Faculty of Navigation, Maritime University of Szczecin, 70-500 Szczecin, West Pomerania, Poland.
iSurvey, Westhill AB32 6FL, UK.
Sensors (Basel). 2020 Nov 13;20(22):6497. doi: 10.3390/s20226497.
The human activities in the offshore oil and gas, renewable energy and construction industry require reliable data acquired by different types of hydrographic sensors: DGNSS (Differential Global Navigation Satellite System) positioning, attitude sensors, multibeam sonars, lidars or total stations installed on the offshore vessel, drones or platforms. Each component or sensor that produces information, unique to its position, will have a point that is considered as the reference point of that sensor. The accurate measurement of the offsets is vital to establish the mathematical relation between sensor and vessel common reference point in order to achieve sufficient accuracy of the survey data. If possible, the vessel will be put on a hard stand so that it can be very accurately measured using the standard land survey technique. However, due to the complex environment and sensors being mobilized when the vessel is in service, this may not be possible, and the offsets will have to be measured in sea dynamic conditions by means of a total station from a floating platform. This article presents the method of transformation by similarity with elements of affine transformation, called Q-ST (Quasi-Similarity Transformation). The Q-ST has been designed for measurements on such unstable substrates when it is not possible to level the total station (when the number of adjustment points is small (4-6 points)). Such situation occurs, among others, when measuring before the offshore duties or during the jack up or semi-submersible rig move. The presented calculation model is characterized by zero deviations at the adjustment points (at four common points). The transformation concerns the conversion of points between two orthogonal and inclined reference frames. The method enables the independent calculation of the scale factor, rotation matrix and system translation. Scaling is performed first in real space, and then both systems are shifted to the centroid, which is the center of gravity. The center of gravity is determined for the fit points that meet the criterion of stability of the orthogonal transformation. Then, the rotation matrix is computed, and a translation is performed from the computational (centroid) to real space. In the applied approach, the transformation parameters, scaling, rotation and translation, are determined independently, and the least squares method is applied independently at each stage of the calculations. The method has been verified in laboratory conditions as well as in real conditions. The results were compared to other known methods of coordinate transformation. The proposed approach is a development of the idea of transformation by similarity based on centroids.
在海上石油和天然气、可再生能源和建筑行业的人类活动中，需要使用各种类型的水文传感器来获取可靠的数据：差分全球导航卫星系统（DGNSS）定位、姿态传感器、多波束声纳、激光雷达或全站仪安装在海上船只上、无人机或平台上。每个产生位置信息的组件或传感器都将有一个点，该点被视为该传感器的参考点。准确测量偏移量对于在传感器和船只公共参考点之间建立数学关系至关重要，以实现测量数据的足够精度。如果可能，船只将被放置在坚硬的底座上，以便使用标准的陆地测量技术进行非常精确的测量。然而，由于复杂的环境和传感器在船只运行时处于移动状态，这可能是不可能的，并且必须在海上动态条件下使用从浮动平台上的全站仪进行测量。本文介绍了一种通过相似变换元素的变换方法，称为 Q-ST（准相似变换）。当无法调平全站仪（当调整点数量较少（4-6 个）时）时，Q-ST 被设计用于在这种不稳定的基座上进行测量。这种情况会出现在海上作业前或自升式或半潜式钻机移动期间等情况下。所提出的计算模型的特点是调整点（在四个公共点）处的零偏差。变换涉及两个正交和倾斜参考系之间的点转换。该方法允许独立计算比例因子、旋转矩阵和系统平移。缩放首先在实空间中执行，然后两个系统都移至质心，即重心。重心是针对满足正交变换稳定性标准的拟合点确定的。然后，计算旋转矩阵，并从计算（质心）空间到实空间执行平移。在应用方法中，变换参数（缩放、旋转和平移）是独立确定的，并且在计算的每个阶段都独立应用最小二乘法。该方法已在实验室条件和实际条件下进行了验证。结果与其他已知的坐标变换方法进行了比较。所提出的方法是基于质心的相似变换思想的发展。
