  This paper investigates the observability of one of the most commonly used
equivalent circuit models (ECMs) for lithium-ion batteries and presents a
method to estimate the state of charge (SOC) in the presence of sensor biases,
highlighting the importance of observability analysis for choosing appropriate
state estimation algorithms. Using a differential geometric approach, necessary
and sufficient conditions for the nonlinear ECM to be observable are derived
and are shown to be different from the conditions for the observability of the
linearised model. It is then demonstrated that biases in the measurements, due
to sensor ageing or calibration errors, can be estimated by applying a
nonlinear Kalman filter to an augmented model where the biases are incorporated
into the state vector. Experiments are carried out on a lithium-ion pouch cell
and three types of nonlinear filters, the first-order extended Kalman filter
(EKF), the second-order EKF and the unscented Kalman filter (UKF) are applied
using experimental data. The different performances of the filters are
explained from the point of view of observability.
