A robust approach to position fixing: Two-dimensional coordinate conformity in engineering surveying

Geomatics instruments have algorithms which derive two-dimensional and three-dimensional coordinates in a local system based on the equipment. The collected coordinates undergo coordinate transformation in order to model the space in question. However, Resident Engineers and geomatics engineers in the Malawian construction industry are still inclined to physical inspection of datasets which may expose some errors. In Malawi, so little use is made of adjustment and error detection in engineering surveys, except in datum transformation and the reconciliation of past and new surveys in cadastral surveying. Thus, this paper implemented a two-dimensional robust approach to fixing the alignment master-points through the implementation of the least squares mathematical approach. Position fixing was carried out by formulating the planimetric transformation between the design coordinates and the as-built survey coordinates using the Lilongwe Western By-Pass Road as a case study. This was validated by performing a re-survey of the stations. The scale factor of the sampled section equated to unity and the positions affected by a rotational angle of 354˚ 46' 32''. The observation quality for the Northings and Eastings was 69 mm and 11 mm, respectively. Outlier detection revealed that 29% of the alignment master stations were geometrically in their actual positions while 71% were out representing a merit in the approach which was impossible with physical inspection. The results also indicated that the approach have profound technical advice to engineering surveyors on the determination of residuals from two sets of coordinates in different coordinate systems.