An efficient digital technique capable o.f arbitrarily high accuracy is developed for implementing discrete-time Bayes-optimal non-linear estimators.
Summary--Practical implementation of discrete-time Bayesoptimal non-linear estimators has not received much attention, since the problems associated with storing probability densities and computing convolution integrals are formidable, and, hence, presumably prohibitive. However, the prevailing technique of designing non-linear estimators based upon Taylor series approximations frequently leads to undesirable, inaccurate or unstable, behavior. Thus there is considerable motivation for proceeding with the development of digital realizations of non-linear filters whose degree of accuracy is under the complete control of the computer program.
In this paper techniques are proposed and discussed which solve the basic two subproblems associated with optimal discrete-time non-linear estimators: density storage and Bayes-law computation. For density storage a point mass representation on a floating rectangular grid of indices is proposed, while for the Bayes-law computation a simple and effective convolution summation involving an ellipsoid tracking technique to determine the important points to include in the summation is developed.
Monte Carlo experiments with the proposed non-linear estimator reveal significant improvement in mean-square error behavior over some conventional approximation realizations. An example is given which illustrates the application of non-linear estimation to tracking and detection systems.
THE THEORY of non-linear filtering is now about 10 years old. It is quite interesting that even with the spectacular success of the linear theory, as indicated in [l], and the clear relevance of the non-linear filter to a wide variety of practical problems, as yet there * The views expressed herein are those of the authors and do not necessarily reflect the views of the United States Air Force or the Department of Defense.