Estimation in a Model that Arises from Linearization in Nonlinear Least Squares Analysis.
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 procedure 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. Since 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. 67 pp. Ref.