Accession Number : AD0725021

Title :   Estimation in a Model That Arises from Linearization in Nonlinear Least Squares Analysis,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Wegner,L. H.

Report Date : APR 1971

Pagination or Media Count : 68

Abstract : The report contains explicit formulas and a JOSS program for obtaining the minimum variance Gauss-Markov or best linear unbiased (BLUE) estimates when a directly observed parameter vector and another parameter vector are related by a possibly nonlinear relationship, and the least squares estimation procedures is linearized. The work was motivated by the need to locate a radar by indirect measurements--either directions or times of arrival of the radar signal--from aircraft whose locations were also indirectly observed by range, azimuth, and range-difference measurements from ground stations--all with some error. However, the results have wide applicability to estimation and error analysis in many real-world situations, such as combining measurements from several trackers. As the covariance matrix of the estimates evaluated at the true values of the estimated quantities generalizes the classical 'propagation of error variance formula,' the computerized covariance matrix is a versatile tool for error analysis of complex systems. (Author)

Descriptors :   (*LEAST SQUARES METHOD, MATHEMATICAL PREDICTION), RADAR TRACKING, ITERATIONS, MATRICES(MATHEMATICS), COMPUTER PROGRAMS, MATHEMATICAL MODELS, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE