1. Introduction
Recent years have witnessed mankind accelerating into a new era of lunar exploration and development [
1], and there will be more and more cislunar activities [
2,
3]. In the future, the number of unmanned lunar probes and manned lunar spacecraft will increase and take more and more “one small step for individuals and one giant step for humankind” [
4,
5,
6].
Cislunar space is a natural extension of the near-Earth orbit space. In a broad sense, it is a region dominated by the gravitational force of the Earth and the Moon, including near-Earth space, lunar gravitational space, and Earth–Moon transfer space; in a narrow sense, it refers to the Earth–Moon transfer space and lunar gravitational space outside the geosynchronous belt [
7,
8,
9,
10]. As the first stop towards deep space, the cislunar space contains various kinds of materials, energy, environments, locations, and other scarce strategic resources [
11], which renders it as a strategic space for human survival and development and the main destination and outpost of space mission activities in the future, including deep space confrontation, in-orbit service and maintenance, deep space science and applications, and support for manned exploration far beyond near-Earth orbit [
12,
13]. It is foreseeable that space activities of all countries will further focus on the cislunar space.
After the announcement of the New Space Exploration Program in the early 21st century [
14], in the future, NASA is planning to launch a nuclear-powered lunar rover to collect more samples from the moon and send them back to Earth by astronauts [
15,
16]. On 28 June 2022, the United States launched a new generation of the lunar probe “Capstone”, the first successful one launched in nearly a decade [
17]. As the forerunner of the Artemis Project, this microwave oven-sized probe is advertised as “the world’s first lunar navigation satellite”, marking the substantial deployment phase of the U.S. version of GPS on the Moon [
18].
Recently, China announced that its manned lunar exploration project has been launched, which plans to achieve the first landing of Chinese people on the moon before 2030. Futhermore, China will promote the fourth phase of the lunar exploration project [
19,
20,
21]: around 2024, the Magpie Bridge-II Relay and CE-6 probe will be launched, to achieve the lunar back sampling return; around 2026 and 2028, CE-7 and CE-8 will be launched, to achieve the lunar south pole resource exploration and constitute the international lunar research station. Meanwhile, China is also demonstrating the construction of a constellation of lunar communication and navigation system—the Magpie Bridge remote integrated constellation system [
22], which will be divided into three phases: pilot phase, basic phase, and expansion phase. The pilot phase will be completed before 2030 to support the fourth phase of the lunar exploration project and international lunar research stations; the basic phase will be accomplished before 2040 to realize regional navigation, service manned lunar exploration, international lunar exploration, etc., which can provide relay communication, navigation, and key information support for future lunar surface operations and more complex lunar exploration tasks [
23].
On 27 December 2022, Korea’s first lunar orbiter, Moonwatch, successfully entered its scheduled orbit around the Moon, and will further help Project Artemis [
24]. In early 2023, the Indian Space Organization announced that India’s third lunar exploration mission will be launched late this year [
25]. The Indian Moonship III lander has successively passed electromagnetic compatibility and critical vibration environment tests and will undertake the relay communication mission and cooperate with the Moonship II propulsion module, thus jointly supporting India’s next lunar exploration mission (the lunar rover will work on the lunar surface for about half a month). Japan’s Shiraito-R, which successfully entered lunar orbit at the end of March 2023, carried the UAE’s first lunar rover and a small Japanese robot into the northern Atlas Crater on the lunar front at the end of April to study the movement of lunar soil, rock and dust, and plasma conditions on the lunar surface [
26]. ESA has likewise launched plans to establish a network of navigation and communication satellites in orbit around the Moon [
27,
28].
In addition, several commercial space companies around the world have announced plans to apply jump robots to survey the lunar surface [
29]. More lunar exploration missions are underway, with the general hope of obtaining rich lunar information and painting a delicate “portrait of the moon goddess” to lay a solid foundation for lunar resource exploration and development, lunar base construction, and long-term human presence on the Moon [
30].
A schematic diagram of the relevant range in cislunar space is shown in
Figure 1 (the figure contains the ground-based Connected Element Interferometry (CEI) observation array as well as non-cooperative spacecraft at significant cislunar orbital altitudes).
Given this, cislunar space has become an important base and destination for deep space explorations, which is also the main starting point of this study. The motivation and existing challenges of this research will be summarized as follows.
As future lunar exploration activities will place higher requirements on lunar probe orbiting accuracy, real-time and applicable scenarios such as Positioning, Navigation, and Timing (PNT) of cislunar space explorations [
31,
32] and the high-precision measurement, orbiting, and positioning of non-cooperative spacecraft in cislunar space will thus become a fundamental and cutting-edge research work. Nevertheless, the current means of determining its orbit still relies on ground-based measurements [
33], including ground-based radar and optical telescopes, which are greatly restricted by geographical location and weather conditions around the stations, ground-based radio ranging, and velocimetry and interferometry, which requires rather long tracking time, especially for the transfer orbit between Earth and Moon [
34].
Recently, the adoption of the short-time alternating differential measurement mode of radio source (Delta Differential One way Ranging,
) has greatly improved the measurement accuracy of deep space probes and has been successfully applied in international deep space exploration missions [
35]. The China VLBI Network (CVN) [
36], led by the Shanghai Observatory of the Chinese Academy of Sciences (SOAS), has been successfully applied in China’s lunar exploration missions to support the high-precision orbit determination of lunar probes [
37]. SOAS has also carried out the same beam interferometry observations of the two spinlets Rstar and Vstar of the Japanese lunar satellite SELENE and obtained differential phase time delays of
magnitude to achieve ultra-high precision interferometry between lunar probes [
38].
Futhermore, the farther the probe is from Earth, the worse geometry of ground-based measurement will become, thus limiting the orbiting accuracy and applicability of merely ground-based methods. With the development of cislunar space exploration, space-based measurement technology has emerged [
39], including interplanetary ranging technology [
40] and satellite-based GNSS leakage signal technology [
41], which have been applied in the current Earth satellite navigation system and will undoubtedly be extended to cislunar space. In this field, a series of frontier explorations have been carried out, including the research of autonomous orbiting of constellations based on lunar leveling point orbit [
42], the joint autonomous orbiting technology of leveling point detector and Earth navigation satellite [
43], the autonomous orbiting of detector of cislunar triangle leveling point [
44], and the autonomous navigation and timing system of cislunar detector based on DRO-LEO formation [
45]. However, the above studies are mainly limited to the realization of the autonomous real-time navigation of the cooperative cislunar spacecraft, and there is still a lack of reliable means for the effective tracking and measurement of the non-cooperative targets in cislunar space.
Conclusively, considering the limitations of existing space-based and ground-based cislunar space target measurement means, this research fully applies the advantages of GNSS interplanetary link signals in flexibility and reliability, with the integration of ground-based radio interferometry means, so as to achieve high-precision cislunar space target tracking and measurement. The specific exploration and verification will be introduced as follows.
As one of the most significant GNSS system, China’s BDS has successfully deployed ISL on BDS-3 series satellites [
46]. One of the main roles of the ISL is to perform precision orbit setting and time synchronization of spacecraft [
47], and the research on orbit and clock difference determination using BDS-3-measured ISL data, refinement of geometric observation models for the ISL, and modeling correction of system errors has just started [
48]. The trajectory of the BeiDou satellites is shown in
Figure 2. The space-division time-division access system and Ka-phase array beam shortening capability of the Beidou ISL system exert a strong ability to expand applications [
49]. The ISL system of the BeiDou-3 harbors the following features [
50,
51]: (i) Ka-band inter-satellite link with high ranging accuracy, strong anti-jamming capability, and good confidentiality; (ii) Space-time division multiple access and double-way ranging (Beidou-3 adopts the space-time division multiple access system, which realizes point-to-point link building between satellites); (iii) High–medium link, medium–medium link, and star-ground link mixed link construction (The Beidou-3 constellation consists of 3 GEO satellites, 3 IGSO satellites, and 24 MEO satellites, each carrying an ISL payload to realize the link construction between high–medium orbit satellites and medium–medium orbit satellites, while the ground is equipped with anchoring station equipment to realize the star-ground link building with the space constellation).
Taking full advantage of the unique characteristics of satellite navigation systems as a time and space reference and global coverage, given that the BeiDou interplanetary link system is fully configurable and rapidly configurable, the user spacecraft is regarded as the expansion node of the BeiDou interplanetary link system to access the BeiDou interplanetary link system and use the on-board processor to process the interplanetary measurement data to get its own orbit, which can theoretically meet the demands of real-time orbiting of cooperative and non-cooperative spacecraft in the cislunar space range [
52,
53].
Based on the above analysis, this paper will utilize the inter-satellite link signal equipped on Beidou-3 satellites, combined with the ground-based CEI equipment, to achieve effective and reliable tracking measurements for non-cooperative spacecraft in cislunar space. The main contributions and structure of this paper are summarized as follows.
- (i)
A non-cooperative cislunar space targets measurement method based on CEI and BDS-3 inter-satellite link signals is proposed, with its general scenario and specific flow discussed in
Section 2. To the best of our knowledge, this is the first time the collaboration of GNSS inter-satellite link signals and interferometry-based technology has been applied in non-cooperative cislunar space target tracking and measurement.
- (ii)
On this basis, in
Section 3, the mathematical models of the proposed method are put forward, which mainly includes four parts: dynamical constraint equations for non-cooperative targets in cislunar space; BDS-based interplanetary link for irradiation of non-cooperative targets; transmission loss equation of BDS-3 inter-satellite link signal in cislunar space; CEI-based precision measurements of targets in cislunar space.
- (iii)
Based on the previous analysis,
Section 4 will focus on the measurement errors of the inter-satellite link signals of Beidou-3 satellites in different orbits during the transmission process in the Earth–Moon space and the CEI observation process of the final received signals reflected by non-cooperative spacecraft. The error correction equation will be introduced to further correct the CEI observation equation of non-cooperative spacecraft in cislunar space.
- (iv)
Based on the above analysis, to give the feasibility demonstration of the proposed method, the link budget analysis and performance evaluation are presented in
Section 5 and
Section 6, which focus on the carrier-to-noise ratio of the measurement of the target, and analysis of the pseudocode ranging and ranging rate of the GNSS-based interplanetary link signal, respectively.
- (v)
The research results of this paper (which are demonstrated by the experiments shown in
Section 7) can achieve effective and reliable tracking and measurement for non-cooperative targets in cislunar space, indicating a promising potential in the increasingly critical cislunar space situational awareness missions in the future.
5. Link Budget Analysis for the Measurements of Non-Cooperative Targets
The complete link schematic of this part is shown in
Figure 6, which mainly includes the analysis of the load-to-noise ratio of the non-cooperative spacecraft tracking and measurement link in Earth–Moon space based on the CEI and BeiDou interplanetary link. The BeiDou-3 satellite transmits the inter-satellite link signal, which is reflected back by the Earth–Moon space target after irradiating it, and the signal is then received by the CEI array on the ground.
The load-to-noise ratio of the non-cooperative spacecraft tracking and measurement link in Earth–Moon space based on the CEI and BeiDou interplanetary link can be expressed as follows:
where
C is the received signal power in
at the CEI receiving array;
is the thermal noise power in
; and the carrier-to-noise ratio
is in
.
The received signal power
C and the thermal noise power
satisfy the following relations, respectively:
where
is the GNSS interstellar link signal transmit power in dBW;
and
are the antenna gain of the GNSS interstellar link transmit and the CEI array receive toward the targets in dBi, respectively;
is the GNSS interstellar link signal reflection loss through the targets in
;
is the GNSS signal transmission loss in
in Earth–Moon space;
is the reception loss in
at the CEI receiving array end;
is Boltzmann constant,
J/K; and
and
are the antenna and amplifier noise temperature in
K, respectively.
in (31) satisfies:
where
is the Beidou interplanetary link signal power,
is the distance between the Beidou-3 satellite transmitting the Beidou interplanetary link signal and the non-cooperative spacecraft, and
is the distance between the non-cooperative spacecraft and the ground-based CEI receiver array.
The antenna noise temperature
and the amplifier noise temperature
in (32) satisfy the following relations, respectively:
where
is the ohmic loss caused by the antenna’s own defects;
is the thermal noise captured by the antenna from the surrounding environment;
is the physical temperature of the antenna;
is the antenna efficiency;
and
are the fixed angles subtracted by the Earth and the Moon, respectively, when the CEI receiving array is the viewing angle;
,
and
are the brightness temperatures of the Earth, the Moon, and the cosmic background, respectively;
is the physical temperature of the amplifier; and
is the amplifier noise factor.
Combining (30) and (35), the load-to-noise ratio equation of the non-cooperative spacecraft tracking and measurement link in Earth–Moon space based on the CEI and BeiDou interplanetary link can be finally expressed as follows:
8. Discussion
For the simplicity of discussion, only Beidou Navigation Satellite signals are applied as the GNSS sources in this research; however, the inter-satellite link signals of other navigation satellites (including global ones such as GPS, GLONASS, and GALILEO and regional ones such as QZSS and IRNSS) can also be used in the proposed method, but only through adjustment of the CEI receiving ends for different signal frequency and signal modulation regimes, with substantially equivalent tracking and measurement accuracy for the high-value cislunar space targets.
Furthermore, the impact of monitoring and measuring cislunar targets when there are interference signals on the GNSS Inter-Satellite Links should be noted. Previous studies have proven that the majority of the interference signals that the GNSS Inter-Satellite Link faces belong to narrow-band interference (NBI), followed by single frequency interference [
57,
58]. Currently, the technology of spread spectrum (SS) is mostly applied to cope with those interference signals, which can be categorized into four types [
59,
60]:
(i) adaptive finite-impulse response (FIR) filtering method, usually consisting of a linear predictive filter and a linear interpolation filter, whose suppression effect will substantially deteriorate on NBI signals, compared with that on single frequency interference ones.
(ii) frequency domain adaptive filtering method, which requires the fast Fourier transform (FFT) operation that greatly increases the computation complexity, and in some cases, spectral leakage may occur.
(iii) infinite impulse response (IIR) notch filtering method, which also increases the computational complexity through FFT and spectrum analysis, and its final interference suppression effect tends to be far from satisfactory as the notch filter bandwidth can hardly be precisely controlled by bandwidth parameters.
(iv) code-aided technique, which requires no prior information on interference, interference detection, and FFTs, as it calculates the antijamming weight based on the received signal and processes the signal directly in the time domain.
Based on the above analysis, the code-aided technique could be a more applicable method to deal with interference signals on the BeiDou-3 Inter-Satellite Link, and the relevant research could be a reference for future lunar missions, especially for the monitoring and measuring of high-value lunar space targets. To suppress narrowband interference (NBI) in direct sequence spread spectrum (DSSS) systems, in [
61], Wang first applied the code-aided interference suppression technique to a direct sequence (DS) UWB system, and then improved the NBI suppression ability of the original code-aided technique by introducing a certain form of spreading sequence. Furthermore, it was suggested in [
62] to use an adaptive code-aided technique based on the RLS algorithm, and an improved method was proposed to modify it for massively parallel signal processing. Meanwhile, [
57] proposes an adaptive narrow-band interference (NBI) suppression approach for the inter-satellite links (ISLs) of GNSS based on a code-aided technique, and the concept of interference influence coefficient is proposed to evaluate the influence of residual interference on the carrier-to-noise ratio (CNR) at the receiving end.
It should also be confirmed that the proposed method in this research uses high-frequency radio frequency inter-satellite links, as they are the most commonly accessible ISL sources among all of the GNSS systems. However, with the emerging advancement of laser communication technology, laser inter-satellite links have appeared in some of the latest generations of GNSS ISL systems, which are expected to be the dominant signal forms for future GNSS ISL systems and could provide enhanced navigation and timing services. In [
63], a laboratory demonstrator was developed to verify the optical inter-satellite linkages of the Kepler constellation, which links satellites in a GNNS constellation for optical range, time transfer, and data transmission. The recent initiatives to create orbits for a constellation of satellites linked by optical links were explored in [
64], including progress on an orbit determination algorithm and a linking rule to schedule communication between constellation components in support of continuous and reliable synchronization capabilities. Considering this, future research could be focused on the application of laser inter-satellite links in the proposed method and the processing of signal sources mixing laser and high-frequency radio frequency ISL signals.
9. Conclusions
Aiming at the urgent requirement for high-precision tracking and reliable cataloging of non-cooperative targets in cislunar space, in this paper, a BeiDou-3 Inter-Satellite Link and Connected Element Interferometry (CEI)-based method is proposed for effective monitoring and measurement of high-value cislunar space targets. The main work of this paper is as follows:
(i) A non-cooperative cislunar space targets measurement method based on CEI and BDS-3 inter-satellite link signals is proposed, with its general scenario and specific flow.
(ii) The mathematical models of the proposed method are put forward, which mainly includes four parts: dynamical constraint equations for non-cooperative targets in cislunar space; BDS-based interplanetary link for irradiation of non-cooperative targets; transmission loss equation of BDS-3 inter-satellite link signal in cislunar space; CEI-based precision measurements of targets in cislunar space.
(iii) Based on the previous analysis, the measurement errors of the entire process has been analyzed, followed by the error correction equations.
(iv) To give the feasibility demonstration of the proposed method, the link budget analysis and performance evaluation are presented.
(v) Simulation results demonstrate that the proposed method could have potential in achieving long-term cataloging, effective tracking, and high-precision measurement of high-value unidentified targets in cislunar space, indicating a promising potential in the increasingly critical cislunar space situational awareness missions in the future.
Further works could be focused on the application of the proposed method to actual unidentified Earth–Moon space target tracking missions.