Methods to compensate estimated phase distortions in multiprobe microwave meters

This paper addresses the problem of the accuracy of contactless relative displacement measurement with the help of a multiprobe measuring line in the microwave range. Attention is given to measurement errors that arise from inaccuracies in the probe placement and probe spacing measurement and inaccuracies in oscillator frequency setting. These inaccuracies can be caused by excessive vibrations and temperature variations. The paper overviews two standard methods: the discrete Fourier transform method and the two-probe method. New approaches based on Prony’s method and the normalized propagation constant correction method are studied. Prony’s method approach uses a modified version of Prony’s method in order to reduce the required number of probes. The novel approach is based on approximating the signal model with the help of a linear approximation of the harmonic component with a shifted value of the normalized propagation constant. The former method significantly reduces the signal distortion, while the latter is sufficient for small distortions and shows a faster computational speed. The methods were first tested on a deterministic noiseless model with phase distortions due to errors in the propagation constant followed by testing them on a model both with propagation constant errors and with additive white Gaussian noise present. The tests gave empirical ranges of applicability of each of the methods including the standard ones based on their performance. For the proposed methods, these ranges are sufficient for real-world applications, and they mainly impose restrictions on the probe spacing measurement accuracy because the oscillator frequency accuracy provided by modern equipment lies well within them. The methods improve the relative displacement measurement accuracy for a waveguide system model subject to vibrations that affect the electrical probe spacing.