ABSTRACT
Nonlinear filters have become an integral part of navigation systems. If the system is linear, the process noise is Gaussian and the pdf of the state is Gaussian, the updated pdf of the next time step is also Gaussian, but with a different mean and a different covariance. But the same is not true for a nonlinear system, the reason why no closed form estimator is available for such cases. For a linear system and with additive noise, the probability density function of the states can be evaluated at any particular instant of time if the initial states are given. Estimating the state-of-charge (SoC) of batteries online is a recent field of application of filtering. It finds major application in electric vehicles where the battery management system should estimate the battery SoC, instantaneous power along with other parameters. The chapter also presents an overview of the key concepts discussed in this book.
