Comparative accuracy assessment of the Bowring, Chord and Power series models for direct and indirect determination of geodetic coordinates

The computation of geodetic coordinates is the basis of geodetic surveying and foundation to modern techniques for geodetic network analyses and design of integrated survey schemes for monitoring and detecting structural deformations. The positional accuracy achievable by Direct and Indirect models of geodetic position determination depends on the varying lengths, azimuths and latitude of the first point of the network of stations. Existing knowledge gaps preclude a comprehensive understanding of the relative accuracies of these methods. Therefore, the aim of this study is to determine the achievable accuracies of three models (Bowring, Chord and Power Series) for direct and indirect position determination vis-a-vis the network configuration. The data comprised of 33 controls in the D-Chain geodetic network located in North-Central Nigeria, with a range of network of lines between 15.530km and 113.254km. Various attributes of the network such as azimuth, angle, distance, and coordinates were computed to a high accuracy and precision using a program written in the Matlab software environment. The results of the direct and indirect computation were summarised using descriptive statistics. Also, the accuracies of the computed coordinates were assessed by comparisons with the provisional (initial) coordinates of the controls. In the analysis of coordinate differences, the positional root mean square error (RMSE) for each of the three models in decreasing order of accuracies are: 4.572639341′′ (Chord), 4.601685022′′ (Power Series) and 4.601701034′′ (Bowring). The positional mean absolute deviation (MAD) for the three models in decreasing order of accuracies are 3.788841258′′ (Chord), 3.813184934′′ (Power Series) and 3.813198679′′ (Bowring) and this agrees with the RMSE trend for the network. This study has shown that the D-chain network configuration favours the use of Chord model for position determination based on the adopted configuration.