How do adaptive forgetting factors in RLS algorithms specifically improve parameter tracking in batteries experiencing capacity fade?

Adaptive forgetting factors in Recursive Least Squares (RLS) algorithms significantly improve parameter tracking in batteries experiencing capacity fade by allowing the algorithm to prioritize recent data over older data, enabling it to quickly adapt to changes in battery parameters that occur as the battery degrades. RLS is an online parameter estimation technique that recursively updates the estimates of a model's parameters based on new measurements. It's used to estimate the parameters of a battery model (e.g., an equivalent circuit model) in real-time. Capacity fade, a key indicator of battery aging, refers to the gradual reduction in the maximum amount of charge that a battery can store. As a battery experiences capacity fade, its parameters, such as internal resistance and open-circuit voltage, change over time. If the parameter estimation algorithm does not account for these changes, the accuracy of the battery model will degrade. The forgetting factor in RLS determines the weight given to past data points in the parameter estimation process. A forgetting factor between 0 and 1 discounts the influence of older data points. A forgetting factor close to 1 means that older data points are given almost as much weight as recent data points, while a forgetting factor close to 0 means that older data points are quickly forgotten. In batteries experiencing capacity fade, the battery parameters are changing over time, so it is important to give more weight to recent data points that reflect the current state of the battery. This is where adaptive forgetting factors come in. An adaptive forgetting factor adjusts its value based on the observed changes in the battery's behavior. When the algorithm detects a sudden change in the battery's voltage response or impedance characteristics, it reduces the forgetting factor to give more weight to recent data points. This allows the algorithm to quickly adapt to the new battery parameters. Conversely, when the battery's behavior is stable, the algorithm increases the forgetting factor to give more weight to past data points, which reduces the impact of noise and improves the accuracy of the parameter estimates. For example, if a battery suddenly experiences a large drop in capacity, the adaptive forgetting factor will decrease to allow the RLS algorithm to quickly update its estimate of the battery's internal resistance to reflect the new capacity. By continuously adjusting the forgetting factor, the RLS algorithm can accurately track the changes in battery parameters that occur as the battery experiences capacity fade, which improves the accuracy of the battery model and the performance of the BMS.