Measurement and C / N ratio analysis method for earth-moon spacecraft based on beidou and cei

Abstract

The application provides a measurement and carrier-to-noise ratio analysis method based on Beidou and CEI, and belongs to the technical field of spacecraft signal measurement and processing; the method combines the use of short baseline interferometric measurement and the inter-satellite link signal equipped on the Beidou-3 satellite system, the inter-satellite link signal of the Beidou-3 satellite is used to irradiate the non-cooperative spacecraft in the earth-moon space, then the method of passively receiving the inter-satellite link signal reflected by the non-cooperative spacecraft in the earth-moon space by using the CEI system, a complete set of tracking and measurement process of the non-cooperative spacecraft in the earth-moon space based on CEI and the inter-satellite link of the Beidou-3 satellite is designed, and the long-term effective monitoring and observation of the high-value non-cooperative spacecraft in the earth-moon space are effectively realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of spacecraft signal measurement and processing, and particularly relates to a measurement and carrier-to-noise ratio analysis method for a geolunar spacecraft based on Beidou and CEI. BACKGROUND

[0002] Geolunar space non-cooperative spacecraft tracking measurement:

[0003] Geolunar space is a natural extension of near-earth orbit space. In a broad sense, geolunar space is a region dominated by the gravity of the Earth and the Moon, including near-earth space, lunar gravity space and geolunar transfer space. In a narrow sense, geolunar space specifically refers to geolunar transfer space and lunar gravity space outside the geosynchronous belt. As the first station for human exploration of deep space, geolunar space has strategic resources such as various materials, energy, environment and location, and is a strategic space for human survival and development in the future for a long period of time. The main applications include space confrontation, on-orbit service and maintenance, space science and application, and support for manned exploration beyond near-earth orbit. In the future for a long period of time, geolunar space will still be the main destination and outpost base for space activities, and on this basis, further exploration of deep space can be carried out. It can be predicted that China's space activities will further focus on geolunar space. High-precision navigation, positioning and timing (PNT) have important application significance in each stage of geolunar space exploration. A schematic diagram of the relevant range of geolunar space is shown in Figure 1 The diagram contains a short baseline interferometric measurement (CEI) observation array on the ground and non-cooperative spacecraft at important orbital altitudes.

[0004] Future lunar exploration activities have higher requirements for lunar probe orbit determination accuracy, real-time performance and applicable scenarios. High-precision measurement, precise orbit determination and positioning of geolunar space non-cooperative spacecraft are basic and cutting-edge research work. So far, the means for orbit determination basically still relies on ground-based measurement technology, including ground-based radio ranging and velocity measurement and interferometric measurement. High-precision orbit determination using ground-based measurement systems requires long-time continuous tracking, especially for the transfer orbit segment between the Earth and the Moon, which requires longer continuous tracking time. Moreover, the farther the probe is from the Earth, the worse the geometry of the ground-based measurement. Therefore, the orbit determination accuracy and applicable range of geolunar space non-cooperative spacecraft based on ground-based measurement technology are limited.

[0005] With the development of the lunar space exploration, the measurement and control means will be changed from the ground-based measurement technology to the space-based measurement technology, including the inter-satellite ranging technology and the space-borne GNSS leakage signal technology, which have been fully applied in the current earth satellite navigation system and will be extended to the lunar space. A series of frontier explorations have been carried out in this field at home and abroad, including the research on the constellation autonomous orbit determination based on the libration point orbit of the moon, the joint autonomous orbit determination technology of the libration point probe and the earth navigation satellite, the autonomous orbit determination of the libration point and the lunar orbit probe, the autonomous orbit determination of the probe of the lunar triangle libration point, and the autonomous navigation and timing system of the lunar probe based on the DRO-LEO formation. However, the above researches are mainly limited to the autonomous real-time navigation of the lunar space spacecraft, and there is still a lack of reliable means for the effective tracking and measurement of the lunar space non-cooperative spacecraft.

[0006] Based on the above analysis, the application will use the inter-satellite link signal of the new generation of Beidou-3 satellite in China, combined with the ground short baseline interferometry (CEI) equipment, to realize the effective and reliable tracking and measurement of the lunar space non-cooperative spacecraft, and to provide strong support for the increasingly severe lunar space situation awareness and other major tasks in the future.

[0007] The ground short baseline interferometry CEI:

[0008] The phase interferometry technology is a passive angle tracking method based on the downlink signal of the spacecraft, and currently there are two kinds of technologies, namely, the very long baseline interferometry (VLBI) and the connected element interferometry (CEI). Compared with the VLBI, the main advantages of the CEI are that the phase delay measurement is relatively simple, the rapid orbit determination of the phase difference can be realized, the real-time angle measurement can be almost achieved, the equipment is simple, the cost is low, and the maintenance and management are convenient.

[0009] Fig. 2(a) shows the basic principle of CEI. The signal of the lunar space spacecraft measured by the CEI correlator is from two geometrically separated ground stations. Therefore, in order to obtain high-precision angle measurement, the measurement precision of the time delay in the interferometry can be improved, which is the basic principle of the high-precision measurement technology of CEI.

[0010] As shown in Fig. 2(b), since the orbital error of the lunar space spacecraft is mostly reflected in its projection in the effective baseline direction, the two CEI orthogonal baselines can determine the two-dimensional angle coordinates of the lunar space spacecraft and the change information thereof.

[0011] Beidou inter-satellite link:

[0012] With the wide application of GNSS, users have higher demands for system accuracy, integrity, reliability and other performance indicators. Inter-satellite link technology is considered as one of the important ways to improve the performance of navigation system. Using inter-satellite link for satellite measurement and communication can shorten the update cycle of navigation message, improve the broadcast ephemeris accuracy; it can provide an independent means to check satellite ephemeris and clock difference parameters, and improve the integrity of the system; it can make up for the defects of regional layout of monitoring stations and improve the navigation satellite orbit determination accuracy; it can reduce the number of ground monitoring stations and injection stations, and reduce the operation and maintenance cost of the system; it can realize the autonomous operation of navigation constellation for a period of time, and enhance the anti-interference and anti-destruction ability of the system.

[0013] China's Beidou navigation satellite system has successfully implemented inter-satellite link (ISL) mutual pseudorange measurement on the new generation of Beidou-3 satellite navigation system. Beidou-3 satellites are equipped with Ka-band inter-satellite two-way ranging technology, which uses Ka phased array antenna. By controlling the phase relationship of each antenna element, it can realize beam scanning in a large space range, quickly switch the antenna beam pointing direction in a short time, and complete the observation task of a single satellite to multiple links, thus forming a dynamic inter-satellite link network with strong agility pointing capability and high precision ranging performance. BDS-3 inter-satellite ranging adopts time division multiple access system. According to the predetermined routing plan, each satellite loops with other visible satellites or ground anchor stations to build links. Each time a link is built, each pair of satellites completes two-way ranging in a short time (3s). Using the epoch-reduced two-way observation values, clock bias-free and geometry-free observations can be decoupled to determine satellite orbit and clock bias.

[0014] The space-time division access system of Beidou inter-satellite link system and the agile capability of Ka phased array beam have strong expansion application capability. Taking full advantage of the unique characteristics of satellite navigation system as time and space reference and the global coverage advantage, under the condition of fully configurable and fast configurable Beidou inter-satellite link system planning, user spacecraft can be connected to Beidou inter-satellite link system as an extension node of Beidou inter-satellite link system, and the onboard processor can process inter-satellite measurement data to obtain its own orbit. In theory, it can meet the real-time orbit determination requirements of spacecraft.

[0015] The inter-satellite link technology system of Beidou-3 networking satellites has the following characteristics:

[0016] 1) Ka-band inter-satellite link ranging has high accuracy, strong anti-interference ability and good security;

[0017] 2) Time-space division multiple access, double one-way ranging;

[0018] The Beidou No. 3 adopts a space-time division multiple access system, and realizes point-to-point link establishment between satellites. Each time slot of the inter-satellite link establishment is 3 seconds, and the first 1.5 seconds are forward measurement and communication of satellite A sending and satellite B receiving, and the last 1.5 seconds are reverse measurement and communication of satellite B sending and satellite A receiving.

[0019] 3) high-middle link, middle-middle link and star-ground link mixed link establishment;

[0020] The Beidou No. 3 constellation is composed of 3 GEO satellites, 3 IGSO satellites and 24 MEO satellites, and each satellite is equipped with an inter-satellite link load, realizing link establishment between high-middle orbit satellites and middle-middle orbit satellites, and at the same time, an anchor station device is provided on the ground to realize star-ground link establishment with the space constellation.

[0021] For the outstanding problems in future space applications, such as lunar space situation awareness, health monitoring of important lunar space assets, and cataloging and monitoring of important non-cooperative targets in lunar space, the traditional monitoring and observation are mainly aimed at cooperative targets in lunar space, and the research on measurement means and observation methods for non-cooperative targets in lunar space is still relatively lacking. SUMMARY

[0022] Therefore, the purpose of the present application is to provide a lunar spacecraft measurement and carrier-to-noise ratio analysis method based on Beidou and CEI, which effectively realizes long-term effective monitoring and observation of high-value non-cooperative spacecraft in lunar space.

[0023] A lunar spacecraft measurement method based on Beidou and CEI, comprising:

[0024] Step 1, establishing a dynamic constraint equation of the non-cooperative spacecraft in lunar space;

[0025] Step 2, irradiating the non-cooperative spacecraft in lunar space based on the inter-satellite link of Beidou;

[0026] (1) Establish the transmission equation of the inter-satellite link signal of Beidou No. 3 satellites located in different orbits in lunar space:

[0027] Based on the inter-satellite link signal of Beidou No. 3 satellites, the pseudo-code ranging equation between Beidou No. 3 satellites located in different orbits and non-cooperative spacecraft in lunar space is as follows:

[0028]

[0029] Wherein, i=1 represents MEO orbit, i=2 represents GEO orbit, and i=3 represents IGSO orbit; t i1 is the time of inter-satellite link transmission of Beidou No. 3 satellites in different orbits, t i2 is the time of arrival of inter-satellite link of different orbits to non-cooperative spacecraft in lunar space; riBD (t i1 ) is the time t i1 Position vector of BeiDou-3 satellite in different orbits in the Earth-Centered Inertial coordinate system, r space (t i2 ) represents the time t i2 Position vector of non-cooperative spacecraft in different orbits in the Earth-Centered Inertial coordinate system; δt space (t i2 ) represents the time t i2 Clock error of non-cooperative spacecraft in different orbits relative to BeiDou system time; δt iBD (t i1 ) represents the time t i1 Clock error of BeiDou-3 satellite in different orbits relative to BeiDou system time; τ iBD Hardware delay of BeiDou-3 satellite in different orbits for inter-satellite link; e i(BD→space) and n i(BD→space) are the error and observation noise of inter-satellite link signal of BeiDou-3 satellite in the Earth-Moon space, which need to be corrected;

[0030] (2) Establish the transmission equation of inter-satellite link signal reflected by non-cooperative spacecraft in the Earth-Moon space and finally received by CEI observation array:

[0031] The inter-satellite link signal of BeiDou-3 satellite irradiated to non-cooperative spacecraft in the Earth-Moon space, after being reflected by non-cooperative spacecraft, the pseudo-code ranging equation between the ground CEI observation array is as follows:

[0032]

[0033] Where, t i3 is the time when the inter-satellite link reflected by non-cooperative spacecraft arrives the ground CEI observation array; r CEI (t i3 ) represents the time t i3 Position vector of CEI observation array on the ground in different orbits in the Earth-Centered Inertial coordinate system; r space (t i2 ) represents the time t i2 Position vector of non-cooperative spacecraft in the Earth-Moon space in different orbits in the Earth-Centered Inertial coordinate system; δt CEI (t i3 ) is the time t i3 Clock error of CEI observation array on the ground in different orbits relative to BeiDou system time; τ iCEI represents the hardware delay of CEI observation array; e i(space→CEI) and n i(space→CEI)The errors and observation noises that need to be corrected during the transmission of the inter-satellite link signals reflected by the non-cooperative spacecraft in the Earth-Moon space and the final reception by the CEI observation array, respectively;

[0034] Step 3, precise measurement of the non-cooperative spacecraft in the Earth-Moon space based on the CEI observation array:

[0035] Based on the inter-satellite link signals of the Beidou-3 satellites, the pseudo-code ranging equations between the Beidou-3 satellites in different orbits and the non-cooperative spacecraft in the Earth-Moon space, and the pseudo-code ranging equations between the inter-satellite link signals of the Beidou-3 satellites irradiated to the non-cooperative spacecraft in the Earth-Moon space and the CEI observation array after being reflected by the non-cooperative spacecraft, the orbit determination equation of the non-cooperative spacecraft in the Earth-Moon space based on the CEI observation array is obtained:

[0036]

[0037]

[0038] Step 4, observation error correction of the whole tracking and measurement process of the non-cooperative spacecraft in the Earth-Moon space based on the CEI observation array and the Beidou inter-satellite link:

[0039] (1) Establish the observation error correction equation of the inter-satellite link signals of the Beidou-3 satellites in different orbits during the transmission in the Earth-Moon space:

[0040] a) The antenna phase center offset of the Beidou-3 satellite transmitting the inter-satellite link is expressed in the Earth-Centered Inertial coordinate system as follows:

[0041]

[0042] wherein, is the antenna phase center offset of the Beidou-3 satellite in different orbits in the satellite-fixed coordinate system, (p x ,p y ,p z ) is the projection of the three coordinate axes in the satellite-fixed coordinate system in the Earth-Centered Inertial coordinate system.

[0043] The antenna phase center offset correction equation of the Beidou-3 satellite is expressed as follows:

[0044]

[0045] wherein, r iBD and r space are the position vectors of the Beidou-3 satellite in different orbits and the non-cooperative spacecraft in the Earth-Moon space in the Earth-Centered Inertial coordinate system, respectively.

[0046] The antenna phase center offset correction equation of the Beidou-3 satellite is obtained by combining equations (17) and (18):

[0047]

[0048] The influence of the clock time bias of the Beidou-3 satellite caused by the relativistic effect on the pseudo-code range value is represented as:

[0049]

[0050] wherein, and are the velocities of the Beidou-3 satellite and the non-cooperative spacecraft in the Earth-centered inertial coordinate system.

[0051] The influence of the gravitational field caused by the general relativistic effect on the pseudo-code range value is represented as:

[0052]

[0053] wherein, γ is the post-Newtonian effect parameter, GM is the Earth's gravitational constant, and r iBD and r space are the distances from the Beidou-3 satellite and the non-cooperative spacecraft in space to the Earth's center; and ρ i(BD→space) is the distance between the Beidou-3 satellite and the non-cooperative spacecraft in space.

[0054] The total error correction equation of the relativistic effect is as follows:

[0055]

[0056] The total observation error correction equation of the inter-satellite link signal in the transmission process of the Beidou-3 satellite in space is obtained as follows:

[0057]

[0058] (2) The observation error correction equation of the CEI observation process of the inter-satellite link signal reflected by the non-cooperative spacecraft is established as follows:

[0059] a) Atmospheric delay error:

[0060] The tropospheric delay correction equation is as follows:

[0061]

[0062] wherein, c dry and c wet are zenith delay correction models of dry delay components and wet delay components, and mapping functions of dry and wet delay components, respectively, the observation elevation angle of the CEI observation array to the non-cooperative spacecraft;

[0063] The ionospheric delay correction equation is as follows:

[0064]

[0065] where f iBD is the carrier frequency of the inter-satellite link of Beidou-3 satellite, N total is the total electron content in zenith direction, R e is the earth radius, and H is the ionospheric layer height;

[0066] b) Error correction of station antenna phase center offset:

[0067] The error correction equation of station antenna phase center offset is as follows:

[0068]

[0069] where, is the station antenna phase center offset in the satellite-fixed coordinate system, (p x , p y , and p z ) are the projections of the three coordinate axes in the satellite-fixed coordinate system in the earth-centered inertial coordinate system, r CEI and r space are the position vectors of the CEI observation array and the non-cooperative spacecraft in the earth-centered inertial coordinate system, respectively;

[0070] c) Relativistic effect

[0071] The error correction equation of the relativistic effect between the non-cooperative spacecraft in the earth-moon space and the CEI observation array is as follows:

[0072]

[0073] where, and are the velocities of the CEI observation array and the non-cooperative spacecraft in the earth-centered inertial coordinate system, respectively, γ is the post-Newtonian effect parameter, GM is the earth gravitational constant, |r CEI | and |r space | are the distances from the CEI observation array and the non-cooperative spacecraft to the earth center, respectively, and ρ i(space→CEI) is the distance between the CEI observation array and the non-cooperative spacecraft in the earth-moon space;

[0074] d) Tidal effect:

[0075] The error correction equation of the tidal effect is as follows:

[0076]

[0077] where GM j is the gravitational constant of the tide-raising body, R and R j are the geocentric positions of the CEI observation array and the tide-raising body, respectively, and the tide-raising body is the moon when j = 1 and the sun when j = 2; and are the unit vectors corresponding to R and R i , respectively, h2 is the Love number, and l2 is the Shida number;

[0078] The total equation for the observation error correction in the CEI observation process of the inter-satellite link signal reflected by the non-cooperative spacecraft is obtained as follows:

[0079]

[0080] Preferably, the specific method of step 1 comprises:

[0081] The earth, the moon, and the non-cooperative spacecraft in the earth-moon space are all regarded as mass points, wherein the line connecting the earth and the moon is taken as the x-axis, and the coordinate origin is the barycenter of the two.

[0082] The distances of the earth and the moon from the barycenter of the two are λ and 1-λ, respectively, and satisfy:

[0083]

[0084]

[0085] where m earth and m moon are the masses of the earth and the moon, respectively; and the distances between the earth and the moon and the lth non-cooperative spacecraft in the earth-moon space satisfy:

[0086]

[0087]

[0088] where x l , y l , and z l are the x, y, and z-axis position coordinates of the lth non-cooperative spacecraft in the earth-moon space, respectively.

[0089] For k non-cooperative spacecraft in the earth-moon space, the state vector containing the velocity and position information is expressed as follows:

[0090]

[0091] where x l , yl l are the x, y, z axis position coordinates of the lth non-cooperative spacecraft in the cis-lunar space, respectively, are the x, y, z axis velocity components of the lth non-cooperative spacecraft in the cis-lunar space, respectively, are the x, y, z axis acceleration components of the lth non-cooperative spacecraft in the cis-lunar space, respectively; satisfy the following relationships:

[0092]

[0093] wherein p l is a potential function, satisfying the following relationship:

[0094]

[0095] According to the formula (1) to formula (7), the dynamic constraint equation of the non-cooperative spacecraft in the cis-lunar space is finally expressed as:

[0096]

[0097] A carrier-to-noise ratio analysis method based on the above-mentioned cis-lunar spacecraft measurement method, comprising:

[0098] The carrier-to-noise ratio of the tracking and measurement link of the non-cooperative spacecraft in the cis-lunar space based on the CEI observation array and the Beidou inter-satellite link is expressed as follows:

[0099] C / N0=C-N0 (30)

[0100] Wherein C is the received signal power of the CEI observation array; N0 is the thermal noise power; the received signal power C and the thermal noise power N0 satisfy the following relationships respectively:

[0101] C=T transmit +G transmit(BD→space) +G receive(space→CEI) -L reflect -L BD→CEI -L receive (31)

[0102] Wherein T transmit is the Beidou inter-satellite link signal transmission power; G transmit(BD→space) is the Beidou No. 3 inter-satellite link transmission antenna gain towards the non-cooperative spacecraft in the cis-lunar space; G receive(space→CEI) is the CEI observation array receiving antenna gain towards the non-cooperative spacecraft in the cis-lunar space; L reflect is the reflection loss of the Beidou inter-satellite link signal through the non-cooperative spacecraft; L BD→CEI is the Beidou inter-satellite link signal transmission loss based on the CEI observation array and the Beidou inter-satellite link in the whole process of tracking and measurement of the non-cooperative spacecraft in the cis-lunar space; L​receive To observe the receiving loss of the CEI array;

[0103] N0 = 10log 10 [k B (T antenna + T amplifier )] (32)

[0104] wherein, k B is the Boltzmann constant, k B = 1.3806452 x 10 -23 J / K; T antenna is the antenna noise temperature; T amplifier is the amplifier noise temperature;

[0105] The total loss L of the Beidou inter-satellite link signal transmission in the whole process of the non-cooperative spacecraft tracking measurement in the earth-moon space in (31) BD→CEI satisfies:

[0106]

[0107] wherein, f iBD is the power of the Beidou inter-satellite link signal, d i(BD→space) is the distance between the Beidou No. 3 satellite transmitting the Beidou inter-satellite link signal and the non-cooperative spacecraft, and d i(space→CEI) is the distance between the non-cooperative spacecraft and the ground CEI observation array;

[0108] The antenna noise temperature T antenna and the amplifier noise temperature T amplifier in (32) respectively satisfy the following relationships:

[0109]

[0110] wherein, the first part T antenna_1 is the ohmic loss caused by the antenna itself defects, and the second part T antenna_2 is the thermal noise captured by the antenna from the surrounding environment; T physical_antenna is the physical temperature of the antenna, e antenna is the antenna efficiency; Ω earth and Ω moon are respectively the fixed angles subtracted by the earth and the moon when viewed from the CEI observation array; T brightness_earth , T brightness_moon and T brightness_cosmic are respectively the brightness temperatures of the earth, the moon and the cosmic background;

[0111]

[0112] wherein, T physical_amplifier is the physical temperature of the amplifier, Nfigure for an amplifier noise figure;

[0113] Based on the CEI observation array and the inter-satellite link of the Beidou satellite, the carrier-to-noise ratio equation of the tracking and measurement link of the lunar-space non-cooperative spacecraft is finally represented as follows:

[0114]

[0115] The present application has the following beneficial effects:

[0116] 1. The present application provides a lunar-space non-cooperative spacecraft tracking and measurement method, which jointly uses the medium-short baseline interferometric measurement (CEI) and the inter-satellite link signal equipped on the Beidou No. 3 satellite system. The inter-satellite link signal of the Beidou No. 3 satellite is used to irradiate the lunar-space non-cooperative spacecraft, and then the CEI system is used to passively receive the inter-satellite link signal reflected by the lunar-space non-cooperative spacecraft. A complete set of tracking and measurement process of the lunar-space non-cooperative spacecraft based on the CEI and the inter-satellite link of the Beidou No. 3 satellite is designed, which effectively realizes the long-term effective monitoring and observation of the high-value lunar-space non-cooperative spacecraft.

[0117] 2. A tracking and measurement model of the lunar-space non-cooperative spacecraft based on the CEI and the inter-satellite link of the Beidou satellite is constructed, and the whole process and key nodes of the present application are analyzed, mainly including the irradiation of the lunar-space non-cooperative spacecraft by the Beidou No. 3 satellite based on the inter-satellite link, the transmission of the signal reflected by the non-cooperative spacecraft in the lunar-space, and the reception of the signal by the ground CEI array.

[0118] 3. A dynamic constraint equation of the tracking and measurement of the lunar-space non-cooperative spacecraft based on the CEI and the inter-satellite link of the Beidou satellite is constructed, and the state vector equation of the lunar-space non-cooperative spacecraft containing position, velocity and acceleration information is established based on the "three-body" problem scenario, i.e. the earth, the moon and the lunar-space non-cooperative spacecraft.

[0119] 4. Based on the irradiation of the lunar-space non-cooperative spacecraft by the inter-satellite link of the Beidou satellite, the transmission equation of the inter-satellite link signal of the Beidou No. 3 satellite in the lunar-space, the transmission equation of the inter-satellite link signal reflected by the non-cooperative spacecraft in the lunar-space, and the reception equation of the inter-satellite link signal reflected by the non-cooperative spacecraft at the receiving end of the CEI array are established.

[0120] 5. Based on the precise measurement of the lunar-space non-cooperative spacecraft by the CEI, the orbit determination equation of the lunar-space non-cooperative spacecraft based on the CEI observation is established based on the pseudo-code ranging equation of the inter-satellite link signal of the Beidou No. 3 satellite established in the third step.

[0121] 6、On this basis, the measurement error of the inter-satellite link signal of the Beidou No.3 satellite located in different orbits in the transmission process in the earth-moon space and the inter-satellite link signal reflected by the non-cooperative spacecraft in the CEI observation process is analyzed, an error correction equation is introduced, and the CEI observation equation of the non-cooperative spacecraft in the earth-moon space is further corrected.

[0122] 7、The link budget of the whole process of tracking and measuring the non-cooperative spacecraft in the earth-moon space based on CEI and Beidou inter-satellite link is analyzed, the inter-satellite link transmission power of the Beidou No.3 satellite located in HEO, GEO and IGSO orbits, the transmission power of the signal reflected by the non-cooperative spacecraft in the earth-moon space and the signal power finally received by the ground CEI array are analyzed, and the carrier-to-noise ratio analysis equation of the tracking and measuring link of the non-cooperative spacecraft in the earth-moon space based on CEI and Beidou inter-satellite link is established.

[0123] 8、On the basis of the above steps, the performance evaluation of the tracking and measuring of the non-cooperative spacecraft in the earth-moon space based on CEI and Beidou inter-satellite link is carried out, mainly including the reception performance evaluation of the CEI receiving array, the geometric accuracy evaluation of the orbit determination of the non-cooperative spacecraft in the earth-moon space based on CEI and Beidou inter-satellite link and the ranging accuracy evaluation of the non-cooperative spacecraft in the earth-moon space based on CEI and Beidou inter-satellite link, so as to realize the cataloging, long-term effective tracking, high-reliable in-orbit monitoring and high-precision observation of abnormal behaviors (such as orbit change, disintegration, etc.) of the high-value non-cooperative spacecraft in the earth-moon space. BRIEF DESCRIPTION OF DRAWINGS

[0124] Figure 1 It is a schematic diagram of the related range of the earth-moon space;

[0125] Fig. 2(a) is a basic principle diagram of CEI measurement;

[0126] Fig. 2(b) is a schematic diagram of precise CEI measurement based on orthogonal baseline;

[0127] Figure 3 It is a total flow chart of the tracking and measuring method of the spacecraft in the earth-moon space based on CEI and Beidou of the present application;

[0128] Figure 4 It is a scene overview diagram of the tracking and measuring of the non-cooperative spacecraft in the earth-moon space based on CEI and Beidou inter-satellite link of the present application;

[0129] Figure 5 It is a schematic diagram of the dynamic constraint of the non-cooperative spacecraft in the earth-moon space of the present application. DETAILED DESCRIPTION

[0130] The present application will be described in detail below with reference to the drawings and examples.

[0131] 1. The method for measuring the earth-moon spacecraft based on Beidou and CEI, mainly comprises the following key steps:

[0132] (1) First, a tracking and measurement model for the earth-moon space non-cooperative spacecraft based on CEI and Beidou inter-satellite link needs to be constructed, and the whole process and key nodes of the signals reflected by the non-cooperative spacecraft and transmitted in the earth-moon space and finally received by the ground CEI array based on the inter-satellite link of the Beidou No. 3 satellite located in the HEO, GEO and IGSO orbits are constructed.

[0133] (2) On the basis of the above step, a dynamic constraint equation for tracking and measuring the earth-moon space non-cooperative spacecraft based on CEI and Beidou inter-satellite link needs to be constructed, and the state vector equation of the earth-moon space non-cooperative spacecraft containing position, velocity and acceleration information is established based on the "three-body" problem scenario, i.e. the earth, the moon and the earth-moon space non-cooperative spacecraft.

[0134] (3) Based on the earth-moon space non-cooperative spacecraft irradiation of the Beidou inter-satellite link, the transmission equation of the inter-satellite link signals of the Beidou No. 3 satellite located in different orbits in the earth-moon space, the transmission equation of the inter-satellite link signals reflected by the non-cooperative spacecraft in the earth-moon space, and the reception equation of the inter-satellite link signals reflected by the non-cooperative spacecraft at the receiving end of the CEI array are established.

[0135] (4) Based on the CEI, the precise measurement of the earth-moon space non-cooperative spacecraft is established based on the pseudo-code ranging equation of the inter-satellite link signals of the Beidou No. 3 satellite in the third step, and the orbit determination equation of the earth-moon space non-cooperative spacecraft based on the CEI observation is established.

[0136] (5) On this basis, the measurement errors in the transmission process of the inter-satellite link signals of the Beidou No. 3 satellite located in different orbits in the earth-moon space and the CEI observation process of the inter-satellite link signals reflected by the non-cooperative spacecraft are analyzed, the error correction equation is introduced, and the CEI observation equation of the earth-moon space non-cooperative spacecraft is further corrected.

[0137] (6) The link budget of the whole process of tracking and measuring the earth-moon space non-cooperative spacecraft based on CEI and Beidou inter-satellite link is analyzed, the transmission power of the inter-satellite link signals of the Beidou No. 3 satellite located in the HEO, GEO and IGSO orbits, the transmission power of the signals reflected by the non-cooperative spacecraft in the earth-moon space and the power of the signals finally received by the ground CEI array are analyzed, and the carrier-to-noise ratio analysis equation of the tracking and measurement link of the earth-moon space non-cooperative spacecraft based on CEI and Beidou inter-satellite link is established.

[0138] (7) On the basis of the above steps, the performance evaluation of the lunar space non-cooperative spacecraft tracking measurement based on CEI and inter-satellite links of Beidou is carried out, mainly including: the receiving performance evaluation of the CEI receiving array, the geometric accuracy evaluation of the lunar space non-cooperative spacecraft orbit determination based on CEI and inter-satellite links of Beidou, and the ranging accuracy evaluation of the lunar space non-cooperative spacecraft based on CEI and inter-satellite links of Beidou.

[0139] As shown in Figure 3 The total flow chart of the lunar space spacecraft tracking measurement method based on Beidou and CEI is shown.

[0140] 2. Construction of the lunar space non-cooperative spacecraft tracking measurement model based on CEI and inter-satellite links of Beidou

[0141] In this model, the focus is on the construction of the whole process and key nodes of the signal reflected by the non-cooperative spacecraft and transmitted in the lunar space and finally received by the ground CEI array based on the inter-satellite links of the Beidou No. 3 satellites located in the HEO, GEO and IGSO orbits. Figure 4 The scene overview of the lunar space non-cooperative spacecraft tracking measurement based on CEI and inter-satellite links of Beidou is shown.

[0142] In this model, first, the Beidou No. 3 satellites located in the HEO, GEO and IGSO orbits will use the inter-satellite link signals to irradiate the lunar space non-cooperative spacecraft in the task gap of the normal inter-satellite link communication of the satellites, based on the previous observation and monitoring data, according to the operation law of the non-cooperative spacecraft. On this basis, the Beidou No. 3 inter-satellite link signals reflected by the non-cooperative spacecraft will be transmitted in the lunar space until reaching the ground. Then, based on the CEI receiving array on the ground, the Beidou No. 3 inter-satellite link signals reflected by the non-cooperative spacecraft will be received, and on the basis of the signal observation error correction, accurate non-cooperative spacecraft tracking measurement information will be obtained.

[0143] At the same time, due to the existence of the troposphere and ionosphere, there is a certain degree of error in the CEI observation signal in this method. Research shows that this error may have a certain impact on the accurate observation model of the lunar space non-cooperative spacecraft based on CEI, which will be corrected in the following accurate measurement of the lunar space non-cooperative spacecraft based on CEI.

[0144] 3. Construction of the dynamic constraint equation of the lunar space non-cooperative spacecraft

[0145] In the research scenario of the application, it is mainly a "four-body" problem, i.e. the Earth, the Moon, the Beidou-3 satellite and the non-cooperative spacecraft in the Earth-Moon space. Compared with the Earth and the Moon, the Beidou-3 satellite is too small in weight, and its gravity on the non-cooperative spacecraft in the Earth-Moon space can be ignored. Therefore, for the convenience of research, the problem can be simplified as a "three-body" problem, i.e. the Earth, the Moon and the non-cooperative spacecraft in the Earth-Moon space, and all of them are regarded as points. The corresponding dynamic constraint diagram of the non-cooperative spacecraft in the Earth-Moon space is shown in Figure 5 . Wherein, the line connecting the Earth and the Moon is taken as the x axis, and the coordinate origin is the barycenter of the two.

[0146] It can be known from Figure 5 that the distances λ and 1-λ of the Earth and the Moon from the barycenter of the two satisfy:

[0147]

[0148]

[0149] Wherein, m earth and m moon are the masses of the Earth and the Moon respectively; the distances between the Earth and the Moon and the lth non-cooperative spacecraft in the Earth-Moon space satisfy:

[0150]

[0151]

[0152] Wherein, x l , y l , z l are the x, y, z axis position coordinates of the lth non-cooperative spacecraft in the Earth-Moon space respectively;

[0153] For the k non-cooperative spacecrafts in the Earth-Moon space, the state vector containing the velocity and position information is expressed as follows:

[0154]

[0155] Wherein, x l , y l , z l are the x, y, z axis position coordinates of the lth non-cooperative spacecraft in the Earth-Moon space respectively, are the x, y, z axis velocity components of the lth non-cooperative spacecraft in the Earth-Moon space respectively, are the x, y, z axis acceleration components of the lth non-cooperative spacecraft in the Earth-Moon space respectively; satisfy the following relationships:

[0156]

[0157] where p l is the potential function, satisfying the following relation:

[0158]

[0159] According to the formula (1) to formula (7), the dynamic constraint equation of the non-cooperative spacecraft in the earth-moon space is finally expressed as:

[0160]

[0161] 4. Illumination of the non-cooperative spacecraft in the earth-moon space based on the inter-satellite link of Beidou: In this step, the transmission equation of the inter-satellite link signal of the Beidou No.3 satellite located in different orbits in the earth-moon space, the transmission and final reception equation of the inter-satellite link signal reflected by the non-cooperative spacecraft in the earth-moon space at the receiving end of the CEI array, and the transmission loss equation of the inter-satellite link will be established, which will be introduced as follows.

[0162] (1) Transmission equation of the inter-satellite link signal of the Beidou No.3 satellite located in different orbits in the earth-moon space:

[0163] Based on the inter-satellite link signal of the Beidou No.3 satellite, the pseudo-code ranging equation between the Beidou No.3 satellite located in different orbits and the non-cooperative spacecraft in the earth-moon space is as follows:

[0164]

[0165] Where i=1 represents the MEO orbit, i=2 represents the GEO orbit, and i=3 represents the IGSO orbit; t i1 is the time when the Beidou No.3 satellite located in different orbital heights transmits the inter-satellite link, t i2 is the time when the inter-satellite link reaches the non-cooperative spacecraft in the earth-moon space; r iBD (t i1 ) is the position vector of the Beidou No.3 satellite located in different orbital heights in the earth-centered inertial coordinate system at time t i1 ; r space (t i2 ) represents the position vector of the non-cooperative spacecraft in the earth-moon space in the earth-centered inertial coordinate system at time t i2 ; δt space (t i2 ) represents the clock error of the non-cooperative spacecraft in the earth-moon space relative to the Beidou system time (BDT) at time t i2 ; δt iBD (t i1 ) represents the clock error of the Beidou No.3 satellite located in different orbital heights relative to the Beidou system time (BDT) at time t i1 ; τ iBDThe hardware delay of the Beidou-3 satellite for the inter-satellite link of different orbital altitudes; e i(BD→space) Other errors that need to be corrected in this process for different orbital altitudes, including antenna phase center offset, relativistic effect, etc., will be given in the specific equation below;n i(BD→space) The observation noise for different orbital altitudes in this process.

[0166] (2) Transmission of the inter-satellite link signal reflected by the non-cooperative spacecraft in the earth-moon space and the reception equation at the receiving end of the CEI array:

[0167] The pseudo-code ranging equation between the inter-satellite link signal of the Beidou-3 satellite irradiated onto the non-cooperative spacecraft in the earth-moon space and the ground CEI receiving array after being reflected by the non-cooperative spacecraft is as follows:

[0168]

[0169] Where, t i3 is the time when the inter-satellite link reflected by the non-cooperative spacecraft reaches the CEI array on the ground; r CEI (t i3 ) represents the position vector of the CEI observation array on the ground at different orbital altitudes in the earth-centered inertial coordinate system at time t i3 r space (t i2 ) represents the position vector of the non-cooperative spacecraft in the earth-moon space at different orbital altitudes in the earth-centered inertial coordinate system at time t i2 δt CEI (t i3 ) is the clock error of the CEI observation array on the ground at different orbital altitudes relative to the Beidou system time (BDT) at time t i3 τ iCEI represents the hardware delay of the CEI observation array; e i(space→CEI) Other errors that need to be corrected in this process for different orbital altitudes, including atmospheric delay error (mainly ionospheric and tropospheric delay error), relativistic effect, station antenna phase center offset, tidal effect, etc., will be given in the specific equation below;n i(space→CEI) The observation noise for different orbital altitudes in this process.

[0170] 5. Precise measurement of the non-cooperative spacecraft in the earth-moon space based on CEI

[0171] In this step, the orbit determination equation of the non-cooperative spacecraft in the earth-moon space based on CEI observation will be established.

[0172] Based on the inter-satellite link signal established in step three, the pseudo-code ranging equation between BeiDou-3 satellites in different orbits and non-cooperative spacecraft in the Earth-Moon space, and the pseudo-code ranging equation between the inter-satellite link signal of the BeiDou-3 satellite illuminating the non-cooperative spacecraft and the ground CEI receiving array after reflection by the non-cooperative spacecraft, the orbit determination equation of the non-cooperative spacecraft in the Earth-Moon space based on CEI observations can be obtained as follows:

[0173]

[0174]

[0175] 6. Observation error correction for the entire process of tracking and measuring non-cooperative spacecraft in Earth-Moon space based on CEI and BeiDou inter-satellite links:

[0176] Based on the above steps, we will focus on analyzing the transmission process of inter-satellite link signals of BeiDou-3 satellites in different orbits in the Earth-Moon space and the measurement errors in the CEI observation process of inter-satellite link signals reflected by non-cooperative spacecraft. We will introduce error correction equations to further revise the CEI observation equations of non-cooperative spacecraft in the Earth-Moon space.

[0177] (1) Observation error correction equations for the transmission of inter-satellite link signals of BeiDou-3 satellites in different orbits in the Earth-Moon space.

[0178] As described in step three, there is an error e in the pseudo-code ranging equation (i.e., formula (1)) between BeiDou-3 satellites in different orbits and non-cooperative spacecraft in the Earth-Moon space that needs to be corrected. i(BD→space) These errors mainly include antenna phase center offset and relativistic effects. This step will focus on analyzing and correcting these errors, with the specific equations shown below.

[0179] a) Error correction for antenna phase center offset of BeiDou-3 satellites that launch inter-satellite links

[0180] The antenna phase center offset of a BeiDou-3 satellite that transmits inter-satellite links can be expressed in a geocentric inertial coordinate system as:

[0181]

[0182] in, The antenna phase center offset of BeiDou-3 satellites at different orbital altitudes in the star-fixed coordinate system, (p x ,p y ,p z ) represents the projection of the three coordinate axes in the star-fixed coordinate system onto the geocentric inertial coordinate system.

[0183] The correction equation for the antenna phase center offset of the BeiDou-3 satellite can be expressed as follows:

[0184]

[0185] where r iBD and r space are the position vectors of the BeiDou-3 satellite and the lunar spacecraft in the geocentric inertial coordinate system, respectively.

[0186] The antenna phase center offset correction equation of the BeiDou-3 satellite can be finally expressed as:

[0187]

[0188] b) Error correction of the relativistic effect

[0189] The influence of the clock time bias of the BeiDou-3 satellite caused by the relativistic effect on the pseudo-range value can be expressed as:

[0190]

[0191] where v and v are the velocities of the BeiDou-3 satellite and the lunar spacecraft in the geocentric inertial coordinate system, respectively.

[0192] The influence of the gravitational field caused by the general relativistic effect on the pseudo-range value can be expressed as:

[0193]

[0194] where γ is the post-Newtonian effect parameter, GM is the Earth's gravitational constant, r iBD and r space are the distances from the BeiDou-3 satellite and the lunar spacecraft to the Earth's center, respectively; and ρ i(BD→space) is the distance between the BeiDou-3 satellite and the lunar spacecraft.

[0195] The total error correction equation of the relativistic effect is as follows:

[0196]

[0197] The total observation error correction equation of the inter-satellite link signal of the BeiDou-3 satellite in the transmission process in the lunar space is obtained as follows:

[0198]

[0199] (2) The observation error correction equation of the CEI observation process of the inter-satellite link signal reflected by the non-cooperative spacecraft is established as follows:

[0200] a) Atmospheric delay error:

[0201] The tropospheric delay correction equation is as follows:

[0202]

[0203] where c dry and c wet are zenith delay correction models of dry delay components and wet delay components respectively, and are mapping functions of dry delay components and wet delay components respectively, is the observation elevation angle of the CEI observation array to the non-cooperative spacecraft;

[0204] The ionospheric delay correction equation is as follows:

[0205]

[0206] where f iBD is the carrier frequency of the inter-satellite link of Beidou-3 satellite, N total is the total electron content in the zenith direction, R e is the radius of the earth, and H is the ionospheric layer height;

[0207] b) Error correction of station antenna phase center offset:

[0208] The error correction equation of the station antenna phase center offset is as follows:

[0209]

[0210] where is the station antenna phase center offset in the star-fixed coordinate system, (p x , p y , p z ) are projections of three coordinate axes in the star-fixed coordinate system in the Earth-centered inertial coordinate system, r CEI and r space are position vectors of the CEI observation array and the non-cooperative spacecraft in the Earth-centered inertial coordinate system respectively;

[0211] c) Relativistic effect

[0212] The error correction equation of the relativistic effect between the non-cooperative spacecraft in the Earth-Moon space and the CEI observation array is as follows:

[0213]

[0214] where and are the velocities of the CEI observation array and the non-cooperative spacecraft in the geocentric inertial coordinate system, respectively, γ is the post-Newtonian effect parameter, GM is the Earth's gravitational constant, r CEI and r space are the distances from the CEI observation array and the non-cooperative spacecraft in the geocentric inertial coordinate system to the Earth's center, respectively; p i(space→CEI) is the distance between the CEI observation array and the non-cooperative spacecraft;

[0215] d) tidal effect

[0216] The tidal effect mainly causes displacement of the CEI observation array, thereby affecting the pseudo-range measurement between the non-cooperative spacecraft and the ground CEI receiving array. The error correction equation of the tidal effect is as follows:

[0217]

[0218] where GM i is the gravitational constant of the tide-causing celestial body (i = 1 for the Moon and i = 2 for the Sun), R and R i (i = 1 for the Moon and i = 2 for the Sun) are the geocentric positions of the CEI observation array and the tide-causing celestial body, respectively, and are the unit vectors corresponding to R and R i , h2 is the Love number, and l2 is the Shida number.

[0219] Based on the above analysis, the total error correction equation of the CEI observation process of the inter-satellite link signal reflected by the non-cooperative spacecraft is obtained as follows:

[0220]

[0221] 7. Analysis of the carrier-to-noise ratio of the tracking and measurement link of the non-cooperative spacecraft in the geocentric space based on the CEI and Beidou inter-satellite links.

[0222] The carrier-to-noise ratio of the tracking and measurement link of the non-cooperative spacecraft in the geocentric space based on the CEI and Beidou inter-satellite links can be expressed as follows:

[0223] C / N0 = C - N0 (30)

[0224] where C is the received signal power at the CEI receiving array end, in dB; N0 is the thermal noise power, in dB; and the carrier-to-noise ratio C / N0 is in dB-Hz. The received signal power C and the thermal noise power N0 satisfy the following relationships, respectively:

[0225] C = T transmit + G transmit(BD→space) + G receive(space→CEI) - L reflect - L BD→CEI-L receive (31)

[0226] wherein, T transmit is the transmitting power of the Beidou inter-satellite link signal, in units of dBW; G transmit(BD→space) is the gain of the transmitting antenna of the Beidou inter-satellite link towards the non-cooperative spacecraft in the Earth-Moon space, in units of dBi; G receive(space→CEI) is the gain of the receiving antenna of the CEI receiving array towards the non-cooperative spacecraft in the Earth-Moon space, in units of dBi; L reflect is the reflection loss of the Beidou inter-satellite link signal by the non-cooperative spacecraft, in units of dB; L BD→CEI is the transmission loss of the Beidou inter-satellite link signal in the whole process of tracking and measurement of the non-cooperative spacecraft in the Earth-Moon space based on the CEI and the Beidou inter-satellite link, in units of dB; L receive is the receiving loss at the end of the CEI receiving array, in units of dB.

[0227] N0 = 10log 10 [k B (T antenna + T amplifier )] (32)

[0228] wherein, k B is the Boltzmann constant, k B = 1.3806452 x 10 -23 J / K; T antenna is the antenna noise temperature, in units of K; T amplifier is the amplifier noise temperature, in units of K.

[0229] The transmission loss L BD→CEI of the Beidou inter-satellite link signal in the whole process of tracking and measurement of the non-cooperative spacecraft in the Earth-Moon space in (31) satisfies:

[0230]

[0231] wherein, f iBD is the power of the Beidou inter-satellite link signal, d i(BD→space) is the distance between the Beidou No. 3 satellite transmitting the Beidou inter-satellite link signal and the non-cooperative spacecraft, d i(space→CEI) is the distance between the non-cooperative spacecraft and the ground CEI receiving array.

[0232] The antenna noise temperature T antenna and the amplifier noise temperature T amplifier in (32) respectively satisfy the following relationships:

[0233]

[0234] wherein, the first part T antenna_1T is the ohmic loss caused by the antenna's own defects, the second part antenna_2 T is the thermal noise captured by the antenna from the surrounding environment; physical_antenna T is the physical temperature of the antenna, e antenna T is the antenna efficiency; Ω earth and Ω moon T and T are the fixed angles subtracted by the Earth and the Moon, respectively, when viewed from the CEI receiving array; T brightness_earth , T brightness_moon and T brightness_cosmic are the brightness temperatures of the Earth, the Moon and the cosmic background, respectively.

[0235]

[0236] where T physical_amplifier is the physical temperature of the amplifier, N figure is the noise figure of the amplifier.

[0237] From (30) to (35), the carrier-to-noise ratio equation of the lunar-space non-cooperative spacecraft tracking and measurement link based on the CEI and the inter-satellite link of Beidou can be finally expressed as follows:

[0238]

[0239] 8. Performance evaluation of lunar-space non-cooperative spacecraft tracking and measurement based on CEI and inter-satellite link of Beidou

[0240] This part mainly includes: reception performance evaluation of CEI receiving array, orbit determination geometric accuracy evaluation of lunar-space non-cooperative spacecraft based on CEI and inter-satellite link of Beidou, and range accuracy evaluation of lunar-space non-cooperative spacecraft based on CEI and inter-satellite link of Beidou. The specific analysis is as follows.

[0241] (1) Reception performance evaluation of CEI receiving array

[0242] The thermal noise in the phase-locked loop and the frequency-locked loop of the receiver of the CEI receiving array affects the accurate measurement of the pseudo-code range and the range rate in the whole process of the lunar-space non-cooperative spacecraft tracking and measurement based on the inter-satellite link signal of Beidou No. 3 and CEI. The corresponding 1σ uncertainty can be expressed as follows:

[0243]

[0244]

[0245] where λ code is the wavelength of the inter-satellite link signal ranging code stream of Beidou No. 3, λ carrier is the carrier wavelength of the inter-satellite link signal of Beidou No. 3, B noise is the ranging code loop noise bandwidth, Bfront-end T is the two-way bandwidth of the loop chip T is the ranging code stream period integration C / N0 is the carrier-to-noise ratio.

[0246] (2) Geometric accuracy evaluation of lunar space non-cooperative spacecraft orbit determination based on CEI and Beidou inter-satellite link

[0247] The geometric accuracy of lunar space non-cooperative spacecraft orbit determination based on CEI and Beidou inter-satellite link is an important indicator for judging the effectiveness of the present application, which can be expressed as follows:

[0248]

[0249] The observation matrix of the orbit determination process of the present application is H, H T The eigenvalue of H is λ i (i=1, 2,..., j), PDOP BD→space→CEI is the geometric accuracy of the whole process of orbit determination.

[0250] (3) Ranging accuracy evaluation of lunar space non-cooperative spacecraft based on CEI and Beidou inter-satellite link

[0251] The ranging accuracy of lunar space non-cooperative spacecraft based on CEI and Beidou inter-satellite link is another important indicator for judging the effectiveness of the present application, which can be expressed as follows:

[0252]

[0253] Where, σ clock_error is the clock difference of Beidou inter-satellite link; σ ephemeris_error is the ephemeris error of Beidou inter-satellite link; σ multipath_error is the multipath error of Beidou inter-satellite link in the whole transmission process; σ receiver_error is the receiver noise and resolution error of CEI receiving array; σ thermal_error is the thermal noise code tracking error, which is a function of the height of the non-cooperative spacecraft, the acquisition and tracking threshold, and the jitter of the signal chip rate.

[0254] In summary, the above is only a preferred embodiment of the present application, and is not intended to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for measuring the earth-moon spacecraft based on Beidou and CEI, characterized in that, The method comprises the following steps: Step 1, establishing a dynamic constraint equation of a non-cooperative spacecraft in a space between the earth and the moon; Step 2, irradiating the non-cooperative spacecraft in the space between the earth and the moon based on an inter-satellite link of Beidou; (1) establishing a transmission equation of an inter-satellite link signal of Beidou satellites located in different orbits in the space between the earth and the moon: Based on the inter-satellite link signal of Beidou satellites, a pseudo-code ranging equation between the Beidou satellites located in different orbits and the non-cooperative spacecraft in the space between the earth and the moon is as follows: Where i=1 represents the MEO orbital, i=2 represents the GEO orbital, and i=3 represents the IGSO orbital; t i1 For the timing of launching inter-satellite links for BeiDou-3 satellites in different orbits, t i2 The time when inter-satellite links in different orbits arrive at non-cooperative spacecraft in Earth-Moon space; r iBD (t i1 (t) represents time t i1 The position vectors, r, of BeiDou-3 satellites in different orbits in the geocentric inertial coordinate system space (t i2 ) represents time t i2 The position vector of non-cooperative Earth-Moon spacecraft in different orbits in the geocentric inertial coordinate system; δt space (t i2 ) represents time t i2 Clock differences between non-cooperative Earth-Moon spacecraft in different orbits and the BeiDou system time; δt iBD (t i1 ) represents time t i1 Clock differences between BeiDou-3 satellites in different orbits and the BeiDou system time; τ iBD Hardware delays for BeiDou-3 satellites during inter-satellite link launches from different orbits; e i(BD→space) and n i(BD→space) These are the errors and observation noise that need to be corrected during the transmission of inter-satellite link signals of BeiDou-3 satellites in the Earth-Moon space. (2) establishing a transmission equation of the inter-satellite link signal reflected by the non-cooperative spacecraft in the space between the earth and the moon and a receiving equation of the signal at a CEI observation array: Based on the inter-satellite link signal of Beidou satellites, a pseudo-code ranging equation between the Beidou satellites located in different orbits and the non-cooperative spacecraft in the space between the earth and the moon is as follows: Among them, t i3 The time when the inter-satellite link, reflected by a non-cooperative spacecraft, reaches the CEI observation array on Earth; r CEI (t i3 ) represents time t i3 The position vectors of the CEI observation arrays on the ground at different orbits in the geocentric inertial coordinate system; r space (t i2 ) represents time t i2 The position vector of non-cooperative Earth-Moon spacecraft in different orbits in the geocentric inertial coordinate system; δt CEI (t i3 (t) represents time t i3 Clock differences between ground-based CEI observation arrays at different orbits and the BeiDou system time; τ iCEI Indicates the hardware latency of the CEI observation array; e i(space→CEI) and n i(space→CEI) These are: the transmission of inter-satellite link signals reflected by non-cooperative spacecraft in Earth-Moon space and the errors and observation noise that need to be corrected during the final reception process by the CEI observation array; Step 3, accurate measurement of the non-cooperative spacecraft in the space between the earth and the moon based on the CEI observation array: Based on the established pseudo-code ranging equation between the Beidou satellites located in different orbits and the non-cooperative spacecraft in the space between the earth and the moon based on the inter-satellite link signal of Beidou satellites and the pseudo-code ranging equation between the CEI observation array and the non-cooperative spacecraft in the space between the earth and the moon based on the inter-satellite link signal of Beidou satellites reflected by the non-cooperative spacecraft, a precise orbit determination equation of the non-cooperative spacecraft in the space between the earth and the moon based on the CEI observation array is obtained: Step 4, observation error correction of the whole tracking and measurement process of the non-cooperative spacecraft in the space between the earth and the moon based on the CEI observation array and the inter-satellite link of Beidou: (1) establishing an observation error correction equation in the transmission process of the inter-satellite link signal of Beidou satellites located in different orbits in the space between the earth and the moon: a) the antenna phase center offset of the Beidou satellite transmitting the inter-satellite link is expressed in the Earth-Centered Inertial coordinate system as follows: wherein, are the antenna phase center offsets of the different orbits of the BeiDou-3 satellites in the star-fixed coordinate system, (p x , y , z are the projections of the three coordinate axes in the star-fixed coordinate system into the geocentric inertial coordinate system; Then, the antenna phase center offset correction equation of the Beidou satellite is expressed as follows: where r iBD and r space are the position vectors of the BeiDou-3 satellite and the non-cooperative spacecraft in the Earth-Centered Inertial (ECI) frame, respectively. The antenna phase center offset correction equation of the Beidou satellite is obtained by combining equations (17) and (18): b) the influence of the clock time deviation of the Beidou satellite caused by the relativistic effect on the pseudo-code ranging value is expressed as follows: wherein, and respectively, are the velocities of the BeiDou-3 satellite and the Earth-Moon space non-cooperative spacecraft in the Earth-centered inertial coordinate system. The influence of the gravitational field caused by the general relativistic effect on the pseudo-code ranging value is expressed as follows: where γ is the post-Newtonian parameter, GM is the Earth's gravitational constant, |r iBD |and |r space |are the distances from the center of the Earth to the BeiDou-3 satellites and the lunar spacecraft, respectively; and ρ i(BD→space) is the distance between the BeiDou-3 satellites and the lunar spacecraft. The total error correction equation of the relativistic effect is as follows: The total error correction equation in the transmission process of the inter-satellite link signal of Beidou satellites located in different orbits in the space between the earth and the moon is obtained as follows: (2) establishing an observation error correction equation in the CEI observation process of the inter-satellite link signal reflected by the non-cooperative spacecraft: a) atmospheric delay error: The tropospheric delay correction equation is as follows: where c dry and c wet are zenith tropospheric delay correction models for dry delay component and wet delay component, respectively, and are mapping functions for dry delay component and wet delay component, respectively, is the observation elevation angle of the CEI observation array to the non-cooperative spacecraft. The ionospheric delay correction equation is as follows: wherein f iBD is the carrier frequency of the inter-satellite link of Beidou-3 satellite, N total is the total electron content in zenith direction, R e is the radius of the earth, and H is the height of ionosphere layer; b) error correction of the station antenna phase center offset: The error correction equation of the station antenna phase center offset is as follows: wherein, is the station antenna phase center offset in the star-fixed coordinate system, x , y , z are the projections of the three coordinate axes in the star-fixed coordinate system in the ECI coordinate system, CEI and r space are the position vectors of the CEI observation array and the non-cooperative spacecraft in the ECI coordinate system, respectively; c) relativistic effect The error correction equation of the relativistic effect between the non-cooperative spacecraft in the space between the earth and the moon and the CEI observation array is as follows: where, and are the velocities of the CEI observer array and the non-cooperative spacecraft in the geocentric inertial frame, respectively, γ is the post-Newtonian effect parameter, GM is the Earth gravitational constant, |r CEI |and |r space |are the distances from the Earth center of the CEI observer array and the non-cooperative spacecraft, respectively; ρ i(space→CEI) is the distance between the CEI observer array and the non-cooperative spacecraft. d) tidal effect: The error correction equation of the tidal effect is as follows: where GM j is the gravitational constant of the tide-causing body, R and R j are the geocentric positions of the CEI observation array and the tide-causing body, respectively, and when j = 1 the tide-causing body is the moon and when j = 2 the tide-causing body is the sun; and are the unit vectors corresponding to R and R j , respectively, h2is the Love number, and l2is the Shida number; The total error correction equation in the CEI observation process of the inter-satellite link signal reflected by the non-cooperative spacecraft is obtained as follows:

2. The method according to claim 1, wherein, The specific method of step 1 comprises: The earth, the moon and the non-cooperative spacecraft in the earth-moon space are regarded as particles, wherein the line connecting the earth and the moon is regarded as the x-axis and the barycenter of the earth and the moon is regarded as the coordinate origin; The distances λ and 1-λ of the earth and the moon from the barycenter of the earth and the moon satisfy: wherein m earth and m moon are the masses of the Earth and the Moon, respectively; the distances between the Earth and the Moon and the first Earth-Moon space non-cooperative spacecraft satisfy: wherein x l y l z l are the x, y, z position coordinates of the lth non-cooperative spacecraft in the Earth-Moon space, respectively; For k non-cooperative spacecraft in the earth-moon space, the state vector containing the velocity and position information is expressed as: wherein x l , y l , z l are the x, y, z axis position coordinates of the lth non-cooperative spacecraft in the cislunar space, respectively, are the x, y, z axis velocity components of the lth non-cooperative spacecraft in the cislunar space, respectively, are the x, y, z axis acceleration components of the lth non-cooperative spacecraft in the cislunar space, respectively; satisfy the following relations: where p l is the potential function, satisfying the relation: According to the equations (1) to (7), the dynamic constraint equation of the non-cooperative spacecraft in the earth-moon space is finally expressed as:

3. A carrier-to-noise ratio analysis method based on the Beidou and CEI-based lunar spacecraft measurement method of claim 1 or 2, characterized in that, It comprises: The carrier-to-noise ratio of the tracking and measuring link of the non-cooperative spacecraft in the earth-moon space based on the CEI observation array and the inter-BDS satellite link is expressed as: C / N0=C-N0 (30) Wherein C is the received signal power of the CEI observation array; N0 is the thermal noise power; the received signal power C and the thermal noise power N0 satisfy the following relationship respectively: C = T transmit +G transmit(BD→space) +G receive(space→CEI) -L reflect -L BD→CEI -L receive (31) wherein, T transmit is the BeiDou inter-satellite link signal transmission power; G transmit(BD→space) is the BeiDou inter-satellite link transmitting antenna gain towards the non-cooperative spacecraft in the geolunar space; G receive(space→CEI) is the CEI observation array receiving antenna gain towards the non-cooperative spacecraft in the geolunar space; L reflect is the reflection loss of the BeiDou inter-satellite link signal by the non-cooperative spacecraft; L BD→CEI is the total transmission loss of the BeiDou inter-satellite link signal in the whole process of tracking and measuring the non-cooperative spacecraft in the geolunar space based on the CEI observation array and the BeiDou inter-satellite link; L receive is the receiving loss of the CEI observation array; N0 = 10 log 10 [k B (T antenna +T amplifier )] (32) where k B is the Boltzmann constant, k B = 1.3806452 x 10 -23 J / K; T antenna is the antenna noise temperature; T amplifier is the amplifier noise temperature; The transmission loss L of the inter-satellite link signal in the whole process of tracking and measuring the non-cooperative spacecraft in the Earth-Moon space in (31) BD→CEI satisfies: wherein f iBD is the power of the BeiDou inter-satellite link signal, d i(BD→space) is the distance between the BeiDou constellation satellite transmitting the BeiDou inter-satellite link signal and the non-cooperative spacecraft, d i(space→CEI) is the distance between the non-cooperative spacecraft and the ground CEI observation array; The antenna noise temperature T in (32) antenna and the amplifier noise temperature T amplifier respectively satisfy the following relationships: Wherein, the first part T antenna_1 is the ohmic loss caused by the antenna itself defects, the second part T antenna_2 is the thermal noise captured by the antenna from the surrounding environment; T physical_antenna is the physical temperature of the antenna, e antenna is the antenna efficiency; Ω earth and Ω moon are the fixed angles subtracted by the earth and the moon respectively when viewed from the CEI observation array; T brightness_earth , T brightness_moon and T brightness_cosmic are the brightness temperatures of the earth, the moon and the cosmic background respectively; where T physical_amplifier is the physical temperature of the amplifier, N figure is the amplifier noise figure; According to the equations (30) to (35), the carrier-to-noise ratio equation of the tracking and measuring link of the non-cooperative spacecraft in the earth-moon space based on the CEI observation array and the inter-BDS satellite link is finally expressed as:

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