Research On GNSS Integer Ambiguity Fast Decorrelation Algorithm

The fast and accurate fixation of the ambiguity in the carrier phase measurement is the key technology of GNSS real-time high-precision positioning.Once the carrier phase ambiguity can be accurately fixed,the carrier phase observations can be converted into accurate distance observations to achieve precise positioning and navigation.With the continuous construction and improvement of the four global satellite navigation and positioning systems,the number of satellites in orbit will increase significantly in the future,resulting in a significant increase in the number of observation equations,which will inevitably bring an increase in the ambiguity dimension.Will affect the efficiency of existing ambiguity resolution methods.In order to improve the efficiency of the existing ambiguity decorrelation algorithm based on the integer least square ambiguity decorrelation adjustment method,this paper starts with related research on how to improve the efficiency and quality of the decorrelation algorithm.The main research content and results as follows.1)The related mathematical models of carrier phase measurement are introduced,including the observation equations of pseudorange measurement and the non-difference of carrier phase measurement,the single-difference between stations and the double-difference between stations,and the observation equations of three common solution modes,as well as how Taylor 's fuzzy.The degree calculation requires the double-difference carrier phase measurement equation to be linearized,as a theoretical basis for the early work of the ambiguity calculation.2)Introduced the mathematical model of integer least squares estimation for ambiguity,discussed the principles of three commonly used decorrelation calculation methods based on integer least squares estimation of LAMBDA algorithm,LLL algorithm and SEQR algorithm,through numerical simulation experiments and measurement of different dimensions in the data experiment,the decorrelation time,search time,overall solution time and condition number of the three algorithms are compared and analyzed.The results show that the SEQR decorrelation algorithm with sorting strategy is more advantageous in solving the ambiguity.3)Aiming at the problem of how the sorting strategy works on the decorrelation algorithm and affects its solving efficiency,the natural ascending strategy,the symmetric rotation strategy,and the perturbing ascending strategy are respectively combined with the integer Gaussian transformation algorithm based on the lower triangular Cholesky decomposition to form three sorting descending correlation algorithm.Through simulation experiments and measured experiments,the decorrelation time,search time,total time,Bootstrapping success rate,and condition number of the three sorted decorrelation algorithms are compared and analyzed.The results show that the key to improving the decorrelation efficiency and quality of the ranking strategy is to sort the conditional variance vector in a certain direction or to reduce the value of the individual elements in the conditional variance vector to different degrees.Subtraction to make the elements in the conditional variance vector approach equal;at the same time,it proves that the condition number cannot well evaluate the quality of the decorrelation.The degree does not improve the search efficiency,but will affect the decorrelation efficiency and the total solution efficiency.4)In order to further quantify the impact of the sorting strategy on the performance of decorrelation,a new index for evaluating the quality of decorrelation is proposed.The comparison experiments of the simulated data and the measured data of the conditional variance standard deviation and search time of the three sorting decorrelation algorithms show that the conditional variance standard deviation and the search time are basically positively correlated,which can reflect the algorithm's decorrelation quality to a certain extent.5)The symmetric rotation sorting strategy and the delayed decorrelation strategy are used to improve the integer Gaussian transform algorithm(LIGT algorithm)based on the lower triangular Cholesky factorization.Through numerical simulation experiments,it can be seen that the symmetric rotation sorting strategy reduces the number of adjacent conditional variance exchanges,and the delayed decorrelation strategy reduces the number of integer Gaussian transformations.The comparison of the solution time of the two sets of measured data experiments shows that under the combined effect of the two improved strategies,the improved algorithm(MLIGT algorithm)will have a significant decorrelation efficiency and total efficiency compared to the LIGT algorithm and the SEQR algorithm.Improvement,and has better stability of solution time.