Rapid Satellite Selection Algorithm Based on Clifford Algebra

GNSS Multi-system provide more visible satellites, however, the amount of computation will increase exponentially and the realtime requirement of navigation solution will be affected when all visible satellites are used for computing the three-dimensional position. Reasonable satellite selection algorithm can meet the accuracy of navigation, as well as the efficiency of navigation. Based on this, according to the characteristics and shortcomings of the elevation angle satellite selection algorithm, combined with the representation advantages of Clifford algebra, a rapid satellite selection algorithm based on Clifford algebra is proposed here. The specific implementation of the algorithm is as follows: taking the station center as the vertex, combining with the regional division of high, medium, and low angle of the elevation angle satellite selection algorithm, an umbrella matching benchmark model for low angle area to select satellites is constructed based on Clifford algebra; the coordinates of the visible satellites about local Cartesian coordinates coordinate system are calculated, and the multi vector set of visible satellites is constructed based on Clifford algebra theory; the matching threshold angle is calculated according to the designed total number of selected satellites and the number of zenith satellites first. Based on Clifford algebra theory, multiple vector sets of visible satellites are constructed. According to the preset total number of selected satellites and the number of top satellites, the matching threshold angle is calculated. Based on the vector angle operation of Clifford algebra, the multiple vector sets visible satellites and the umbrella model are matched and selected satellites. When the total number of the low elevation angle area and the high elevation area visible satellites is smaller than the designed total number, the visible satellites of the medium elevation angle area will be added, until the number of visible satellites meets the total number of selected satellites for the design. The experiment results about BDS/GPS/GLONASS show that when the number of selected satellites reaches 8, the result of this algorithm is close to that of the minimum GDOP method. When selecting the quantity of satellite is not less than 13, the algorithm selected satellite GDOP value is less than 2, show that the algorithm can meet the accuracy requirement of high precision navigation. Moreover, the calculation efficiency of this algorithm is much better than using the minimum GDOP method.