An alternative method for estimating densification point velocity based on back propagation artificial neural networks

The establishment of Turkish National Fundamental GPS Network (TNFGN) was completed in 2001 and Large Scale Map and Map Information Production Regulation (LSMMIPR) came into force in 2005 in parallel with the establishment of TNFGN and the increase in the use of GPS applications. TNFGN has been designed as first order GPS network and it comprises second-, third- and fourth-order GPS densification networks. LSMMIPR has required determining the positions of first-, second- and third-order GPS densification (C1, C2 and C3) points with the reference epoch besides the measurement epoch. Therefore, it is necessary to estimate the velocity vectors of the densification points. In practise, the velocity vectors of C1, C2 and C3 points are estimated from TNFGN points or higher-order densification points velocity vectors by interpolation methods but LSMMIPR did not specify the interpolation method for this procedure. The objective of this study is to use a back propagation artificial neural network (BPANN) that has been more widely applied in engineering among all other neural network models for estimating the velocity of the densification point as an alternative to the interpolation methods. BPANN and selected ten interpolation methods are evaluated over a test area, in terms of root mean square error (RMSE). The results showed that the employment of BPANN estimated the densification point velocity (V_X,Y,Z) with a better accuracy (±5.0 mm, ±4.0 mm, ±3.9 mm, respectively) than the interpolation methods in the test area and indicated that BPANN can be a useful tool for estimating point velocity in the densification networks as a real alternative to the interpolation methods.