An Approximate Analytic Solution to the Wiener-Hopf Integral Equation

摘要

It is known that the solution for the optimum filter in the Kalman-Bucy filter theory for continuous data can be obtained by solving a Wiener-Hopf integral equation. Analytic solutions to the integral equation are available for only limited classes of kernels. Numerical techniques which solve matrix inversions may also present computational problems. In this paper it is shown how the application of quasilinearization to the solution of a Riccati differential equation gives an approximate solution which can be represented analytically in terms of quadrature operations on known functions. Further refinements to the solution can be obtained by an iterative numerical technique which can be specified as an algorithm. The accuracy of the solution is then limited by computational error propagation problems. (Author)