An Evaluation of the Static, Dynamic, and Static-dynamic Geodetic , Densification Models on a Part of the Kenyan Geodetic Network

Abstract

A fundamental consideration in densification of geodetic networks is how to handle the position values of the already established datum stations. The question is: shall they be considered as stochastic or as fixed, non-stochastic entities? Different densification models have been put forward as solutions to the question above. These are distinguished by the manner in which higher order net points are handled within the densification process. Presented herein is a study aimed at evaluating three densification approaches, namely; static, dynamic, and static dynamic densification models with a view to identifying their strengths and weaknesses as models for densification of geodetic networks. In the static densification model, existing stations are held fixed and assumed errorless, while in the dynamic densification model, the existing datum parameters are treated as stochastic. The static-dynamic model treats datum parameters as stochastic prior information, while at the same time keeping them numerically and stochastically unchanged. To evaluate these models, each was used to adjust a network at two levels of densification. The adjustment process involved' estimation of parameters for secondary and tertiary densification networks built on a datum defined by adjusting the primary network within the framework of a free network. For each model and at every level of densification, the resulting parameters, standard errors of points and their correspondi~g standard error ellipses were 'compared against each other. Through analysis of these results the strength and weaknesses of each densification model have been appraised. A real network forming a part of the geodetic network of Kenya was adopted as the test network. The network consists of eight primary control stations, fifteen secondary stations, and twentytwo tertiary stations. Using original field data the test network is densified in two levels using the three densification models above. The results indicate that standard errors and point error ellipses from the static model are the smallest, followed by those from the static-dynamic model, and finally those from the dynamic model. The standard errors for the static model are expected to be small algebraically because they are based on a fixed and errorless datum; with the datum being stochastic these results are not representative enough. The dynamic and static-dynamic densification models incorporate stochasticity of datum parameters, in the staticdynamic model datum parameters are maintained definitive, while in the dynamic model all parameters are estimated afresh, thus resulting in the loss of the concept of datum. It is on the basis of the stronger theoretical and practical qualities of the static dynamic model that the model would ordinarily be recommended for geodetic densification of networks. The results in general demonstrate that the static-dynamic model gives more realistic estimates than the static and dynamic models hence it is a more suitable approach to the densification of geodetic networks.