多站大尺寸测量仪坐标系转换的Procrustes方法

Procrustes method in coordinate transformation on multi-station of large scale measurement

提出了用7参数Procrustes方法建立了具有尺度因子的7参数坐标转换模型对多站大尺寸坐标测量仪坐标数据进行转换。首先,根据大尺寸测量仪坐标转换的原理,建立了7参数大尺寸坐标转换的非线性模型,并具体分析了Procrustes方法及其对坐标转换的适用性和重心法的转换过程。然后,列出了7参数Procrustes坐标转换方法的具体算法步骤;最后,利用该方法对一台Faro激光跟踪仪在移站前后的实际测量数据进行了坐标转换验证。对所得结果与激光跟踪仪配套软件移站的结果以及重心法的测量结果进行了比较,还利用所得的转换参数对一已知长度的基准尺两端坐标值进行转换验证。结果表明:利用7参数Procrustes方法得到坐标转换后x、y、z三个轴的最大误差分别为24.5μm、42.5μm和32.8μm,转换结果的中误差为17.1μm,远远高于配套软件以及重心法的转换精度。另外,用转换后的坐标值计算基准尺长度的极差为36μm。该坐标转换方法也可用于不同种类的坐标测量仪的数据匹配。

A 7 parameter Procrustes method with scale factors was proposed and a coordinate conver-sion model was established to transform coordinate data for a multi-station in large scale coordinate measurement.First,according to the coordinate transformation principle of large-size measuring instrument,the 7 parameter non-linear model in coordinate transformation was established,the Procrustes method and its applicability for coordinate transformation were analyzed and the transformation process of the center method was introduced.Then,the working steps of the 7 parameter Procrustes algorithm were listed.Finally,this method was used to test and verify the measuring data from a Faro laser tracker.The obtained results were compared with those from the laser tracker supporting software in a transfer station and center method and also the conversion parameters were used to transform the coordinates for both ends of a scale bar with a given length.The results show that the maximum error of the 7 parameters method in three axes of x,y,z are 24.5μm,42.5μm and 32.8μm and the mean error of this method is 17.1 μm,better than that of the supporting software and the center method.Moreover,the error range of the scale bar＇s length is 36μm in transformed coordinates of this method.The method is also suitable for other coordinate transform instruments to implement data matching.