Pose estimation of a fast tumbling space noncooperative target using the time-of-flight camera

This article proposes a pose estimation method for a fast tumbling space noncooperative target. The core idea of this method is to extract the target’s body-fixed coordinate system by using the geometric characteristics of the target’s point cloud and then by the body-fixed coordinate system to realize pose initialization and pose tracking of the target. In the extraction of the body-fixed coordinate system, a point cloud of the target, which can be obtained by a time-of-flight camera, can be divided into small plane point clouds firstly; then the geometric information of these plane point clouds can be utilized to extract the target’s descriptive structures, such as the target surfaces and the solar panel supports; and finally the body-fixed coordinate system can be determined by the geometric characteristics of these structures. The body-fixed coordinate system obtained above can be used to determine the pose of consecutive point clouds of the target, that is, to realize the pose initialization and the pose tracking, and accumulated bias often emerges in the pose tracking. To mitigate the accumulated bias, a pose graph optimization method is adopted. In the end of this article, the performance of the proposed method is evaluated by numerical simulations. Simulation results show that when the distance between the target and the chaser is 10 m, the errors of the estimation results of the target’s attitude and position are 0.025° and 0.026 m, respectively. This means that the proposed method can achieve high-precision pose estimation of the noncooperative target.

An Energy Bound in the Affine Group

We prove a nontrivial energy bound for a finite set of affine transformations over a general field and discuss a number of implications. These include new bounds on growth in the affine group, a quantitative version of a theorem by Elekes about rich lines in grids. We also give a positive answer to a question of Yufei Zhao that for a plane point set $P$ for which no line contains a positive proportion of points from $P$, there may be at most one line, meeting the set of lines defined by $P$ in at most a constant multiple of $|P|$ points.

An Innovative Detection Method of High-Speed Railway Track Slab Supporting Block Plane Based on Point Cloud Data from 3D Scanning Technology

The dimension detection of high-speed railway track slabs is one of the most important tasks before the track slabs delivery. Based on the characteristics of a 3D scanner which can acquire a large amount of measurement data continuously and rapidly in a short time, this paper uses the integration of 3D scanner and the intelligent robot to detect the CRTSIII (China Railway Track System) track slab supporting block plane, then the dense and accurate supporting block plane point cloud data is obtained, and the point cloud data is registered with the established model. An improved Random Sample Consensus (RANSAC) plane fitting algorithm is also proposed to extract the data of supporting block plane point cloud in this paper. The detection method is verified and the quality analysis of the detection results is assessed by a lot of real point cloud data obtained on site. The results show that the method can meet the quality control of CRTSIII finished track slab and the detection standard. Compared with the traditional detection methods, the detection method proposed in this paper can complete the detection of a track slab in 7 min, which greatly improves the detection efficiency, and has better reliability. The method has wide application prospects in the field of railway component detection.

Evaluation of tax audit strategies

It should be noted that the tax audit topic is relevant – during the last years quantity of tax audits accomplished by state authorities is still growing. Especially in this way is attempted to combat against tax avoidance and evasion, informal economy prevailed in the country. For committing it only helps to have regular inspections of taxpayers i.e. tax audits. Tax audits are divided under the verification time, as it is classified into a complex, a thematic inspection and an operational check. However, despite the existing differences between the various types of tax audit, a key moment of choosing strategy is a tax audit organization. In practice there are distinguished two tax audit strategies – “line-plane-point“ and “point-line-plane“. The first one indicates that before the initial analysis of data examination, it is necessary to investigate whether the company's tax accounting does not have indications for increased risk of error existence. For its practical application is necessary to execute a thorough collection and analysis of the evidence, and the most important is objective and correct assessment of indicators for an increased risk of errors. For this purpose suspicious taxpayers usually are selected and under the tax audit all of the data that can distort selected dubious indicators are checked. In application of the second strategy, if the execution of a company is suspected of tax evasion, it will be forwarded to the additional tax audit services, which will continue the investigation and will explore the additional information. Accomplished practical research have shown that the more of these indicators are observed during initial tax audit stage, the “point-line-plane“ method is more likely to be chosen. Accordingly, to choose one or another tax strategy correctly and adapt it properly it is necessary to take into account the indicators linked to the need for a tax audit.