Estimation of stationary and non-stationary moving average processes in the correlation domain

Abstract

This paper introduces a novel approach for the offline estimation of stationary moving average processes, further extending it to efficient online estimation of non-stationary processes. The novelty lies in a unique technique to solve the autocorrelation function matching problem leveraging that the autocorrelation function of a colored noise is equal to the autocorrelation function of the coefficients of the moving average process. This enables the derivation of a system of nonlinear equations to be solved for estimating the model parameters. Unlike conventional methods, this approach uses the Newton-Raphson and Levenberg–Marquardt algorithms to efficiently find the solution. A key finding is the demonstration of multiple symmetrical solutions and the provision of necessary conditions for solution feasibility. In the non-stationary case, the estimation complexity is notably reduced, resulting in a triangular system of linear equations solvable by backward substitution. For online parameter estimation of non-stationary processes, a new recursive formula is introduced to update the sample autocorrelation function, integrating exponential forgetting of older samples to enable parameter adaptation. Numerical experiments confirm the method’s effectiveness and evaluate its performance compared to existing techniques.