Journal of Surveying Engineering

A kinematic deformation analysis (KDA) model is mostly preferred to estimate the displacement, velocity, and acceleration parameters in deformation analysis. Different models, such as linear and quadratic, are used in KDA. The displacement, velocity, and acceleration parameters are generally determined by the least-squares estimation (LSE) method. The LSE method smears the effects of the displaced points to the other nondisplaced points. Therefore, it should be noted that although the point is flagged as displaced from the KDA, it may not actually be displaced. Additionally, this may result in incorrect estimation of the velocity or acceleration. In this article, the reliability of the results of different models estimated by the KDA is discussed. To investigate the reliability of the models, different deformation scenarios were simulated in the Global Navigation Satellite Systems (GNSS) network. Different velocity and acceleration parameters were taken into account in these scenarios. The reliability of the KDA models was measured by the mean success rate (MSR). Different approaches for linear and quadratic models—namely, deduction, induction, and quadratic—were considered. According to the results, the solutions of the quadratic model are more successful when the acceleration is considered as zero and nonzero. Also, the MSRs of the induction and deduction models are very similar when the loaded acceleration is considered as zero.

When using the free station method, a total station (TS) is established by performing distance and angle observations toward a number of control points (CPs). The quality of the establishment is crucial for the quality of subsequent measurements. The optimal horizontal location of the TS has been investigated in previous studies. The vertical precision also is important in many applications, especially with significant height variations. Therefore, this study focused on the optimality of the vertical location of the TS. The sum of TS coordinates and orientation variances was used as an optimality criterion. To investigate the optimization problem, an analytical and a trial-and-error method were developed. Results from both methods show that the height component has no significant influence on the optimal vertical placement of the TS. Inspection of results from the trial-and-error method, where the CPs were moved in different height layers, indicates differences in the height uncertainty of the establishment in the micrometer range, which is negligible for most engineering applications.