Performance of dual one-way measurements and precise orbit determination for BDS via inter-satellite link

2.1 GPS ISL

In order to enhance the survivability of GPS in a fiercely confrontational environment, e.g., high-altitude nuclear events, GPS autonomous navigation based on the ISLs was proposed in the 1980s (Codik 1985). By 1990, the theoretical designs and data simulations of ISLs for GPS Block IIR were basically completed, which enable the ability to broadcast satellite position and clock data for 180 days (without ground contracts) with an accuracy of 6 m user ranging error (URE) (Ananda et al. 1990). The ephemeris observability issues were also addressed later in 1994 (Menn and Bernstein 1994), and it was verified that the user navigation accuracy would not be seriously degraded despite the unobservability of the rotational ephemeris errors. The first Block IIR satellite was launched in 1997, while the AutoNav on-orbit background testing had not been started until early 2000 (Wu 1999), and analysis of the on-orbit range measurements indicated that AutoNav processing with the use of highly precise ground-based references, referred to as “AutoNav with Anchor,” would yield a URE less than 3 m (Rajan et al. 2003).

The 12 Block IIF satellites deployed between 2010 and 2016 have been optimized and improved with the updated ISL technology. In addition to the data exchange required for AutoNav, ISLs can also be used to transmit TT&C or downlink navigation information, which would provide a backup means for satellites to handle anomalies. The accuracy of AutoNav for 180 days remained URE better than 6 m, and when all satellites in the constellation were upgraded to Block IIF, the URE would be improved to 3 m (Fisher and Ghassemi 1999).

With further driver of increased capacity for improved communications, GPS III satellites have been considered to move from the easily interfered and crowded UHF band to the Ka (22.55–23.55 GHz) or V (59.3–64 GHz). The high-speed ISLs will feature a cross-linked command and control architecture to realize the concept of “contact one satellite, contact all satellites,” allowing the entire GPS constellation to be updated simultaneously from a single ground station. ISLs in the V band were finally reported to the International Telecommunication Union (ITU) after the full demonstration of Ka and V bands around 2010. The GPS III A will continue to use the ISL in the UHF band, whereas the future GPS III B will introduce the V band link. GPS has launched five Block III satellites by far, but has not disclosed the on-orbit status of their ISLs (Lazar 2002, Luba et al. 2005, Ollie et al. 2003, Maine et al. 2003, Maine et al. 2003).

2.2 GLONASS ISL

The Russian GLONASS tested ISLs in S-band with an operating frequency of 2212.5 MHz. Within each 5 s, the TDMA system divides the 24 satellites into 4 groups, with one group transmitting and the other three receiving signals. In this way, each group completes a measurement polling of transmission and reception within 40 s. Each ranging procedure last 5 min, and then, the next ranging procedure is performed at 10 min intervals. GLONASS-K satellites carried onboard laser ISLs, using a fixed topology to achieve high-precision inter-satellite ranging and data exchange, with the data exchange rate of 50 Kbps and measurement noise better than 10.0 cm, which will result in an enhanced POD performance with orbital position error less than 0.5 m, radial error less than 1.0 cm, and clock error less than 2.0 ns (Ignatovich and Schekutjev 2008, Roscosmos State Space Corporation 2020).

2.3 Galileo ISL

There have been various proposals for Galileo ISLs. Around 2010, the ESA “GNSS+” and ADVISE Projects (Sánchez et al. 2008, Fernández 2011) were initiated successively to assess the capability of ISLs and its corresponding onboard POD/TS processing to enhance the orbit and clock prediction accuracy and to reduce the Galileo system dependency from ground infrastructure. The GNSS+ project planned to perform dual-frequency pseudo-range measuring between satellites in C-band from 8.1 to 10.1 GHz. The TDMA system schedules 5 min for all the range measurements and all the necessary inter-satellite and medium earth orbit (MEO) to Galileo Sensor Station (GSS) communications, which is specifically one duty-cycle of 100 s for ranging and two duty-cycles of 200 s for communications. Although the orbit and clock determination processes are not continuous, the AutoNav scenario is supposed to achieve an accuracy of 1.0 m after 14 days of AutoNav, relying on the dual-frequency pseudo-range of 1.0 cm measuring accuracy; in the nominal scenario, when one ground station used, the average position error is in order of 8.0–12.0 cm (Sánchez et al. 2008).

On the basis of the GNSS+ Project, ADVISE Project optimized the mass and RF power of the ISL payload. This project canceled the MEO to GSS link in GNSS+, and adopts only the conventional GNSS L-band, which allows halving the power consumption and reducing the mass of ISL payload. The estimator processes the conventional L-band ranging data and uses the inter-satellite two-way ranging data to correct it, so as to reduce the ground dependence, and the POD accuracy is better than 12.0 cm when only 6 L-band stations are employed (Fernández 2011).

Another concept with ISLs has recently been developed by the German Aerospace Center (DLR). A navigation system named Kepler was proposed which consists of 24 Galileo-like MEO and 6 LEO satellites and uses optical ISLs for communication, high precision ranging and satellite clocks synchronization. Simulated POD results based on ISLs and even a single ranging station would yield the radial orbit accuracy of below 1.0 cm, without considering errors of GNSS antenna phase center offset, GNSS multipath, clock synchronization noise, and ISL range biases, while the ISL range biases up to 5.0 and 20.0 mm would lead to increase of signal-in-space range errors (SiSRE) to 0.74 and 1.67 cm, respectively (Schlicht et al. 2020, Michalak et al. 2021).

2.4 BDS ISL

ISLs were proposed to BDS as early as the very beginning phase of the global constellation project. Considering the new state of technology and the high level of complexity (Wang et al. 2020, Lei 2020, Chujo et al. 2020, Guo et al. 2021), BDS launched five test satellites from 2015 to 2016 to perform on-orbit testing of a multitude of innovative technologies, such as the network topology, communication protocol, antenna design, and AutoNav algorithm etc. Both reflector antennas and phased-array antennas were tested onboard the test satellites, while only the later were adopted by the new generation BDS, noted as BDS-3, taking full advantage of the agile pointing capability and high-precision ranging performance of the phased-array antennas (Ren et al. 2017, Xie et al. 2021).

The nominal BDS global constellation consists of 30 satellites at different altitudes, including three GEO satellites, three inclined geosynchronous orbit (IGSO) satellites at an altitude of 35,786 km, and the Walker 24/3/1 MEO constellation at an altitude of 21,528 km (Xie and Zhang 2020, Yang et al. 2020). All satellites carry onboard a set of phased-array antennas to set up ISLs, allowing the range measurements between MEOs or between MEOs and GEOs/IGSOs with a decimeter precision. Pointing toward the center of the earth, the phased-array antennas connect with other visible satellites within its beam scanning range (−60° and 60°) (Xie et al. 2019). Therefore, each MEO satellite can establish a total of eight permanent links with other MEOs according to its geometric visibility, with four in the orbital plane and the other four out of the orbital plane, besides from some dynamic links with GEOs/IGSOs. Furthermore, each satellite only needs one hop to connect to the ground based on an optimized routing. Figure 1 demonstrates the BDS-3 ISL network, including the topology of a single MEO satellite and the whole framework of three layers of links.

Figure 1

BDS ISL: topology of an MEO satellite (left) and three layers of links (right).

The TDMA system schedules a time slot of 3 s for each pair of satellites, with first 1.5 s for transmitting and another 1.5 s for receiving. The dual one-way measurement process is described as Figure 2. At first, satellite A sends a signal at its local time t A , 1 , and the corresponding system time (i.e., BDS time, BDST for short) is t 1 . After the hardware delay of c A , 1 and c B , 2 and the spatial propagation path delay τ A B , it is detected by satellite B at its local time t B , 2 , and the corresponding BDST is t 2 . So, the time delay noted as T A B measured by satellite B is t B , 2 − t A , 1 , which consists of all spatial path delays, such as ionospheric refraction and multipath effects, while the actual signal propagation delay from sending to receiving is t 2 − t 1 , which is generally far less than 1.5 s, and the most of the remaining time will be spent transferring data. For the next 1.5 s, satellite B sends a ranging signal at local time t B , 3 (system time t 3 ); after a similar process of the spatial propagation path delay τ B A , as well as hardware delay of c B , 3 and c A , 4 , satellite A detects this signal at the moment t A , 4 (system time t 4 ). Therefore, the time delay T B A measured by satellite A should be t A , 4 − t B , 3 .

Figure 2

The dual one-way measurement process of the ISL.

Then, these dual one-way pseudo-range measurements are written as

where τ A B and τ B A represent the geometric distance between the antenna phase centers of A and B; τ rel , AB and τ rel , BA represent the relativistic effect delay; and ε is the measurement noise. Obviously, the raw pseudo-range observations are functions of orbital positions and clock information of two associated satellites.

3.1 Data processing methods

Using pseudo-range observations for POD and TS is one of the fundamental purposes of establishing ISLs between satellites in GNSS. Therefore, the on-orbit performance of ISLs can be generally analyzed from these two processes. It has been investigated that as the original observation Eqs. (1) and (2) involve variables of two related satellites, such as the orbits, clock corrections, and hardware delays, these variables of different satallites need to be parameterized and estimated integratelly. Basically, two technical routes have been formed in the processing of observation data of ISLs.

The conventional method is to transfer the two bidirectional observations in the same time short slot to the same epoch so that parameters (orbital parameters, hardware delay, and clock corrections as epoch parameters) for a specific satellite are the same in two pseudo-range observation equations. Then, they can be combined to form a clock-free (CF) or geometry-free (GF) observation, thereby decoupling the orbit and clock parameters. In this way, the POD and TS processes are carried out independently by using two different sets of combined observations, i.e., CF observations and GF observations, respectively. As a result, satellite clock corrections derived in this way will be isolated from orbital errors, which provide potentially an independent two-way time comparison technology for GNSS. Actually, this method is originally proposed for the GPS AutoNav process and has been employed for ISL process of BDS. A comparative analysis of the satellites’ clock corrections from the L satellite-ground two-way observations with the Ka ISLs derived clock corrections has been conducted in references (Rajan 2002, Zhu et al. 2013), and the results show that the two have good consistency. However, all bidirectional observations in this process need to be paired, yet data that cannot be paired will be discarded. In addition, the noise of the combined observations is amplified compared to the raw data.

Nonetheless, the raw data contain much richer information. For example, the hardware delay parameters can be identified separately according to the receiving and sending channels via the raw one-way observations. Therefore, a second method of processing raw one-way observation data has been developed in recent years. All the dynamic parameters, epoch parameters, and geometric parameters for the whole constellation should be set up in one estimator, and the estimation is done by filtering the raw data.

3.1.3 Hardware delay calibration

The hardware delay is ISLs’ inherent characteristic due to the implementation differences in the signal processing system of each satellite. Although the ground-based calibration values will be given before the satellite is launched, they will change due to the complex factors in space, so that it is necessary to be calibrated on orbit. A reference should be set up by specifying the ISL receiver or transmitter of a certain satellite, and then, others can be derived. The hardware delays for each receiver or transmitter are usually parameterized as a constant variable and estimated with other parameters during the POD process. By processing one-way measurements, the hardware delay of the receiver or transmitter can be parameterized separately; however, only the sums ( c A , 1 + c A , 4 ) and ( c B , 2 + c B , 3 ) are estimated during the processing of combined dual one-way measurements. The hardware delay is one of the most important indicators of ISL measurement performance. Figure 3 exhibits the ISLs’ estimation accuracy of the hardware delays at the receiver and transmitter of the BDS ISLs, with average rms of 27 satellites below 0.3 ns and standard deviation (std) around 0.1 ns.

Figure 3

Statistical accuracy of estimated hardware delay via on-orbit data.

3.2 Measuring performance evaluation

The on-orbit operation of the Beidou-3 satellite provides favorable conditions for the performance evaluation of the BDS ISLs. From the perspective of POD and TS, the performance that affects the accuracy of the orbit and clock error mainly includes two aspects: (i) the spatial geometric constraints in terms of the position dilution of precision (PDOP), continuity and integrity of measurement process, and success rate of dual one-way pairing; (ii) measurement accuracy of the ISLs, in terms of the signal-to-noise ratio and measurement noise level, the accuracy, and posterior observation residuals, etc. Since the launch of the BDS test satellites, the on-orbit performance of the ISLs has attracted much attention, mostly focusing on the application of the ISLs to improve the accuracy of satellites’ orbit and clock corrections. Corresponding to three phases of BDS-3 construction, there are classified as the test satellites (Chen et al. 2016, Pan et al. 2018, Tang et al. 2018, Yang et al. 2021), the basic system of 18 MEOs (Zhou et al. 2018, Bai et al. 2020), and the global system BDS-3 (Xie et al. 2019, Yang et al. 2021, Yang et al. 2021).

3.2.1 Space geometry

After the constellation configuration is confirmed, the relative positional relationship between satellites is determined. PDOP is generally employed to describe the spatial geometry of the ranging measurement constraints, and early simulations showed that the PDOP of the ISLs for BDS-like Walker 24/3/1 MEO constellation varies between 1.2 and 1.3. However, measurement discontinuity in on-orbit operations would degrade the practical space geometric constrains. Since AutoNav adopts a dual one-way data pairing scheme, only the paired dual one-way pseudo-ranges can be used in POD or TS, and the pairing rate will also affect the continuity of the effective observations. Figures 4 and 5 show the typical statistical results of the Beidou IGSO/MEO ISL from Day of Year (DOY) 244 to 257 in 2021, respectively.

Figure 4

Statistics of BDS dual one-way ISLs.

Figure 5

Statistical PDOPs of BDS satellites via ISLs.

The success rate of ISLs refers to the ratio of the actual links to the planned links (i.e., linking rate), and the pairing rate refers to the actual dual one-way links versus total realized links, which is an intuitive indicator of on-orbit operation while playing an important role in POD for BDS. As shown in Figure 4, the linking rate of 99% means good onboard operation and the same as the pairing rate of over 98%. The quantified spatial geometry imposed by ISLs is expressed in PDOP, with the statistical mean of 0.9 for MEOs and 1.46 for IGSOs. In addition, for GEOs, the PDOPs imposed by ISLs range from 1.30 to 1.95 with a mean value of 1.56, although not listed in the figure. These PDOPs indicate good spatial geometric constraints on the satellite orbit.

3.2.2 SIS quality

The SIS quality of ISLs is evaluated in terms of signal-to-noise ratio, measurement noise, and bias. The measurement noise can be obtained by fitting the one-way measurements or by removing clock corrections from the combined GF measurements. The typical ISLs’ one-way ranging noise of BDS is between 0.1 and 0.2 ns, as shown in Figure 6, where the discontinuity of the MEO-to-IGSO link is very significant. Figure 6 also lists the carrier-to-noise ratio, which is normalized by the nominal value, and the result of the MEO-to-MEO link all above 1.0 shows a perfect performance.

Figure 6

Measurement noise and normalized carrier-to-noise ratio of BDS dual one-way ISLs.

Since the measuring performance can affect POD accuracy seriously, SIS quality of ISLs can also be evaluated in terms of the POD posterior residuals and orbital accuracy. For BDS satellites, an arc length of three days is generally suitable for POD. All ISLs’ dual one-way measurements and L-band measurements from international GNSS Monitoring and Assessment System (iGMAS) stations are collected, while only data from a regional network of eight stations located in China are collected to be fused with ISL data. Figure 7 shows that most of the posterior residuals’ RMS errors are around 5 cm after POD, which is larger than the noise level of the ISL measurement, and so that indicates unmodeled errors still remaining to be eliminated. Figure 8 lists the statistical POD accuracy in terms of overlap orbital differences, with radial RMS error of MEOs and IGSOs less than 1.0 and 2.4 cm, respectively, and the three-dimensional RMS error less than 15.0 cm. POD for GEOs is not involved in this evaluation due to its special characteristics, which has been investigated in our previous literature (Huyan et al. 2020). The results mentioned above are slightly worse than results derived from the global networks of iGMAS (Li et al. 2020), but enhance the regional network-based POD significantly (Zhu et al. 2013). This is exactly why ISLs are crucial for BDS to provide global high-precision continuous services while relying on regional ground infrastructures.

Figure 7

The posterior residuals of ISLs’ pseudo-range after POD.

Figure 8

POD accuracy of BDS satellites via ISL measurements.