Research On The Application Of Some Artificial Intelligent Techniques To Geodetic Coordinate Transformation

Global Navigation Satellite Systems(GNSS)have been widely adopted in geospatial sciences and its related disciplines for geodetic purposes.Over the years,the means to facilitate the usage of GNSS acquired data in countries like Ghana where there is continual use of non-geocentric datums has been a major research focus in the geodetic community.Since its arrival,GNSS has become an indispensable technology with most countries having migrated from astro-geodetic datum to geocentric datum.However,the adoption of such datum requires the need to transform old geospatial data in the astro-geodetic datum into the established geocentric datum.In addition,countries that are still using the non-geocentric datum are also required to transform GNSS acquired data into their local geodetic datum.Reliable estimation of transformed coordinates between global and local datums is one of the fundamental problems in geodetic sciences.Several authors have attributed such problems to:i.the data collection procedures employed when establishing the local geodetic datum;ii.computational adjustment techniques applied to adjust and unify the local geodetic reference networks;iii.the quality of the data set collected in the local geodetic reference network;andiv.lack of ellipsoidal height for the local geodetic datum.These challenges have contributed to the heterogeneity in the data related to the local geodetic networks.Countries that are yet to establish and migrate onto the geocentric datum are often confronted with the above-mentioned concerns.To circumvent the situation,conventional transformation techniques which are parametric and thus require a fixed functional form to the co-located point coordinates as well as the non-parametric methods of artificial intelligent have been the most widely used for two and three-dimensional coordinate transformation.Studies have shown that the artificial intelligent methods have the capability of adequately transforming coordinates to a reliable degree of accuracy.Specifically,most scholars have focussed mainly on the following artificial intelligent methods: backpropagation and radial basis function neural networks,fuzzy neural network,fuzzy logic and genetic programming.Consequently,as a means to apply novel techniques for the purposes of coordinate conversion and transformation,the following studies were conducted.The first study applied and assessed for the first time the forward coordinate conversion performance of backpropagation and radial basis function neural networks as well as multiple linear regression technique.The essence of this study was to investigate whether the aforementioned techniques could serve as alternative method to the standard forward equation based on the supervised learning technique.The following statistical indicators were used to evaluate the methods prediction adequacy: mean squared error,correlation coefficient,coefficient of determination,mean bias error,mean absolute error,Legates and McCabe index,relative error correction,mean horizontal positional error,standard deviation,maximum and minimum horizontal positional error.The overall analyses revealed standard deviation values of 5.184E-04 and 1.008E-03 m furnished by the radial basis function neural network and multiple linear regression technique.The backpropagation neural network,on the other hand,achieved 0.089 m.Taking into account the maximum horizontal positional errors,0.004,0.011,and 0.627 m were obtained by the radial basis function neural network,multiple linear regression and backpropagation neural network.The study further concluded that for forward conversion of geodetic coordinates to cartesian coordinates in the study area,the radial basis function neural network should be adopted.In the second study,backpropagation neural network,radial basis function neural network and generalized regression neural network were applied to develop a novel approach capable of improving the results produced by geocentric translation model.The proposed novel approach known as the artificial neural network-error compensation model(ANN-ECM)has been duly presented.The essence of this new technique is to hybrid the geocentric translation model transformed coordinates as the inputs in the artificial neural network model by predicting its residuals as the outputs.The predicted residuals by the artificial neural network were then added to the existing transformed coordinates by the geocentric translation model.The results revealed that the most widely used arithmetic mean for estimating the geocentric translation model parameters produced a maximum horizontal positional error of 1.99 m.This was reduced significantly to approximately 0.9 m by the proposed techniques.It must be stated here that the 0.9 m obtained by the proposed models agreed with the horizontal positional error tolerance for cadastral surveying and plan production as specified by the Ghana Survey and Mapping Division of Lands Commission.In this third study,a novel hybrid approach of total least squares(TLS)and radial basis function neural network(RBFNN)hereafter TLS-RBFNN has been proposed and applied to carry out coordinate transformation in Ghana's geodetic reference network.This hybrid combined the function approximation and nonlinear modelling capabilities of TLS and RBFNN during its implementation.Moreover,using the total least squares as an optimization tool in this context,improved the performance of the radial basis function neural network in many aspects such as training speed,reduction in the size of the network leading to fast convergence and satisfactory transformation results.The proposed approach could be categorized as a combination of knowledge based system and empirical model.The findings reported in this study revealed that 0.3631,0.4587 and 0.6074 m was the overall transformation accuracy achieved by TLS-RBFNN,RBFNN and TLS based on the testing data,respectively.This clearly shows that the hybrid model is superior to applying each method separately.To further assess the strength of the TLS-RBFNN,the Bayesian information criterion was applied.The TLS-RBFNN obtained the least Bayesian information criterion value and thus was selected as the most suitable model to be used for transforming coordinates between WGS84 and Ghana's War Office 1926 ellipsoidIn the fourth study,support vector machine(SVM),least square support vector machine(LS-SVM),multivariate adaptive regression spline(MARS)and extreme learning machine(ELM)was applied for the first time to perform coordinate transformation.These novel techniques were applied to co-located points in the Ghana geodetic reference network.The SVM,LS-SVM,MARS and ELM results were compared with the backpropagation neural network(BPNN),radial basis function neural network(RBFNN),2D conformal and 2D affine model,respectively.The statistical analyses carried out showed that the LS-SVM,MARS,ELM,BPNN and RBFNN all produced good and better transformation results than the SVM,2D conformal and 2D affine model.The overall analyses showed that the RBFNN produced more accurate results by having a transformation accuracy of 0.137 m.The MARS,LS-SVM,ELM and BPNN,respectively,had transformation accuracy of 0.157,0.198,0.246,and 0.258 m.The SVM and 2D affine,on the other hand,gave identical transformation accuracy of 0.433 m while,0.474 m was achieved by the 2D conformal model.Consistent with the maximum horizontal positional error,approximately 0.59,0.63,0.84,and 0.93 m were given by RBFNN,MARS,LS-SVM,and ELM based on the entire testing data.Their corresponding minimum horizontal positional errors realised were 0.005,0.018,0.03 and 0.008 m respectively.For the purposes of cadastral applications in Ghana,RBFNN,MARS,LS-SVM and ELM results satisfied the horizontal positional error tolerance limit of approximately ± 0.9 m set by the Ghana Survey and Mapping Division.On the contrary,the BPNN had 1.624 and 0.04 m as its maximum and minimum horizontal positional errors.The SVM and 2D affine,conversely,had 2.153 m coupled with the 2D conformal model that gave 2.642 m.Although the BPNN,SVM,2D affine and 2D conformal obtained maximum horizontal positional errors does not conform to the stipulated ± 0.9 m,the methods can still be used in less demanding accuracy survey works such as GIS data collection for geodatabase generation,small scale topographic mapping surveys and transforming thematic data for example vegetation,soil type and geology.The presented research is based on three papers published in SCI indexed journals out of this thesis as well as unpublished studies by the author.