An on-orbit calibration method and system for an antenna phase center of a microwave ranging system

Abstract

The application discloses an on-orbit calibration method and system for an antenna phase center of a microwave ranging system, and relates to the technical field of microwave measurement. The method comprises the following steps: determining a maneuvering angle of a main satellite in a single direction according to a maneuvering period, a maneuvering initial offset angle and a maneuvering angle amplitude of the satellite; constructing an observation equation between two satellites, and performing differential processing on the observation equation; obtaining an estimated state of a main satellite phase center in a satellite center-of-mass system at a current moment according to the observation equation after the differential processing; and calibrating the estimated state of the main satellite phase center in the satellite center-of-mass system at the current moment by using the maneuvering angle of the satellite in the single direction at the current moment. The application can inhibit the influence of satellite attitude disturbance and improve test precision.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of microwave measurement technology, in particular to a method and system for on-orbit calibration of an antenna phase center of a microwave ranging system. BACKGROUND

[0002] In high-precision radio measurement systems represented by the micro-meter level precision ranging system (KBR) of a gravity measurement satellite and GNSS receivers, an antenna is the reference point for signal reception, transmission and measurement value output. If the phase center of the antenna changes during the measurement period of interest, the output ranging value will be erroneous. Accurate determination of the antenna phase center position is very important for online and offline calibration of the ranging value, ranging accuracy evaluation, optimal configuration of the ranging system, etc.

[0003] Due to errors in the installation of the antenna of the ground KBR system, the relative position between the phase center and the center of mass of the KBR system changes when the satellite operates in the space vacuum ionized environment after being launched, so on-orbit calibration of the phase center of the KBR system is of great significance.

[0004] The existing typical on-orbit phase center calibration method of the KBR antenna can be divided into three categories: one is to use satellite attitude maneuver to realize on-orbit calibration of the KBR phase center, taking the relationship between the distance and distance rate measured by the KBR system and the satellite rotation angle as the starting point and designing the satellite attitude maneuver law. The second method is to convert the on-orbit phase center calibration problem into the solution of the satellite attitude quaternion. The third method is to estimate the KBR phase center by using the Kalman filtering algorithm.

[0005] However, the least squares method is often used for phase estimation, and the optimal solution is often not obtained in engineering practice, and the calculation amount is huge. Moreover, the common noises in on-orbit phase estimation include K-band ranging system phase (distance) observation noise, satellite relative position determination error and attitude quaternion error, all of which will reduce the accuracy of the phase center determination.

[0006] The calibration purpose of the K-band system is to determine the phase center of each formation satellite microwave antenna. The attitude and orbit control system (AOCS) can adjust the attitude direction of two satellites to make the phase centers of the antennas of the two formation satellites and the centers of mass of the two satellites approximately on the same straight line, and allow post-processing of the phase measurement value to obtain the biased distance of the centers of mass of the two satellites. For the case of periodic oscillation maneuver for K-band system calibration, the required data includes K-band observation data, star sensor observation data and precise orbit determination (POD) data of GPS.

[0007] The observation data of the star sensor is directly used to determine the attitude orientation of the two satellites. The observation noise and the misalignment of the star sensor frame can bring certain errors to the determination of the phase center. The global positioning system receiver component on each satellite can accurately determine the position of the satellite. However, only the relative position is obtained in the distance observation, and the position error of a single satellite can be partially offset due to some similar disturbances. In addition, during the K-band calibration, the combination of magnetic torque and thruster torque is used to make the satellite oscillate around the bias angle.

[0008] Therefore, it is very urgent to invent a method for on-orbit calibration of the phase center of the KBR antenna to suppress the influence of attitude disturbance. SUMMARY

[0009] The purpose of the present application is to provide a method and system for on-orbit calibration of the phase center of a microwave ranging system antenna, which can suppress the influence of satellite attitude disturbance and improve test accuracy.

[0010] To achieve the above-mentioned purpose, the present application provides the following solutions:

[0011] A method for on-orbit calibration of the phase center of a microwave ranging system antenna, comprising:

[0012] determining the maneuver angle of the primary star in a single direction according to the maneuver period, the initial bias angle and the maneuver angle amplitude of the satellite;

[0013] constructing an observation equation between the two satellites, and performing Fourier transform and difference processing on the observation equation;

[0014] obtaining the estimated state of the phase center of the primary star in the satellite center-of-mass system at the current time according to the observation equation after difference processing;

[0015] calibrating the estimated state of the phase center of the primary star in the satellite center-of-mass system at the current time using the maneuver angle of the satellite in a single direction at the current time.

[0016] Optionally, the determination of the maneuver angle of the primary star in a single direction according to the maneuver period, the initial bias angle and the maneuver angle amplitude of the satellite specifically comprises:

[0017] determining the maneuver angle of the primary star in a single direction using the formula .

[0018] wherein θ(t) represents the single-direction maneuver angle of a single satellite at time t, T represents the maneuver period, θ0 represents the initial bias angle, and Θ represents the maneuver angle amplitude, Θ=kT 2 , k is a constant.

[0019] Optionally, the construction of the observation equation between the two satellites, and the Fourier transform and difference processing on the observation equation specifically comprises:

[0020] The observation equation between the two satellites is constructed by using the formula

[0021] The observation equation after Fourier transform is determined by using

[0022] The observation equation after difference processing is determined by using the formula

[0023] The convolution kernel of the observation equation after difference processing is determined

[0024] The vector is constructed according to the convolution kernel

[0025] The estimated state is determined according to the vector

[0026] wherein f(x) represents a fitting function of the on-orbit center-of-mass distance measurement, represents the center-of-mass spatial relative distance of the two satellites obtained by the differential GPS, q1 and q2 represent attitude quaternions of the two satellites, represents a matrix conversion corresponding to the attitude quaternion, respectively represent phase centers of the two satellites, Θ(·) represents a vectorized phase center, R br ,R nr respectively represent constant bias and random noise, Poly(n) represents a polynomial fitting term, δ1f(x), δ2f(x) and δ3f(x) respectively represent a first-order difference function, a second-order difference function and a third-order difference function of the fitting function of the on-orbit center-of-mass distance measurement, F[·] represents a Fourier transform operation, represents an n-th order differential of f(x), ω represents an angular rate in the frequency domain, x represents an estimated state, i is an imaginary unit, and is a square root value of -1.

[0027] Optionally, the vector is constructed according to the convolution kernel, and specifically includes:

[0028] The vector is constructed by using the formula y = [δ1f(x) δ2f(x) δ3f(x)] T

[0029] wherein y represents the vector.

[0030] Optionally, the estimated state is determined according to the vector, and specifically includes:

[0031] The estimated state is determined by using the formula

[0032] wherein H represents a first-order partial derivative matrix of f(x) with respect to the state, R represents a measurement random error, and t0 represents a time t0.

[0033] ​​​​​Optionally, the estimation state of the main star phase center in the satellite center of mass system at the current moment is calibrated by using the maneuvering angle of the satellite single direction at the current moment, and specifically includes:

[0034] The calibrated components of the main star phase center in the satellite center of mass system in the x direction and the z direction are determined by using the formula

[0035] Wherein, d 1x , d 1z represent the components of the main star phase center in the satellite center of mass system in the x direction and the z direction, a f , a 2f represent the maneuvering frequency Fourier component amplitude and the twice maneuvering frequency Fourier component amplitude, respectively.

[0036] An on-orbit calibration system for the antenna phase center of a microwave ranging system, comprising:

[0037] A maneuvering angle determination module is configured to determine the maneuvering angle of the main star single direction according to the maneuvering period, the maneuvering initial offset angle and the maneuvering angle amplitude of the satellite.

[0038] An observation equation construction and processing module is configured to construct the observation equation between two satellites and perform Fourier transform and difference processing on the observation equation.

[0039] An estimation state determination module is configured to obtain the estimation state of the main star phase center in the satellite center of mass system at the current moment according to the observation equation after difference processing.

[0040] A calibration module is configured to calibrate the estimation state of the main star phase center in the satellite center of mass system at the current moment by using the maneuvering angle of the satellite single direction at the current moment.

[0041] An on-orbit calibration system for the antenna phase center of a microwave ranging system, comprising at least one processor, at least one memory and computer program instructions stored in the memory, when the computer program instructions are executed by the processor, the method is realized.

[0042] A storage medium having computer program instructions stored thereon, when the computer program instructions are executed by a processor, the method is realized.

[0043] According to the specific embodiments of the present application, the following technical effects are provided:

[0044] ​The application provides an on-orbit calibration method and system for an antenna phase center of a microwave ranging system. BRIEF DESCRIPTION OF DRAWINGS

[0045] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort on the basis of these drawings.

[0046] Figure 1 The application provides an on-orbit calibration method and system for an antenna phase center of a microwave ranging system.

[0047] Figure 2 The application provides an on-orbit calibration method and system for an antenna phase center of a microwave ranging system.

[0048] Figure 3 The application provides an on-orbit calibration method and system for an antenna phase center of a microwave ranging system. DETAILED DESCRIPTION

[0049] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without any creative effort belong to the protection scope of the present application.

[0050] The application provides an on-orbit calibration method and system for an antenna phase center of a microwave ranging system, which can suppress the influence of satellite attitude disturbance and improve the test accuracy.

[0051] In order to make the above objectives, characteristics and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the drawings and specific embodiments.

[0052] As shown in Figure 1 , the method comprises the following steps:

[0053] S101, determining the maneuvering angle of the main satellite in a single direction according to the maneuvering period, the initial offset angle and the amplitude of the maneuvering angle; and maneuvering the two satellites in the pitch and yaw directions according to the characteristics of the KBR antenna. The maneuvering angle is selected comprehensively according to the on-orbit calibration requirement of the KBR antenna phase center, the signal-to-noise ratio of each satellite load data and the actual maneuvering capability of the satellite. The maneuvering angle realizes the distance change of the line-of-sight direction of the phase centers of the two antennas and senses the phase center information.

[0054] Specifically, the method comprises the following steps:

[0055] S101, determining the maneuvering angle of the main satellite in a single direction according to the maneuvering period, the initial offset angle and the amplitude of the maneuvering angle; and maneuvering the two satellites in the pitch and yaw directions according to the characteristics of the KBR antenna. The maneuvering angle is selected comprehensively according to the on-orbit calibration requirement of the KBR antenna phase center, the signal-to-noise ratio of each satellite load data and the actual maneuvering capability of the satellite. The maneuvering angle realizes the distance change of the line-of-sight direction of the phase centers of the two antennas and senses the phase center information.

[0056] Wherein, θ(t) represents the single-direction maneuvering angle of a single satellite at time t, T represents the maneuvering period, θ0 represents the initial offset angle, and Θ represents the amplitude of the maneuvering angle, Θ=kT 2 , k is a constant.

[0057] The selection of the periodic maneuvering drives the change of the antenna in the polarization angle direction, improves the sensitivity in this direction, and on the other hand, drives the distance change of the phase centers of the two satellites, which is reflected by the KBR distance change measurement and provides input for the phase center estimation algorithm.

[0058] As a specific embodiment, the maneuvering parameters are set as follows: the initial offset angle is 2 deg, the amplitude of the maneuvering angle is 1 deg, the maneuvering period is 250 s, and the maneuvering time length is 3000 s. The selection of the maneuvering parameters comprehensively considers the moment of inertia of the whole satellite, the execution capability of the attitude control system, and comprehensively considers the single-direction swing sensitivity characteristics of the antenna phase center and the actual attitude control system constraint of the satellite.

[0059] S102, constructing the observation equation between the two satellites, and performing Fourier transform and difference processing on the observation equation; the difference-based data processing idea is similar to the two-way comparison principle of the KBR, and the signal-to-noise ratio of the useful signal is obtained through the difference.

[0060] S102 specifically comprises the following steps:

[0061] S102, constructing the observation equation between the two satellites, and performing Fourier transform and difference processing on the observation equation; the difference-based data processing idea is similar to the two-way comparison principle of the KBR, and the signal-to-noise ratio of the useful signal is obtained through the difference.

[0062] ​​​The observation equation after Fourier transform is determined; through Fourier transform, the signal-to-noise ratio of measurement information can be improved, that is, the low-frequency amplitude is suppressed and the high-frequency amplitude is increased in the time domain.

[0063] The observation equation after differential processing is determined The observation equation after differential processing is determined; through differential processing, the disturbance term can be effectively eliminated, and the useful signal information is improved.

[0064] The convolution kernel corresponding to δ1f(x), δ2f(x), δ3f(x) is [1, -1], [1, -2, 1], [1, -3, 3, -1] respectively. Through frequency response analysis, it can be known that the convolution kernel can suppress low-frequency noise and appropriately increase high-frequency noise. The measurement fitting value is constructed into a vector y = [δ1f(x) δ2f(x) δ3f(x)] T At the same time, it is found that:

[0065]

[0066] Among them, the state H represents the first-order partial derivative matrix of f(x) with respect to the state, and R represents the measurement random error. For differential processing, it can be regarded as a linear operation of the coefficient matrix, and does not affect the row space, that is, the differential operation is constant for the estimated state.

[0067] Among them, f(x) represents the fitting function of the on-orbit phase center distance measurement, represents the relative distance between the two satellite mass centers in space, q1, q2 represents the attitude quaternion of the two satellites, represents the matrix conversion corresponding to the attitude quaternion, respectively represent the phase centers of the two satellites, Θ(·) represents the vectorized phase center, R br ,R nr respectively represent the constant bias and random noise, Poly(n) represents the polynomial fitting term, δ1f(x), δ2f(x), δ3f(x) respectively represent the first-order differential function, the second-order differential function and the third-order differential function of the on-orbit phase center distance measurement fitting function, F[·] represents the Fourier transform operation, represents the n-order differential of f(x), ω represents the angular rate in the frequency domain, x represents the estimated state, i is the imaginary unit, and is the square root of -1.

[0068] S103, according to the observation equation after differential processing, the estimated state of the main star phase center in the satellite mass center system at the current time is obtained;

[0069] S104: calibrate the estimated state of the primary satellite phase center in the satellite mass center system at the current moment using the satellite's unidirectional maneuvering angle at the current moment.

[0070] The projection of the star phase center vector on the inter-satellite line vector is the x component of the phase center vector. Its Taylor expansion can be expressed as:

[0071]

[0072] Among them, d 1x , d 1y , d 1z represents the three components of the main satellite phase center vector in the satellite mass center system, d 2x , d 2y , d 2z represents the three components of the phase center vector from the satellite in the satellite mass center system, ρ sinu Indicates a maneuver signal.

[0073] The maneuvering signal generated by the x-axis component of the KBR antenna phase center during the maneuvering process is mainly the bias term and periodic terms The bias term cannot be effectively extracted, and because both Θ and θ are small, the amplitude of the periodic term corresponding to the x-axis component is much smaller than that of the periodic terms corresponding to the y and z axes. Therefore, under the current maneuvering conditions, the x-axis result cannot be accurately calibrated.

[0074] The amplitude of the Fourier component of the motor frequency cos(4πft) and the amplitude of the Fourier separation of twice the motor frequency sin(2πft) are respectively denoted as a f ,a 2f , then the above formula can be written as an equation:

[0075]

[0076] In this way, the x and z direction components of the satellite phase center vector are calculated and the phase center calibration is completed.

[0077] The following is an example of actual space maneuvering and phase center calibration:

[0078] On a certain day, a space maneuver was carried out. Satellite B performed a pitch angle maneuver with an amplitude of about 1.5 degrees, initially -1 degrees. Then, it performed an azimuth angle maneuver with an amplitude of about 2 degrees, initially -2 degrees, with a period of 250 seconds. The actual data of the two maneuver angles are as follows Figure 2 After taking the third-order difference of the above angles, Fourier transform is performed to obtain the spectrum information, as shown in Figure 3 shown.

[0079] After the difference, the low frequency component of the maneuver angle is effectively suppressed, and the signal-to-noise ratio of the useful information in the maneuver is improved. Because of the pitch and azimuth maneuver, the phase center estimation can pay attention to the y direction and z direction values, and after the data is processed in three sections and arranged and combined, the deviation angle caused by the phase center yz direction is shown in Table 1. From the results, it can be seen that the method is superior to the traditional batch processing estimation algorithm by 0.3mrad, and the accuracy is obviously improved.

[0080] Table 1 Analysis table of deviation angle after three groups of data yz value combination replacement

[0081]

[0082] The antenna phase center high-precision on-orbit calibration method provided by the application solves the problem of phase center deviation caused by satellite on-orbit attitude disturbance, achieves the purpose of accurately calibrating the antenna phase center on-orbit, and has the advantages of simple and convenient method and low complexity.

[0083] The observation set required for calibrating the phase center includes K-band range data, star-sensitive camera data and PODs from GPS observation. From the perspective of data processing, the main difference from linear drift K-band calibration is that the attitude dynamics motion equation is no longer needed, and the range observation value is processed instead of range rate.

[0084] Based on the differential data processing idea, the signal-to-noise ratio of the useful signal is obtained through difference, and the disturbance term can be effectively eliminated and the useful signal information can be improved.

[0085] As another specific embodiment, the application also provides an on-orbit calibration system for an antenna phase center of a microwave ranging system, comprising:

[0086] The maneuver angle determination module is configured to determine the maneuver angle of the main satellite in a single direction according to the maneuver period of the satellite, the maneuver initial offset angle and the maneuver angle amplitude.

[0087] The observation equation construction and processing module is configured to construct an observation equation between the two satellites, and perform Fourier transform and difference processing on the observation equation.

[0088] The estimation state determination module is configured to obtain the estimation state of the main satellite phase center in the satellite center of mass system at the current time according to the observation equation after difference processing.

[0089] The calibration module is configured to calibrate the estimation state of the main satellite phase center in the satellite center of mass system at the current time by using the maneuver angle of the satellite in a single direction at the current time.

[0090] In order to implement the method corresponding to the above-mentioned embodiment one to achieve the corresponding functions and technical effects, the application further provides a system for on-orbit calibration of an antenna phase center of a microwave ranging system, comprising at least one processor, at least one memory and computer program instructions stored in the memory, which, when executed by the processor, implement the method.

[0091] Based on the above description, the technical solutions of the application, in essence, or the parts of the technical solutions that contribute to the prior art, or the parts of the technical solutions, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method of each embodiment of the application. The aforementioned computer storage medium includes a U disk, a mobile hard disk, a read-only memory, a random access memory, a magnetic disk, or an optical disk, and various media that can store program codes.

[0092] The embodiments in the specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method part.

[0093] The principles and implementation manners of the application are described by using specific examples in this paper. The above embodiment description is only used to help understand the method of the application and its core idea. For those skilled in the art, according to the idea of the application, the specific implementation manner and application range can be changed. In summary, the content of the specification should not be understood as a limitation of the application.

Claims

1. An on-orbit calibration method for the phase center of a microwave ranging system antenna, characterized in that: include: Determine the master satellite's unidirectional maneuvering angle based on the satellite's maneuvering period, initial maneuvering offset angle, and maneuvering angle amplitude; constructing an observation equation between the two satellites, and performing Fourier transform and difference processing on the observation equation; According to the observation equation after differential processing, the estimated state of the main satellite phase center in the satellite mass center system at the current moment is obtained; The estimated state of the main satellite phase center in the satellite mass center system at the current moment is calibrated using the satellite's unidirectional maneuvering angle at the current moment; The constructing of the observation equation between the two satellites and performing Fourier transform and differential processing on the observation equation specifically includes: Using the formula Construct the observation equation between the two satellites; use Determine the observation equation after Fourier transformation; Determine using the formula Observation equation after difference processing; Determine the convolution kernel of the observation equation after difference processing; Construct a vector based on the convolution kernel; determining an estimated state based on the vector; Where f(x) represents the fitting function of the on-orbit phase center distance measurement, Indicates the relative distance between the center of mass of the two satellites obtained by differential GPS, q1, q2 represent the attitude quaternions of the two satellites, Represents the matrix transformation corresponding to the attitude quaternion, They represent the phase centers of the two satellites, Θ(·) represents the phase center after vectorization, and R br ,R nr denote constant deviation and random noise respectively, Poly(n) denotes the polynomial fitting term, δ1f(x), δ2f(x), δ3f(x) denote the first-order difference function, second-order difference function and third-order difference function of the fitting function of on-orbit phase center distance measurement respectively, F[·] denotes Fourier transform operation, represents the nth-order differential of f(x), ω represents the angular rate in the frequency domain, x represents the estimated state, and i is the imaginary unit, which is the square root of -1.

2. The on-orbit calibration method for the phase center of a microwave ranging system antenna according to claim 1, characterized in that: Determining the maneuvering angle of the master satellite in one direction according to the maneuvering period, the initial maneuvering offset angle, and the maneuvering angle amplitude of the satellite specifically includes: Using the formula Determine the maneuvering angle of the main satellite in one direction; Where θ(t) represents the single-direction maneuvering angle of a single satellite at time t, T represents the maneuvering period, θ0 represents the initial maneuvering offset angle, Θ represents the maneuvering angle amplitude, and Θ = kT 2 , k is a constant.

3. The on-orbit calibration method for the phase center of a microwave ranging system antenna according to claim 2, characterized in that: The constructing of a vector according to the convolution kernel specifically includes: Using the formula y = [δ1f(x) δ2f(x) δ3f(x)] T Construct vector; Here, y represents a vector.

4. The on-orbit calibration method for the phase center of a microwave ranging system antenna according to claim 3, characterized in that: Determining the estimated state according to the vector specifically includes: Using the formula Determine the estimated status; Where H represents the first-order partial derivative matrix of f(x) with respect to the state, R represents the measurement random error, and t0 represents the time.

5. The on-orbit calibration method for the phase center of a microwave ranging system antenna according to claim 2, characterized in that: The method of calibrating the estimated state of the primary satellite phase center in the satellite mass center system at the current moment by using the satellite's unidirectional maneuvering angle at the current moment specifically includes: Using the formula Determine the components of the main satellite phase center in the x-direction and z-direction in the calibrated satellite mass center system; Among them, d 1x , d 1z represents the components of the main satellite phase center in the x and z directions under the satellite mass center system, a f ,a 2f represent the amplitude of the Fourier component of the maneuvering frequency and the amplitude of the Fourier separation of twice the maneuvering frequency, respectively.

6. An on-orbit calibration system for the phase center of a microwave ranging system antenna, used to implement the on-orbit calibration method for the phase center of a microwave ranging system antenna according to any one of claims 1 to 5, characterized in that: include: The maneuvering angle determination module is used to determine the maneuvering angle of the master satellite in one direction according to the satellite's maneuvering period, maneuvering initial offset angle and maneuvering angle amplitude; An observation equation construction and processing module is used to construct the observation equation between the two satellites and perform Fourier transform and differential processing on the observation equation; The estimated state determination module is used to obtain the estimated state of the main satellite phase center in the satellite mass center system at the current moment according to the observation equation after differential processing; The calibration module is used to calibrate the estimated state of the main satellite phase center in the satellite mass center system at the current moment using the satellite's unidirectional maneuvering angle at the current moment.

7. An on-orbit calibration system for the phase center of a microwave ranging system antenna, characterized in that: include: At least one processor, at least one memory, and computer program instructions stored in the memory, which, when executed by the processor, implement the on-orbit calibration method for the phase center of a microwave ranging system antenna according to any one of claims 1 to 5.

8. A storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, an on-orbit calibration method for the phase center of a microwave ranging system antenna is implemented as described in any one of claims 1 to 5.

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