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# Evaluation of strategies for estimating residual neutral-atmosphere propagation delay in high precision Global Positioning System data analysis

## Description

The research described in this thesis compares and evaluates techniques for the estimation of residual neutral-atmosphere propagation delay of Global Positioning System (GPS) measurements in high precision geodetic relation positioning applications. Three techniques were analysed: (1) a conventional weighted least squares adjustment, (2) a sequential weighted least squares adjustment, and (3) Kalman filtering. The University of New Brunswick Differential Positioning Program (DIPOP) package was extensively modified to estimate residual neutral-atmosphere delay parameters for the three techniques under investigation. A data set of five baselines of regional length, 50 to 700 KM, was analysed with the new DIPOP software. Ten days of data were analysed to determine the sensitivity of baseline component estimates to a priori constraints, and to provide an estimate of the precision and accuracy of the three techniques. Short-term repeatability of estimated baseline components were compared with the International Earth Rotation Service (IERS) Terrestrial Research Frame of 1993 (ITRF93). Particular attention was given to the vertical component of the baselines, since the vertical component of a GPS geodetic baseline is up to three times more sensitive to residual neutral-atmospheric delay than the horizontal components. Mapping the repeatability of the estimated baseline components against a priori constraints showed that baseline component estimates are significantly sensitive to the initial constraints place on the estimated residual delay parameters. The three techniques are capable of estimating geodetic parameters at approximately the same level of accuracy and precision. The sequential weighted least squares approach was found to be equivalent to the Kalman filtering approach for estimating residual delays when the random walk model was used to characterise the delay variability. However, the equivalence breaks down when a stochastic process with time correlated states is used in the sequential weighted least squares technique. The precision analysis revealed: (1) baseline component estimates are significantly sensitive to the a priori constraints placed on the estimated delay parameters; (2) the three techniques are capable of operating at the same level of precision; (3) empirical determination (sensitivity testing) of the stochastic process coefficients and constraints for the least squares residual delay parameters is necessary due to a lack of correlation between optimal residual delay parameter coefficients and baseline vector components; (4) precision for the conventional weighted least squares case ranged in magnitude from 5.6 mm to 13.0 mm in the height component, and 2.4 mm to 9.5 mm in the length component; (5) precision for the Kalman filter Gauss-Markov case ranged in magnitude from 5.8 mm to 9.8 mm in the height component, and 2.4 mm to 9.0 mm in the length component; and (6) precision for the Kalman filter random walk case ranged in magnitude from 5.9 mm to 10.1 mm in the height component, and 2.4 mm to 9.6 mm in the length component. The accuracy assessment revealed: (1) the three techniques are capable of estimating baseline components at approximately the same level of accuracy; (2) two of the five estimated baseline vectors agree well (within a factor of 2 times their short term repeatability) in terms of height and length with the ITRF93 coordinates; (3) three of the five baseline vectors showed large height discrepancies (of the order of 4 to 9 cm); however, they agree well in the length component estimates.