Total capacity is often estimated using ordinary-least-squares (OLS) methods. This week, you will learn that this is a fundamentally incorrect approach, and will learn that a total-least-squares (TLS) method should be used instead. You will learn how to derive a weighted OLS solution, to use as a benchmark, and how to derive a weighted TLS solution also.

Unfortunately, the weighted TLS solution you learned in week 2 is not well suited for efficient computation on an embedded system like a BMS. As an intermediate step toward finding an efficient weighted TLS method, you will first learn a proportionally weighted TLS method this week. You will then learn how to generalize this to an "approximate weighted TLS" (AWTLS) method, which gives good estimates, and is feasible to implement on a BMS.

So far this course, you have learned a number of methods for estimating total capacity. This week, you will learn how to implement those methods in Octave code. You will also explore different simulation scenarios to benchmark how well each method works, in comparison with the others. The scenarios are representative of hybrid-electric-vehicle (HEV) and battery-electric-vehicle (BEV) applications, but the principles learned can be extrapolated to other similar application domains.

In the third course of the specialization, you learned how to use extended Kalman filters (EKFs) and sigma-point Kalman filters (SPKFs) to estimate the state of a battery cell. In this honors week, you will learn how to extend those concepts to apply EKF and SPKF to estimating the parameters of a battery-cell model if the state is known, and also how to simultaneously estimate both the state and parameters of a cell model.

You have learned several different total-capacity estimation methods. Some of these methods work better than others in general, but any method is only as good as the data you give it. In this project, you will explore a different way to determine the "x" and "y" data you use as input to the total-capacity estimation methods.