Research On The Total Least Squares Collocation Algorithm And Its Applications

The least square method and the total least square method are the common methods for measuring data processing.In order to satisfy the needs of field with data processing,we take the observation data and prior information into the adjustment criteria,made the observation data and prior information can be used.In order to improve the precision of parameter estimation is becoming the research direction by many scholars.The least square method does not consider the coefficient matrix error caused by the observation data in parameter estimation,so the parameter estimation is no longer unbiased.The total least square method takes the coefficient matrix error and the observation vector error into account,and the parameter estimation model is more rigorous and reliable.The least square collocation method takes the prior information of the observation data to be adjusted into the adjustment criterion,but ignores the random error of the observation vector and the coefficient matrix.The basic task of measurement adjustment is to obtain the real value of the observed object,and to evaluate the accuracy of data processing by using some criteria.Studying the theory and method of data taking into account the error of observation data and the information of prior constraints at the same time,it can enrich the theoretical system of the total least square data processing and expand the scope of application,and has important practical significance.In this paper,it considers both the prior information and the coefficient matrix error of the observed data,and the adjustment model is applied to the estimation of the parameters.Researched on the total least squares collocation method adjustment criterion,calculating method and formula of accuracy,the iterative derived of total least square collocation method calculation formula.Specific examples of selected is height anomaly,gravity estimation and bursa model three-dimensional coordinate transformation to experiment the algorithm.Combining the concrete application,the influence of the coefficient matrix with the error and the prior information of the parameter on the adjustment result is analyzed.The example analysis shows that the least squares collocation height anomaly fitting precision is the same with least square collocation method,but higher than the plane fitting method;3D coordinates of the application with total least squares collocation method conversion model parameters calculation accuracy is higher than the least square collocation method and the classical least squares method;estimation accuracy is higher than the least square collocation method in the estimation of gravity fitting by using the total least squares collocation method.