Finite difference implementation of distributed parameter filters

The numerical problems associated with the full three-dimensional (spatial) distributed parameter filters demand a novel technique that maintains accuracy and efficiency for the complex partial differential Riccati equation governing the filter variance. The filters can be successfully implemented by using numerical operators that can, in various ways, be factored. Use of the finite difference method having this property increases the accuracy and efficiency of the implementation.

This paper outlines a time-splitting technique for the numerical implementation of distributed parameter filters. The paper provides rationales to the square root and U-D factorizations of the distributed parameter filter by means of the time-splitting finite difference method.