Process noise quantification in Kalman filters with application to electrochemical Lithium-ion battery state estimation

Abstract

Accurate state estimation of Lithium-ion batteries (LIBs) can enable improved hybrid and electric vehicles. A Battery Management System (BMS) can use electrochemical models in conjunction with Kalman filter approaches to estimate internal battery states from current and voltage measurements. For Kalman filters, the process noise is assumed to be Gaussian and independent across states, resulting in a diagonal covariance matrix. To the best of our knowledge, these assumptions have never been validated for battery dynamics, nor has any detailed calculation of variance of each model state been presented. This paper proposes a novel method for quantifying process noise in electrochemical battery models that can be generalized to other system applications. The method is derived analytically by mapping a true high-fidelity model to a reduced model and comparing differences in concentration states. The electrochemical model used is an enhanced Single Particle Model (eSPM), where parameters were experimentally identified for a Li-NMC cell. An investigation of process noise carried out using the proposed approach shows that the covariance matrix is not diagonal and gaussian only in first approximation (but only for the diagonal terms).