Parameter estimation in 3D affine and similarity transformation: implementation of variance component estimation

摘要: Three-dimensional (3D) coordinate transformations, generally consisting of origin shifts, axes rotations, scale changes, and skew parameters, are widely used in many geomatics applications. Although some geodetic applications simplified transformation models based on the assumption small other fields such parameters indeed large. The algorithms two recent papers weighted total least-squares (WTLS) problem for 3D transformation. methodology can be applied to case when large which no approximate values required. Direct linearization rotation is thus not WTLS formulation employed take into consideration errors both start target systems estimation parameters. Two well-known methods, namely affine (12, 9, 8 parameters) similarity (7 6 handled using theory subject hard constraints. Because method formulated by standard with constraints, covariance matrix directly provided. above characteristics implemented presence different variance components, estimated least squares component estimation. In particular, estimability components investigated. efficacy proposed verified real data sets.