An autoregressive (AR) model based stochastic unknown input realization and filtering technique

TL;DR

This paper introduces an AR model-based approach for realizing and filtering stochastic unknown inputs in linear discrete-time systems, enabling effective state estimation without prior input information.

Contribution

It proposes a novel AR model-based unknown input realization method combined with ERA and Kalman filtering, reducing computational cost with a reduced order model.

Findings

The method accurately recovers input statistics from output data.

The approach effectively estimates states in numerical examples.

The reduced order filter decreases computational complexity.

Abstract

This paper studies the state estimation problem of linear discrete-time systems with stochastic unknown inputs. The unknown input is a wide-sense stationary process while no other prior informaton needs to be known. We propose an autoregressive (AR) model based unknown input realization technique which allows us to recover the input statistics from the output data by solving an appropriate least squares problem, then fit an AR model to the recovered input statistics and construct an innovations model of the unknown inputs using the eigensystem realization algorithm (ERA). An augmented state system is constructed and the standard Kalman filter is applied for state estimation. A reduced order model (ROM) filter is also introduced to reduce the computational cost of the Kalman filter. Two numerical examples are given to illustrate the procedure.