Enhanced maximal precision increment method for network measurement optimization

Optimization of the measurements is an important theme of the geodesy and especially engineering surveying nowadays. The optimization can be categorized into orders, from the zero to the third order. The zero order design is the coordinate system selection, the first order is the configuration optimization, the second order is the optimization of the number of the repetitions, the third order is the improvement of the existing network by adding point and/or observations. In the engineering surveying the second order design need to be addressed. Thus there are known possible locations of network points, the desired accuracy, possible measurements within the existing situation, and it is necessary to choose such measurements and their numbers of repetition, so that their number was minimal (resp. used energy on their implementation) and yet the required accuracy was met. There were many attempts to meet this objective, but usually by the deployment of general mathematical optimization methods that do not respect the character of geodetic measurements and rational optimization results demands. There was designed a new method which, in our opinion, meets these requirements and is based on gradual selection of the most beneficial measurement to meet the accuracy requirements. The method was successfully tested on the levelling network optimization firstly. Adding of the measurements by one do not allow to use this method successfully on the terrestrial length and angle measurement, because one direction on new station cannot bring precision improvement and thus no new stations are used-except the necessary ones. In this paper was presented newly designed procedure of the optimization using the original principle of the method enhanced by the initial determination based on the least squares method optimization of the whole network, which identifies the initial skeleton for further improvements by the maximal precision increment method. The results of the successful testing of the method on model networks is presented too, including some levelling network (in comparison with the results of the previous method version and brute force perfect solution) and some two dimensional terrestrial networks measured by the total station.