Theoretical Performance Evaluation of Battery Equivalent Circuit Model Parameter Estimators

Equivalent circuit model (ECM) based approaches are widely used by Li-ion battery management systems. In the ECM approach, the voltage drop within a battery is modelled using resistive and capacitive electrical components. Numerous approaches were reported to estimate the parameters of ECM based on the voltage and current measurements from the battery. Battery ECM parameter estimation is done based on both voltage and current measurements. The measurement noise in these applications results in a doubly noisy observation model and makes theoretical analysis challenging. In this paper, theoretical performance bounds are derived for ECM parameter estimation in batteries where the effect of both voltage and current measurement noises are objectively analyzed. The performance bound is derived in the form of Cramer-Rao lower bound (CRLB) by considering the doubly noisy observation model that represent ECM parameter estimation in batteries. It is shown that traditional least square estimation approach becomes biased and inefficient at low signal to noise ratio (SNR) levels. A new approach, based on the total least squares (TLS) method, is developed for low SNR conditions. It is shown through simulation experiments that the TLS approach can be efficient for ECM parameter estimation. The proposed approach is validated through data collected from cylindrical Li-ion battery cells.