Research On Beidou/GNSS Star Selection Algorithm Based On Helmert Multi System Weighted Optimization

With a long time of development,the number of satellites in orbit of Beidou /GNSS system reached 100.In the near earth area,GNSS receiver will receive 30-40 navigation satellites at the same time.How to effectively use the Beidou / GNSS multi system data,to ensure the navigation accuracy,and to improve the real-time and reliability,is worth studying and solving.If all visible stars participate in the solution,there will be huge data redundancy,and the data solution rate will be greatly affected.In order to ensure the accuracy and speed of the data solution,it is one of key problems in navigation applications to select the appropriate navigation satellite by using the appropriate satellite selection algorithm to ensure the accuracy of the data solution and the real-time data calculation.In view of this,the main contents of this paper are as follows:Under the MATLAB 2017 b programming plat,a data solution platform based on the RINEX format is established,which realizes the data solution of BDS,GPS,GLONASS,satellite clock difference correction,coordinate system unification,time system unification,and finally the three clock differences and receiver coordinates based on the least square principle.(1)Using Helmert’s variance component estimation theory to solve the weight determination problem of Beidou / GNSS multi-system,the least square solution of the weight optimization of BDS / GPS / GLONASS three navigation systems is carried out.Helmert variance estimation can reasonably distribute the weights of Beidou / GNSS multi-system observations in the positioning solution through weight matrix optimization,so as to minimize the variance of unknown parameters and improve the accuracy of navigation and positioning.However,the traditional Helmert variance estimation optimization process needs multiple iterations to achieve the minimum variance,which takes a lot of time.For this reason,combined with the operation law of navigation satellite,a weight matrix optimization method is proposed,which takes the result of the above one epoch as the initial value of the latter one,reduces the number of iterations and improves the calculation efficiency.The experimental results show that the average number of iterations of the improved Helmert variance component estimation weighting algorithm is reduced from the traditional 8 times to 4 times,and the algorithm is relatively stable,and its positioning accuracy is better than the equal weight positioning method.(2)In Beidou / GNSS multi-system star selection calculation,there is a problem of large-scale matrix calculation.Principal component analysis can use eigenvalues and eigenvectors to reveal the relationship between large-scale matrix and influencing factors.In order to improve the efficiency of star selection,combined with coordinate rotation theory,a fast star selection algorithm based on principal component analysis is proposed.Specific ideas: firstly,the coefficient matrix of visible star is decomposed into matrix,the eigenvector and eigenvector are calculated,then a new coordinate system is constructed based on this eigenvector,and the coordinates of each satellite in the new coordinate system are obtained through coordinate rotation transformation;considering that the positioning accuracy is affected by the direction derivatives of three coordinate axes and the clock difference of receiver,the star selection combining the new coordinate value and the eigenvalue is given Finally,based on Sherman Morrison formula,the number of stars selected can be reasonably estimated without human intervention.(3)The experimental data of the above algorithm theory are verified.Aiming at Beidou Xingtong and Hexinxingtong UB4B0 M boards,real-time data transmission,storage and calculation programs are compiled by MATLAB 2017 b platform.The real-time data transmission and solution are realized.The results show that when the number of selected stars reaches 12,the GDOP value of most star selection algorithms based on similar principal component has been less than 2,which meets the requirements of high-precision navigation and positioning;when the number of selected stars continues to increase,the GDOP value has not decreased significantly,but the calculation amount is increasing;the number of independent star selection algorithms based on Sherman Morrison formula also shows that the number of selected stars reaches 12 At 93.54% probability,GDOP is less than 2,which further shows that Sherman Morrison formula can assist the star selection algorithm based on similar principal components to achieve the effect of autonomously determining the number of stars.