A MACSYMA/Expert System for Nonlinear Filtering

A prototype “expert” system for the treatment of certain nonlinear filtering problems is described with illustrative examples. The system is written in MACSYMA. It accepts user input in symbolic form; it carries out the basic analysis of the user’s problem in symbolic form (e.g., computing the Zakai equation and the estimation Lie algebra for nonlinear filtering problems); and it produces output in the form of automatically generated FORTRAN code for the final numerical reduction of the problem, e.g., FORTRAN code for the conditional statistics of the signal given the observation process. The system is also capable of testing the well-posedness of a limited class of filtering problems by setting up the robust form of the Zakai equation and applying some known theorems for well-posedness of that system. This is done in symbolic form directly in the MACSYMA code. In addition, the system has a module which generates FORTRAN code for the computation of the likelihood ratio arising in connection with the filtering problem. This code implements a sophisticated approximation for the Feynmann-Kac (or Kallianpur-Streibel) representation of the conditional density in the estimation problem. Sample terminal sessions are presented to illustrate its operation. The status of the system and plans for its further development are described.