Reliability Evaluation Of Transformation Results Of Coordinate System Based On Global Least Squares

Coordinate transformation is common problem in the measurement,and it is widely used in geodetic surveying,engineering surveying,photogrammetry and remote sensing.The coordinate transformation model of common main constraint adjustment is based on the least squares criterion.With the rapid development of science and technology,the higher accuracy of the data requirements is required,the traditional least squares model considering only the error in observed value,and most of the time,it can not meet the requirement of the high precision,so overall least squares adjustment model that can simultaneously consider observation error and error of coefficient matrix of the whole least squares adjustment model is developed quickly including the Partial-EIV and the Gauss-TLS Helmert model and so on as well as the calculation of the TLS method:singular value decomposition method,the Lagrange function method.This paper compares LS and TLS by enumerating examples.The coordinate transformation model based on various TLS models is developed.The paper discusses the situation of large and small rotation angles as well as the universal TLS coordinate transformation model.The least square criterion is a commonly used method in measuring data processing.It has good effect on parameter estimation.Before calculating mathematical model adjustment,if the observation data contains coarse difference,the adjustment result of the least squares will be seriously distorted,and its good effect will be greatly reduced.Therefore,it is more important to find out the coarse difference correctly.The research on reliability theory is very necessary,which mainly includes internal reliability and external reliability.In this paper,the overall least square reliability of EIV model is studied through the cofactor matrix solved by the error propagation rule,and the hypothesis test of the coarse difference is given.By EIV model considering the gross error may exist in the coefficient matrix,the redundant observation value of the reliability distribution in the coefficient matrix and the observation vector,according to the data under the constraints of the strength of the different data redundant observation of the size is different,and the corresponding numerical and controllability for observed value is inversely proportional to the relationship.The controllability value can be used as a measure to describe the internal reliability size,which is mainly related to the medium error multiple,and reflects the relationship between the lower boundary value and the middle error multiple.According to the example,the control value of the general internal reliability is at least 3.5 to 5 times of the error,which is consistent with the minimum of our common coarse difference.The lower bound value of the inner reliability is proportional to the controllability value,and therefore its relation with the middle error is also multiplied.By comparing the reliability of Gauss-Markov model,the superiority of EIV model reliability is verified.