Recursive Total Least-Squares Algorithm Based on Inverse Power Method and Dichotomous Coordinate-Descent Iterations

TL;DR

This paper introduces a novel recursive total least-squares algorithm using inverse power method and DCD iterations, offering improved efficiency and stability for errors-in-variables system identification.

Contribution

The paper presents the DCD-RTLS algorithm, which reduces computational complexity and enhances performance over existing RTLS methods based on line-search techniques.

Findings

DCD-RTLS outperforms previous RTLS algorithms in accuracy and efficiency.

The algorithm is asymptotically unbiased and stable in the mean.

Theoretical steady-state MSD matches simulation results.

Abstract

We develop a recursive total least-squares (RTLS) algorithm for errors-in-variables system identification utilizing the inverse power method and the dichotomous coordinate-descent (DCD) iterations. The proposed algorithm, called DCD-RTLS, outperforms the previously-proposed RTLS algorithms, which are based on the line-search method, with reduced computational complexity. We perform a comprehensive analysis of the DCD-RTLS algorithm and show that it is asymptotically unbiased as well as being stable in the mean. We also find a lower bound for the forgetting factor that ensures mean-square stability of the algorithm and calculate the theoretical steady-state mean-square deviation (MSD). We verify the effectiveness of the proposed algorithm and the accuracy of the predicted steady-state MSD via simulations.