we propose a method to estimate the initial state of a linear dynamical system with noisy observation. The method allows the user to have estimations in real time, that is, to have a new estimation for each new observation. Moreover, at each step, the covariance matrix of the error is known and it is proved that the dynamic of the state estimator error is always Lyapunov stable. Also, %necessary and sufficient conditions are given to guarantee asymptotic stability for the error dynamics of an LTI dynamical system, which is itself an LTV system.