Application of Chebechev´s inequality theorem in the design of optimal non-linear filters

Chebechev´s inequality theorem from the theory of probability and statistics provides an upper bound for the amount of probability in the “tails” of any given probability density function. This theorem has interesting applications in the numerical solution of the Fokker-Planck-Kolmogorov equation (FPKE) as shown in this paper. Numerical solution of FPKE is an essential component of the design of optimal nonlinear filters. The solution of the FPKE in conjunction with the Bayes´ conditional density lemma provides optimal (minimum variance) state estimates of any general stochastic dynamic system (SDS)