V3I5P125

Gaussian Bayesian Estimation in State-Space Models for Linear Dynamic Systems under Correlated Noise Influence 

Do Hoai Nam^1*

Abstract

This paper presents a unified framework for state estimation in linear dynamic systems subjected to time-correlated noise. Based on Gaussian Bayesian theory, a set of generalized and explicit expressions is constructed to describe the propagation of mean and state covariance as well as the update of information when discrete measurements occur in phase space. The noise models considered include process noise and measurement noise, in which the measurement noise is modeled by a linear noise-generation system to accurately characterize temporal correlation. The paper establishes the entire estimation algorithm in a generalized matrix form and subsequently develops specific implementations for multi-state systems. The result is a systematic, rigorous set of formulas capable of being applied to control systems, sensors, or aerospace vehicles that require high-accuracy state estimation. The proposed method contributes to improving estimation reliability in environments where noise models can no longer be assumed white, and expands applicability to practical problems with strongly correlated measurement noise.

Keywords:

Bayesian estimation, phase space, linear dynamic systems, correlated noise, Gaussian distribution, state estimation, noise modeling, covariance propagation, discrete measurement.