# Carrier Phase Dual One-Way Ranging Method Based on a Frequency Hopping Signal
## 1 Introduction  
A navigation satellite constellation can construct a high-precision, spatial-temporal reference that provides navigation and location services to users [1]. The spatial reference is obtained through orbit determination, and the temporal reference is transferred via a ground time reference [2]. In the Global Navigation Satellite System (GNSS), to enhance orbit determination and time synchronization accuracy, the BeiDou system and GPS adopt intersatellite links (ISLs) [3]. The ISLs refer to the effective expansion of the telemetry, tracking, and command (TT&C) and communications range of ground stations [4; 5] by establishing communication and measurement links between satellites. On the one hand, measurements via ISLs can effectively improve orbit determination and time synchronization performance in GNSSs; on the other hand, ground stations can control satellites that cannot be directly linked to ground stations [6]. Improving the precision of the measurement method, reducing measurement errors, and employing an advanced data processing algorithm for ISLs can enhance orbit determination and time synchronization accuracy. In the GPS and BeiDou system (BDS), the ISLs adopt dual one-way ranging (DOWR) to measure the distance and time difference between different satellites [7]. The accuracy of satellite orbit determination and time synchronization is restricted by the precision of ISL measurements. The radio ISL adopts pseudonoise (PN) code, a carrier phase, and a binary offset carrier (BOC) signal to measure the distance between different satellites [7; 8]. The receiving satellite measures the PN code offset, carrier phase offset, and square wave offset, which represent the distance and time delay between the transmitter and receiver, respectively. The K-band ranging system (KBR) in the GRACE project of the U.S. calculates the orbit andrange change rate of low-orbit satellites. At a distance of 200 km between satellites, the speed measurement accuracy is 1 \(\upmu\)m/s, and the ranging variance is 1-2 mm [9]. In addition, [PERSON] et al. proposed a satellite dynamic DOWR algorithm that uses a combination of intersatellite pseudodistance fitting and time difference fitting to determine the relative temporal difference between satellites. The performance of the related method reached a time synchronization error within 5 ns [10]. [PERSON] et al. discussed a time synchronization algorithm based on single-point pseudorange conversion, which can be applied to DOWR between satellites in highly dynamic environments [11]. [PERSON] combined the satellite ground clock deviation data collected using the bidirectional time-frequency transmission equipment of the BeiDou experiment and the relative clock deviation obtained from the intersatellite link to achieve in-orbit calibration of the transmission delay of the intersatellite link channel. The delay calculation accuracy is better than 0.3 ns [12]. Due to the accuracy improvement requirement, [PERSON] adopted a laser DOWR whose accuracy was at the femtosecond level [13]. However, laser ISLs are limited by laser pointing, which cannot provide flexible access services to users. In addition, to improve the anti-interference performance and mitigate the autocorrelation function (ACF) ambiguity of dual-frequency multiplexing modulation, [PERSON] adopted a frequency hopping alternated binary offset carrier [14; 15]. To achieve high-accuracy measurements and flexible access services, radio phase measurements are employed for ISL communication. The carrier phase ranging between the satellite and the ground mainly utilizes precise single-point positioning techniques and multifrequency carrier phase measurements. The former can obtain high-precision carrier phase positioning results via satellite orbit, messages, etc. [16; 17]. Multifrequency carrier phase measurements transmit signals simultaneously at multiple frequency points via satellites. [PERSON] et al.