Overparameterized Least-Squares Adjustment with Linear Models for Geodetic and Surveying Applications

Abstract

Least-squares (LS) estimation is a standard tool for the optimal processing of geodetic and surveying observations. In many applications, additional nuisance parameters are frequently included within the LS adjustment process in order to account for unknown instrumental biases and other external disturbances that have affected the input data. Moreover, in view of the availability of more precise instruments and data sensors, the enhancement of the mathematical models with additional parameters is justified on the basis of detecting new higher-order systematic effects from the optimal inversion of progressively more accurate data sets. The objective of this paper is to expose an important trade off in the LS adjustment with linear models which are augmented with additional parameters in the presence of unknown systematic effects in the input data. In particular, a condition is derived that quantifies the necessary reduction in the data noise level which ensures the improvement in the estimation accuracy for the original model parameters, when a linear(-ized) model enhancement takes place.