On the Identification of Electrical Equivalent Circuit Models Based on Noisy Measurements

TL;DR

This paper evaluates and improves methods for identifying electrical circuit models from noisy data, proposing a total least squares approach combined with a Kalman filter for better accuracy in low signal-to-noise conditions.

Contribution

It introduces a total least squares-based parameter estimation method and a recursive total Kalman filter for more accurate electrical model identification under noisy conditions.

Findings

Least squares is unbiased at high SNR but biased at low SNR.

Total least squares is asymptotically unbiased at low SNR.

Total Kalman filter improves convergence and accuracy.

Abstract

Real-time identification of electrical equivalent circuit models is a critical requirement in many practical systems, such as batteries and electric motors. Significant work has been done in the past developing different types of algorithms for system identification using reduced equivalent circuit models. However, little work was done in analyzing the theoretical performance bounds of these approaches. Proper understanding of theoretical bounds will help in designing a system that is economical in cost and robust in performance. In this paper, we analyze the performance of a linear recursive least squares approach to equivalent circuit model identification and show that the least squares approach is both unbiased and efficient when the signal-to-noise ratio is high enough. However, we show that, when the signal-to-noise ratio is low - resembling the case in many practical applications - the least squares estimator becomes significantly biased. Consequently, we develop a parameter estimation approach based on total least squares method and show it to be asymptotically unbiased and efficient at practically low signal-to-noise ratio regions. Further, we develop a recursive implementation of the total least square algorithm and find it to be slow to converge; for this, we employ a Kalman filter to improve the convergence speed of the total least squares method. The resulting total Kalman filter is shown to be both unbiased and efficient in equivalent circuit model parameter identification. The performance of this filter is analyzed using real-world current profile under fluctuating signal-to-noise ratios. Finally, the applicability of the algorithms and analysis in this paper in identifying higher order electrical equivalent circuit models is explained.