Different-orbit inter-satellite communication link beam pointing error calculation method

Abstract

The invention discloses a different-orbit inter-satellite communication link beam pointing error calculation method, which relates to the technical field of communication, introduces high-order perturbation modeling, solar radiation pressure, earth tidal effect and moon gravitational perturbation items, effectively simulates orbit change of a satellite disturbed by external gravitational force for a long time, reduces the accumulation effect of errors, and improves the accuracy of beam pointing error calculation. In long-time or high-orbit satellite communication, pointing errors caused by simplified perturbation can be effectively reduced, relative motion models of two different-orbit satellites are combined, orbit change of a single satellite is integrated, change of relative speed is taken into calculation, wave beam pointing can be dynamically adjusted when the relative position and the speed of the satellites change, and the method is suitable for large-scale popularization and application. Errors caused by relative movement are reduced, meanwhile, a coupling model of frequency deviation and beam pointing angle deviation is constructed, the influence of the Doppler effect on beam pointing is predicted and corrected in real time, the beam pointing is dynamically adjusted through coupling correction, communication signals are kept on the optimal transmission path, and frequency deviation is avoided.

Description

Technical Field

[0001] The present invention relates to the field of communication technology, and in particular to a method for calculating beam pointing errors of inter-satellite communication links in different orbits. Background Art

[0002] In inter-satellite communication links with different orbits, beam pointing errors directly affect the quality and stability of the communication links. As the distance between satellites increases, the differences in orbits increase, and the relative speed changes, precise beam alignment becomes extremely challenging.

[0003] Satellites in different orbits are affected by a variety of orbital perturbations, such as the Earth's non-spherical gravitational field, solar radiation pressure, lunar gravity, and Earth's tidal effects. Due to the cumulative effect of orbital perturbations, the relative positions of satellites in different orbits will deviate over time. These deviations will directly affect the alignment accuracy of the beam. Traditional beam pointing error calculation methods are mostly based on simplified orbital models, assuming that the orbital parameters of the satellite are stable, or only consider low-order perturbation effects, such as the J2 gravitational field. Under this simplified treatment, the pointing error is compensated by static or semi-dynamic correction, relying on pre-calculated orbital data or adjusting based on short-term orbit predictions.

[0004] Orbital perturbation effects are dynamic and accumulate over long periods of time. Simplified perturbation models cannot capture the long-term impact of complex perturbation factors, resulting in a gradual increase in beam pointing errors in long-term communication links. In addition, traditional schemes mostly rely on pre-calculated or simplified predicted orbital parameters and cannot respond in real time to subtle position changes caused by orbital perturbations, resulting in insufficient real-time correction capabilities. In long-distance orbit environments, high-order perturbation effects, such as J4, J6 items, and solar wind, have a greater impact on satellite positions. Traditional methods are difficult to effectively compensate for these factors. Therefore, a beam pointing error calculation method for inter-orbital communication links is urgently needed to solve such problems. Summary of the invention

[0005] In view of the above existing problems, the present invention is proposed.

[0006] The present invention provides a beam pointing error calculation method for an inter-orbital satellite communication link to solve the problem that a simplified model used in orbit perturbation error processing is difficult to cope with the influence of long-term accumulation and high-order perturbations.

[0007] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0008] The present invention provides a method for calculating beam pointing errors of inter-satellite communication links in different orbits, which comprises:

[0009] Step S1, orbital perturbation high-order modeling,

[0010] Establish an orbital perturbation model including multiple perturbation factors;

[0011] Step S2, orbital perturbation combined with relative motion,

[0012] Based on the orbit perturbation model of step S1, a relative motion model between two satellites in different orbits is established, and an error prediction model evolving over time is derived;

[0013] The model not only considers the impact of orbital perturbations on a single satellite, but also takes into account the impact of orbital perturbations on the relative velocity changes of the two satellites. It combines orbital perturbations with relative motion to form an error prediction model that evolves over time, and predicts the relative position deviation and velocity changes of the two satellites under orbital perturbations.

[0014] Step S3, Doppler effect and pointing angle error correction,

[0015] Based on the relative motion model of step S2, the Doppler effect is calculated in combination with the relative velocity change;

[0016] Step S4, adaptive filtering dynamic correction,

[0017] Adaptive filtering technology is introduced for dynamic adjustment. Based on the error prediction model of step S2 and the angle deviation correction model of step S3, a particle filter is used to correct the beam pointing in real time.

[0018] Furthermore, the perturbation term in step S1 includes:

[0019] The Earth's non-spherical gravitational field, higher-order terms J2 to J6,

[0020] Solar radiation pressure,

[0021] Tidal effects,

[0022] And the external perturbations of the moon's gravity.

[0023] Furthermore, in step S1, the orbital perturbation high-order modeling method is:

[0024] Define satellite acceleration:

[0025] Among them, a grav represents the acceleration caused by the earth's gravity, G represents the gravitational constant, M represents the mass of the earth, and r represents the distance from the satellite to the center of the earth.

[0026] Introducing the non-spherical perturbation of the earth, items J2 to J6:

[0027] Among them, a J2J6 represents the non-spherical perturbation acceleration of the Earth, J n represents the nth order normalized coefficient of the Earth's gravitational field, R erepresents the average radius of the Earth, P n (sinφ) is the Legendre polynomial, φ represents the satellite's geocentric latitude,

[0028] Define the perturbation of solar radiation pressure, the acceleration of solar radiation pressure is:

[0029] Among them, a SRP represents the acceleration of solar radiation pressure, P SR represents the solar radiation pressure constant per unit area, A represents the satellite light receiving area, C r represents the reflection coefficient, which characterizes the satellite's ability to reflect solar radiation, m represents the satellite's mass,

[0030] Define the earth's tidal effect perturbation, and the tidal effect acceleration expression is:

[0031] Among them, a tide represents the acceleration caused by tidal effect, k2 represents the earth tidal stiffness coefficient, M m represents the mass of the moon, r m represents the distance from the moon to the earth,

[0032] Define the lunar gravitational perturbation, the acceleration formula of the lunar gravity is:

[0033] in,

[0034] a moon is the acceleration caused by the moon's gravity, M m represents the mass of the moon, r m represents the distance from the satellite to the moon, r·r m represents the dot product of the satellite and moon position vectors,

[0035] Define the total perturbation acceleration: a total =a grav +a J2J6 +a SRP +a tide +a moon , where a total is the total perturbation acceleration.

[0036] Furthermore, in step S2, the orbital perturbation and relative motion are combined in the following manner:

[0037] Assume that the orbits of the two satellites are represented by position vectors r1(t) and r2(t), respectively, and the relative position vector of the two satellites is Δr(t), that is, Δr(t)=r2(t)-r1(t), where r1(t) represents the instantaneous position vector of satellite 1 relative to the center of the earth, r2(t) represents the instantaneous position vector of satellite 2 relative to the center of the earth, and Δr(t) represents the instantaneous relative position between the two satellites.

[0038] The relative velocity vector Δv(t) of the two satellites is expressed as the difference in the speed of the two satellites,

[0039] Δv(t)=v2(t)-v1(t), where v1(t) is the instantaneous velocity vector of satellite 1, v2(t) is the instantaneous velocity vector of satellite 2, and Δv(t) represents the instantaneous relative velocity between the two satellites.

[0040] The orbital perturbation model in step S1 is introduced. Based on the perturbation effect, the orbital accelerations of the two satellites are defined as a1(t) and a2(t), respectively. The relative acceleration is expressed as:

[0041] Δa(t)=a2(t)-a1(t), where a1(t) represents the acceleration of satellite 1 under perturbation, a2(t) represents the acceleration of satellite 2 under perturbation, and Δa(t) represents the relative acceleration between the two satellites, based on various perturbation terms;

[0042] The relative position and velocity changes of the two satellites are expressed as:

[0043] in, It represents the second-order derivative of the relative position of the two satellites, that is, the acceleration of the relative position over time, and Δa(t) is the relative acceleration of the two satellites.

[0044] Furthermore, in step S2, the orbital perturbation and relative motion combination method further includes:

[0045] The perturbation term of the relative acceleration is calculated by combining the orbital perturbations of the two satellites:

[0046] Among them, J n represents the nth order term of the Earth's non-spherical gravitational field, r1 and r2 are the distances from the two satellites to the Earth's center, and P n (sinφ1),P n (sinφ2) are the Legendre polynomials of satellite 1 and satellite 2, respectively, φ1 and φ2 are the geocentric latitudes of the two satellites;

[0047] Define the relative position Δr0 and relative velocity Δv0 of the satellite at the initial time t0, and the time evolution of the relative position is expressed as:

[0048] Among them, Δr(t) represents the relative position at time t, Δr0 represents the relative position at the initial time, Δv0 represents the relative velocity at the initial time, and Δa(t) represents the relative acceleration evolving over time.

[0049] The time evolution of the relative velocity is expressed as:

[0050] Δv(t)=Δv0+Δa(t)·t, where Δv(t) represents the relative velocity at time t. Combined with the relative acceleration Δa(t), an error prediction model is established.

[0051] Furthermore, in step S3, the Doppler effect calculation includes:

[0052] Using relative velocity to predict the frequency offset of communication signals,

[0053] Establish a Doppler effect correction model for beam pointing angle deviation;

[0054] Since the Doppler effect will cause the communication frequency to shift, the frequency change will affect the beam pointing accuracy of the communication antenna. Therefore, a coupling model of frequency offset and beam pointing angle deviation is constructed to predict the impact of the Doppler effect on the pointing angle in real time, dynamically calculate the angle error, and generate preliminary beam correction instructions.

[0055] Furthermore, in step S3, the Doppler effect and the pointing angle error correction method is:

[0056] The frequency offset Δf(t) is expressed using the Doppler frequency shift formula:

[0057] Where Δf(t) represents the Doppler frequency shift at time t, f0 represents the carrier frequency of the transmitted signal, and v rel (t) represents the relative radial velocity between the two satellites, that is, the velocity difference between the two satellites along the signal propagation direction at time t, and c represents the speed of light;

[0058] Calculate the relative radial velocity v rel (t), assuming that the instantaneous position vectors of the two satellites are r1(t) and r2(t), the relative position vector is Δr(t) = r2(t) - r1(t), and the relative radial velocity v rel (t) is expressed as the projection of the relative velocity of the two satellites in the direction of their relative positions:

[0059] Where v1(t) represents the velocity vector of satellite 1 at time t, v2(t) represents the velocity vector of satellite 2 at time t, Δr(t) represents the instantaneous relative position vector between the two satellites, |Δr(t)| represents the modulus of the relative position vector Δr(t), that is, the distance between the two satellites, and v rel (t) represents the relative velocity of the two satellites in the relative radial direction at time t.

[0060] Furthermore, in step S3, the Doppler effect and pointing angle error correction method further includes:

[0061] Incorporating perturbations:

[0062] Among them, a J2J6，1 (t) and a J2J6，2 (t) are the accelerations of satellite 1 and satellite 2 caused by the perturbation of the Earth’s non-spherical gravitational field (items J2 to J6), a SRP，1 (t) and a SRP，2 (t) are the accelerations of satellite 1 and satellite 2 due to solar radiation pressure;

[0063] Assuming that the beam width of the communication signal is θ(t), the beam pointing angle error Δθ(t) caused by the Doppler frequency shift is:

[0064] Where Δθ(t) represents the beam pointing angle error at time t, Δf(t) represents the Doppler frequency shift at time t, and f0 represents the carrier frequency of the transmitted signal. represents the wavelength of the signal, c is the speed of light, and D represents the aperture of the satellite antenna;

[0065] Based on the coupling relationship between Doppler frequency shift and beam pointing angle, the beam pointing error caused by frequency offset is quantified. As the relative speed changes, the beam pointing will have an angular deviation, which is corrected here.

[0066] Based on the Doppler frequency shift and beam angle deviation, the beam pointing angle θ is dynamically adjusted corrected (t) Compensation for deviation caused by Doppler effect:

[0067] θ corrected (t)=θ0(t)-Δθ(t), where, θ corrected (t) represents the corrected beam pointing angle at time t, θ0(t) represents the uncorrected beam pointing angle, and Δθ(t) represents the beam pointing angle error caused by the Doppler effect;

[0068] The correction model dynamically adjusts the pointing angle of the beam to offset the angle deviation caused by relative velocity changes and the Doppler effect, thereby maintaining the stability of the communication link and the signal quality.

[0069] Furthermore, the input of the filter in step S4 includes,

[0070] Satellite attitude sensor data,

[0071] Relative speed sensor data,

[0072] Orbit perturbation error and frequency offset data.

[0073] Furthermore, in step S4, the adaptive filtering dynamic correction method is:

[0074] Define the system state vector x t , including relative position, relative velocity and beam pointing angle status:

[0075] Among them, Δr(t) represents the relative position vector of the two satellites, Δv(t) represents the relative velocity vector of the two satellites, and θ(t) represents the pointing angle of the beam;

[0076] Use particle filter to filter the system state x t Make real-time estimates, predictions, updates and continuous adjustments to the beam pointing angle;

[0077] The prediction stage predicts the state at the next moment, and the state transfer equation is:

[0078] x t =f(x t-1 )+w t , where f(x t-1 ) represents the state transition function, which is the state x at the previous moment. t-1 Evolved to the current state at time t, w t represents the process noise,

[0079] Make predictions for multiple particles and get different possible states That is, the state represented by the i-th particle:

[0080]

[0081] Δv(t)=Δv(t-1)+a total (t-1)·Δt, where Δr(t) represents the relative position vector at the current time t, Δv(t) represents the relative velocity vector at the current time t, and a total (t-1) represents the relative acceleration of the two satellites at time t-1, Δt represents the time step,

[0082] Update the state of each particle to obtain the predicted state at the current time t In the update phase, the particle filter combines the observed data z t Each particle is weighted and its weight is updated. The observation data includes the satellite's attitude, relative speed, and angle deviation. The weight update formula is:

[0083] in, represents the weight of the i-th particle at time t, represents the weight of the i-th particle at time t-1, Represents the state of a given particle The observed likelihood function represents the observed data z t With particle state The degree of matching,

[0084] Use Gaussian distribution to describe the likelihood function

[0085] in, Represents the observation model, representing the particle state The predicted observed value, z t represents the actual observation value at the current moment, σ represents the standard deviation of the observation noise,

[0086] Particle Weight Adjust according to the match between the particle state and the actual observed value,

[0087] After each filter update, the particle filter uses weighted average to estimate the state of the system, and the final estimate is is the weighted sum of all particles:

[0088] in, represents the system state estimation at the current moment, including relative position, relative velocity and beam pointing angle, N represents the total number of particles, represents the weight of the i-th particle, represents the state vector of the i-th particle;

[0089] According to the final state estimate The beam pointing angle in The actual pointing direction of the beam is corrected in real time to compensate for errors caused by factors such as the Doppler effect and orbital perturbations.

[0090] The beneficial effects of the present invention are:

[0091] The present invention introduces high-order perturbation modeling, solar radiation pressure, earth tidal effects and lunar gravitational perturbation terms to effectively simulate the orbital changes of satellites caused by long-term external gravitational disturbances, reduce the accumulation effect of errors, and effectively reduce the pointing errors caused by simplified perturbations in long-term or high-orbit satellite communications.

[0092] The present invention combines the relative motion model of two satellites in different orbits, integrates the orbit change of a single satellite, and incorporates the change of relative speed into the calculation. It can dynamically adjust the beam pointing when the relative position and speed of the satellites change, thereby reducing the error caused by relative motion.

[0093] The present invention constructs a coupling model of frequency offset and beam pointing angle deviation, predicts and corrects the influence of Doppler effect on beam pointing in real time, dynamically adjusts beam pointing through coupling correction, keeps communication signals on the optimal transmission path, and avoids frequency offset.

[0094] The present invention introduces a particle filter, combines actual observations to estimate and correct the system state in real time, continuously updates the beam pointing state by weighted averaging, adapts to the beam error caused by orbital perturbations and relative velocity changes in real time, and greatly improves the stability of the communication link. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0096] Figure 1 The present invention is a flow chart of a method for calculating beam pointing errors of inter-satellite communication links in different orbits. DETAILED DESCRIPTION

[0097] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the accompanying drawings.

[0098] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0099] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive with other embodiments.

[0100] Example 1, reference Figure 1 This embodiment provides a method for calculating beam pointing errors of inter-satellite communication links in different orbits, comprising the following steps:

[0101] Step S1, orbital perturbation high-order modeling,

[0102] Establish an orbital perturbation model including multiple perturbation factors;

[0103] The perturbation terms in step S1 include,

[0104] The Earth's non-spherical gravitational field, higher-order terms J2 to J6,

[0105] Solar radiation pressure,

[0106] Tidal effects,

[0107] and external perturbations such as the moon's gravity.

[0108] The high-order modeling method of orbital perturbations is:

[0109] Define satellite acceleration:

[0110] Among them, a grav represents the acceleration caused by the earth's gravity, G represents the gravitational constant, M represents the mass of the earth, and r represents the distance from the satellite to the center of the earth.

[0111] Introducing the non-spherical perturbation of the earth, items J2 to J6:

[0112] Among them, a J2J6 represents the non-spherical perturbation acceleration of the Earth, J n represents the nth order normalized coefficient of the Earth's gravitational field, R e represents the average radius of the Earth, P n (sinφ) is the Legendre polynomial, φ represents the satellite's geocentric latitude,

[0113] Define the perturbation of solar radiation pressure, the acceleration of solar radiation pressure is:

[0114] Among them, a SRP represents the acceleration of solar radiation pressure, P SR represents the solar radiation pressure constant per unit area, A represents the satellite light receiving area, Cr represents the reflection coefficient, which characterizes the satellite's ability to reflect solar radiation, m represents the satellite's mass,

[0115] Define the earth's tidal effect perturbation, and the tidal effect acceleration expression is:

[0116] Among them, a tide represents the acceleration caused by tidal effect, k2 represents the earth tidal stiffness coefficient, M m represents the mass of the moon, r m represents the distance from the moon to the earth,

[0117] Define the lunar gravitational perturbation, the acceleration formula of the lunar gravity is:

[0118] in,

[0119] a moon is the acceleration caused by the moon's gravity, M m represents the mass of the moon, r m represents the distance from the satellite to the moon, r·r m represents the dot product of the satellite and moon position vectors,

[0120] Define the total perturbation acceleration: a total =a grav +a J2J6 +a SR P+a tide +a moon , where a total is the total perturbation acceleration;

[0121] Specifically, the introduction of high-order orbital perturbation models, Doppler effect correction and adaptive filters can greatly improve the stability and accuracy of inter-satellite communications, effectively deal with the long-term cumulative errors caused by orbital perturbations, and significantly improve the accuracy of communication links.

[0122] Step S2, orbital perturbation combined with relative motion,

[0123] Based on the orbit perturbation model of step S1, a relative motion model between two satellites in different orbits is established, and an error prediction model evolving over time is derived;

[0124] The model not only considers the impact of orbital perturbations on a single satellite, but also takes into account the impact of orbital perturbations on the relative velocity changes of the two satellites. It combines orbital perturbations with relative motion to form an error prediction model that evolves over time, and predicts the relative position deviation and velocity changes of the two satellites under orbital perturbations.

[0125] In step S2, the orbital perturbation and relative motion are combined in the following manner:

[0126] Assume that the orbits of the two satellites are represented by position vectors r1(t) and r2(t), respectively, and the relative position vector of the two satellites is Δr(t), that is, Δr(t)=r2(t)-r1(t), where r1(t) represents the instantaneous position vector of satellite 1 relative to the center of the earth, r2(t) represents the instantaneous position vector of satellite 2 relative to the center of the earth, and Δr(t) represents the instantaneous relative position between the two satellites.

[0127] The relative velocity vector Δv(t) of the two satellites is expressed as the difference in the speed of the two satellites,

[0128] Δv(t)=v2(t)-v1(t), where v1(t) is the instantaneous velocity vector of satellite 1, v2(t) is the instantaneous velocity vector of satellite 2, and Δv(t) represents the instantaneous relative velocity between the two satellites.

[0129] The orbital perturbation model in step S1 is introduced. Based on the perturbation effect, the orbital accelerations of the two satellites are defined as a1(t) and a2(t), respectively. The relative acceleration is expressed as:

[0130] Δa(t)=a2(t)-a1(t), where a1(t) represents the acceleration of satellite 1 under perturbation, a2(t) represents the acceleration of satellite 2 under perturbation, and Δa(t) represents the relative acceleration between the two satellites, based on various perturbation terms;

[0131] The relative position and velocity changes of the two satellites are expressed as:

[0132] in, It represents the second-order derivative of the relative position of the two satellites, that is, the acceleration of the relative position over time, Δa(t) is the relative acceleration of the two satellites;

[0133] In step S2, the orbital perturbation and relative motion combination method further includes:

[0134] The perturbation term of the relative acceleration is calculated by combining the orbital perturbations of the two satellites:

[0135] Among them, J n represents the nth order term of the Earth's non-spherical gravitational field, r1 and r2 are the distances from the two satellites to the Earth's center, and P n (sinφ1),P n (sinφ2) are the Legendre polynomials of satellite 1 and satellite 2, respectively, φ1 and φ2 are the geocentric latitudes of the two satellites;

[0136] Define the relative position Δr0 and relative velocity Δv0 of the satellite at the initial time t0, and the time evolution of the relative position is expressed as:

[0137] Among them, Δr(t) represents the relative position at time t, Δr0 represents the relative position at the initial time, Δv0 represents the relative velocity at the initial time, and Δa(t) represents the relative acceleration evolving over time.

[0138] The time evolution of the relative velocity is expressed as:

[0139] Δv(t)=Δv0+Δa(t)·t, where Δv(t) represents the relative velocity at time t, and combined with the relative acceleration Δa(t), an error prediction model is established;

[0140] In addition, due to the differences in orbital altitude and orbital type, the relative speed of satellites in different orbits changes greatly during the orbital period. This relative speed change will produce the Doppler effect, affecting the frequency of the communication signal. At the same time, there is a coupling relationship between the frequency offset of the signal and the angle deviation of the beam pointing. In a high dynamic environment, ignoring the Doppler effect may cause an angle error in the beam pointing.

[0141] Traditional Doppler effect processing relies on real-time monitoring of Doppler frequency offset and frequency compensation mechanism, using the frequency tuning system of the ground station or the satellite itself to correct the frequency offset of the communication link. At the same time, for the relative speed change between satellites, the traditional method assumes that it has little effect on beam pointing, and often ignores the coupling effect of the Doppler effect on pointing accuracy.

[0142] Traditional solutions mostly focus on frequency compensation and ignore the impact of Doppler frequency shift on the beam pointing angle. When the relative speed is large, the actual pointing of the beam may deviate from the expected direction. In certain specific relative orbital phases of off-orbit satellites, the speed changes rapidly. Traditional frequency correction methods cannot quickly adapt to the error changes in this high-dynamic environment, resulting in a decrease in the signal quality of the communication link. For this reason, the present invention introduces the Doppler effect and pointing angle error correction for optimization.

[0143] Step S3, Doppler effect and pointing angle error correction,

[0144] Based on the relative motion model of step S2, the Doppler effect is calculated in combination with the relative velocity change;

[0145] In step S3, the Doppler effect calculation includes:

[0146] Using relative velocity to predict the frequency offset of communication signals,

[0147] Establish a Doppler effect correction model for beam pointing angle deviation;

[0148] Since the Doppler effect will cause the communication frequency to shift, the change in frequency will affect the beam pointing accuracy of the communication antenna. Therefore, a coupling model of frequency shift and beam pointing angle deviation is constructed to predict the impact of the Doppler effect on the pointing angle in real time, dynamically calculate the angle error, and generate preliminary beam correction instructions.

[0149] In step S3, the Doppler effect and pointing angle error correction method is:

[0150] The frequency offset Δf(t) is expressed using the Doppler frequency shift formula:

[0151] Where Δf(t) represents the Doppler frequency shift at time t, f0 represents the carrier frequency of the transmitted signal, and v rel (t) represents the relative radial velocity between the two satellites, that is, the velocity difference between the two satellites along the signal propagation direction at time t, and c represents the speed of light;

[0152] Calculate the relative radial velocity v rel (t), assuming that the instantaneous position vectors of the two satellites are r1(t) and r2(t), the relative position vector is Δr(t) = r2(t) - r1(t), and the relative radial velocity v rel (t) is expressed as the projection of the relative velocity of the two satellites in the direction of their relative positions:

[0153] Where v1(t) represents the velocity vector of satellite 1 at time t, v2(t) represents the velocity vector of satellite 2 at time t, Δr(t) represents the instantaneous relative position vector between the two satellites, |Δr(t)| represents the modulus of the relative position vector Δr(t), that is, the distance between the two satellites, and v rel (t) represents the relative speed of the two satellites in the relative radial direction at time t,

[0154] Incorporating perturbations:

[0155] Among them, a J2J6，1 (t) and a J2J6，2 (t) are the accelerations of satellite 1 and satellite 2 caused by the perturbation of the Earth’s non-spherical gravitational field (items J2 to J6), a SRP，1 (t) and a SRP，2 (t) are the accelerations of satellite 1 and satellite 2 due to solar radiation pressure;

[0156] Assuming that the beam width of the communication signal is θ(t), the beam pointing angle error Δθ(t) caused by the Doppler frequency shift is:

[0157] Where Δθ(t) represents the beam pointing angle error at time t, Δf(t) represents the Doppler frequency shift at time t, and f0 represents the carrier frequency of the transmitted signal. represents the wavelength of the signal, c is the speed of light, and D represents the aperture of the satellite antenna;

[0158] Based on the coupling relationship between Doppler frequency shift and beam pointing angle, the beam pointing error caused by frequency offset is quantified. As the relative speed changes, the beam pointing will have an angular deviation, which is corrected here.

[0159] Based on the Doppler frequency shift and beam angle deviation, the beam pointing angle θ is dynamically adjusted corrected (t) Compensation for deviation caused by Doppler effect:

[0160] θ corrected (t)=θ0(t)-Δθ(t), where, θ corrected (t) represents the corrected beam pointing angle at time t, θ0(t) represents the uncorrected beam pointing angle, and Δθ(t) represents the beam pointing angle error caused by the Doppler effect;

[0161] The correction model dynamically adjusts the pointing angle of the beam to offset the angle deviation caused by the relative speed change and the Doppler effect, thereby maintaining the stability of the communication link and the signal quality.

[0162] Specifically, combined with the satellite relative motion model, the coupling influence of the Doppler effect on the beam pointing angle is introduced into the calculation, the beam pointing of the communication link is dynamically adjusted, and the beam pointing deviation caused by the relative speed change is compensated in real time to ensure the directionality and intensity of signal transmission. The beam accuracy is greatly improved, and the risk of communication interruption can be significantly reduced in the orbital segments where the relative speed between satellites is large.

[0163] Step S4, adaptive filtering dynamic correction,

[0164] Adaptive filtering technology is introduced for dynamic adjustment. Based on the error prediction model in step S2 and the angle deviation correction model in step S3, a particle filter is used to correct the beam pointing in real time.

[0165] The input of the filter in step S4 includes,

[0166] Satellite attitude sensor data,

[0167] Relative speed sensor data,

[0168] Orbit perturbation error and frequency offset data,

[0169] The adaptive filtering dynamic correction method is:

[0170] Define the system state vector x t , including relative position, relative velocity and beam pointing angle status:

[0171] Among them, Δr(t) represents the relative position vector of the two satellites, Δv(t) represents the relative velocity vector of the two satellites, and θ(t) represents the pointing angle of the beam;

[0172] Use particle filter to filter the system state x t Make real-time estimates, predictions, updates and continuous adjustments to the beam pointing angle;

[0173] The prediction stage predicts the state at the next moment, and the state transfer equation is:

[0174] x t =f(x t-1 )+w t , where f(x t-1 ) represents the state transition function, which is the state x at the previous moment. t-1 Evolved to the current state at time t, w t represents the process noise,

[0175] Make predictions for multiple particles and get different possible states That is, the state represented by the i-th particle:

[0176]

[0177] Δv(t)=Δv(t-1)+a total (t-1)·Δt, where Δr(t) represents the relative position vector at the current time t, Δv(t) represents the relative velocity vector at the current time t, and a total (t-1) represents the relative acceleration of the two satellites at time t-1, Δt represents the time step,

[0178] Update the state of each particle to obtain the predicted state at the current time t In the update phase, the particle filter combines the observed data z t Each particle is weighted and its weight is updated. The observation data includes the satellite's attitude, relative speed, and angle deviation. The weight update formula is:

[0179] in, represents the weight of the i-th particle at time t, represents the weight of the i-th particle at time t-1, Represents the state of a given particle The observed likelihood function represents the observed data z t With particle state The degree of matching,

[0180] Use Gaussian distribution to describe the likelihood function

[0181] in, Represents the observation model, representing the particle state The predicted observed value, z t represents the actual observation value at the current moment, σ represents the standard deviation of the observation noise,

[0182] Particle Weight Adjust according to the match between the particle state and the actual observed value,

[0183] After each filter update, the particle filter uses weighted average to estimate the state of the system, and the final estimate is is the weighted sum of all particles:

[0184] in, represents the system state estimation at the current moment, including relative position, relative velocity and beam pointing angle, N represents the total number of particles, represents the weight of the i-th particle, represents the state vector of the i-th particle;

[0185] According to the final state estimate The beam pointing angle in Make real-time corrections to the actual pointing direction of the beam to compensate for errors caused by factors such as the Doppler effect and orbital perturbations;

[0186] Specifically, adaptive filtering technology is introduced and particle filters are used to effectively deal with the influence of nonlinearity and noise. This filtering mechanism can not only respond to error changes in complex orbital environments in real time, but also estimate and correct errors in real time by combining observation data.

[0187] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for calculating beam pointing error of inter-satellite communication link in different orbits, characterized by: include, Step S1, orbital perturbation high-order modeling, establishing an orbital perturbation model including multiple perturbation factors; Step S2, combining orbital perturbation with relative motion, establishing a relative motion model between two satellites in different orbits based on the orbital perturbation model of step S1, and deriving an error prediction model that evolves over time; Step S3, Doppler effect and pointing angle error correction, based on the relative motion model of step S2, the Doppler effect is calculated in combination with the relative speed change; Step S4, adaptive filtering dynamic correction, introduces adaptive filtering technology for dynamic adjustment, based on the error prediction model of step S2 and the angle deviation correction model of step S3, uses a particle filter to correct the beam pointing in real time.

2. The method for calculating beam pointing error of inter-satellite communication link in different orbit according to claim 1, characterized in that: The perturbation terms in step S1 include, The Earth's non-spherical gravitational field, higher-order terms J2 to J6, Solar radiation pressure, Tidal effects, And the external perturbations of the moon's gravity.

3. The method for calculating beam pointing error of inter-satellite communication link in different orbit according to claim 2, characterized in that: In step S1, the orbital perturbation high-order modeling method is: Define satellite acceleration: Among them, a grav represents the acceleration caused by the earth's gravity, G represents the gravitational constant, M represents the mass of the earth, and r represents the distance from the satellite to the center of the earth. Introducing the non-spherical perturbation of the earth, items J2 to J6: Among them, a J2J6 represents the non-spherical perturbation acceleration of the Earth, J n represents the nth order normalized coefficient of the Earth's gravitational field, R e represents the average radius of the Earth, P n (sinφ) is the Legendre polynomial, φ represents the satellite's geocentric latitude, Define the perturbation of solar radiation pressure, the acceleration of solar radiation pressure is: Among them, a SRP represents the acceleration of solar radiation pressure, P SR represents the solar radiation pressure constant per unit area, A represents the satellite light receiving area, C r represents the reflection coefficient, which characterizes the satellite's ability to reflect solar radiation, m represents the satellite's mass, Define the earth's tidal effect perturbation, and the tidal effect acceleration expression is: Among them, a tide represents the acceleration caused by tidal effect, k2 represents the earth tidal stiffness coefficient, M m represents the mass of the moon, r m represents the distance from the moon to the earth, Define the lunar gravitational perturbation, the acceleration formula of the lunar gravity is: in, a moon is the acceleration caused by the moon's gravity, M n represents the mass of the moon, r m is the distance from the satellite to the moon, r·r m represents the dot product of the satellite and moon position vectors, Define the total perturbation acceleration: a total =a grav +a J2J6 +a SRP +a tide +a moon , where a total is the total perturbation acceleration.

4. The method for calculating beam pointing error of inter-satellite communication link in different orbit according to claim 3, characterized in that: In step S2, the orbital perturbation and relative motion are combined in the following manner: Assume that the orbits of the two satellites are represented by position vectors r1(t) and r2(t), respectively, and the relative position vector of the two satellites is Δr(t), that is, Δr(t)=r2(t)-r1(t), where r1(t) represents the instantaneous position vector of satellite 1 relative to the center of the earth, r2(t) represents the instantaneous position vector of satellite 2 relative to the center of the earth, and Δr(t) represents the instantaneous relative position between the two satellites. The relative velocity vector Δv(t) of the two satellites is expressed as the difference in the speed of the two satellites, Δv(t)=v2(t)-v1(t), where v1(t) is the instantaneous velocity vector of satellite 1, v2(t) is the instantaneous velocity vector of satellite 2, and Δv(t) represents the instantaneous relative velocity between the two satellites. The orbital perturbation model in step S1 is introduced. Based on the perturbation effect, the orbital accelerations of the two satellites are defined as a1(t) and a2(t), respectively. The relative acceleration is expressed as: Δa(t)=a2(t)-a1(t), where a1(t) represents the acceleration of satellite 1 under perturbation, a2(t) represents the acceleration of satellite 2 under perturbation, and Δa(t) represents the relative acceleration between the two satellites, based on various perturbation terms; The relative position and velocity changes of the two satellites are expressed as: in, It represents the second-order derivative of the relative position of the two satellites, that is, the acceleration of the relative position over time, and Δa(t) is the relative acceleration of the two satellites.

5. The method for calculating beam pointing error of inter-satellite communication link in different orbit according to claim 4, characterized in that: In step S2, the orbital perturbation and relative motion combination method further includes: The perturbation term of the relative acceleration is calculated by combining the orbital perturbations of the two satellites: Among them, J n represents the nth order term of the Earth's non-spherical gravitational field, r1 and r2 are the distances from the two satellites to the Earth's center, and P n (sinφ1),P n (sinφ2) are the Legendre polynomials of satellite 1 and satellite 2, respectively, φ1 and φ2 are the geocentric latitudes of the two satellites; Define the relative position Δr0 and relative velocity Δv0 of the satellite at the initial time t0, and the time evolution of the relative position is expressed as: Among them, Δr(t) represents the relative position at time t, Δr0 represents the relative position at the initial time, Δv0 represents the relative velocity at the initial time, and Δa(t) represents the relative acceleration evolving over time. The time evolution of the relative velocity is expressed as: Δv(t)=Δv0+Δa(t)·t, where Δv(t) represents the relative velocity at time t. Combined with the relative acceleration Δa(t), an error prediction model is established.

6. The method for calculating beam pointing error of inter-satellite communication link in different orbit according to claim 5, characterized in that: In step S3, the Doppler effect calculation includes: Using relative velocity to predict the frequency offset of communication signals, A model for correcting beam pointing angle deviation due to Doppler effect is established.

7. The method for calculating beam pointing error of inter-satellite communication link in different orbit according to claim 6, characterized in that: In step S3, the Doppler effect and pointing angle error correction method is: The frequency offset Δf(t) is expressed using the Doppler frequency shift formula: Where Δf(t) represents the Doppler frequency shift at time t, f0 represents the carrier frequency of the transmitted signal, and v rel (t) represents the relative radial velocity between the two satellites, that is, the velocity difference between the two satellites along the signal propagation direction at time t, and c represents the speed of light; Calculate the relative radial velocity v rel (t), assuming that the instantaneous position vectors of the two satellites are r1(t) and r2(t), the relative position vector is Δr(t) = r2(t) - r1(t), and the relative radial velocity v rel (t) is expressed as the projection of the relative velocity of the two satellites in the direction of their relative positions: Where v1(t) represents the velocity vector of satellite 1 at time t, v2(t) represents the velocity vector of satellite 2 at time t, Δr(t) represents the instantaneous relative position vector between the two satellites, |Δr(t)| represents the modulus of the relative position vector Δr(t), that is, the distance between the two satellites, and v rel (t) represents the relative velocity of the two satellites in the relative radial direction at time t.

8. The method for calculating beam pointing error of inter-satellite communication link in different orbit according to claim 7, characterized in that: In step S3, the Doppler effect and pointing angle error correction method further includes: Incorporating perturbations: Among them, a J2J6,1 (t) and a J2J6,2 (t) are the accelerations of satellite 1 and satellite 2 caused by the perturbation of the non-spherical gravitational field of the Earth, a SRP,1 (t) and a SRP,2 (t) are the accelerations of satellite 1 and satellite 2 due to solar radiation pressure; Assuming that the beam width of the communication signal is θ(t), the beam pointing angle error Δθ(t) caused by the Doppler frequency shift is: Where Δθ(t) represents the beam pointing angle error at time t, Δf(t) represents the Doppler frequency shift at time t, and f0 represents the carrier frequency of the transmitted signal. represents the wavelength of the signal, c is the speed of light, and D represents the aperture of the satellite antenna; Based on the Doppler frequency shift and beam angle deviation, the beam pointing angle θ is dynamically adjusted corrected (t) Compensation for deviation caused by Doppler effect: θ corrected (t)=θ0(t)-Δθ(t), where, θ corrected (t) represents the corrected beam pointing angle at time t, θ0(t) represents the uncorrected beam pointing angle, and Δθ(t) represents the beam pointing angle error caused by the Doppler effect.

9. The method for calculating beam pointing error of inter-satellite communication link in different orbit according to claim 8, characterized in that: The input of the filter in step S4 includes, Satellite attitude sensor data, Relative speed sensor data, Orbit perturbation error and frequency offset data.

10. The method for calculating beam pointing error of inter-satellite communication link in different orbit according to claim 9, characterized in that: In step S4, the adaptive filtering dynamic correction method is: Define the system state vector x t , including relative position, relative velocity and beam pointing angle status: Among them, Δr(t) represents the relative position vector of the two satellites, Δv(t) represents the relative velocity vector of the two satellites, and θ(t) represents the pointing angle of the beam; Use particle filter to filter the system state x t Make real-time estimates, predictions, updates and continuous adjustments to the beam pointing angle; The prediction stage predicts the state at the next moment, and the state transfer equation is: x t =f(x t-1 )+w t , where f(x t-1 ) represents the state transition function, which is the state x at the previous moment. t-1 Evolved to the current state at time t, w t represents the process noise, Make predictions for multiple particles and get different possible states That is, the state represented by the i-th particle: Δv(t)=Δv(t-1)+a total (t-1)·Δt, where Δr(t) represents the relative position vector at the current time t, Δv(t) represents the relative velocity vector at the current time t, and a total (t-1) represents the relative acceleration of the two satellites at time t-1, Δt represents the time step, Update the state of each particle to obtain the predicted state at the current time t In the update phase, the particle filter combines the observed data z t Each particle is weighted and its weight is updated. The observation data includes the satellite's attitude, relative speed, and angle deviation. The weight update formula is: in, represents the weight of the i-th particle at time t, represents the weight of the i-th particle at time t-1, Represents the state of a given particle The observed likelihood function represents the observed data z t With particle state The degree of matching, Use Gaussian distribution to describe the likelihood function in, Represents the observation model, representing the particle state The predicted observed value, z t represents the actual observation value at the current moment, σ represents the standard deviation of the observation noise, Particle Weight Adjust according to the match between the particle state and the actual observed value, After each filter update, the particle filter uses weighted average to estimate the state of the system, and the final estimate is is the weighted sum of all particles: in, represents the system state estimation at the current moment, including relative position, relative velocity and beam pointing angle, N represents the total number of particles, represents the weight of the i-th particle, represents the state vector of the i-th particle; According to the final state estimate The beam pointing angle in The actual pointing direction of the beam is corrected in real time.

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