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Kalman filtering is a multiple-input, multiple-output filter that can optimally estimate the states of a system, and applicable for deformation analysis. The states are all the variables needed to completely describe the system behavior of the deformation process as a function of time (such as position, velocity etc.). The standard Kalman filter estimates the state vector where the measuring process is described by a linear system. In order to process a non-linear system an optimized aspect of Kalman filter is required. The main purpose of this research is to evaluate the optimized Kalman filter (OKF) as a non-robust method versus the iterative weighted similarity transformation (IWST) as a rigorous (also called robust) method. To satisfy this objective, first a detailed description on executing the optimized Kalman filter using the observation of angles and distances directly is provided. Then, 2-D total station data observations comprising distances and angles are used to demonstrate the OKF. For detecting the deformation, a real point-related test (single point test) is applied for every point as a local test. Consequently, the findings from OKF are compared and evaluated against the results from the IWST method. In general, the outcome of the Kalman filter algorithm is close to the preliminary results from the IWST method. The maximum and minimum differences in computed displacements are 0.2 and 2 millimeters respectively. Finally, Kalman filter approaches, having some properties, are recognized as suitable techniques for deformation analysis.

Optimized Kalman filter versus rigorous method in deformation analysis