The Method Of Total Least Squares For3D Datum Transformation In The Arbitrary Rotational Angle

In3D datum transformation, classic linear Bursa-Wolf model is suitable of solving seven parameters in the case of the enough small rotational angle. As the development of survey technology, in many practical applications, such as the image matching in photogrammetry and the point cloud registering in3D Laser Scanning, the principle of them are essentially the solving parameters of the3D datum transformation with arbitrary rotational angle and more cases are the rotational angle would be Large in generally. On the condition of small rotational angle, the coefficient matrix, from the error equation of Bursa-Wolf model, is constituted with a series of common point coordinates. Even if these common point coordinates are the result after adjustment, it will still be affected by random error and the case don’t correspond the precondition of Least Squares (LS). Total Least Squares (TLS) is the method that demands to do global analysis and total considering not only observation vectors but also coefficient matrix.Based on the Gauss-Markov model of classic LS, linear model and nonlinear model of3D datum transformation are researched and verified by the simulation experiment. The result of experiment display:in the small rotational angle, it is equivalent between linear model and nonlinear model, but in the large rotational angle, the results of linear model are severe infidelity and the nonlinear model is relatively better.Aimed at classic LS never considering that the coefficient matrix wouldn’t include or be never affected by the random error, it is introduced the Error-in-variables (EIV) model and give its fundamental form and the criterion of estimation. Base on EIV model, both Weighted TLS (WTLS) iterative algorithm are researched and derived in detail.In order to straight line fitting as an example, the solving result display the precise of both iterative algorithms is equivalent and the solving result of WTLS is obviously superior to LS, which the slope a and the intercept b have improved62.33%and66.80%respectively.This paper explored and researched the TLS method of3D datum transformation with the arbitrary rotational angle based on the seven parameters model and the iterative algorithm of WTLS and proposed the WTLS orthogonal constraint model based on Newton-Gauss. In this paper, at first, setting simulation experiment and selecting the Root Mean Square Error (RMSE) as the index of precise assessment, in contrast to the precise of solving parameters from LS, the translation parameters AX, AY and AZ improve75.29%,61.08%and65.98%respectively; the scale parameter K improve68.01%; the rotational parameters εx,εy and εz improve71.89%,70.80%and68.49%respectively. It is to reveal the advantage of TLS, and meanwhile verify the validity and reasonability of WTLS orthogonal constraint model.In addition, utilizing the case data of actual measurement, it aimed at proofing the universal property of the model. The results of experiment indicate the model improve the precise of3D datum transformation to same extent and has the rapid convergence, universal property and easy achievement, which has the definite application value and guiding significance in the actual production.