A fast algorithm for GPS dynamic data processing based on integer reversible ambiguity transformation and probability calculation in Journal of Surveying and Mapping Xiong Yongliang, Huang f, Zhang Xianzhou, Liu Wenxi (Department of Surveying Engineering, Southwest Jiaotong University, Chengdu 610031, China) combined with Kalman filtering technology proposed a new GPS dynamic data Fast algorithm for processing fast algorithms based on probability calculation (Probability BasedFastAmbiguity-nesoiutionTechnique, PBFAT method for short) The algorithm directly rounds the floating point ambiguity when the rounding success probability is greater than the given limit; if the rounding probability is less than the given value, it will proceed! A range of fuzzy search. Experiments show that the calculation speed of this method is higher than that of the traditional method, and the required ambiguity has a clear confidence level.
Fund Project: The project supported by the National Natural Science Foundation of China (49771062) has a small transformation of the correlation coefficient. If all elements of L and L + 1 are integers, then L is called an integer reversible ambiguity transformation. The key issue of Gauss high-precision baseline solution for short is correct solution of ambiguity over the entire week. The correct solution of ambiguity depends on many factors such as the quality of observations, the number and distribution of satellites, the length of observation time, the size of multipath, the length of baseline, ionosphere, and troposphere. Over the years, many scholars at home and abroad have done a lot of research in this area, and put forward many algorithms, which are mainly divided into rounding method and search method. The rounding method is simple and fast, but requires a higher correlation between the accuracy and ambiguity of the floating-point solution. The search method is currently the main method of ambiguity decomposition. It includes the search method in the ambiguity space (typically the FARA method, LAMBDA method) and the search method in the coordinate space (such as the ambiguity function method). The search method has good robustness. But most of them are time-consuming. The shape and size of the search space in the fuzzy degree domain are completely determined by the structure of the fuzzy degree variance matrix. For short-term observations, the ambiguities are strongly correlated. The semi-axes of the ambiguity confidence ellipsoids vary greatly, so the search efficiency in the original ambiguity space is very low, the resolution of the ambiguities is particularly difficult, and the success rate is low. The LAMBDA method utilizes integer reversible ambiguity transformation (referred to as integer Gauss transformation for short) to transform the ambiguity into another fuzzy space and then conduct a conditional least squares search. Since the correlation coefficient between ambiguities in the new space becomes smaller and the accuracy is improved, this method greatly improves the search efficiency and success rate of ambiguities.
For GPS dynamic data processing, it is necessary to decompose the ambiguity of each epoch. Therefore, the resolution speed of ambiguity is very important, especially when online real-time calculation is required. This paper combines the advantages of the rounding method and the search method, using integer Gauss transformation, combined with Kalman filtering technology, a new fast algorithm for dynamic resolution of ambiguity is proposed. The algorithm uses the Kalman filter to obtain the ambiguity floating-point solution, and calculates the success probability P of the rounding method. When P is sufficiently close to 1, the rounding method is used. When P is less than the given probability Po, the algorithm shifts to the search method. The actual calculation example shows that the algorithm has higher calculation efficiency than LAMBDA, and the ambiguity of the algorithm has a clear confidence level.
2 Integer reversible ambiguity transformation is provided with m double-difference phase observations. Its linear combination can form m new observations, that is, == LAX + LBN + e, the corresponding combined ambiguity is: y = LN, L is Linear transformation operator, different transformations L will result in linear combination observations with different properties. In actual application, according to different application purposes, choose different transform matrix L. For fuzzy transform.
It is easy to prove that the identity matrix is ​​the simplest Gauss transform; the double-difference transform matrix obtained after changing the satellite and the integer triangular matrix with a diagonal element of 1 are both Gauss transforms; the inverse, transpose, and product of the Gauss transform are also Gauss transforms .
2.1 The construction method of integer reversible ambiguity transformation matrix 2.1.12-dimensional integer reversible ambiguity transformation Let the fuzzy degree floating-point solution and its variance matrix be respectively transformed. It is easy to prove that the correlation coefficient of the ambiguity after the above transformation is 0, and after the transformation The highest degree of ambiguity accuracy of 1 transform formula (4) is also Gauss transform, we call it Z2 transform. 2.1.2 There are two ways to construct the n-dimensional integer reversible ambiguity transformation matrix. One is to realize the construction of the n-dimensional Gauss transformation matrix through the continuous 2-dimensional Gauss transformation, and the second is to construct the n-dimensional Gauss transformation through the continuous dish T decomposition method. Formation. In this paper, the former is improved, and the following algorithm is designed. Comparison with other methods shows that this method is superior to other methods in reducing the correlation coefficient of ambiguity and improving the accuracy of ambiguity after transformation. For n ambiguities, set its variance matrix to Qv, and set Q = Qv at the same time, there are the following improved algorithms: n) the row i and column j corresponding to the largest of the n; the degree of decomposition should be selected to make the transformed baboon Well, it's just as good as it is. For example, the 2-dimensional variance matrix / sub corresponding to v! Construction 2.) Use the Zi transform. If you use the Z2 transform and fill its corresponding elements into the corresponding position of the n-dimensional unit matrix, get the n-dimensional Gauss transform Tk; -iT! ', The largest of which is less than 0.5, then it ends; otherwise letk = k + 1, repeat steps 2, 3; 6. Find the integer reversible ambiguity transformation T: 3 the probability of success of the rounding method Let N be the true value of the ambiguity vector, 7V is its floating-point solution. 々 is the direct integer solution. The probability of success of the integer method is P. When the ambiguities are not related, () the death of surveying and mapping scientist educator Wang Zhizhuo academician bookmark14 senior academician of the Chinese Academy of Sciences and professor of Wuhan University The treatment of the disease was ineffective. He died in Wuhan on May 18, 2002 at the age of 93.
Professor Wang Zhizhuo, as a well-known educator in China, is the main founder of Chinese surveying and mapping education and devoted his whole life to the surveying and mapping education in China. He is a learned and highly respected scholar. He has been rigorous in his life, selfless dedication, Tao Liman all over the world, and his achievements are remarkable. Professor Wang Zhizhuo's pioneering spirit and truth-seeking and pragmatic spirit in his career are our role models forever.
Professor Wang Zhizhuo has been a member of the editorial committee of the two journals for a long time since the publication of the Bulletin of Surveying and Mapping and the Journal of Surveying and Mapping, and has made positive contributions to the construction and development of the two journals.
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