Hello All,
For those unfamiliar with the equations or filters mentioned, let me explain:
The Fokker Planck Kolmogorov equation (FPKE) and the Chapman-Kolmogorov equation (CKE) are both equations which are used to propagate processes with probabilistic initial conditions or processes with random forcing/terms in the dynamics.
These are idea/concepts often encountered in statistical mechanics and statistical thermodynamics, if you're a physics major, or estimation/stochastic processes, if you're a math or engineering major, although curriculum variability could lead to different paths.
The linear filters I'm referring to are the two commonly used forms of the Kalman filter, the Unscented Kalman filter, and the Extended Kalman filter. These filters are used to propagate probabilistic processes as Gaussian distributions (they only take into account the first two moments).
Since the FKPE and CKE are very general probabilistic propagation equations, it seems reasonable that the simpler approximations, the EKF and the UKF, should stem from these equations. My questions is, does any one know of a source that details these derivations?
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