# Fast Screening Algorithm for Satellites Based on Multi-Constellation System
## 1 Introduction  
The successful launch of the last BeiDou-3 satellite in 2020 marked a new addition to the group of global satellite navigation systems in the world, which now are the Global Positioning System (GPS) of the United States, the BeiDou Navigation Satellite System (BDS) of China, the Galileo Satellite Navigation System of the European Union, and the GLONASS system of Russia. At the same time, due to the combination of multi-satellite systems, the number of visible stars at the same epoch moment has gradually increased from 6-10 to nearly 40 [1]. However, the redundancy of navigation information caused by too much observation information does not significantly increase the positioning accuracy, and instead, the large amount of data put a great burden on the receiver system and may even cause a lag in the positioning solution results. Therefore, a satellite selection method with the ability to identify and eliminate faulty stars under a multi-constellation system and provide optimal navigation constellations is particularly important. The satellite selection method mainly accomplishes two tasks: The first part is to detect the coarseness in the observation information and then exclude the faulty stars, i.e., the screening algorithm. The main goal of this part is to ensure that the faulty stars will not participate in the localization as far as possible and, at the same time, to reduce the amount of computation. The second part is to select the suboptimal observation constellations among the remaining satellites after screening, i.e., the star selection algorithm. The goal of this part is to select a combination of better-configured satellites in the remaining constellations to significantly reduce the computational burden on the computer while ensuring that the positioning accuracy remains within acceptable limits [2]. Among them, reference [3] proposes a satellite screening called the user equivalent range error (UERE) model that takes into account multiple types of errors. The system computation elapsed time for a single-calendar element has been significantly reduced, which greatly improves the real-time performance of the positioning system, but the increase in the geometric dilution of precision (GDOP) value is also more pronounced, and the positioning error is larger. Considering that different satellites are located in different spatialpositions, the ranging error has some differences [4]. Considering the heteroskedasticity of satellite pseudo-range measurement errors on the basis of the least squares (LS) method, the screening probability of faulty satellites is further improved by using the weighted least squares (WLS) algorithm. Reference [5] proposes a satellite selection method using the minimum GDOP combined Walker configuration, which maintains the GDOP value better, but the requirements for the receiver location are more demanding and only applicable to the mid-latitude region. Using the symmetric positive definiteness of the measurement matrix, reference [6] proposes a GDOP solution based on the UT decomposition of the matrix to solve the problem of large computation and poor numerical stability in the matrix inversion process in the star selection process of GDOP. [PERSON] and [PERSON] et al. [7] take the altitude angle as the starting point of star selection and categorize the visible stars into a high-elevation zone, middle-elevation zone, and low-elevation zone according to the altitude angle information. Through the combination verification, it is concluded that the optimal combination is mainly concentrated in the high-elevation angle region and low-elevation angle region and the number ratio is close to 1:3. In summary, based on the analysis of GDOP value of a multi-system, combined navigation system, this paper proposes a fast star selection algorithm based on multi-threshold optimization, which judges, analyzes, and screens for the elevation angle, direction angle, and satellite carrier-to-noise ratio and selects a suitable navigation constellation.