A method for calculating the beam pointing error of an inter-satellite communication link with different orbits

Abstract

The present invention discloses a method for calculating the beam pointing error of an inter-satellite communication link in different orbits, which relates to the field of communication technology. The present invention introduces high-order perturbation modeling, solar radiation pressure, earth tide effect and lunar gravitational perturbation terms to effectively simulate the orbital changes of satellites affected by external gravitational perturbations for a long time, reduce the accumulation effect of errors, and can effectively reduce the pointing error caused by simplified perturbations in the communication of long-time or high-orbit satellites. Combining the relative motion model of two satellites in different orbits, comprehensively considering the orbital changes of a single satellite, and incorporating the change of relative velocity into the calculation, it can dynamically adjust the beam pointing when the relative position and velocity of the satellites change, reduce the error caused by relative motion. At the same time, a coupling model between frequency offset and beam pointing angle deviation is constructed to predict and correct the influence of Doppler effect on beam pointing in real time. Through coupling correction, the beam pointing is dynamically adjusted to keep the communication signal on the optimal transmission path and avoid frequency offset.

Description

Technical Field

[0001] The present invention relates to the field of communication technologies, and particularly to a method for calculating the beam pointing error of an inter-orbit inter-satellite communication link. Background Art

[0002] In an inter-orbit inter-satellite communication link, the beam pointing error directly affects the quality and stability of the communication link. With the increase in the distance between satellites, the increase in orbital differences, and the change in relative velocity, the precise alignment of the beam becomes extremely challenging.

[0003] Inter-orbit satellites are affected by various orbital perturbation factors, such as the non-spherical gravitational field of the Earth, solar radiation pressure, lunar gravity, and Earth tide effect. Due to the cumulative effect of orbital perturbations, the relative positions of inter-orbit satellites will deviate over time, and these deviations will directly affect the alignment accuracy of the beam. Most traditional methods for calculating the beam pointing error are based on simplified orbital models, assuming that the orbital parameters of the satellites are stable, or only considering low-order perturbation effects, such as the J2-term gravitational field. Under this simplified treatment, the pointing error is compensated through static or semi-dynamic correction, relying on pre-calculated orbital data or adjusted based on short-term orbital predictions;

[0004] The orbital perturbation effect is dynamic and accumulates over a long term. The simplified perturbation model cannot capture the long-term effects of complex perturbation factors, resulting in the gradual increase of the beam pointing error in a long-term communication link. In addition, traditional solutions mostly rely on pre-calculated or simplified predicted orbital parameters and cannot respond in real time to the subtle position changes brought about by orbital perturbations, resulting in insufficient real-time correction ability. In a long-distance orbital environment, high-order perturbation effects, such as J4, J6 terms, and solar wind, have a greater impact on the satellite position, and it is difficult for traditional methods to effectively compensate for these factors. Therefore, there is an urgent need for a method for calculating the beam pointing error of an inter-orbit inter-satellite communication link 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 method for calculating the beam pointing error of an inter-orbit inter-satellite communication link to solve the problem that the simplified model adopted for dealing with orbital perturbation errors is difficult to cope with the influence of long-term accumulation and high-order perturbations.

[0007] To solve the above technical problems, the present invention provides the following technical solutions:

[0008] The present invention provides a method for calculating the beam pointing error of an inter-orbit inter-satellite communication link, which includes,

[0009] Step S1, high-order modeling of orbital perturbations,

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

[0011] Step S2, combining orbital perturbation and relative motion

[0012] Based on the orbital perturbation model in Step S1, establish a relative motion model between two satellites in different orbits, and derive an error prediction model that evolves over time;

[0013] This model not only synthesizes the influence of orbital perturbation on a single satellite, but also incorporates the influence of orbital perturbation on the relative velocity change of the two satellites into the calculation, combines orbital perturbation and relative motion, forms an error prediction model that evolves over time, and predicts the relative position deviation and velocity change of the two satellites under orbital perturbation;

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

[0015] Based on the relative motion model in Step S2, calculate the Doppler effect in combination with the relative velocity change;

[0016] Step S4, adaptive filtering dynamic correction

[0017] Introduce adaptive filtering technology for dynamic adjustment. Based on the error prediction model in Step S2 and the angle deviation correction model in Step S3, use a particle filter to correct the beam pointing in real time.

[0018] Furthermore, the perturbation factors in Step S1 include

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

[0020] Solar radiation pressure

[0021] Tidal effect

[0022] And external perturbation factors of lunar gravity

[0023] Furthermore, in Step S1, the high-order modeling method of orbital perturbation is as follows:

[0024] Define the satellite acceleration:

[0025] where 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 Earth's center

[0026] Introduce the non-spherical perturbation of the Earth, J2 to J6 terms:

[0027] where 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 edenotes the average radius of the Earth, P n (sinφ) is the Legendre polynomial, φ represents the geocentric latitude of the satellite,

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

[0029] where, a SRP represents the acceleration of solar radiation pressure, P SR represents the solar radiation pressure constant per unit area, A represents the light-receiving area of the satellite, C r represents the reflection coefficient, characterizing the reflection ability of the satellite to solar radiation, m represents the mass of the satellite,

[0030] Define the perturbation of the Earth tide effect. The expression of the tide effect acceleration is:

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

[0032] Define the perturbation of lunar gravity. The acceleration formula of lunar gravity is:

[0033] where,

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

[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 combination method of orbit perturbation and relative motion is:

[0037] Suppose the orbits of two satellites in different orbits are represented by the 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 earth's center, r2(t) represents the instantaneous position vector of satellite 2 relative to the earth's center, 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 velocities 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] Introduce the orbit perturbation model in step S1. Based on the perturbation effect, define the orbit accelerations of the two satellites as a1(t) and a2(t) respectively, and 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 factors.

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

[0043] Among them, represents the second derivative of the relative position of the two satellites, that is, the acceleration of the relative position with respect to time, and Δa(t) is the relative acceleration of the two satellites.

[0044] Furthermore, in step S2, the combination method of orbit perturbation and relative motion also includes:

[0045] Expand by combining the orbit perturbations of the two satellites to calculate the perturbation factors of the relative acceleration:

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

[0047] Define the relative position Δr0 and relative velocity Δv0 of the satellites 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 moment, Δv0 represents the relative velocity at the initial moment, and Δa(t) represents the relative acceleration evolving with 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. Combining the relative acceleration Δa(t), an error prediction model is established.

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

[0052] predicting the frequency offset of the communication signal using the relative velocity

[0053] establishing a correction model for the beam pointing angle deviation caused by the Doppler effect;

[0054] Since the Doppler effect will cause the offset of the communication frequency, and the change in frequency 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 influence of the Doppler effect on the pointing angle in real time, dynamically calculate the angle error, and generate a preliminary beam correction instruction.

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

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

[0057] Among them, Δf(t) represents the Doppler frequency shift at time t, f0 represents the carrier frequency of the transmitted signal, v rel (t) represents the relative radial velocity between 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) respectively, 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 relative position direction:

[0059] Among them, 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 also includes:

[0061] Including perturbation factors:

[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 (J2 to J6 terms) respectively, and a SRP,1 (t) and a SRP,2 (t) are the accelerations of satellite 1 and satellite 2 caused by solar radiation pressure respectively;

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

[0064] Among them, Δθ(t) represents the beam pointing angle error at time t, Δf(t) represents the Doppler frequency shift at time t, 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 the Doppler frequency shift and the beam pointing angle, quantify the beam pointing error caused by frequency offset. As the relative velocity changes, the beam pointing will have an angular deviation, and it is corrected here;

[0066] Based on the Doppler frequency shift and the beam angle deviation, dynamically adjust the beam pointing angle θ corrected (t) to compensate for the deviation caused by the 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 calibration model cancels the angular deviation caused by the relative velocity change and Doppler effect by dynamically adjusting the pointing angle of the beam, and maintains 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 velocity sensor data

[0072] orbital 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] where 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 a particle filter to perform real-time estimation of the system state x t and continuously adjust the beam pointing angle through prediction and update;

[0077] In the prediction stage, predict the state at the next moment, and the state transition equation is:

[0078] x t = f(x t-1 ) + w t , where f(x t-1 ) represents the state transition function, evolving from the state x at the previous moment t-1 to the state at the current moment t, and w t represents the process noise,

[0079] Predict multiple particles to obtain 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 moment t, Δv(t) represents the relative velocity vector at the current moment t, a total (t - 1) represents the relative acceleration of the two satellites at the (t - 1)-th moment, and 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 observation data z t Weight each particle to update the weight of the particle. The observation data includes the attitude of the satellite, the relative velocity, and the angular deviation. The weight update formula is:

[0083] where, 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 observation likelihood function given the particle state and represents the matching degree between the observation data z t and the particle state ;

[0084] The likelihood function is described by a Gaussian distribution

[0085] where, represents the observation model, which represents the predicted observation value according to the particle state , z t represents the actual observation value at the current time, and σ represents the standard deviation of the observation noise,

[0086] The particle weight is adjusted according to the matching degree between the particle state and the actual observation value,

[0087] After each filtering update, the particle filter uses weighted averaging to estimate the state of the system. The final estimated value is the weighted sum of all particles:

[0088] where, represents the system state estimate at the current time, including the 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 beam pointing angle in the final state estimate the actual pointing of the beam is corrected in real time to compensate for errors caused by factors such as the Doppler effect and orbital perturbation.

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

[0091] The present invention introduces high-order perturbation modeling, solar radiation pressure, earth tide effect, and lunar gravitational perturbation factors, effectively simulates the orbital changes of satellites affected by external gravitational perturbations in the long term, reduces the cumulative effect of errors, and can effectively reduce the pointing errors caused by simplified perturbations in the communication of long-duration or high-orbit satellites.

[0092] The present invention combines the relative motion models of two non-coplanar satellites, comprehensively considers the orbital changes of a single satellite, incorporates the changes in relative velocity into the calculation, and can dynamically adjust the beam pointing when the relative position and velocity of the satellites change, reducing the errors caused by relative motion.

[0093] The present invention constructs a coupling model between frequency offset and beam pointing angle deviation, predicts and corrects in real time the influence of the Doppler effect on the beam pointing, dynamically adjusts the beam pointing through coupling correction, keeps the communication signal 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 through weighted averaging, and adapts in real time to the beam errors caused by orbital perturbations and changes in relative velocity, greatly improving the stability of the communication link. Description of the Drawings

[0095] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0096] Figure 1 It is a schematic flow chart of the method for calculating the beam pointing error of a non-coplanar inter-satellite communication link of the present invention. Detailed Embodiments

[0097] To make the above objects, features, and advantages of the present invention more obvious and understandable, the detailed embodiments of the present invention will be described in detail below with reference to the drawings in the specification.

[0098] Many specific details are set forth in the following description to facilitate a thorough understanding of the present invention. However, the present invention can also be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the connotation of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below.

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

[0100] Embodiment 1, referring to Figure 1 , this embodiment provides a method for calculating the beam pointing error of an inter-satellite communication link in different orbits, including the following steps:

[0101] Step S1, high-order modeling of orbit perturbation,

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

[0103] The perturbation factors in step S1 include,

[0104] The non-spherical gravitational field of the earth, high-order terms J2 to J6,

[0105] Solar radiation pressure,

[0106] Tidal effect,

[0107] And external perturbation factors such as lunar gravity,

[0108] The high-order modeling method of orbit perturbation is:

[0109] Define satellite acceleration:

[0110] Where, 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 earth's center,

[0111] Introduce the non-spherical perturbation of the earth, J2 to J6 terms:

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

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

[0114] Where, a SRP Represents the acceleration of solar radiation pressure, P SR Represents the solar radiation pressure constant per unit area, A represents the light-receiving area of the satellite, Cr denotes the reflection coefficient, which characterizes the reflection ability of the satellite to solar radiation. \(m\) represents the mass of the satellite,

[0115] Define the perturbation of the earth tide effect. The acceleration expression of the tide effect is:

[0116] where, \(a\) tide denotes the acceleration caused by the tide effect, \(k_2\) represents the earth tide stiffness coefficient, \(M\) m represents the mass of the moon, \(r\) m denotes the distance from the moon to the earth,

[0117] Define the perturbation of the lunar gravity. The acceleration formula of the lunar gravity is:

[0118] where,

[0119] \(a\) moon denotes the acceleration caused by the lunar gravity, \(M\) m represents the mass of the moon, denotes the distance from the satellite to the moon, denotes the dot product of the position vectors of the satellite and the moon,

[0120] 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;

[0121] Specifically, by introducing a high-order orbit perturbation model, Doppler effect correction, and an adaptive filter, the stability and accuracy of satellite-to-satellite communication are greatly improved, the long-term cumulative errors caused by orbit perturbation can be effectively addressed, and the accuracy of the communication link is significantly improved.

[0122] Step S2, combining orbit perturbation and relative motion,

[0123] Based on the orbit perturbation model in Step S1, establish a relative motion model between two satellites in different orbits, and derive an error prediction model that evolves over time;

[0124] This model not only comprehensively considers the influence of orbit perturbation on a single satellite, but also incorporates the influence of orbit perturbation on the relative velocity change of the two satellites into the calculation, combines orbit perturbation and relative motion, forms an error prediction model that evolves over time, and predicts the relative position deviation and velocity change of the two satellites under orbit perturbation;

[0125] In Step S2, the way of combining orbit perturbation and relative motion is:

[0126] Suppose the orbits of two non - coplanar 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 earth's center, r2(t) represents the instantaneous position vector of satellite 2 relative to the earth's center, 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 velocities 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] Introduce the orbit perturbation model in step S1. Based on the perturbation effect, define the orbit accelerations of the two satellites as a1(t) and a2(t) respectively, and 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 factors;

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

[0132] Among them, represents the second - order derivative of the relative position of the two satellites, that is, the acceleration of the relative position with respect to time, and Δa(t) is the relative acceleration of the two satellites;

[0133] In step S2, the combination method of orbit perturbation and relative motion also includes:

[0134] Expand by combining the orbit perturbations of the two satellites to calculate the perturbation factors of the relative acceleration:

[0135] Among them, J n represents the n - th 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 respectively, and P n (sinφ1), P n (sinφ2) are the Legendre polynomials of satellite 1 and satellite 2 respectively, and φ1 and φ2 are the geocentric latitudes of the two satellites;

[0136] Define the relative position Δr0 and relative velocity Δv0 of the satellites 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 moment, Δv0 represents the relative velocity at the initial moment, and Δa(t) represents the relative acceleration evolving with 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. Combining the relative acceleration Δa(t), an error prediction model is established.

[0140] In addition, due to the differences in orbital altitude and orbital type of non - co - orbital satellites, their relative velocities change significantly within an orbital period. This change in relative velocity will produce the Doppler effect, affecting the frequency of communication signals. At the same time, there is also a coupling relationship between the frequency offset of the signal and the angular deviation of the beam pointing. In a high - dynamic environment, the beam pointing that ignores the Doppler effect may have an angular error.

[0141] Traditional Doppler effect processing relies on the real - time monitoring of Doppler frequency offset and the frequency compensation mechanism. The ground station or the satellite's own frequency tuning system is used to correct the frequency offset of the communication link. At the same time, for the change in the relative velocity between satellites, the traditional method assumes that its impact on the beam pointing is small and often ignores the coupling effect of the Doppler effect on the 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 velocity is large, the actual pointing of the beam may deviate from the expected value. In some specific relative orbital stages of non - co - orbital satellites, the velocity changes rapidly, and the traditional frequency correction method cannot quickly adapt to the error changes in this high - dynamic environment, resulting in a decline in the signal quality of the communication link. Therefore, the present invention introduces the correction of the Doppler effect and the pointing angle error for optimization.

[0143] Step S3: Correction of the Doppler effect and the pointing angle error

[0144] Based on the relative motion model in step S2, the Doppler effect is calculated by combining the change in relative velocity.

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

[0146] Predict the frequency offset of the communication signal using the relative velocity.

[0147] Establish a correction model for the deviation of the beam pointing angle caused by the Doppler effect.

[0148] Due to the Doppler effect causing a shift in the communication frequency, 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 in real time the impact of the Doppler effect on the pointing angle, dynamically calculate the angle error, and generate a preliminary beam correction instruction.

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

[0150] The frequency shift 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, 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). Assume that the instantaneous position vectors of the two satellites are r1(t) and r2(t) respectively, and the relative position vector is Δr(t) = r2(t) - r1(t). The relative radial velocity v rel (t) is expressed as the projection of the relative velocity of the two satellites in the direction of the relative position:

[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 velocity of the two satellites in the relative radial direction at time t,

[0154] Incorporate perturbation factors:

[0155] where a J2J6,1 (t) and a J2J6,2 (t) are the accelerations of satellite 1 and satellite 2 respectively caused by the perturbation of the non-spherical gravitational field of the Earth (J2 to J6 terms), and a SRP,1 (t) and a SRP,2 (t) are the accelerations of satellite 1 and satellite 2 respectively caused by solar radiation pressure;

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

[0157] Among them, Δθ(t) represents the beam pointing angle error at time t, Δf(t) represents the Doppler frequency shift at time t, 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 the Doppler frequency shift and the beam pointing angle, the beam pointing error caused by the frequency offset is quantified. As the relative velocity changes, the beam pointing will have an angular deviation, and it is corrected here;

[0159] Based on the Doppler frequency shift and the beam angle deviation, the pointing angle θ of the beam is dynamically adjusted corrected (t) to compensate for the deviation caused by the 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 beam pointing angle before correction, and Δθ(t) represents the beam pointing angle error caused by the Doppler effect;

[0161] This correction model cancels the angular deviation caused by the relative velocity change and the Doppler effect by dynamically adjusting the beam pointing angle, maintaining the stability of the communication link and the signal quality;

[0162] Specifically, combined with the satellite relative motion model, the coupling effect 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 velocity change is compensated in real time, ensuring the directivity and intensity of signal transmission, greatly improving the beam accuracy, and significantly reducing the risk of communication interruption in the orbital segment where the relative velocity between satellites is large.

[0163] Step S4, adaptive filtering dynamic correction,

[0164] The 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, the particle filter is used to correct the beam pointing in real time;

[0165] The inputs of the filter in step S4 include,

[0166] Satellite attitude sensor data,

[0167] Relative velocity 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 states:

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

[0172] Adopt a particle filter to perform real-time estimation on the system state x t and continuously adjust the beam pointing angle through prediction and update;

[0173] In the prediction stage, predict the state at the next moment, and the state transition equation is:

[0174] x t = f(x t-1 ) + w t , where f(x t-1 ) represents the state transition function, evolving from the state x t-1 at the previous moment to the state at the current moment t, and w t represents the process noise,

[0175] Predict multiple particles to obtain 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 moment t, Δv(t) represents the relative velocity vector at the current moment t, a total (t - 1) represents the relative acceleration of the two satellites at the (t - 1)-th moment, and Δt represents the time step,

[0178] Update the state of each particle to obtain the predicted state at the current moment t In the update stage, the particle filter combines the observation data z t to weight each particle and update the weight of the particle. The observation data includes the attitude, relative velocity, and angle deviation of the satellite. The weight update formula is:

[0179] Among them, represents the weight of the i-th particle at the moment t, represents the weight of the i-th particle at the moment t - 1, represents the observation likelihood function given the particle state , representing the observation data z t and the particle state Degree of matching

[0180] The likelihood function is described using a Gaussian distribution

[0181] Wherein Represents the observation model, which represents the predicted observation value z according to the particle state The actual observation value at the current moment is represented by z, and σ represents the standard deviation of the observation noise t The particle weights

[0182] Are adjusted according to the matching degree between the particle state and the actual observation value

[0183] After each filtering update, the particle filter uses weighted averaging to estimate the state of the system. The final estimated value Is the weighted sum of all particles

[0184] Wherein Represents the system state estimate 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 beam pointing angle in the final state estimate The actual pointing of the beam is corrected in real time to compensate for errors caused by factors such as the Doppler effect and orbital perturbation

[0186] Specifically, an adaptive filtering technique is introduced, and a particle filter is used to effectively handle the influence of non-linearity and noise. This filtering mechanism can not only respond to the error changes in a complex orbital environment in real time but also estimate and correct the errors in real time by combining the observation data

[0187] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention​​

Claims

1. A method for calculating the beam pointing error of an inter-satellite communication link with different orbits, characterized in that: including, Step S1, high-order modeling of orbital perturbation, establishing an orbital perturbation model containing multiple perturbation factors; Step S2, combining orbital perturbation and relative motion, based on the orbital perturbation model in Step S1, establishing a relative motion model between two non-coplanar satellites, and deriving an error prediction model evolving with time; Step S3, Doppler effect and pointing angle error correction, based on the relative motion model in Step S2, calculating the Doppler effect in combination with the change of relative velocity, and establishing a correction model of the Doppler effect on the beam pointing angle deviation, specifically including: Assuming that the beam width of the communication signal is θ(t), calculating the beam pointing angle error Δθ(t) caused by the Doppler frequency shift: Among them, Δθ(t) represents the beam pointing angle error at time t, Δf(t) represents the Doppler frequency shift at time t, 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; Dynamically adjust the pointing angle θ of the beam based on the Doppler shift and beam angle deviation corrected (t) Compensate for the deviation caused by the 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 beam pointing angle without correction, and Δθ(t) represents the beam pointing angle error caused by the Doppler effect; Step S4, adaptive filtering dynamic correction, introducing adaptive filtering technology for dynamic adjustment, and based on the error prediction model in Step S2 and the angle deviation correction model in Step S3, using a particle filter to perform real-time correction of the beam pointing.

2. The method for calculating the beam pointing error of an inter-satellite communication link with different orbits according to claim 1, characterized in that, The perturbation factors in Step S1 include, the non-spherical gravitational field of the Earth, high-order terms J2 to J6, solar radiation pressure, tidal effect, and external perturbation factors of lunar gravity.

3. A method for calculating the beam pointing error of an inter-satellite communication link with different orbits according to claim 2, characterized in that, In Step S1, the high-order modeling method of orbital perturbation is: Defining the satellite acceleration: where 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, terms 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 mean radius of the Earth, P n (sinφ) is the Legendre polynomial, and φ represents the geocentric latitude of the satellite. Defining the perturbation of solar radiation pressure, and 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 light-receiving area of the satellite, C r represents the reflection coefficient, characterizing the reflection ability of the satellite to solar radiation, m represents the mass of the satellite Defining the perturbation of the Earth's tidal effect, and the expression of the tidal effect acceleration is: Among them, a tide represents the acceleration caused by the tidal effect, k2 represents the Earth's tidal stiffness coefficient, M m represents the mass of the moon, r m represents the distance from the moon to the Earth, Defining the perturbation of lunar gravity, and the acceleration formula of lunar gravity is: Among them, a moon represents the acceleration caused by the lunar gravity, M m represents the mass of the moon, represents the distance from the satellite to the moon, represents the dot product of the position vectors of the satellite and the moon, 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. A method for calculating the beam pointing error of an inter-satellite communication link with different orbits according to claim 3, characterized in that In Step S2, the combination method of orbital perturbation and relative motion is: Assuming that the orbits of two non-coplanar 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 geocenter, r2(t) represents the instantaneous position vector of satellite 2 relative to the geocenter, 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 velocities 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, Introducing the orbital perturbation model in Step S1, based on the perturbation effect, defining the orbital accelerations of the two satellites as a1(t) and a2(t) respectively, and 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 factors; The relative position and velocity changes of the two satellites are expressed as: Among them, represents the second derivative of the relative position of the two satellites, that is, the acceleration of the relative position with respect to time, and Δa(t) is the relative acceleration of the two satellites.

5. A method for calculating the beam pointing error of an inter-satellite communication link with different orbits according to claim 4, characterized in that, In Step S2, the combination method of orbital perturbation and relative motion also includes: Combining the orbital perturbations of the two satellites to expand the perturbation factors for calculating the relative acceleration: 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 respectively. 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; Defining the relative position Δr0 and relative velocity Δv0 of the satellites 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 with 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. Combining the relative acceleration Δa(t), an error prediction model is established.

6. A method for calculating the beam pointing error of an inter-satellite communication link with different orbits according to claim 5, characterized in that In step S3, the Doppler effect calculation includes predicting the frequency offset of the communication signal using the relative velocity, and establishing a correction model for the beam pointing angle deviation caused by the Doppler effect.

7. A method for calculating the beam pointing error of an inter-satellite communication link with different orbits according to claim 6, characterized in that, In step S3, the method for correcting the Doppler effect and the pointing angle error is: expressing the frequency offset Δf(t) using the Doppler frequency shift formula: Among them, 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 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). Assume that the instantaneous position vectors of the two satellites are r1(t) and r2(t) respectively, 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 the relative position: Among them, \(v_1(t)\) represents the velocity vector of satellite 1 at time \(t\), \(v_2(t)\) represents the velocity vector of satellite 2 at time \(t\), \(\Delta r(t)\) represents the instantaneous relative position vector between the two satellites, \(|\Delta r(t)|\) represents the magnitude of the relative position vector \(\Delta r(t)\), 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. A method for calculating the beam pointing error of an inter-satellite communication link with different orbits according to claim 7, characterized in that In step S3, the method for correcting the Doppler effect and the pointing angle error also includes: incorporating perturbation factors: where a J2J6,1 (t) and a J2J6,2 (t) are the accelerations of satellite 1 and satellite 2 respectively caused by the perturbation of the non-spherical gravitational field of the Earth, and a SRP,1 (t) and a SRP,2 (t) are the accelerations of satellite 1 and satellite 2 respectively caused by the solar radiation pressure.

9. A method for calculating the beam pointing error of an inter-satellite communication link with different orbits according to claim 8, characterized in that, The inputs to the filter in step S4 include satellite attitude sensor data, relative velocity sensor data, orbital perturbation error and frequency offset data.

10. A method for calculating the beam pointing error of an inter-satellite communication link with different orbits 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 states: where Δr(t) represents the relative position vector of two satellites, Δv(t) represents the relative velocity vector of two satellites, and θ(t) represents the pointing angle of the beam; Use a particle filter to estimate the system state x t in real time, and continuously adjust the beam pointing angle by prediction and update; predicting the state at the next moment in the prediction stage, and the state transition equation is: x t = f(x t-1 ) + w t , where f(x t-1 ) represents the state transition function, evolving from the state x at the previous moment t-1 to the state at the current moment t, and w t represents the process noise Predict multiple particles to obtain 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, a total (t - 1) represents the relative acceleration of the two satellites at the (t - 1)-th moment, and 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 observation data z t Weight each particle to update its weight. The observation data includes the attitude of the satellite, relative velocity, and angular deviation. The weight update formula is as follows: Wherein, 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 given particle state of the observation likelihood function, representing the observation data z t and the particle state matching degree, Use the Gaussian distribution to describe the likelihood function Among them, represents the observation model, representing the predicted observation value according to the particle state z t represents the actual observation value at the current moment, and σ represents the standard deviation of the observation noise. Particle weight Adjusted according to the matching degree between the particle state and the actual observation value After each filtering update, the particle filter uses weighted averaging to estimate the state of the system, and the final estimate is the weighted sum of all particles: Among them, 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 of the beam pointing angle perform real-time correction on the actual pointing of the beam.

Images