Covariance and One-Step Error Prediction of Difference Equations Through Convolution and Deconvolution

Abstract

This paper determines a cohesive framework for addressing the algorithmic filtering drawback faced in filtering the noise in the digital filter. Digital filters for nonlinear time-varying systems victimizing the noise reduction and this can be established through difference equations. The new generalized projected filter is adopted into the algorithmic filter structure administrated by identifying two different embedded systems of stochastic type and Riccati type nonlinear random equations. The gain matrix of the proposed filter is calculated by minimizing the covariance trace of the filtering error   ^th element. Simultaneously the gain of the filter is identified and minimizing the filtering error . Taking this partial differential coefficient and its first derivative of  with relevancy  and set the derivative to zero, at some stage the higher order coefficient leads to the reduction of the noise in the digital filter. Further the, solutions to the non homogeneous difference equation problem using convolution and deconvolution methods are analyzed along with the numerical examples.