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.
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