I’ve found a research paper that would allow me to implement a Kalman filter to estimate state of charge for a LiPo battery, but cannot make sense of some of the symbols as I’m a first year. Can anybody give a rough description of the process used (for the Sigma Point Kalman Filter detailed) and what some of the symbols in the augmented state covariance mean. We have some understanding but do not fully understand the meaning of some of the positive and negative symbols in the superscript and subscript mean.

Need to get an overview so we can finish develop a working model in Matlab.

Here is a link to the paper: https://www.researchgate.net/publication/308672015_State-of-charge_estimation_based_on_microcontroller-implemented_sigma-point_Kalman_filter_in_a_modular_cell_balancing_system_for_Lithium-Ion_battery_packs

Cheers.