Parameter adaptive estimation of random processesThis paper is concerned with the parameter adaptive least squares estimation of random processes. The main result is a general representation theorem for the conditional expectation of a random variable on a product probability space. Using this theorem along with the general likelihood ratio expression, the least squares estimate of the process is found in terms of the parameter conditioned estimates. The stochastic differential for the a posteriori probability and the stochastic differential equation for the a posteriori density are found by using simple stochastic calculus on the representations obtained. The results are specialized to the case when the parameter has a discrete distribution. The results can be used to construct an implementable recursive estimator for certain types of nonlinear filtering problems. This is illustrated by some simple examples.
Document ID
19770029602
Acquisition Source
Legacy CDMS
Document Type
Conference Proceedings
Authors
Caglayan, A. K. (Virginia Polytechnic Inst. and State Univ. Blacksburg, VA, United States)
Vanlandingham, H. F. (Virginia Polytechnic Institute and State University Blacksburg, Va., United States)