The stochastic model for Global Navigation Satellite Systems and terrestrial laser scanning observations: A proposal to account for correlations in least squares adjustment

Abstract

Abstract The best unbiased estimates of unknown parameters in linear models have the smallest expected mean-squared errors as long as the residuals are weighted with their true variance–covariance matrix. As this condition is rarely met in real applications, the least-squares (LS) estimator is less trustworthy and the parameter precision is often overoptimistic, particularly when correlations are neglected. A careful description of the physical and mathematical relationships between the observations is, thus, necessary to reach a realistic solution and unbiased test statistics. Global Navigation Satellite Systems and terrestrial laser scanners (TLS) measurements show similarities and can be both processed in LS adjustments, either for positioning or deformation analysis. Thus, a parallel between stochastic models for Global Navigation Satellite Systems observations proposed previously in the case of correlations and functions for TLS range measurements based on intensity values can be drawn. This comparison paves the way for a simplified way to account for correlations for a use in LS adjustment.