## 1 Introduction  
The Global Positioning System (GPS) uses radio waves to provide users with positioning, navigation, and timing (PNT) services. GPS navigation signals have numerous applications in space weather, biology, and everyday life [1]. GPS is one of several Global Navigation Satellite Systems (GNSS), which include the Russian Global Navigation Satellite System (GLONASS), the European Galileo, and the Chinese BeiDou systems (BDS) [2]. IS-GPS-200 [3] illustrates receivers could solely use legacy L1C/A signals for positioning before GPS modernization. The modernization of GPS brings quite a few benefits to civil GPS users. The first IIR-M satellite launched in 2005 brought a new civil signal L2C that was primarily to meet commercial use and was open to civilians. Thereafter, all satellites launched by GPS would transmit L2C [4]. Subsequently, the third generation civil signal of GPS, the L5 signal started broadcasting in a protected aeronautical radio navigation service band that was mainly for safety-of-life transportation. The full L5 signal has been implemented with the launch of the first block IIF in May 2010 [5]. Despite the unprecedented success of GPS, this planning and technical foundation from the 1970s has its own shortcomings in terms of anti-interference, safety and rapid response to constellation abnormal time. [PERSON] [6] reports that the US Congress approved a plan in 2000 to establish a new GPS, called GPS III, which would greatly improve civilian and military navigation capabilities. GPS III deploys a signal compatible with other GNSS such as Galileo and BDS at the L1 frequency and is also the fourth generation civil signal, called L1C [7]. The first satellite of the GPS III was launched in December 2018. The Quasi-Zenith Satellite System (QZSS) is a Japanese regional satellite positioning system operated by the Japan Aerospace Exploration Agency (JAXA). Take advantage of the high elevation of a highly elliptical orbit, QZSS has been developed as a GPS-complementary system to increase the availability, reliability, integrity and accuracy of positioning performance in the Asia-Oceania region, especially in urban canyons and mountainous areas [8]. QZS-1, the first satellite of QZSS, is in orbit since 2010. In 2017, Japan launched three satellites to join QZSS, including QZS-2, QZS-3 and QZS-4 [9; 10], which indicates that it is now feasible to carry out positioning based on QZSS. These four satellites transmit all GPS civil signals since the modernization of GPS, including L1C/A, L1C, L2C and L5 [11]. IS-GPS-800 [12] illustrates the L1C signal consisting of data (L1 CD) and pilot (L1 CP). They are unequally distributed power in 1:3. The novel BOC modulation and TMBOC modulation are used in the GPS III L1C signal, which is virtually seamless interoperability with L1C from QZSS. The navigation message modulated on the L1C signal uses advanced Low Density Parity Check (LDPC) coding, Bose, Chaudhuri, and Hocquenghem (BCH) coding and interleaving to reduce the bit error rate caused by L1 CD accounting for 25% of the signal power [13; 14]. A theoretical research [15] reports that the new spread spectrum modulation in the pilot component improve the acquisition and tracking performance, especially against interference and noise. As of May 2019, there are a total of five satellites broadcasting L1C signal in orbit, one of which belongs to GPS III and four of which belong to QZSS. A GPS III satellite with a code number of 4 is called Vespucci. The other four satellites of QZSS called QZS-1, QZS-2, QZS-3, QZS-4 use the code number 193, 194, 199, 195 respectively. It should be noted that QZS-1, the first satellite launched by QZSS, differs from GPS III when it comes to modulation and phase. QZS-1 uses BOC(1,1) modulation for both data and pilot, and its pilot advances data by 90 degrees (in phase quadrature). In GPS III and three other QZSS satellites, L1 CD uses BOC(1,1) modulation, and L1 CP uses TMBOC(6,1,4/33) modulation. And they are in the same phase.