Decomposition of nonlinear non-Gaussian process and its application to nonlinear filter and predictor design

An approach for decomposing of a Nonlinear Non-Gaussian Process (NNGP) is presented. A set of adjoin processes alpha's are first constructed based on the orthogonal principle so that the linear and nonlinear part of the process can be completely separated by a correlation operation without the statistical assumption on the process (i.e., it is not necessarily a Gaussian Process). The linear and nonlinear filters or predictors can then be designed and implemented independently and the consistency of parameters is guaranteed. An algorithm is given for a second order nonlinear process, and it can easily be extended to higher order cases if necessary. The method is first demonstrated by applying it to a nonlinear filter design problem, i.e., system identification. Finally, the necessity of a proposed decomposition procedure is proven by applying it to an example in which the parameters of a signal model are extracted from a version which is distorted due to the nonlinearity of the channel.