ABSTRACT
The theory of nonlinear filtering has been in development since the beginning of the 1960s. Nonlinear filtering results are mainly the theoretical solution of the general estimation problem that deals with the extraction of the useful information from the measurement data that are contaminated by noise processes. This general estimation problem covers many problems in the field of communication, and power systems, control, and aerospace engineering: suppression or reduction of the noise by filtering, estimation of the states/parameters of nonlinear stochastic dynamic systems, parameter estimation of algebraic or dynamic systems, and often joint state/parameter estimation in robotics. The Kushner–Stratonovich equation takes the measurements into account and represents the theoretical solution of the nonlinear filtering problem in the continuous time domain. The chapter considers the estimation problem for discrete time dynamic systems with discrete time measurements. The differential equations that govern most practical real-life dynamic systems and processes are nonlinear.
