Perspective Chapter: Insights from Kalman Filtering with Correlated Noises Recursive Least-Square Algorithm for State and Parameter Estimation

TL;DR

This paper introduces a novel Kalman filtering algorithm that utilizes noise correlation to improve the joint estimation of states and parameters in linear stochastic systems, supported by theoretical analysis and numerical validation.

Contribution

The study proposes the KF-CN-RGELS algorithm, which exploits noise correlation in Kalman filtering to enhance estimation accuracy for states and parameters.

Findings

Estimation accuracy increases with positive noise correlation.

The proposed algorithm outperforms standard Kalman filters in simulations.

Theoretical analysis confirms the impact of noise correlation on estimation precision.

Abstract

This article explores the estimation of parameters and states for linear stochastic systems with deterministic control inputs. It introduces a novel Kalman filtering approach called Kalman Filtering with Correlated Noises Recursive Generalized Extended Least Squares (KF-CN-RGELS) algorithm, which leverages the cross-correlation between process noise and measurement noise in Kalman filtering cycles to jointly estimate both parameters and system states. The study also investigates the theoretical implications of the correlation coefficient on estimation accuracy through performance analysis involving various correlation coefficients between process and measurement noises. The research establishes a clear relationship: the accuracy of identified parameters and states is directly proportional to positive correlation coefficients. To validate the efficacy of this algorithm, a comprehensive comparison is conducted among different algorithms, including the standard Kalman filter algorithm and the augmented-state Kalman filter with correlated noises algorithm. Theoretical findings are not only presented but also exemplified through a numerical case study to provide valuable insights into practical implications. This work contributes to enhancing estimation accuracy in linear stochastic systems with deterministic control inputs, offering valuable insights for control system design and state-space modeling.