Total Least Squares State of Charge Estimation for Lithium-Ion Batteries: An Efficient Moving Horizon Estimation Approach

This paper proposes a computationally efficient moving horizon approach for total least squares (TLS) battery state of charge (SOC) estimation. Much of the existing SOC estimation literature assumes that uncertainties arise mainly from (i) unmodeled dynamics and (ii) output measurement noise. In contrast, the total least squares (TLS) estimation problem explicitly examines the added noise affecting both output and input measurements. This increases the computational burden associated with TLS estimation by necessitating input trajectory estimation. We address this challenge by exploiting the differential flatness of a temperature-dependent equivalent circuit battery model to improve the computational speed of TLS estimation. Since the model is differentially flat, one can represent its underlying dynamics in terms of the time history of a single flat output. The exploitation of differential flatness improves the computational efficiency of moving horizon estimation (MHE) in two ways: (i) it decreases the number of decision variables significantly and (ii) eliminates battery dynamics-related equality constraints. A simulation study compares the proposed work to a benchmark unscented Kalman filter (UKF), and shows that the proposed flatness-based MHE framework can provide more accurate SOC estimates.