Application Of Least Square Method And Its Extension Method In Surveying And Mapping

Least squares method is one of the commonly used methods to deal with the measurement data and is the main way to complete measurement adjustment. Currently, with the development of computer technology and the demand for high precision measurement data, the least squares method has been fully developed and been widely used in the conventional measurement techniques, but compared to the new problems emerging in the practice of Surveying and mapping and the higher requirements of the new measurement technology, new methods and new theory still need to been further explored and developed based on the least squares methods. This paper introduces the least squares principle and the derivation of formulas under the condition of linear and nonlinear. And then takes the time series parameters and the surface fitting as examples to analyze the application of the least squares under the condition of linear and nonlinear. The main researches are as follows:1) Classical least squares can give a better fitting result for the model which is known based on the observation vector error, but in practical work, the measurement data error makes it difficult to obtain better data accuracy, can not meet the certain actual needs. So this paper put forward the weighted least squares method based on previous studies, and takes the transformation of the three-dimensional space rectangular coordinate and solving the contradictory equations as examples respectively to explain the using method of the weighted least squares method.2) According to the error of coefficient matrix in the actual measurement data processing, the classical least squares method is difficult to play a role, but the total least squares method can give more accurate calculation and evaluation in this condition. Therefore, this paper further studies the mathematical model of total least squares adjustment, the adjustment criteria, calculating formula, accuracy assessment and other issues combining with the characteristics of the measured data. Finally, specific applications and precision are discussed with examples.3) For the condition of measurement data processing process has not been defined a complete mathematical model, the classical least squares method and the total least squares method can hardly play a role, because they must dependent on the existing mathematical model (that is, first to determine the existing model which will be used, and then to obtain the relevant parameters of the known model based on measurement data). But the moving least squares method can make up for this defect. In this paper, moving least squares formula is derived and the work method of moving least squares at two and three dimensions is shown with the sinking data of mining subsidence and the interpolation of grid point elevation data as examples. And the corresponding program is compiled by programming software.4) According to the problem of looking for a relationship between independent variables and the dependent variable from complex data problems, this paper proposes the partial least squares method. Firstly, the paper introduces the concept of partial least squares method, then takes the mining subsidence work as example to search for the relationship between the basic parameters of working face which is regarded as the independent variable and the predicting parameters of the probability integral method which is regarded as the dependent variable. Finally it is proved the validity and practicability of the method.Finally, this paper summarizes the differences between the various methods and their advantages and disadvantages, and then analyzes the use of various methods, which provides a reference for the actual measurement data processing in various surveying adjustment work.