A large-scale space debris tracking measurement method based on CEI

Abstract

The application provides a large-scale space debris tracking measurement method based on CEI and belongs to the technical field of satellite signal measurement and processing. Firstly, a large-scale space debris tracking measurement overall scene based on CEI and Beidou satellite signals is constructed. Then, for large-scale space debris of different orbital heights, low-orbit and high-orbit large-scale space debris tracking measurement models based on CEI and Beidou satellite signals are established. Expressions of in-orbit running speeds, maximum Doppler speeds and maximum Doppler frequency shifts of large-scale space debris on low-orbit and high-orbit and Beidou satellites on medium-orbit are obtained. By substituting the most common orbital heights and signal frequency bands in actual tasks into the above expressions, in-orbit running speeds, maximum Doppler speeds and maximum Doppler frequency shift data of large-scale space debris and Beidou satellites in typical tasks are given. Thus, cataloging, long-term effective tracking measurement and timely early warning of abnormal behaviors of large-scale space debris are realized.

Description

Technical Field

[0001] This invention belongs to the field of satellite signal measurement and processing technology, specifically relating to a large-scale space debris tracking and measurement method based on CEI. Background Technology

[0002] Phase interferometry is a passive angle measurement and tracking method based on the downlink signal of an aircraft. Currently, there are two main types: Very Long Baseline Interferometry (VLBI) and Connected Element Interferometry (CEI). Compared to VLBI, the main advantages of CEI are: simpler phase delay measurement, rapid orbit determination based on phase differences, near real-time angle measurement, simpler equipment, lower cost, and easier maintenance and management. It is particularly suitable for enhancing and supplementing existing tracking and control methods for geostationary orbit and smaller Earth satellites.

[0003] Figure 1 The diagram shows the basic principle of CEI (Cyclic Electron Identifier). The high-orbit satellite signal processed by the CEI measurement correlator originates from two geometrically separated ground stations. The time difference between the arrival of the wavefront of the signal emitted by the high-orbit satellite at both ends of the baseline is approximately:

[0004] (1)

[0005] In the formula, For the time difference, The baseline vector is the strip from the first station to the second station. The direction vector of the high-orbit satellite. and The included angle is According to equation (2), when the baseline is determined, by Caused by measurement error The angle measurement error is expressed as:

[0006] (2)

[0007] From equation (2), it can be seen that the angle measurement error Compared with baseline The length is inversely proportional to, and with Measurement error It is directly proportional. Therefore, to obtain high-precision angle measurements, the measurement accuracy of the interferometric delay can be improved, which is the basic principle of CEI high-precision measurement technology.

[0008] like Figure 2As shown, since the majority of satellite orbital errors are reflected in its projection along the effective baseline direction, the two CEI orthogonal baselines can determine the two-dimensional angular coordinates and their variations of the high-orbit satellite. The signal emitted by the satellite is used to establish measurement equations according to the spherical wave propagation mode. For ease of analysis, the measurement equations are established using stations 1 and 2 as examples, as shown below: (3)

[0009] In the formula, and These are phase observations and integer ambiguity, respectively. The signal wavelength for the satellite downlink band; and , These are the position vectors of the high-orbit satellite and stations 1 and 2 at both ends of baseline 1, respectively. The difference between the clock differences of the two stations; The residual error is the atmospheric propagation delay between stations; Distance error caused by instrument delay; To observe noise.

[0010] Space debris, also known as "space junk," refers to abandoned man-made objects in outer space. This includes defunct spacecraft, discarded rocket stages, ejected and leaked materials from space launches, and fragments of man-made objects broken in various forms. It can be mainly categorized into large-scale space debris (greater than 10 cm in low Earth orbit and greater than 1 meter in geostationary orbit), medium-scale space debris (1-10 cm in low Earth orbit), small-scale space debris (1-10 mm), and micro-scale space debris (less than 1 mm). The relative speed between space debris and orbiting spacecraft can reach several kilometers per second, posing a significant threat to the safe operation of spacecraft. Collisions between large-sized space debris, such as defunct spacecraft or rocket bodies, and orbiting spacecraft can cause devastating damage such as explosions, fractures, and structural disintegration. Centimeter-sized space debris can also completely destroy a spacecraft; millimeter-sized debris can cause perforations or craters on the spacecraft surface, antenna deformation, and leaks in pressure vessels or sealed compartments; the cumulative impact effect of micrometer-sized space debris can lead to surface erosion, decreased functionality, or even failure of photosensitive or thermosensitive devices on the spacecraft.

[0011] For spacecraft, protective barriers can be installed on their surfaces to withstand the impact of collisions from objects with a diameter of less than 1 cm. However, for objects with a diameter of 1 cm to 10 cm, a collision with a spacecraft could potentially destroy it. Installing excessively thick protective layers would reduce the spacecraft's actual load factor, and for high-orbit missions, this would undoubtedly increase fuel consumption significantly. In some regions of space, debris density has reached a very high level, and a collision could lead to the "Kessler effect."

[0012] The existing space debris tracking measurement means are mainly based on optical, radar, laser and other detection equipment, and the radar means mainly include traditional target detection radars and imaging radars represented by SAR and ISAR. However, the existing means have the following outstanding problems. The optical, radar, laser and other means will be discussed below.

[0013] The existing space debris tracking measurement technology based on optical means has the following problems: there are a large amount of noises in the observation image, and in the tracking observation mode, the space debris target is also a point-like target similar to the noise, which can be submerged by the noise. At the same time, the stray light can also change the image contrast, and even cover the space target. It is difficult to realize the accurate detection of the space debris by the optical means in the dynamic environment. When observing the space debris at a long distance, the space debris has small size, no obvious geometric features and low brightness on the optical image, so it is difficult to extract the weak space debris target features and realize the space debris tracking. According to the laser ranging principle, the more the number of returned light photons received by the system, the better the ranging performance. However, the surface of the measured space target diffusely reflects the incident laser beam, so that the returned laser signal is weak, resulting in great difficulty in measurement. Low false alarm rate.

[0014] The existing space debris tracking measurement technology based on radar means has the following problems: for the space debris with a size of centimeter level, in order to achieve the required signal-to-noise ratio for detection, a radar antenna with large size and high transmission power is needed. In the spaceborne environment, these two conditions are difficult to guarantee. On the other hand, due to the high-speed motion state of the target and the radar, the target has a large range of distance migration, so the effect of traditional coherent accumulation is very limited, and new motion target detection technology needs to be researched. In the spaceborne condition, there is high-speed radial and lateral motion between the radar and the space debris, so it is difficult to establish the tracking measurement process of "searching-capturing-tracking-target motion parameter estimation-orbit measurement". At the same time, due to the limited action distance of the radar, it is difficult to obtain the orbit information from the short track of the target based on the sequential scanning of the antenna beam, so new target orbit measurement method needs to be researched. Due to the need to use a multi-antenna structure, and the need to accurately decompose the target velocity under the condition of limited baseline, the radar also needs to have high resolution, so such a space debris observation radar system is actually relatively complex.

[0015] The existing space debris tracking measurement technology based on laser means has the following problems: according to the laser ranging principle, the more the number of returned light photons received by the system, the better the ranging performance. However, when the surface of the measured space target diffusely reflects the incident laser beam, the returned laser signal is weak, resulting in great difficulty in measurement. SUMMARY

[0016] Therefore, the present application aims to provide a CEI-based large-scale space debris tracking measurement method, which realizes long-term cataloging and effective tracking measurement of large-scale space debris in the orbit of important spacecrafts such as low-orbit and high-orbit spacecrafts.

[0017] A CEI-based large-scale space debris tracking measurement method comprises the following steps:

[0018] Step 1: Construct a CEI and Beidou satellite signal-based large-scale space debris tracking measurement model, thereby establishing a maximum Doppler frequency shift equation of a direct signal of a downlink of a Beidou satellite, a maximum Doppler frequency shift equation of an indirect signal of the downlink of the Beidou satellite reflected by a large-scale space debris in a low orbit, and a maximum Doppler frequency shift equation of the indirect signal of the downlink of the Beidou satellite reflected by a large-scale space debris in a high orbit, and then obtaining corresponding maximum Doppler frequency shift data.

[0019] Step 2: Based on the tracking measurement model, obtain an expression of a downlink signal of a Beidou No. 3 satellite, and obtain expressions of a direct signal and an indirect signal finally obtained at a CEI observation array end.

[0020] Step 3: According to direct and indirect downlink signal data of a Beidou satellite received by the CEI, based on the maximum Doppler frequency shift data of the direct signal and the indirect signal of the downlink of the Beidou No. 3 satellite at the CEI receiving end in step 1, eliminate the direct signal received by the CEI and retain the indirect signal.

[0021] Step 4: Based on the indirect signal obtained in step 3, obtain angle measurement information and time delay estimation information of a space large-scale debris, thereby constructing a space large-scale debris information database; and based on the information database, track and measure the large-scale space debris.

[0022] Preferably, in step 1, the maximum Doppler frequency shift equation of the direct signal in the large-scale space debris tracking measurement model of the low-orbit and high-orbit spacecrafts is as follows: ;

[0023] wherein, is a maximum carrier frequency of a Beidou No. 3 satellite of the B1 type, represents a maximum Doppler velocity: ;

[0024] wherein, is an on-orbit running speed of the Beidou satellite, is an earth radius, is a distance of the Beidou satellite from the center of the earth.

[0025] Preferably, in step 1, the maximum Doppler frequency shift equation of the indirect signal in the large-scale space debris tracking measurement model of the low-orbit spacecraft is as follows:

[0026] ;

[0027] wherein, represents the maximum Doppler velocity of the low-orbit large-scale space debris; is the maximum carrier frequency of the Beidou-3 satellite of B1 type.

[0028] Preferably, in the step one, the maximum Doppler frequency shift equation of the indirect signal in the high-orbit large-scale space debris tracking measurement model is:

[0029] ;

[0030] wherein, represents the maximum Doppler velocity of the high-orbit large-scale space debris; is the maximum carrier frequency of the Beidou-3 satellite of B1 type.

[0031] Preferably, in the step two, the direct signal and the indirect signal finally obtained at the CEI observation array end are expressed as follows:

[0032] wherein, the subscripts and respectively represent the direct signal and the indirect signal; and are the expressions of the direct signal and the indirect signal, respectively; is the relationship expression between the direct signal and the indirect signal; is the number of the Beidou satellites transmitting downlink signals, is a time variable, is the number of output integrations; represents the phase of the indirect signal, is the observation noise; represents the width of the data chip, is an integer; represents the received signal power of the indirect signal; represents the navigation data bit value of the indirect signal; represents the navigation data bit value of the direct signal; and respectively represent the spreading codes of the direct signal and the indirect signal; and are the relative Doppler frequency and the phase difference between the weak signal and the strong signal, respectively.

[0033] The present application has the following beneficial effects: The purpose of the present application is to provide a large-scale space debris tracking measurement method based on CEI. In view of the problem that the on-orbit running speed, maximum Doppler velocity and maximum Doppler frequency shift of large-scale space debris in low orbit and high orbit and Beidou satellites in medium orbit are significantly different, the present application firstly constructs a large-scale space debris tracking measurement overall scene based on CEI and Beidou satellite signals. On this basis, the tracking measurement model of large-scale space debris in low orbit and high orbit based on CEI and Beidou satellite signals is established for large-scale space debris in different orbital heights. In the present model, the expression of the on-orbit running speed, maximum Doppler velocity and maximum Doppler frequency shift of large-scale space debris in low orbit and high orbit and Beidou satellites in medium orbit is derived, and the on-orbit running speed, maximum Doppler velocity and maximum Doppler frequency shift data of large-scale space debris and Beidou satellites in typical tasks are given by substituting the most common orbital height and signal frequency band in actual tasks into the above expression for the convenience of expression of the present method.

[0034] In view of the problem that the downlink signal of the currently networked Beidou-3 satellite constellation needs to be utilized, and the CEI observation technology is combined to realize effective tracking and measurement of large-scale space debris, the expression of the downlink signal of the Beidou-3 satellite is given, and the expression of the direct signal and indirect signal finally obtained at the CEI observation array end is given in combination with the related measurement equation and processing method of the CEI observation array.

[0035] On the basis of the above steps, the CEI receiving signal processing is realized based on the Doppler frequency offset difference of the direct signal and indirect signal of the Beidou-3 downlink at the CEI receiving end: according to the Doppler difference of the direct signal and indirect signal, the direct signal is eliminated, and only the indirect signal is left.

[0036] On this basis, the construction of the space large-scale debris information library in the key orbital height is realized. Thus, the cataloging, long-term effective tracking measurement and timely early warning of abnormal behavior (collision with on-orbit spacecraft of ours, disintegration, etc.) of large-scale space debris are realized. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 It is a basic principle diagram of CEI measurement;

[0038] Figure 2 It is a schematic diagram of CEI accurate measurement based on orthogonal baseline;

[0039] Fig. 3 (a) and Fig. 3 (b) are schematic diagrams of the running track of Beidou satellites for 48 hours;

[0040] Figure 4 It is a total flow chart of the space non-cooperative satellite measurement method based on CEI of the present application;

[0041] Figure 5 A large-scale space debris tracking measurement scene overview diagram based on CEI and Beidou satellite signals;

[0042] Figure 6 A low-orbit large-scale space debris tracking measurement model schematic diagram based on CEI and Beidou satellite signals;

[0043] Figure 7 A high-orbit large-scale space debris tracking measurement model schematic diagram based on CEI and Beidou satellite signals. DETAILED DESCRIPTION

[0044] The present application will be described in detail below with reference to the accompanying drawings and embodiments.

[0045] For the future space application, the space situation awareness, the safe and stable on-orbit operation of important orbit spacecraft, the cataloging and effective tracking measurement of large-scale space debris, and the collision risk prediction of large-scale space debris and on-orbit spacecraft, the traditional monitoring and observation means for on-orbit cooperative spacecraft cannot realize the cataloging and effective monitoring of space non-cooperative large-scale space debris, and the related measurement means and observation method research is currently still relatively lacking, so that the growing space debris poses a great challenge to the safe and stable operation of on-orbit spacecraft. The present method comprehensively utilizes the medium-short baseline interferometric measurement (CEI) and Beidou satellite signals, based on the method that the CEI observation array passively receives the direct signals of the Beidou satellite downlink and the indirect signals reflected by the low-orbit and high-orbit large-scale space debris, a complete set of large-scale space debris tracking measurement process based on CEI and Beidou satellite signals is designed, and the long-term cataloging and effective tracking measurement of large-scale space debris on the important spacecraft on-orbit operation orbit of low-orbit and high-orbit is relatively effectively realized.

[0046] A large-scale space debris tracking measurement method based on CEI of the present application, as shown in Figure 4 The overall process is as follows:

[0047] (1) First, a large-scale space debris tracking and measurement model based on CEI and BeiDou satellite signals needs to be constructed. This model will construct CEI and BeiDou satellite signal observation scenarios for large-scale space debris in low Earth orbit and high Earth orbit respectively, focusing on establishing the on-orbit velocity, maximum Doppler velocity, and maximum Doppler frequency shift equations for large-scale space debris at different orbital altitudes. Based on this, the orbital altitude and signal frequency band most common in actual missions are substituted into the above expressions, and the on-orbit velocity, maximum Doppler velocity, and maximum Doppler frequency shift data of large-scale space debris and BeiDou satellites in typical missions are given. The above establishes a large-scale space debris tracking and measurement model based on CEI and BeiDou satellite signals.

[0048] (2) Based on the established tracking and measurement model, the downlink signal expression of Beidou-3 satellite is given. Combined with the relevant measurement equations and processing methods of CEI observation array, the expressions of direct and indirect signals finally obtained at the CEI observation array are given, thereby realizing the reception of direct and indirect downlink signals of Beidou satellite based on CEI.

[0049] (3) For the Beidou satellite direct and indirect downlink signal data obtained in the previous step based on CEI, based on the Doppler frequency offset difference of the direct and indirect signals of the Beidou-3 downlink at the CEI receiver, the signal processing of the direct and indirect signals received by CEI is realized: according to the Doppler difference between the direct and indirect signals, the direct signal is removed, leaving only the indirect signal.

[0050] (4) Based on the accurate angle measurement information and time delay estimation information of large-scale space debris obtained in the above steps, the results are compiled and summarized into a large-scale space debris information database. On this basis, the construction of a large-scale space debris information database at key orbital altitudes is realized. This enables the cataloging of large-scale space debris, long-term effective tracking and measurement, and timely early warning of abnormal behavior (collision, disintegration, etc. of orbital spacecraft).

[0051] The specific steps of the large-scale space debris tracking and measurement method based on CEI of this invention are as follows:

[0052] I. Construction of a large-scale space debris tracking and measurement model based on CEI and BeiDou satellite signals

[0053] Studies show that most of the world's spacecraft currently in orbit are concentrated in low Earth orbit (LEO) and high Earth orbit (HEO), resulting in a concentration of large-scale space debris, which poses the greatest threat to these spacecraft, in these two regions. However, by utilizing BeiDou satellite signals distributed at medium Earth orbit (MEO) altitudes, combined with CEI observation technology, it is possible to effectively track and measure large-scale space debris located at these two key orbital altitudes.

[0054] Therefore, the present method mainly aims at these two orbital height large-scale space debris, and constructs a large-scale space debris tracking measurement model based on CEI and Beidou satellite signals, as shown below:

[0055] 1.1. Large-scale space debris tracking measurement overall scene based on CEI and Beidou satellite signals

[0056] The downlink signal emitted by the Beidou satellite located in the medium orbit height is encoded with timing information to facilitate accurate ranging. The CEI observation array located on the ground can achieve high-precision estimation of the distance from the position of the Beidou satellite to the CEI array. In the present method, the CEI array will receive two types of signals. One is the downlink signal emitted by the Beidou satellite, which directly reaches the CEI receiving array. For the convenience of discussion, this type of signal will be referred to as direct signal in the present method. The other is the downlink signal emitted by the Beidou satellite, which first reaches the large-scale space debris to be observed, and then is emitted from the observed object to the CEI receiving array on the ground. For the convenience of discussion, this type of signal will be referred to as indirect signal in the present method.

[0057] In the present method, the above direct signal and indirect signal will be received by the CEI observation array together, and through the following processing techniques, that is, by analyzing the differences in key information such as delay and Doppler shift of the direct signal and indirect signal, the position and velocity of the reflecting object (i.e. the low-orbit and high-orbit large-scale space debris which need to be observed with high precision) can be obtained, thereby achieving effective tracking measurement of large-scale space debris in important orbits. The above large-scale space debris tracking measurement overall scene based on CEI and Beidou satellite signals is shown in Figure 5 .

[0058] For any global navigation satellite system (GNSS) satellite, when it passes above the observation device, the distance between the signal observation receiver and the satellite will change, and the rate of this change reflects the constant change of the Doppler frequency shift of the satellite signal. Among them, the maximum Doppler velocity occurs when the navigation satellite passes through the horizontal line where the ground observation station is located and rises along the orbit where the satellite is located. In the present method, in order to distinguish the characteristics of the direct signal and the indirect signal and thereby achieve high-precision tracking measurement of low-orbit large-scale space debris, the typical feature used is the significant difference in Doppler frequency shift between the direct signal and the indirect signal. Therefore, in the present model, the low-orbit and high-orbit large-scale space debris tracking measurement scene based on CEI and Beidou satellite signals under the maximum Doppler velocity will be mainly studied. The specific construction of the large-scale space debris tracking measurement model will be carried out below for the low-orbit and high-orbit scenarios.

[0059] 1.2. Construction of low-orbit large-scale space debris tracking measurement model based on CEI and Beidou satellite signals

[0060] Figure 6 The figure shows the CEI observation array receiving direct and indirect signals of Beidou satellites and the signal transmission path, relative velocity, geometry and corresponding Doppler effect between the signal transmitter located at different orbital heights. The signal transmitters of this model include: large-scale space debris located in low earth orbit, reflecting the downlink signals of Beidou satellites, and Beidou satellites located in medium earth orbit, directly transmitting downlink signals to the CEI array and at the same time transmitting downlink signals to the low earth orbit target to be observed.

[0061] (1) The maximum Doppler frequency shift of the direct signal in the low earth orbit large-scale space debris tracking measurement model

[0062] For Beidou satellites located in medium earth orbit, the on-orbit running speed satisfies the following relationship:

[0063] (4)

[0064] wherein is the on-orbit running speed of Beidou satellites, is the distance from the Beidou satellite to the center of the earth, is the running period of the Beidou satellite, satisfying the following relationship:

[0065] (5)

[0066] Combining equations (4) and (5), we have:

[0067] (6)

[0068] wherein the gravitational constant , the mass of the earth , are all constants. According to the geometric relationship, the Doppler velocity between the Beidou satellite and the ground CEI observation array satisfies:

[0069] (7)

[0070] wherein is the angle between and .

[0071] As mentioned above, the maximum Doppler velocity between the Beidou satellite and the ground CEI observation array occurs when the Beidou satellite just passes through the horizontal line of the ground observation station, so there is the following relationship:

[0072] (8)

[0073] in, For this time and The angle between them For the Earth's radius, This refers to the altitude of the BeiDou satellite above the Earth's surface. For BeiDou satellites located in the medium Earth orbit, Therefore, from equations (6) and (8), we can obtain the on-orbit speed of the Beidou satellite in this model. Maximum Doppler velocity .

[0074] Furthermore, due to the relative motion between the BeiDou satellites and the ground-based CEI observation array, the magnitude of the Doppler frequency shift is as follows:

[0075] (9)

[0076] (10)

[0077] in, This refers to the downlink signal transmission frequency of the BeiDou satellite. This refers to the signal receiving frequency of the ground-based CEI observation array. The Doppler frequency offset of the received signal relative to the transmitted signal. The speed is the speed of light. Therefore:

[0078] (11)

[0079] The BeiDou-3 satellite constellation is now fully operational. Therefore, this invention will primarily focus on BeiDou-3 satellite signals, which are mainly distributed across the following three frequency bands. For the B1 type BeiDou-3 satellite signal, its carrier frequency is: For the B2 type Beidou-3 satellite signal, its carrier frequency is: For the B3 type Beidou-3 satellite signal, its carrier frequency is: Therefore, from equation (11), we can obtain:

[0080] (12)

[0081] (13)

[0082] (14)

[0083] To investigate the maximization difference in Doppler frequency offset between direct and indirect signals, the following will focus on... The maximum Doppler frequency shift of the direct signal is shown in the following equation: .

[0084] (2) The maximum Doppler frequency shift of the indirect signal in the tracking and measurement model of large-scale space debris in low earth orbit

[0085] Research shows that large-scale space debris in low earth orbit is distributed in a wide range from the ground to . For the convenience of research, two typical low earth orbits are selected in this scenario: the international space station at and the starlink system at .

[0086] Following equation (4), (5) are:

[0087] (15)

[0088] where is the running speed of large-scale space debris in low earth orbit, is the distance from the large-scale space debris to the center of the earth. According to the geometric relationship, the Doppler velocity between the large-scale space debris and the ground CEI observation array satisfies:

[0089] (16)

[0090] where is the angle between and .

[0091] Following equation (8), the maximum Doppler velocity between the large-scale space debris in low earth orbit and the ground CEI observation array is shown as follows:

[0092] (17)

[0093] where is the angle between and .

[0094] For large-scale space debris located at and two orbital altitudes, , , so from equation (15), (17) we can get:

[0095] The running speed of large-scale space debris in this model is respectively:

[0096] ; ;

[0097] The corresponding maximum Doppler velocities are respectively:

[0098] , .

[0099] The Doppler frequency offset of the received signal with respect to the reflected Beidou satellite downlink signal of the large-scale space debris is shown as follows:

[0100] (18)

[0101] Therefore, combining formula (18), formula (12) to (14) can be obtained:

[0102] (19)

[0103] (20)

[0104] In summary, for a CEI observation array on the ground that is approximately static, the maximum Doppler frequency shift of the reflected Beidou satellite downlink indirect signal of the large-scale space debris on the low earth orbit is about .

[0105] For convenience of illustration, the orbital height of the large-scale space debris and the Beidou satellite and the signal frequency band of the Beidou No. 3 satellite in the actual task are substituted into the expression, and the on-orbit running speed, the maximum Doppler velocity and the maximum Doppler frequency shift data of the large-scale space debris and the Beidou satellite in the typical task are given. In fact, for the large-scale space debris, as long as the corresponding regional orbital height of the low earth orbit and the high earth orbit is met, it can be substituted; for the Beidou No. 3 satellite signal, five types of signals (B1I, B1C, B2a, B2b, B3I) can be substituted.

[0106] 2.3, High-orbit large-scale space debris tracking measurement model based on CEI and Beidou satellite signals

[0107] Figure 7 The high-orbit large-scale space debris tracking measurement model based on CEI and Beidou satellite signals is shown. The figure shows the CEI observation array on the ground receiving the direct and indirect signals of the Beidou satellite, the signal transmission path, the relative velocity, the geometric shape and the corresponding Doppler effect between the signal transmitter located at different orbital heights. The signal transmitter of the model includes the large-scale space debris located at the high earth orbit, reflecting the Beidou satellite downlink signal, and the Beidou satellite located at the medium earth orbit, directly sending the downlink signal to the CEI array and at the same time sending the downlink signal to the high-orbit target to be observed

[0108] (1) The maximum Doppler frequency shift of the direct signal in the tracking and measurement model of large-scale space debris in high orbit

[0109] This part is exactly the same as in low orbit, and will not be repeated.

[0110] (2) The maximum Doppler frequency shift of the indirect signal in the tracking and measurement model of large-scale space debris in high orbit

[0111] Research shows that large-scale space debris in high orbit are mainly concentrated in the geosynchronous orbit and its adjacent space where spacecraft are most concentrated, and the space debris in this position have the most significant impact on high-orbit spacecraft. For the convenience of research, this typical high-orbit height is mainly selected in this scenario: .

[0112] Following formula (15), the running speed of large-scale space debris in high orbit satisfies the following relationship:

[0113] (21)

[0114] wherein, is the distance from the large-scale space debris in high orbit to the center of the Earth. According to the geometric relationship, the Doppler velocity between the large-scale space debris in high orbit and the ground CEI observation array satisfies:

[0115] (22)

[0116] wherein, is the angle between and .

[0117] Following formula (17), the maximum Doppler velocity between the large-scale space debris in high orbit and the ground CEI observation array is as follows: (23)

[0118] wherein is the angle between and at this time. For large-scale space debris located in this orbital height , , thus from formula (21), (23), the running speed of large-scale space debris in this model is , and the maximum Doppler velocity is .

[0119] Following formula (18), the Doppler frequency offset of the received signal relative to the reflected Beidou satellite downlink signal of large-scale space debris is as follows:

[0120] (24)

[0121] Therefore, combined with formula (24), formula (19) to (20) can be obtained as follows:

[0122] (25)

[0123] In summary, for the CEI observation array on the ground which is approximately static, the maximum Doppler frequency shift of the indirect signal of the Beidou satellite downlink reflected by the large-scale space debris on the high orbit is about .

[0124] In this step, for the CEI observation array on the ground which is approximately static, the maximum Doppler frequency shift of the direct signal of the Beidou satellite downlink is about ; the maximum Doppler frequency shift of the indirect signal of the Beidou satellite downlink reflected by the large-scale space debris on the low orbit is about ; the maximum Doppler frequency shift of the indirect signal of the Beidou satellite downlink reflected by the large-scale space debris on the high orbit is about It can be seen that, based on the model established in the application, the direct signal of the Beidou satellite downlink and the indirect signal reflected by the large-scale space debris on the low orbit and the high orbit are received by the CEI observation array on the ground, and the maximum Doppler frequency shift of each signal is significantly different, so that after the subsequent processing process of the application, the low-orbit and high-orbit large-scale space debris can be effectively tracked and measured.

[0125] Thirdly, the link budget of the direct and indirect downlink signals of the Beidou satellite received by the CEI is also studied in the application, which can assist in identifying the indirect signal when necessary. In order to realize the detection of the direct and indirect downlink signals of the Beidou satellite received by the CEI observation array, especially the detection of the indirect signal reflected by the large-scale space debris, on the basis of the "low-orbit and high-orbit large-scale space debris tracking and measurement model based on CEI and Beidou satellite signals" established in the previous step, the link budget of the "Beidou signal transmitter-low-orbit and high-orbit large-scale space debris-ground CEI receiving array signal receiver" needs to be carried out as shown below, and the specific process is as follows:

[0126] 3.1, Link budget determination of the direct downlink signal of the Beidou satellite received by the CEI

[0127] For the direct downlink signal of the Beidou satellite received by the CEI, the received power of the signal receiver of the CEI observation array satisfies the following relationship:

[0128] (26)

[0129] where is the transmit power of the BDS downlink signal, and are the gains of the BDS satellite signal transmitter and the CEI observation array signal receiver, respectively, is the path loss in the signal transmission process, is other loss in the signal transmission process.

[0130] On this basis, the effective isotropic radiated power of the BDS satellite downlink signal transmitter can be expressed as follows:

[0131] (27)

[0132] The available signal power on the receiving antenna of the CEI observation array depends on the effective area of the receiving antenna, which is related to the gain of the antenna. Based on this, the gain of the CEI observation array signal receiver in equation (26) satisfies the following relationship:

[0133] (28)

[0134] where, is the carrier wavelength of the BDS satellite downlink signal, is the effective area of the receiving antenna of the CEI observation array.

[0135] At the same time, the path loss in the signal transmission process in equation (26) satisfies the following relationship:

[0136] (29)

[0137] where, is the distance between the BDS satellite downlink signal transmitter and the CEI observation array signal receiver.

[0138] Combining equations (26) to (29), the final expression for the received power of the CEI received BDS satellite direct downlink signal by the signal receiver of the CEI observation array is obtained as follows:

[0139] (30)

[0140] 3.2, Link budget determination of the CEI received BDS satellite indirect downlink signal reflected by large-scale spatial fragments

[0141] For the BeiDou satellite indirect downlink signals reflected by the large-scale space debris received by the CEI, it largely depends on the radar scattering cross section coefficient of the space debris. Thus, following the derivation in the direct signal in the previous part, for the indirect signal, the received power of the signal receiver of the CEI observation array satisfies the following relationship: (31)

[0142] wherein, is the distance between the BeiDou satellite downlink signal transmitter and the low-orbit or high-orbit large-scale space debris, is the distance between the large-scale space debris and the signal receiver of the CEI observation array, is the radar scattering cross section coefficient of the large-scale space debris, is other losses in the present scenario.

[0143] In this step, combining equations (30) and (31), it can be obtained that the received powers of the direct signal and the indirect signal at the signal receiver of the CEI observation array satisfy the following relationship (for the convenience of research, in combination with the measurement actuality, it can be considered that and ):

[0144] (32)

[0145] According to the above link analysis method given by the present application, according to the orbital height of the BeiDou satellite and the to-be-observed large-scale space debris in the actual task scenario and the radar scattering cross section coefficient of the debris, the present link budget analysis step can be completed.

[0146] Thus, the link budget determination of the direct and indirect downlink signals of the BeiDou satellite received by the CEI is completed.

[0147] Four, BeiDou satellite direct and indirect downlink signal reception based on CEI

[0148] On the basis of the large-scale space debris tracking and measurement model based on the CEI, in the present step, the direct and indirect downlink signal reception of the BeiDou satellite based on the CEI will be completed.

[0149] ​At present, the Beidou-3 satellite constellation has completed networking and opened services, so in the present application, the main research is to use the downlink signals of the Beidou-3 satellite, combined with the CEI observation technology, to realize effective tracking and measurement of large-scale space debris. The navigation signals of the Beidou-3 satellite are mainly generated by modulating the carrier, the spread spectrum code, the navigation message and the like in the form of complex envelope, as described above, which mainly have three types of signals, namely B1, B2 and B3. For the convenience of description, the following takes the I branch of the Beidou-3 B2b signal in the 20.46MHz bandwidth centered on the carrier frequency of 1207.14MHz as an example to discuss the CEI-based Beidou satellite direct and indirect downlink signal reception in the present application.

[0150] B2b signal I branch component from navigation message data and ranging code modulation, as shown below:

[0151] (33)

[0152] Navigation message data in formula (33) and ranging code respectively satisfy the following relationships:

[0153] (34)

[0154] (35)

[0155] wherein, is the navigation message data code of the B2b signal I branch, is the corresponding data chip width, is a rectangular pulse with a width of ; wherein, is the ranging code sequence of the I branch component, is the ranging code length of the corresponding component, is the ranging code chip width of the B2b signal I branch, is a rectangular pulse with a width of .

[0156] Combining formulas (33) to (35) can obtain:

[0157] (36)

[0158] The above is the expression of the downlink signal of the Beidou satellite. Based on the above downlink signal of the Beidou satellite, the correlation measurement equation and processing method of the CEI observation array are shown in formulas (1) to (3), and the final expressions of the direct signal and the indirect signal obtained at the end of the CEI observation array are as follows: (37)

[0159] Subscript and These represent direct signals and indirect signals, respectively. and These are the expressions for direct signals and indirect signals, respectively; This is the expression representing the relationship between direct and indirect signals; The number of BeiDou satellites transmitting downlink signals. For time variables, To output the number of integrals; Indicates the phase of the indirect signal. To observe noise; Indicates the width of the data chip. It is an integer; This indicates the received signal power of the indirect signal; Navigation data bit values ​​representing indirect signals; This represents the navigation data bit values ​​of the direct signal; and Spread codes representing direct and indirect signals, respectively; and These represent the relative Doppler frequency and phase difference between the weak and strong signals, respectively.

[0160] Thus, the direct and indirect downlink signal reception of BeiDou satellites based on CEI was completed. For ease of description, this step uses the I branch of the BeiDou-3 B2b type signal within a 20.46MHz bandwidth centered at a carrier frequency of 1207.14MHz as an example to illustrate the direct and indirect downlink signal reception of BeiDou satellites based on CEI in this invention. In fact, all five types of BeiDou-3 satellite signals (B1I, B1C, B2a, B2b, and B3I) can be substituted for the corresponding calculations.

[0161] V. CEI Received Signal Processing Based on Doppler Frequency Offset Difference

[0162] After completing the previous step of "Receiving Direct and Indirect Downlink Signals from BeiDou Satellites Based on CEI," the received direct and indirect signals will be input into this step for CEI received signal processing based on Doppler frequency offset differences. In the model established in the second step, it was discussed that the direct downlink signal from BeiDou satellites and the indirect signal reflected from large-scale space debris in low and high orbits exhibit significant differences in maximum Doppler frequency shift after being received by the ground-based CEI observation array. Therefore, in this step, based on the Doppler difference between the direct and indirect signals, the direct signal will be eliminated, leaving only the indirect signal.

[0163] Six, space large scale debris information library construction

[0164] On the basis of the accurate related information of the indirect signals of the large scale space debris reflection of the downlink of the Beidou satellite obtained in each step, a space large scale debris information library based on the CEI and the Beidou satellite signals is constructed, including the space debris type, the catalog number, the orbit height, the radius size, the motion law, the threat degree to the spacecraft and the potential early warning time, etc.

[0165] To sum up, the above is only a preferred embodiment of the present application, and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A large-scale space debris tracking and measurement method based on CEI, characterized in that, include: Step 1: Construct a large-scale space debris tracking and measurement model based on the CEI observation array and BeiDou satellite signals. Based on this model, establish the maximum Doppler frequency shift equation for the direct downlink signal of BeiDou satellite, the maximum Doppler frequency shift equation for the indirect downlink signal of BeiDou satellite reflected by large-scale space debris in low Earth orbit, and the maximum Doppler frequency shift equation for the indirect downlink signal of BeiDou satellite reflected by large-scale space debris in high Earth orbit, and then obtain the corresponding maximum Doppler frequency shift data. Step 2: Based on the established tracking and measurement model, the downlink signal expression of the BeiDou-3 satellite is obtained, and the direct and indirect signal expressions are finally obtained at the CEI observation array. Step 3: Based on the direct and indirect downlink signal data of BeiDou satellites received by the CEI observation array, and based on the maximum Doppler frequency shift data of the direct and indirect signals of the BeiDou-3 downlink at the CEI observation array receiver in Step 1, remove the direct signals received by the CEI observation array and retain the indirect signals. Step 4: Based on the indirect signals obtained in Step 3, acquire the angle measurement information and time delay estimation information of large-scale space debris, thereby constructing a large-scale space debris information database; Tracking and measuring large-scale space debris based on a database; In step one, the maximum Doppler frequency shift equation for the direct signal in the large-scale space debris tracking and measurement models for both low-Earth orbit and high-Earth orbit is: ; in, This refers to the maximum carrier frequency of the B1 type Beidou-3 satellite; Indicates the maximum Doppler velocity: ; in, For the on-orbit operating speed of BeiDou satellites, For the Earth's radius, This refers to the distance of a BeiDou satellite from the Earth's center. In step one, the maximum Doppler frequency shift equation for the indirect signal in the low-orbit large-scale space debris tracking and measurement model is: ； in, Represents the speed of light; This represents the maximum Doppler velocity of large-scale space debris in low Earth orbit; This refers to the maximum carrier frequency of the B1 type Beidou-3 satellite; In step one, the maximum Doppler frequency shift equation for the indirect signal in the high-orbit large-scale space debris tracking and measurement model is: ； in, Represents the speed of light; This represents the maximum Doppler velocity of large-scale space debris in high orbit; This is the maximum carrier frequency for the B1 type Beidou-3 satellite.

2. The large-scale space debris tracking and measurement method based on CEI as described in claim 1, characterized in that, In step two, the expressions for the direct and indirect signals finally obtained at the CEI observation array are as follows: Subscript and These represent direct signals and indirect signals, respectively. and These are the expressions for direct signals and indirect signals, respectively; This is the expression representing the relationship between direct and indirect signals; The number of BeiDou satellites transmitting downlink signals. For time variables, To output the number of integrals, Indicates the phase of the indirect signal. To observe the noise, Indicates the width of the data chip. It is an integer; This indicates the received signal power of the indirect signal. The navigation data bit values ​​representing indirect signals. The navigation data bit values ​​represent the direct signals. and These represent the spreading codes for direct and indirect signals, respectively. and These represent the relative Doppler frequency and phase difference between the weak and strong signals, respectively.

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