
Accession Number : AD0766846
Title : FixedPoint Nonlinear Smoothing.
Descriptive Note : Doctoral thesis,
Corporate Author : CALIFORNIA UNIV IRVINE SYSTEMS ENGINEERING AND OPERATIONS RESEARCH GROUP
Personal Author(s) : Eng,Robert
Report Date : JUN 1973
Pagination or Media Count : 117
Abstract : Smoothing is a generic term describing any technique that estimates a state or parameter at a point in time prior to a most recent noisy measurement which is related to the state. Attention in this dissertation is focused on the derivation and application of a recursive forwardtime fixedpoint smoothing algorithm. This algorithm is for discretetime nonlinear dynamic systems driven by Gaussian, white noise wherein the measurements are nonlinear functions of the state in the presence of additive Gaussian white noise. Using the marginal maximum likelihood approach, the author obtains the smoothing algorithm. It is found that the derived algorithm depends on the past filtered estimates; thus the fixedpoint smoothing problem is solved by simultaneously implementing the filtering and smoothing algorithms. The smoothing algorithm contains terms involving the secondorder partial derivatives of the system dynamics. The associated filtering algorithm includes the secondorder partial derivatives of the nonlinear measurement function. Both filtering and smoothing estimates are computed recursively by iterative solution of the algorithms. A nontrivial example in data smoothing is presented to illustrate the application of the theory. (Modified author abstract)
Descriptors : (*ADAPTIVE CONTROL SYSTEMS, MATHEMATICAL MODELS), LINEAR SYSTEMS, NONLINEAR SYSTEMS, PROBABILITY DENSITY FUNCTIONS, RANDOM VARIABLES, WHITE NOISE, STATISTICAL ANALYSIS, APPROXIMATION(MATHEMATICS), ALGORITHMS, THESES
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE