# Research on Improving Satellite Positioning Precision Based on Multi-Frequency Navigation Signals
## 1 Introduction  
In satellite positioning systems, positioning precision of the receiver is mainly affected by spatial layout of navigation satellites constellation and measurement errors [1]. Measurement errors generally include satellite clock error, ephemeris error, and errors caused by ionospheric delay, troposphere delay, multipath effect, and receiver thermal noise. The methods such as wide-area difference technology, local-area difference technology, navigation message enhancement, high-precision orbit/clock correction, atmospheric delay correction, and measurement noise suppression are generally adopted to eliminate or weaken the pseudo-range observation error and improve the positioning precision of the receiver. In papers [2; 3; 4], they introduced the methods of wide-area difference and local-area difference and client performance evaluation. In papers [5; 6; 7], the observation residual caused by atmospheric delay was improved by improving modeling accuracy. In paper [8], a particle filter tracking algorithm was proposed to suppress multi-path errors under strong and weak signals. The spatial layout of satellite constellation has an important influence on the system performance and positioning precision, and dilution of precision (DOP) is the main parameter to measure the geometric relationship between satellite and receiver. In paper [9; 10], the relationship between satellite positioning error and optimal constellation layout was analyzed. By adding satellites and improving the constellation structure, the DOP value and positioning precision can be improved. In the paper [11], a satellite selection method based on NSGA-II genetic algorithm is proposed, which takes into account the Geometric DOP (GDOP) value and the number of selected satellites. In paper [12], a GNSS multi-constellation selection method and an improved GPS real-time satellite selection algorithm were proposed. In paper [13], a constellation selection scheme for the regional satellite positioning system was proposed. In paper [14], it analyzed the influence of multi-constellation on the performance of the navigation system. In paper [15], it demonstrated that the Position DOP (PDOP) value of the GNSS system and the positioning precision can be improved by using LEO satellites. In paper [16], it introduced a GNSS analysis software based on MATLAB software for evaluating positioning results, such as positioning error, number of satellites, DOP value, etc. In paper [17], the weighted GDOP (WDOP) was proposed as an indicator for selecting stars and evaluating positioning precision. Chinese Area Positioning System (CAPS) is a satellite positioning system based on communication satellites. Satellite navigation signals are broadcast from ground stations and forwarded by communication satellites to reach ground receivers to achieve positioning and navigation [18]. The principle of implementation of the system is shown in Figure 1. The communication satellites in the system include geostationary orbit (GEO) satellites and small inclined geostationary orbit (SIGSO) satellites. During the CAPS system test from 2019 to 2021, the ASIASAT-3S, CHINASAT-10, CHINASAT-12, and APSTAR-6C communication satellites were selected as navigation satellites. Each satellite has more than 20 communication transponders used to transmit CAPS navigation signals. The developed CAPS receiver has 48 signal channels and can simultaneously receive 48 downlink navigation signals. When the constellation layout is not good, three communication satellites can be used to achieve positioning with the aid of elevation [19; 20]; when the constellation layout is good, the conventional least squares method can be used to achieve positioning. Combining the forwarding characteristics of the CAPS system and the resource advantages of communication satellites, [PERSON] et al. proposed the virtual clock method to effectively eliminate or greatly weaken the ephemeris error of the CAPS system [21]. [PERSON] et al.