How can the Unscented Kalman Filter (UKF) improve SOC estimation accuracy compared to the standard Kalman Filter (KF) in highly non-linear battery systems?

The Unscented Kalman Filter (UKF) improves State of Charge (SOC) estimation accuracy compared to the standard Kalman Filter (KF) in highly non-linear battery systems by better handling the non-linear relationships between battery states (like SOC) and measurements (like voltage and current). The standard KF relies on a linearization process to approximate non-linear functions. This linearization involves calculating the Jacobian matrix, which represents the partial derivatives of the system equations. However, this linearization can introduce significant errors when the system is highly non-linear, meaning the relationship between the states and measurements is not a straight line. Batteries often exhibit non-linear behavior, especially during charging and discharging, and at varying temperatures. The UKF addresses this limitation by using a technique called the unscented transformation (UT). Instead of linearizing the system equations, the UKF selects a set of carefully chosen sample points, called sigma points, that represent the probability distribution of the system states. These sigma points are then passed through the non-linear system equations, and the resulting transformed points are used to estimate the mean and covariance of the state distribution after the non-linear transformation. This approach avoids the need for linearization and better captures the effects of non-linearity on the state estimation process. For instance, if the battery voltage has a highly non-linear relationship with SOC, especially near full charge or full discharge, the KF's linearization may lead to inaccurate SOC estimates in these regions. The UKF, by propagating sigma points through the non-linear voltage-SOC relationship, can more accurately estimate the mean and covariance of the SOC distribution, resulting in improved SOC estimation accuracy. The UKF also avoids the need to calculate Jacobian matrices, which can be computationally expensive and prone to errors, especially for complex battery models. While the UKF is more computationally intensive than the standard KF due to the need to propagate multiple sigma points, the improved accuracy in highly non-linear systems often outweighs the increased computational cost. In summary, the UKF provides a more accurate and robust SOC estimation in non-linear battery systems by avoiding linearization and better capturing the effects of non-linearity on the state estimation process through the use of the unscented transformation.