
Accession Number : AD0713098
Title : AN EXACT SOLUTION TO AN ADAPTIVE LINEAR ESTIMATION PROBLEM,
Corporate Author : FRANK J SEILER RESEARCH LAB UNITED STATES AIR FORCE ACADEMY COLO
Personal Author(s) : Senne,Kenneth D.
Report Date : SEP 1970
Pagination or Media Count : 37
Abstract : An exact analysis of a particular form of adaptive estimator is presented. The result is the explicit evolution of the mean square estimation errors in general timevarying environments, as well as necessary and sufficient conditions for convergence of the estimates and explicit corresponding solutions in the presence of step changes in signal statistics. The estimator in question involves a gradientfollowing algorithm for recursively computing the solution to a discrete aprroximation to the WienerHopf integral equation. The term adaptive is used to indicate that the gradientfollowing is permitted to continue indefinitely resulting in the capability of adjusting to sudden or unexpected evolutionary changes in process statistics at any time. Convergence of the estimates is defined in terms of the fractional excess mean square error or misadjustment maintained by the random estimator weights. Adaptive estimator convergence is intentionally weaker than stochastic approximation convergence so that precise knowledge of the timevarying nature of f the statistics is not required in order to obtain satisfactory meansquareerror performance. The specific problem which is analyzed exactly involves zeromean, mutually gaussian distributed, independent sample vectors. The assumption of intersample independence is in part justified by the detailed analytical results which provide for the first time a prototype for the synthesis of adaptive estimators suitable for truly nonstationary environments. (Author)
Descriptors : (*INFORMATION THEORY, DECISION THEORY), ADAPTIVE SYSTEMS, CONTROL SYSTEMS, INTEGRAL EQUATIONS, ALGORITHMS, THEOREMS, THESES
Subject Categories : Cybernetics
Distribution Statement : APPROVED FOR PUBLIC RELEASE