Heuristics and H-optimum Estimators in a Model with Type-I Constraints

Abstract

The aim in linear statistical models is to determine an estimator of the unknown parameters on the basis of the observation vector. One possible approach used mainly in geodetic measurements is known as $\mathbf H$-optimum estimator.

This paper deals with problem of connecting measurements where boundaries of estimators dispersion are previously known. The $\mathbf H$- optimum estimators seem to be appropriate for reducing the influence of B-type metrological uncertainty on the estimator in connecting measurement. However in this case, general $\mathbf H$-optimum estimators do not solve the problem of bounded dispersion completely.

Heuristic methods such as algorithm complex method help us to extend $\mathbf H$-optimum estimator theory so given dispersion boundaries could be satisfied. Presented paper describes standard theory of $\mathbf H$-optimum estimators and its extension with heuristics utilization. Finally, qualities of extended $\mathbf H$-optimum estimator are shown by solving illustration example.