Sigma-point Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 2: Simultaneous state and parameter estimation

We have previously described algorithms for a battery management system (BMS) that uses Kalman filtering (KF) techniques to estimate such quantities as: cell self-discharge rate, state-of-charge, nominal capacity, resistance, and others. Since the dynamics of electrochemical cells are not linear, we used a nonlinear extension to the original KF called the extended Kalman filter (EKF).Now, we introduce an alternative nonlinear Kalman filtering technique known as “sigma-point Kalman filtering” (SPKF), which has some theoretical advantages that manifest themselves in more accurate predictions. The computational complexity of SPKF is of the same order as EKF, so the gains are made at little or no additional cost.This paper is the second in a two-part series. The first paper explored the theoretical background to the Kalman filter, the extended Kalman filter, and the sigma-point Kalman filter. It explained why the SPKF is often superior to the EKF and applied SPKF to estimate the state of a third-generation prototype lithium-ion polymer battery (LiPB) cell in dynamic conditions, including the state-of-charge of the cell.In this paper, we first investigate the use of the SPKF method to estimate battery parameters. A numerically efficient “square-root sigma-point Kalman filter” (SR-SPKF) is introduced for this purpose. Additionally, we discuss two SPKF-based methods for simultaneous estimation of both the quickly time-varying state and slowly time-varying parameters. Results are presented for a battery pack based on a fourth-generation prototype LiPB cell, and some limitations of the current approach, based on the probability density functions of estimation error, are also discussed.