Recursive approximate weighted total least squares estimation of battery cell total capacity

Battery cell total capacity refers to the total amount of charge that can be extracted from a fully charged cell. Knowledge of the present total capacity value is important to being able to calculate the maximum energy storage capability of a battery pack, the remaining energy in a battery pack, and as an indicator of the battery’s state of health. We show that traditional methods of estimating battery cell total capacity, which consider noises only in the accumulated ampere hour measurement, are biased. Battery cell total capacity must be estimated with knowledge of both the noises on the state of charge estimates and on the accumulated ampere hour measurements used to compute the total capacity estimate. We demonstrate how total least squares gives better results than traditional methods, and derive an approximate weighted total least squares algorithm that is suitable for implementation in an embedded battery management system.