Noise-resistant signal processing in a ballistic laser gravimeter with a symmetrical way of measuring the gravitational acceleration

Abstract

The paper considers methods for noise-resistant processing of signals in a ballistic laser gravimeter (BLG) with a symmetrical way of measuring the gravitational acceleration (GA).Seismic oscillations of the ground surface are the main source of errors when measuring the GA using a BLG. Gravimeters with the symmetrical way of measuring have a relatively short bump of the catapult, which causes basis oscillations, called auto-seismic. Systematic error of measuring the GA appears due to such the oscillations. In addition, it is necessary to take into account the influence of the discretization noises that appear when measuring trajectory parameters of the test body.The least squares (LS) method, traditionally used in ballistic gravimeters, is optimal only for the case of uncorrelated additive noise and under the condition of homoscedasticity. The mentioned conditions are not met for ballistic gravimetry. Thus, the problem of developing new methods of signal processing in a BLG is relevant.Our main attention is focused on synthesizing gravimeter weight functions aimed at minimizing the influence of the following types of additive noise: 1) external seismic noise; 2) auto-seismic noise; 3) discretization noise.A combination of quality factors was used to comprehensively take into account various noises. To determine weights of observation, the weighted least squares (WLS) method was used in this paper. The WLS method allows to use window functions, in particular the Hann window. In contrast to known methods of regression analysis, the form of such the window functions is determined not by variation of the noise variance, but rather to be selected to maximize suppression of the noise impact on the result of measuring the GA.Properties of gravimeter weight functions are given. Analysis of the impact of the form of the Hann window functions on the factors of noise resistance of the BLG is performed. It was shown that increase in the speed of window function drop from the center to the tails leads to significant decrease in the auto-seismic component of the error of measuring the GA at the expense of some negligible increase in other noise-resistance factors. The impact of omission of observations around the highest point of the test body trajectory on results of GA measurements is investigated. It is shown that fulfillment of the Nyquist condition for the weight function of the gravimeter allows to decrease the auto-seismic component of the GA measurement error.