Local geoid determination using a generalized regression neural network and interpolation methods: A case study in Kars, Turkey

Abstract

This study aimed to determine the most suitable local geoid model based on 641 GNSS/leveling points within the borders of Kars Province in eastern Turkey using the generalized regression neural network (GRNN), weighted average (WA), multiquadric (MQ), inverse multiquadric (IMQ) function, and local polynomial (LP) method. Among these methods used in local geoid determination, the studies conducted with the GRNN method are very limited in the literature. To test the performance of the model, 169 GNSS/leveling points were selected as test data. When selecting reference points and test points, care was taken to distribute these points homogeneously within the study area. The criteria of root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R 2 ) were used to assess the accuracy and error rates of the results achieved using the different methods. According the results of analysis, GRNN method yielded better results than other interpolation methods. These results have showed that GRNN method can be taken into account in modeling various geodesy problems.

Prediction of geoid undulations: Random forest versus classic interpolation techniques

“…In the LP method, the most suitable polynomial degree to be used is generally sought via experimentation. If the error in the model starts to rise when using a polynomial degree, the next lowest polynomial degree is then selected 35 . The polynomials expressed above are represented as 1st, 2nd, and 3rd‐degree polynomials.…”

“…If the error in the model starts to rise when using a polynomial degree, the next lowest polynomial degree is then selected. 35 The polynomials expressed above are represented as 1st, 2nd, and 3rd-degree polynomials. When the function is expressed as a 1st, 2nd, or 3rd degree, it is formulated as follows, respectively.…”