I am learning about state estimation and I am having difficulty understanding the difference between Bayesian filters such as Kalman filter and particle filters compared to adaptive filters. According to this tutorial, adaptive filters are stochastic approximators such as LMS and RLS and they assume that state varies very slowly with unknown dynamics. Could you please explain the main differences between these state estimation categories?
I don't know what "adaptive filters" are, but from a statistical standpoint
- recursive least squares is a special case of the Kalman filter for models with state dynamics that are noiseless, and
- particle filters are simulation-based approximations to the filtering recursions. Instead of keeping track of several numbers that change from time point to time point (the Kalman filter keeps track of a mean vector and a covariance matrix), they keep track of a large collection of weighted samples. They are much slower, more difficult to program, and harder to justify mathematically than closed-form filters, so they should really only be used for models where, say, the Kalman filter isn't suitable. This might happen, for instance, when either the state transition and/or the observation equation aren't normal, or one of them isn't "linear".