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

Document Type


Publication Date


Publication Title

IEEE Transactions on Instrumentation and Measurement




Battery equivalent circuit model (ECM), battery impedance, battery management system, Kalman filter, measurement errors, recursive least squares (RLS) estimation, total least squares estimation


Real-Time identification of electrical equivalent circuit models (ECMs) 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-order ECMs. However, little work was done in analyzing the theoretical performance bounds of these system identification approaches. Given that both voltage and current are measured with error, proper understanding of theoretical bounds will help in designing a system that is economical in cost and robust in performance. In this article, we analyze the performance of a linear recursive least squares (RLS) approach to ECM identification and show that the LS 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 LS estimator becomes significantly biased. Consequently, we develop a parameter estimation approach based on the total LS 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 LS method. The resulting total Kalman filter (TKF) is shown to be both unbiased and efficient in ECM identification. The performance of this filter is analyzed using real-world current profiles under fluctuating signal-To-noise ratios. Finally, the applicability of the algorithms and analysis in this article in identifying higher-order electrical ECMs is explained.