Vibration error compensation algorithm in the development of laser interference absolute gravimeters

Measurement error arising from vibration interference is recognized as the primary obstacle limiting the accuracy and stability of laser interference absolute gravimeters. The present work addresses this issue by proposing a global search optimization algorithm that determines the optimal absolute value of gravity based on the measured time–displacement coordinates of a falling body and the signal obtained from the passive vibration isolation system of the inertial reference corner cube in a laser interference absolute gravimeter. Results of numerical calculations conducted under vibration interference conditions with added white noise resulting in a signal-to-noise ratio of 40 dB demonstrate the following. The accuracy and standard deviation of the gravimeter obtained using the proposed algorithm are −0.04 µGal (1µGal=1×10-8 m s−2) and 0.24 µGal, respectively, while those values obtained by the standard least-squares solution are 10.19 and 154.11 µGal, respectively. The test results indicate that the average response of the reference value of acceleration due to gravity superimposed by a disturbance of 1.00 µGal is 1.01 µGal using the proposed algorithm and 0.87 µGal using the standard least-squares solution.

On the general strong fuzzy solutions of general fuzzy matrix equation involving the Core-EP inverse

<abstract><p>The inconsistent or consistent general fuzzy matrix equation are studied in this paper. The aim of this paper is threefold. Firstly, general strong fuzzy matrix solutions of consistent general fuzzy matrix equation are derived, and an algorithm for obtaining general strong fuzzy solutions of general fuzzy matrix equation by Core-EP inverse is also established. Secondly, if inconsistent or consistent general fuzzy matrix equation satisfies $ X\in R(S^{k}) $, the unique solution or unique least squares solution of consistent or inconsistent general fuzzy matrix equation are given by Core-EP inverse. Thirdly, we present an algorithm for obtaining Core-EP inverse. Finally, we present some examples to illustrate the main results.</p></abstract>

Algebraic Techniques for Least Squares Problems in Elliptic Complex Matrix Theory and Their Applications

In this study, we introduce concepts of norms of elliptic complex matrices and derive the least squares solution, the pure imaginary least squares solution, and the pure real least squares solution with the least norm for the elliptic complex matrix equation AX=B by using the real representation of elliptic complex matrices. To prove the authenticity of our results and to distinguish them from existing ones, some illustrative examples are also given. Elliptic numbers are generalized form of complex and so real numbers. Thus, the obtained results extend, generalize and complement some known least squares solutions results from the literature.

Vibration error compensation algorithm in the development of the laser interference absolute gravimeter

Measurement error arising from vibration interference is recognized as the primary obstacle limiting the accuracy and stability of laser interference absolute gravimeters. The present work addresses this issue by proposing a global search optimization algorithm that determines the optimal absolute value of gravity based on the measured time-displacement coordinates of a falling body and the signal obtained from the passive vibration isolation system of the inertial reference corner-cube in a laser interference absolute gravimeter. Results of numerical calculations conducted under vibration interference conditions with added white noise resulting in a signal-to-noise ratio of 40 dB demonstrate the following. (1) The accuracy and standard deviation of the gravimeter obtained using the proposed algorithm are −0.04 μGal (1 μGal = 1 × 10−8 m/s2) and 0.24 μGal, respectively, while those values obtained by the standard least-squares solution are 10.19 μGal and 154.11 μGal, respectively. (2) The resolution of the test results shows that the average response of the reference value of acceleration due to gravity superimposed by a disturbance of 1.00 μGal is 1.01 μGal using the proposed algorithm and 0.87 μGal using the standard least-squares solution.