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When photoelectric measuring equipment is used to track satellites, the extraction of the short-term or long-term target often fails because the target is weak, clouds block the target, and/or the sun’s angle is too small, resulting in the loss of the tracking target. In this study, an improved Laplacian satellite tracking method based on the Kalman filter is proposed. Firstly, the improved Laplacian algorithm was used for the initial fitting of the equation of motion of a small amount of measurement data. Judgment of the validity and Kalman filtering was carried out on the current frame’s measurement data to calculate the optimal estimate of the current frame’s orbit data, and the accurate equation of motion was iteratively fitted to obtain high-precision data for predicting the satellite’s orbit frame by frame. Numerical tracking of the equipment was carried out. This method was experimentally validated on an actual optical measurement device. The test results showed that this method can make up for the frequent loss of short-term targets. Under the condition that the maximum deviation is less than 3″, the length of extrapolated data can be up to 30 s and the length of the measurement data was less than 30 s. This method may improve the stability of tracking equipment as well as the accuracy and integrity of the measurement data.

In soft soil engineering projects, the building loads are always required to be symmetrically distributed on the surface of the foundation to prevent uneven settlement. Even if the buildings and soft clay are controlled by engineers, it can still lead to the rheology of the foundation. The analytical solution based on the Laplace integral transformation method has positive significance for providing a simple and highly efficient way to solve engineering problems, especially in the long-term uneven settlement deformation prediction of buildings on soft soil foundations. This paper proposes an analytical solution to analyze the deformation of soft soil foundations. The methodology is based on calculus theory, Laplace integral transformation, and viscoelastic theory. It combines an analytical solution with finite theory to solve the construction sequences and loading processes. In addition, an improved quantum genetic algorithm is put forward to inverse the parameters of soft soil foundations. The analytical solution based on Laplace integral transformation is validated through an engineering case. The results clearly illustrate the accuracy of the method.

The topic of this article is one-sided hypothesis testing on the means of two populations when there is uncertainty as to which population a datum is drawn. Along with each datum, a probability is given as to which of the populations the datum emanated. Such situations arise, for example, in the use of Bayesian imputation methods to assess racial and ethnic disparities with certain survey, health, and financial data. By use of a Bayesian framework and Markov Chain Monte Carlo sampling from the joint posterior distribution of the population means, the probability of a disparity hypothesis is estimated. This approach extends sample size limitations of previous methods given in the literature from a few dozen to well into the thousands. Four methods are developed and compared. Three methods are implemented in R codes and one method in WinBUGS. All the codes are provided in the appendices.