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Abstract

This paper proposes a modification of the classical process for evaluating the statistical significance of displacements in the case of heterogeneous (e.g. linear-angular) control networks established to deformation measurements and analysis. The basis for the proposed solution is the idea of local variance factors. The theoretical discussion was complemented with an example of its application on a simulated horizontal control network. The obtained results showed that the evaluation of the statistical significance of displacements in the case of heterogeneous control networks should be carried out using estimators of local variance factors.
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Abstract

The paper deals with frequency estimation methods of sine-wave signals for a few signal cycles and consists of two parts. The first part contains a short overview where analytical error formulae for a signal distorted by noise and harmonics are presented. These formulae are compared with other accurate equations presented previously by the authors which are even more accurate below one cycle in the measurement window. The second part contains a comparison of eight estimation methods (ESPRIT, TLS, Prony LS, a newly developed IpDFT method and four other 3-point IpDFT methods) in respect of calculation time and accuracy for an ideal sine-wave signal, signal distorted by AWGN noise and a signal distorted by harmonics. The number of signal cycles is limited from 0.1 to 3 or 5. The results enable to select the most accurate/ fastest estimation method in various measurement conditions. Parametric methods are more accurate but also much slower than IpDFT methods (up to 3000 times for the number of samples equal to 5000). The presented method is more accurate than other IpDFT methods and much faster than parametric methods, which makes it possible to use it as an alternative, especially in real-time applications.
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