An antenna calibration method, apparatus, device, and medium

Abstract

The application relates to an antenna calibration method and device, comprising the following steps: selecting qualified visible satellites from GNSS satellites based on carrier phase observations, calculating unit observation vectors of the visible satellites, and determining reference satellites of each epoch according to the unit observation vectors of all the visible satellites; constructing a set of triple difference phase center error measurements; constructing a spherical harmonic function fitting model according to the set of triple difference phase center error measurements, and obtaining a phase pattern of the antenna to be calibrated after solving. The application is suitable for large-scale calibration of low-cost antennas. The carrier phase ambiguity is eliminated, the complex ambiguity resolution and verification process is avoided, the complexity of the phase center error calibration is reduced, the influence of triple difference noise on the fitting accuracy of the phase pattern is reduced, and the accuracy of the antenna calibration result is improved. The application also relates to an equipment and a storage medium.

Description

Technical Field

[0001] This invention relates to the field of antenna technology, and in particular to an antenna calibration method, apparatus, device, and medium. Background Technology

[0002] There are three conventional antenna calibration methods: microwave anechoic chamber calibration, absolute field calibration, and relative field calibration. Microwave anechoic chamber calibration is performed indoors, using absorbing materials to create an ideal environment that effectively suppresses reflected signals. The antenna under test (DUT) is fixed to a precisely rotating and tilting mechanical device. By continuously adjusting the DUT's attitude, the phase center error in different signal incident directions is measured. While this method allows for absolute calibration under near-ideal conditions, the construction of the anechoic chamber and the associated equipment are costly, and the calibration results are subject to slight deviations. Absolute field calibration, performed in an open area, uses both the DUT and a reference antenna to simultaneously collect observations from a real satellite. Phase center error measurements are constructed, and a phase pattern is fitted to achieve absolute calibration. This method currently offers the highest accuracy in phase center error calibration, but it requires customized calibration robots and other equipment, resulting in extremely high costs. The relative field calibration method utilizes real satellite observations to construct phase center error measurements and fit the phase pattern, thus solving the problems of high cost and low accuracy associated with the microwave anechoic chamber calibration method. Furthermore, compared to the absolute field calibration method, the relative field calibration method eliminates the need for a calibration robot, controlling calibration costs. Among the three existing antenna calibration methods, the relative field calibration method is the lowest-cost method and is suitable for large-scale calibration of low-cost antennas.

[0003] Existing calibration methods primarily utilize double-difference carrier phase observations for ambiguity resolution. However, for low-cost antennas with significant phase center errors, the reliability of the ambiguity resolution results is low. Furthermore, different satellite observations typically possess varying degrees of accuracy, a factor that current antenna calibration algorithms do not consider. Summary of the Invention

[0004] To achieve high-precision antenna calibration, this invention provides an antenna calibration method, apparatus, device, and medium.

[0005] In a first aspect, the present invention provides an antenna calibration method, the method comprising:

[0006] Acquire the carrier phase observations of the antenna to be calibrated and the carrier phase observations of the reference antenna on the GNSS satellite within a preset time period;

[0007] Based on the carrier phase observations of the GNSS satellite by the antenna to be calibrated and the carrier phase observations of the GNSS satellite by the reference antenna, visible satellites that meet the preset conditions are selected from the GNSS satellites within each epoch of the preset time period. The unit observation vector of the visible satellite is calculated, and the reference satellite for each epoch is determined based on the unit observation vectors of all the visible satellites. Based on the carrier phase observations of the reference satellite for each epoch by the antenna to be calibrated and the carrier phase observations of the reference satellite for each epoch by the reference antenna, the three-difference phase center error measurement values ​​for all epochs are constructed.

[0008] Based on the satellite unit observation vectors that constitute the three-difference phase center error measurements, a spherical quadrilateral is constructed. The weight of each three-difference phase center error measurement is set according to the area of ​​the spherical quadrilateral. A spherical harmonic function weighted fitting model is constructed based on the weights of the three-difference phase center error measurements, and the spherical harmonic fitting function weighted model is solved to obtain the phase pattern of the antenna to be calibrated.

[0009] Based on the above technical solution, further, the acquisition of the carrier phase observations of the GNSS satellite by the antenna to be calibrated and the carrier phase observations of the GNSS satellite by the reference antenna within a preset time period specifically includes:

[0010] Acquire the carrier phase observations of the antenna to be calibrated for the GNSS satellite. and the carrier phase observations of the GNSS satellite by the reference antenna.

[0011]

[0012] Among them, r1 s The geometric distance from the antenna to be calibrated to the GNSS satellite is... Let be the geometric distance from the reference antenna to the GNSS satellite, c be the speed of light, and δt1, δt2, and δt be the distances from the reference antenna to the GNSS satellite. s denoted as clock errors of the first receiver, the second receiver, and the GNSS satellite, respectively; I as ionospheric error; T as tropospheric error; λ as carrier wavelength; N as carrier phase integer ambiguity; ξ(azi,ele) as phase center error; azi as satellite azi in the antenna body coordinate system; ele as satellite elevation in the antenna body coordinate system; and ε as carrier phase measurement noise.

[0013] Based on the above technical solution, further, the step of selecting visible satellites that meet preset conditions from the GNSS satellites within each epoch of the preset time period based on the carrier phase observations of the GNSS satellites by the antenna to be calibrated and the carrier phase observations of the GNSS satellites by the reference antenna, calculating the unit observation vector of the visible satellites, and determining the reference satellite for each epoch based on the unit observation vectors of all the visible satellites, specifically includes:

[0014] S21. Mark the carrier phase observations of the GNSS satellite by the antenna to be calibrated and the carrier phase observations of the GNSS satellite by the reference antenna that contain cycle slips;

[0015] S22. Select visible satellites from the GNSS satellites that have no cycle slip in the current time difference interval;

[0016] S23. If the number of visible satellites is greater than the preset number, calculate the coordinates of the visible satellites, and derive the geometric distance from the antenna to the visible satellites and the unit observation vector of the visible satellites.

[0017] Otherwise, continue processing the next epoch and repeat step S22 until all epochs have been processed;

[0018] S24. Based on the unit observation vector of each of the visible satellites at the time difference interval T diff For the varying angular distance within the range, select a reference satellite.

[0019] Based on the above technical solution, step S24 further includes:

[0020] Calculate epoch tT diff The angular distance Δθ of the motion of the visible satellite s is obtained by taking the dot product of the unit observation vector of the visible satellite at epoch t. s (t):

[0021] Δθ s (t)=e s (t)e s (tT diff )

[0022] Where: e s Let be the unit observation vector from the antenna to the visible satellite s. [x s y s z s [x1y1z1] represents the precise coordinates of the visible satellite s, and [x1y1z1] represents the coordinates of the antenna to be calibrated.

[0023] Comparison at time difference interval T diff The reference satellite is determined by the angular distances of all visible satellites within the range.

[0024] The reference satellite r is

[0025] Based on the above technical solution, further, the construction of the three-difference phase center error measurement values ​​for all epochs based on the carrier phase observation of the reference satellite at each epoch by the antenna to be calibrated and the carrier phase observation of the reference satellite at each epoch by the reference antenna specifically includes:

[0026] The carrier phase observations of the antenna to be calibrated and the reference antenna relative to the visible satellite s are subtracted to obtain the single-difference carrier phase observation.

[0027] Based on the single-difference carrier phase observation The relative phase center error Ξ of the visible satellite s along the incident direction is obtained. s ;

[0028] For the antenna to be calibrated and the reference antenna at epoch tT diff The first relative phase center error Ξ is obtained by subtracting the carrier phase observations of the visible satellite s and the reference satellite r from the epoch t. s (t), Second relative phase center error Ξ r (t), Third relative phase center error Ξ s (tT diff ) and the fourth relative phase center error Ξ r (tT diff ), where the first relative phase center error Ξ s (t) is the relative phase center error of the visible satellite s at epoch t, ​​and the second relative phase center error Ξ r (t) is the relative phase center error of the reference satellite r at epoch t, ​​and the third relative phase center error Ξ s (tT diff ) is a visible satellite s in epoch tT diff The relative phase center error, the fourth relative phase center error Ξ r (tT diff () is the reference satellite r at epoch tT diff The relative phase center error;

[0029] The difference between the first relative phase center error and the second relative phase center error is used to obtain the first double-difference phase center error measurement value Ξ. sr (t), the difference between the third relative phase center error and the fourth relative phase center error is used to obtain the second double-difference phase center error measurement value Ξ. sr (tT diff ):

[0030] The first double-difference phase center error measurement value Ξ sr (t) and the second double-difference phase center error measurement value Ξ sr (tT diff By performing a difference operation, the measured value of the three-difference phase center error Ξ is obtained. sr (t,tT diff ),Right now

[0031] in, For triple-difference carrier phase observations, It is a triple-difference noise component. It is the tri-difference antenna-satellite geometric distance;

[0032] After processing all the observations for all epochs, the set of three-difference phase center error measurements Ω is obtained. Ξ ,

[0033] Ω Ξ ={Ξ sr (t,tT diff )|s=1,2,...,r-1,r+1,...;t=T diff +1,T diff +2,...}.

[0034] Based on the above technical solution, further, the step of constructing a weighted fitting model of the spherical harmonic function according to the weights of the measured values ​​of the three-difference phase center error, and solving the weighted fitting model of the spherical harmonic function to obtain the phase pattern of the antenna to be calibrated, specifically includes:

[0035] The measured values ​​of the three-difference phase center error are expanded using spherical harmonic functions to form a weighted fitting model of the spherical harmonic function. The formula for the expansion of the spherical harmonic function is as follows:

[0036]

[0037] Where: n max Let m′ be the highest order of the spherical harmonic function, and m′ = max(m max ,n),m max Let m be the highest degree of the spherical harmonic function. max ≤n max , For a normalized adjoint Legendre polynomial of degree m, a nm and b nm Let be the spherical harmonic coefficients to be determined;

[0038] Calculate the area of ​​the spherical quadrilateral formed by the unit observation vectors corresponding to the relative phase center error measurements that constitute the three-difference phase center error measurements;

[0039] Based on the area of ​​the spherical quadrilateral corresponding to each of the three-difference phase center error measurements, determine the weight matrix W of the three-difference phase center error measurements. Ξ ;

[0040] The set of three-difference phase center error measurements Ω Ξ As input data, the least squares method is used, based on the weight matrix W of the three-difference phase center error measurements. Ξ Solve for the spherical harmonic coefficients a nm and b nm The model for the phase center error is obtained as follows:

[0041]

[0042] The phase center error at the grid points in the model is calculated to obtain the phase pattern, which is the calibration result of the phase center error of the antenna to be calibrated.

[0043] Secondly, the present invention also provides an antenna calibration device, the device comprising:

[0044] The first calculation module is used to obtain the carrier phase observation of the antenna to be calibrated to the GNSS satellite and the carrier phase observation of the reference antenna to the GNSS satellite within a preset time period.

[0045] The second calculation module is used to select visible satellites that meet preset conditions from the GNSS satellites within the preset time period based on the carrier phase observations of the GNSS satellites by the antenna to be calibrated and the carrier phase observations of the GNSS satellites by the reference antenna, calculate the unit observation vector of the visible satellites, determine the reference satellite for each epoch based on the unit observation vectors of all the visible satellites, and construct the three-difference phase center error measurement values ​​for all epochs based on the carrier phase observations of the reference satellites by the antenna to be calibrated and the carrier phase observations of the reference satellites by the reference antenna for each epoch.

[0046] The third calculation module is used to construct a spherical quadrilateral based on the satellite unit observation vector of the observations constituting the three-difference phase center error measurement value, set the weight of each three-difference phase center error measurement value according to the area of ​​the spherical quadrilateral, construct a spherical harmonic function weighted fitting model according to the weight of the three-difference phase center error measurement value, and solve the spherical harmonic fitting function weighted model to obtain the phase pattern of the antenna to be calibrated.

[0047] Based on the above technical solution, further, the first calculation module is specifically used to acquire the carrier phase observations of the antenna to be calibrated for the GNSS satellite. and the carrier phase observations of the GNSS satellite by the reference antenna.

[0048]

[0049] Among them, r1 s The geometric distance from the antenna to be calibrated to the GNSS satellite is... Let be the geometric distance from the reference antenna to the GNSS satellite, c be the speed of light, and δt1, δt2, and δt be the distances from the reference antenna to the GNSS satellite. s denoted as clock errors of the first receiver, the second receiver, and the GNSS satellite, respectively; I as ionospheric error; T as tropospheric error; λ as carrier wavelength; N as carrier phase integer ambiguity; ξ(azi,ele) as phase center error; azi as satellite azi in the antenna body coordinate system; ele as satellite elevation in the antenna body coordinate system; and ε as carrier phase measurement noise.

[0050] Based on the above technical solution, the second computing module further includes:

[0051] The first submodule is used to mark the carrier phase observations of the GNSS satellite by the antenna to be calibrated and the carrier phase observations of the GNSS satellite by the reference antenna that contain cycle slips.

[0052] The second submodule is used to select visible satellites without cycle slips in the current time difference interval from the GNSS satellites;

[0053] The third submodule is used to calculate the coordinates of the visible satellites and derive the geometric distance from the antenna to the visible satellites and the unit observation vector of the visible satellites when the number of visible satellites is greater than a preset number.

[0054] Otherwise, continue processing the next epoch, repeating the second submodule until all epochs have been processed;

[0055] The fourth submodule is used to perform time difference interval T based on the unit observation vector of each of the visible satellites. diff For the varying angular distance within the range, select a reference satellite.

[0056] Based on the above technical solution, the fourth submodule is further configured to:

[0057] Calculate epoch tT diff The angular distance Δθ of the motion of the visible satellite s is obtained by taking the dot product of the unit observation vector of the visible satellite at epoch t. s (t):

[0058] Δθ s (t)=e s (t)e s (tT diff )

[0059] Where: e s Let be the unit observation vector from the antenna to the visible satellite s. [x s y s z s [x1y1z1] represents the precise coordinates of the visible satellite s, and [x1y1z1] represents the coordinates of the antenna to be calibrated.

[0060] Comparison at time difference interval T diff The reference satellite is determined by the angular distances of all visible satellites within the range; the reference satellite r is...

[0061] Based on the above technical solution, the third computing module is further configured to:

[0062] The carrier phase observations of the antenna to be calibrated and the reference antenna relative to the visible satellite s are subtracted to obtain the single-difference carrier phase observation.

[0063] Based on the single-difference carrier phase observation The relative phase center error Ξ of the visible satellite s along the incident direction is obtained. s ;

[0064] For the antenna to be calibrated and the reference antenna at epoch tT diff The first relative phase center error Ξ is obtained by subtracting the carrier phase observations of the visible satellite s and the reference satellite r from the epoch t. s (t), Second relative phase center error Ξ r (t), Third relative phase center error Ξ s (tT diff ) and the fourth relative phase center error Ξ r (tT diff ), where the first relative phase center error Ξ s (t) is the relative phase center error of the visible satellite s at epoch t, ​​and the second relative phase center error Ξ r (t) is the relative phase center error of the reference satellite r at epoch t, ​​and the third relative phase center error Ξ s (tT diff ) is a visible satellite s in epoch tT diff The relative phase center error, the fourth relative phase center error Ξ r (tT diff () is the reference satellite r at epoch tT diff The relative phase center error;

[0065] The difference between the first relative phase center error and the second relative phase center error is used to obtain the first double-difference phase center error measurement value Ξ. sr (t), the difference between the third relative phase center error and the fourth relative phase center error is used to obtain the second double-difference phase center error measurement value Ξ. sr (tT diff ):

[0066] The first double-difference phase center error measurement value Ξ sr (t) and the second double-difference phase center error measurement value Ξ sr (tT diff By performing a difference operation, the measured value of the three-difference phase center error Ξ is obtained. sr (t,tT diff ),Right now

[0067] in, For triple-difference carrier phase observations, It is a triple-difference noise component. It is the tri-difference antenna-satellite geometric distance;

[0068] After processing all the observations for all epochs, the set of three-difference phase center error measurements Ω is obtained. Ξ Ω Ξ ={Ξ sr (t,tT diff )|s=1,2,...,r-1,r+1,...;t=T diff +1,T diff +2,...}.

[0069] Based on the above technical solution, the fourth calculation module is further configured to:

[0070] The measured values ​​of the three-difference phase center error are expanded using spherical harmonic functions to form a weighted fitting model of the spherical harmonic function. The formula for the expansion of the spherical harmonic function is as follows:

[0071]

[0072] Where: n max Let m′ be the highest order of the spherical harmonic function, and m′ = max(m max ,n),m max Let m be the highest degree of the spherical harmonic function. max ≤n max , For a normalized adjoint Legendre polynomial of degree m, a nm and b nm Let be the spherical harmonic coefficients to be determined;

[0073] Calculate the area of ​​the spherical quadrilateral formed by the unit observation vectors corresponding to the relative phase center error measurements that constitute the three-difference phase center error measurements;

[0074] Based on the area of ​​the spherical quadrilateral corresponding to each of the three-difference phase center error measurements, determine the weight matrix W of the three-difference phase center error measurements. Ξ ;

[0075] The set of three-difference phase center error measurements Ω Ξ As input data, the least squares method is used, based on the weight matrix W of the three-difference phase center error measurements. Ξ Solve for the spherical harmonic coefficients a nm and b nm The model for the phase center error is obtained as follows:

[0076]

[0077] The phase center error at the grid points in the model is calculated to obtain the phase pattern, which is the calibration result of the phase center error of the antenna to be calibrated.

[0078] Thirdly, the present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement an antenna calibration method as described in any one of the first aspects.

[0079] Fourthly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements an antenna calibration method as described in any one of the first aspects.

[0080] This invention provides an antenna calibration method, comprising: selecting qualified visible satellites from GNSS satellites based on carrier phase observations; calculating the unit observation vector of the visible satellites; determining the reference satellite for each epoch based on the unit observation vectors of all visible satellites; constructing a set of triple-difference phase center error measurements; constructing a spherical harmonic function fitting model based on the set of triple-difference phase center error measurements; and obtaining the phase pattern of the antenna to be calibrated after solving the model. This invention is applicable to large-scale calibration of low-cost antennas and can help promote the high-precision application of low-cost antennas. In the process of constructing phase center error measurements, the carrier phase ambiguity is directly eliminated by using triple-difference combination, avoiding complex ambiguity resolution and verification processes, and reducing the complexity of phase center error calibration. In the process of phase pattern fitting, the weight matrix of the triple-difference phase center error measurements is constructed using the area of ​​a spherical quadrilateral, reducing the impact of triple-difference noise on the accuracy of phase pattern fitting and improving the accuracy of antenna calibration results. Attached Figure Description

[0081] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0082] In the attached diagram:

[0083] Figure 1 This is a flowchart illustrating an antenna calibration method provided in an embodiment of the present invention;

[0084] Figure 2 This is a schematic flowchart illustrating the construction of a three-difference phase center error measurement value according to another embodiment of the present invention;

[0085] Figure 3 This is a schematic diagram of the configuration of the three-difference combination in an antenna calibration method provided by another embodiment of the present invention;

[0086] Figure 4 This is a schematic diagram of the spherical quadrilateral formed by the endpoints of four unit satellite observation vectors in an antenna calibration method provided in another embodiment of the present invention;

[0087] Figure 5 This is a schematic diagram of an antenna calibration device provided in another embodiment of the present invention. Detailed Implementation

[0088] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other.

[0089] The following detailed description is exemplary and intended to provide further detailed explanation of the invention. Unless otherwise specified, all technical terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used in this invention is for describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention.

[0090] The following will be combined with the appendix Figure 1 This invention provides a detailed description of an antenna calibration method, which includes the following steps:

[0091] 100. Obtain the carrier phase observations of the antenna to be calibrated and the carrier phase observations of the reference antenna on the GNSS satellite within a preset time period;

[0092] 200. Based on the carrier phase observations of the GNSS satellite by the antenna to be calibrated and the carrier phase observations of the GNSS satellite by the reference antenna, select visible satellites that meet the preset conditions in each epoch within the preset time period from the GNSS satellites, calculate the unit observation vector of the visible satellites, and determine the reference satellite for each epoch based on the unit observation vectors of all the visible satellites. Based on the carrier phase observations of the reference satellite for each epoch by the antenna to be calibrated and the carrier phase observations of the reference satellite for each epoch by the reference antenna, construct the three-difference phase center error measurement values ​​for all epochs.

[0093] 300. Construct a spherical harmonic function fitting model based on the measured values ​​of the three-difference phase center error, and obtain the phase pattern of the antenna to be calibrated by solving the spherical harmonic fitting function.

[0094] Based on the above embodiments, step 100 further includes:

[0095] Acquire the carrier phase observations of the antenna to be calibrated for the GNSS satellite. and the carrier phase observations of the GNSS satellite by the reference antenna.

[0096]

[0097] Among them, r1 s The geometric distance from the antenna to be calibrated to the GNSS satellite is... Let be the geometric distance from the reference antenna to the GNSS satellite, c be the speed of light, and δt1, δt2, and δt be the distances from the reference antenna to the GNSS satellite. s denoted as clock errors of the first receiver, the second receiver, and the GNSS satellite, respectively; I as ionospheric error; T as tropospheric error; λ as carrier wavelength; N as carrier phase integer ambiguity; ξ(azi,ele) as phase center error; azi as satellite azi in the antenna body coordinate system; ele as satellite elevation in the antenna body coordinate system; and ε as carrier phase measurement noise.

[0098] Based on the above embodiments, further, in step 200, based on the carrier phase observations of the GNSS satellite by the antenna to be calibrated and the carrier phase observations of the GNSS satellite by the reference antenna, visible satellites meeting preset conditions are selected from the GNSS satellites within each epoch of the preset time period; the unit observation vector of the visible satellite is calculated; and the reference satellite for each epoch is determined based on the unit observation vectors of all the visible satellites. Specifically, this includes:

[0099] 210. Mark the carrier phase observations of the GNSS satellite by the antenna to be calibrated and the carrier phase observations of the GNSS satellite by the reference antenna that contain cycle slips;

[0100] 220. Select from the GNSS satellites any visible satellites that have no cycle slip in the current time difference interval;

[0101] 230. If the number of visible satellites is greater than a preset number, calculate the coordinates of the visible satellites, derive the geometric distance from the antenna to the visible satellites and the unit observation vector of the visible satellites;

[0102] Otherwise, continue processing the next epoch and repeat step 220 until all epochs have been processed;

[0103] 240. Based on the unit observation vector of each of the visible satellites at a time difference interval T diff For the varying angular distance within the range, select a reference satellite.

[0104] Based on the above technical solution, step 240 further includes:

[0105] Calculate epoch tT diff The angular distance Δθ of the motion of the visible satellite s is obtained by taking the dot product of the unit observation vector of the visible satellite at epoch t. s (t):

[0106] Δθ s (t)=e s (t)e s (tT diff )

[0107] Where: e s Let be the unit observation vector from the antenna to the visible satellite s. [x s y s z s [x1y1z1] represents the precise coordinates of the visible satellite s, and [x1y1z1] represents the coordinates of the antenna to be calibrated.

[0108] Comparison at time difference interval T diff The reference satellite is determined by the angular distances of all visible satellites within the range; the reference satellite r is...

[0109] Based on the above embodiments, further, in step 200, based on the carrier phase observation of the reference satellite at each epoch by the antenna to be calibrated and the carrier phase observation of the reference satellite at each epoch by the reference antenna, the three-difference phase center error measurement values ​​for all epochs are constructed, specifically including:

[0110] The carrier phase observations of the antenna to be calibrated and the reference antenna relative to the visible satellite s are subtracted to obtain the single-difference carrier phase observation.

[0111] Based on the single-difference carrier phase observation The relative phase center error along the incident direction of the visible satellite s is denoted as Ξ. s ;

[0112] For the antenna to be calibrated and the reference antenna at epoch tT diff The first relative phase center error Ξ is obtained by subtracting the carrier phase observations of the visible satellite s and the reference satellite r from the epoch t. s (t), Second relative phase center error Ξ r (t), Third relative phase center error Ξ s (tT diff ) and the fourth relative phase center error Ξ r (tT diff ), where the first relative phase center error Ξ s (t) is the relative phase center error of the visible satellite s at epoch t, ​​and the second relative phase center error Ξ r (t) is the relative phase center error of the reference satellite r at epoch t, ​​and the third relative phase center error Ξ s (tT diff ) is a visible satellite s in epoch tT diff The relative phase center error, the fourth relative phase center error Ξ r (tT diff () is the reference satellite r at epoch tT diff The relative phase center error;

[0113] The difference between the first relative phase center error and the second relative phase center error is used to obtain the first double-difference phase center error measurement value Ξ. sr (t), the difference between the third relative phase center error and the fourth relative phase center error is used to obtain the second double-difference phase center error measurement value Ξ. sr (tT diff ):

[0114] The first double-difference phase center error measurement value Ξ sr (t) and the second double-difference phase center error measurement value Ξ sr (tT diff By performing a difference operation, the measured value of the three-difference phase center error Ξ is obtained. sr (t,tT diff ),Right now

[0115] in, For triple-difference carrier phase observations, It is a triple-difference noise component. It is the tri-difference antenna-satellite geometric distance;

[0116] After processing all the observations for all epochs, the set of three-difference phase center error measurements Ω is obtained. Ξ ,

[0117] Ω Ξ ={Ξ sr (t,tT diff )|s=1,2,...,r-1,r+1,...;t=T diff +1,T diff +2,...}. Based on the above embodiments, step 400 further includes:

[0118] The measured values ​​of the three-difference phase center error are expanded using spherical harmonic functions to form a weighted fitting model of the spherical harmonic function. The formula for the expansion of the spherical harmonic function is as follows:

[0119]

[0120] Where: n max Let m′ be the highest order of the spherical harmonic function, and m′ = max(m max ,n),m max Let m be the highest degree of the spherical harmonic function. max ≤n max , For a normalized adjoint Legendre polynomial of degree m, a nm and b nm Let be the spherical harmonic coefficients to be determined;

[0121] Calculate the area of ​​the spherical quadrilateral formed by the unit observation vectors corresponding to the relative phase center error measurements that constitute the three-difference phase center error measurements;

[0122] Based on the area of ​​the spherical quadrilateral corresponding to each of the three-difference phase center error measurements, determine the weight matrix W of the three-difference phase center error measurements. Ξ ;

[0123] The set of three-difference phase center error measurements Ω Ξ As input data, the least squares method is used, based on the weight matrix W of the three-difference phase center error measurements. Ξ Solve for the spherical harmonic coefficients a nm and b nm The model for the phase center error is obtained as follows:

[0124]

[0125] The phase center error at the grid points in the model is calculated to obtain the phase pattern, which is the calibration result of the phase center error of the antenna to be calibrated.

[0126] This embodiment provides an antenna calibration method, including selecting qualified visible satellites from GNSS satellites based on carrier phase observations, calculating the unit observation vector of the visible satellites, and determining the reference satellite for each epoch based on the unit observation vectors of all visible satellites; constructing a set of three-difference phase center error measurements; constructing a spherical harmonic function fitting model based on the set of three-difference phase center error measurements, and obtaining the phase pattern of the antenna to be calibrated after solving the model. This invention is applicable to large-scale calibration of low-cost antennas and can help promote the high-precision application of low-cost antennas. In the process of constructing phase center error measurements, the carrier phase ambiguity is directly eliminated by using a three-difference combination, avoiding complex ambiguity resolution and verification processes, and reducing the complexity of phase center error calibration. In the process of phase pattern fitting, the weight matrix of the three-difference phase center error measurements is constructed using the area of ​​a spherical quadrilateral, reducing the impact of three-difference noise on the accuracy of phase pattern fitting and improving the accuracy of the antenna calibration results.

[0127] It should be understood that this invention aims to design a phase center error calibration method suitable for low-cost antennas. For low-cost antennas, the phase center errors of antennas of the same model vary greatly, and the average calibration result is not practically meaningful. Therefore, in order to effectively eliminate phase center errors, each phase-distorted antenna needs to be calibrated individually. Among the three existing phase center error calibration methods, the microwave anechoic chamber calibration method and the absolute field calibration method are costly, limiting the individual calibration of large-scale antennas. The relative field calibration method, on the other hand, does not require dedicated calibration equipment and can effectively reduce costs. Therefore, this invention designs a relative field calibration method.

[0128] Compared with existing antenna calibration methods, this invention makes improvements in the following two aspects:

[0129] 1. Construct the phase center error measurement value using a three-difference combination;

[0130] 2. A characteristic of low-cost antennas is their large phase center error, leading to low accuracy in carrier phase observations and making them unsuitable for high-precision positioning. During antenna calibration, a large phase center error reduces the success rate of carrier phase ambiguity resolution. To address this issue, this invention utilizes the characteristic that carrier phase ambiguity remains unchanged between adjacent epochs (under the condition of no cycle slip), using a three-difference combination to directly eliminate carrier phase ambiguity, avoiding complex ambiguity resolution and verification processes, and reducing the complexity of phase center error calibration.

[0131] 3. Use the area of ​​a spherical quadrilateral to set the weight;

[0132] Compared to the double-difference combination used in conventional antenna calibration methods, the triple-difference combination contains greater random errors. To address this issue, this invention constructs a spherical quadrilateral using four satellite unit observation vectors during the spherical harmonic function fitting process. The accuracy of the phase center error measurement is evaluated based on the area of ​​this quadrilateral, and a weight matrix for the triple-difference phase center error measurement is constructed. This design reduces the impact of triple-difference noise on the phase pattern fitting accuracy and improves the accuracy of the antenna calibration results.

[0133] To address the issue of large phase center error amplitude in phase-distorted antennas, this invention proposes a phase center error calibration method based on a triple-difference combination and spherical quadrilateral area weighting. In implementation, firstly, a calibration environment is set up in an open test site, and raw observation data is collected continuously for several days (two days for GPS and 14 days for BeiDou). Then, using the collected raw observation data, a set of phase center error measurements is constructed using a triple-difference combination. Finally, the phase center error measurements are weighted and fitted to obtain the calibration result, i.e., the phase radiation pattern. The weighting of the phase center error measurements is based on the area of ​​a spherical quadrilateral.

[0134] The following describes each step of antenna calibration:

[0135] 1. Calibration environment setup and data acquisition

[0136] The steps for setting up the antenna phase center error calibration environment are as follows:

[0137] Ensure that all equipment, including GNSS receivers, antennas, and necessary power supplies, cables, and connectors, is ready and configured so that the receivers can fully record the collected satellite observation data.

[0138] Select a suitable calibration site that is open and free from obstructions such as buildings within the upper hemisphere of the antenna. Additionally, gravel or absorbing materials can be laid on the calibration site to suppress reflected signals from the ground.

[0139] Two antennas are horizontally mounted on two concrete piers or tripods: one is the antenna to be calibrated, and the other is a reference antenna with a pre-calibrated phase pattern. The two antennas are then connected to two measurement receivers.

[0140] The two receivers operated continuously for several days, recording the complete raw satellite observation data. The sampling rate of the observations was 1 Hz, which means 3600 epochs per hour.

[0141] When calibrating the antenna phase pattern using GPS satellite observations, data is collected continuously for two days. After collecting 24 hours of data, both the antenna under test and the reference antenna are rotated horizontally by 180°, and another 24 hours of data are collected.

[0142] When using BeiDou satellite observations to calibrate the antenna phase pattern, data is collected continuously for 14 days. After collecting 148 hours of data, both the antenna under test and the reference antenna are rotated horizontally by 180°, and another 148 hours of data are collected.

[0143] Carrier phase observations of satellite s from antennas 1 and 2 and They are respectively:

[0144]

[0145] Where: r1 s and δt1, δt2, and δt are the geometric distances from antenna 1 and antenna 2 to the satellite, respectively; c is the speed of light; δt1, δt2, and δt are the geometric distances from antenna 1 and antenna 2 to the satellite, respectively ... is the speed of light; δt1, δt2, and s denoted by , respectively, the clock errors of receiver 1, receiver 2, and satellite s; I and T are the ionospheric error and tropospheric error, respectively; λ is the carrier wavelength; N is the carrier phase integer ambiguity; ξ(azi,ele) is the phase center error; azi is the satellite aziel angle in the antenna body coordinate system; ele is the satellite elevation angle in the antenna body coordinate system; ε is the carrier phase measurement noise.

[0146] Save and organize the collected raw satellite observation data to prepare for the construction of phase center error measurement values.

[0147] 2. Construction of phase center error measurement values

[0148] The process for constructing phase center error measurement values ​​is as follows: Figure 2 As shown below, the detailed steps for constructing the phase center error measurement are as follows:

[0149] Cycle slip detection is performed on carrier phase observations to identify those containing cycle slips. Existing mature techniques such as cycle slip detection algorithms based on lock-out identifiers, higher-order difference methods, and triple-difference residual methods can be used for cycle slip detection.

[0150] Reasonable setting of time difference interval T diff (Based on experience, it can be set to 3600 epochs). From epoch t = T diff Starting with +1, filter out available satellites for epoch t, ​​i.e., within consecutive T... diff Within each epoch (from epoch tT) diff A satellite with no cycle slip (up to epoch t).

[0151] If more than two satellites are available, calculate the satellite coordinates using precise ephemeris, and derive the antenna-satellite geometric distance and the satellite unit observation vector; otherwise, proceed to step 2 to continue processing the next epoch.

[0152] Calculate the observation vector of each satellite in time period T diff For the varying angular distance within the range, select a reference satellite.

[0153] The angular distance of the satellite motion, Δθ, can be obtained by calculating the inner product of epoch t-Tdiff and the satellite unit observation vector at epoch t. s (t) is:

[0154] Δθ s (t)=e s (t)e s (tT diff (3)

[0155] Where: e s Let be the unit observation vector of satellite s from the antenna. [x s y s z s [x1y1z1] represents the precise coordinates of the satellite; [x1y1z1] represents the coordinates of antenna 1.

[0156] By comparing the angular distances of all continuously visible satellites from epoch t-Tdiff to epoch t, ​​a reference satellite is selected, and the reference satellite r is:

[0157]

[0158] Construct the measurement value of the three-difference phase center error.

[0159] The composition of the three-difference combination is as follows: Figure 3 As shown in the figure, r represents the reference satellite, and Tdiff represents the time interval of the difference between epochs. The eight carrier phase observations are obtained by antenna 1 and antenna 2 measuring the signals of satellite r and satellite s at epoch t and epoch t-Tdiff, respectively, and can be written in the form of equation (1) and equation (2). The three-difference phase center error measurement is composed of the eight carrier phase observations.

[0160] Since both antennas are placed horizontally, the signal propagation paths from the same satellite to both the antenna under test and the reference antenna can be considered parallel, i.e., and This is valid. The relative phase center error (Ξ) can be obtained by subtracting the phase center errors of the two antennas. s for:

[0161] Ξ s =ξ1(azi s ,eles )-ξ2(azi s ,ele s (5)

[0162] Dividing equations (1) and (2) by difference, we can obtain the single-difference carrier phase observation. for:

[0163]

[0164] A measurement of the relative phase center error can be obtained through a simple transformation:

[0165]

[0166] Similarly, by subtracting the observations of the same satellite from two antennas at the same time, four relative phase center error measurements Ξ can be obtained. s (t), Ξ r (t), Ξ s (tT diff ) and Ξ r (tT diff ), respectively:

[0167]

[0168] Based on this, by subtracting the relative phase center error measurements of the same satellite at two different epochs, a double-difference phase center error measurement Ξ can be constructed. sr (t) and Ξ sr (tT diff ), respectively:

[0169]

[0170] Among them: Ξ sr (·)=Ξ s (·)-Ξ r (·); It represents double-difference ambiguity.

[0171] It is a combination of antenna-satellite geometric distances at different epochs, namely:

[0172]

[0173] Where: r1 s (·) represents the geometric distance between antenna 1 and satellite s at epoch ·. r1 can be calculated using the receiving antenna coordinates and the precise satellite coordinates. s (·), antenna coordinates can use prior calibration values, and satellite precise coordinates use precise ephemeris.

[0174] To Ξ sr (t) and Ξ sr (tT diff By performing a difference operation, the measured value of the three-difference phase center error Ξ can be obtained. sr (t,tT diff That is:

[0175]

[0176] in: This is a three-difference carrier phase observation; This is a triple-difference noise component.

[0177] Proceed to step 2, construct the triple-difference phase center error measurement values ​​using the observations at epoch t+1, and continue until all observations have been processed, obtaining the set of triple-difference phase center error measurement values ​​Ω. Ξ That is:

[0178] Ω Ξ ={Ξ sr (t,tT diff )|s=1,2,...,r-1,r+1,...;t=T diff +1,T diff +2,...} (12)

[0179] 3. Fitting of phase pattern

[0180] The steps for phase pattern fitting are as follows:

[0181] The measured values ​​of the three-difference phase center error are expanded using spherical harmonic functions to construct a spherical harmonic function fitting model. The formula for the spherical harmonic function expansion is:

[0182]

[0183] Where: n max The highest order of the spherical harmonic function; m′=max(m max ,n); m max Let m be the highest degree of the spherical harmonic function. max ≤n max ; For a normalized adjoint Legendre polynomial of degree m, order n; a nm and b nm Let be the spherical harmonic coefficients to be determined.

[0184] Calculate the area of ​​the spherical quadrilateral.

[0185] Depend on Figure 3 It can be seen that the three-difference phase center error measurement values ​​consist of relative phase center error measurements in four different directions, and the unit observation vectors corresponding to the four directions. like Figure 4 As shown in the figure, the four satellite icons represent the positions of two different satellites at different epochs. The endpoints of the four unit observation vectors form a spherical quadrilateral ACBD.

[0186] Divide the spherical quadrilateral into two spherical triangles, △ABC and △ABD, and calculate their areas. For accurate area calculation, △ABC and △ABD should not intersect. Geometrically, if the great circle arc AB is the common side of the two spherical triangles, then when constructing a plane passing through A, B, and the origin O, points C and D should be on opposite sides of the plane. Therefore, first find the equation of the plane passing through any two points and the origin O, then substitute the coordinates of the remaining two points into the plane equation. If the calculated results have opposite signs, then take the two selected points as the common points and divide the spherical quadrilateral into two spherical triangles, △ABC and △ABD.

[0187] Use equation (3) to calculate the three sides a, b and c of the spherical triangle △ABC.

[0188] Using the law of cosines of the sphere, calculate the three spherical angles A, B, and C, which are:

[0189]

[0190] According to spherical trigonometry, the area S of spherical triangle △ABC can be calculated. ΔABC :

[0191] S ΔABC = (A+B+C-π)×R 2 (15)

[0192] Where R is the radius of the antenna hemisphere, R = 1.

[0193] Similarly, the area S of the spherical triangle △ABD can be calculated. ΔABD Adding the areas of the two spherical triangles gives the area S of the spherical quadrilateral ACBD. quad :

[0194] S quad =S ΔABC +S ΔABD (16)

[0195] Set the weights for the three-difference phase center error measurements.

[0196] After calculating the area of ​​the spherical quadrilateral corresponding to each triple-difference phase center error measurement, a weight matrix W is set for the triple-difference phase center error measurement. Ξ for:

[0197]

[0198] in: Let be the area of ​​the spherical quadrilateral corresponding to the k-th triple-difference phase center error measurement value.

[0199] The set of three-difference phase center error measurements Ω Ξ Using the least squares method as input data, the spherical harmonic coefficients a are calculated. nm and b nm The model for the phase center error is obtained as follows:

[0200]

[0201] The phase center error at the grid points is calculated using equation (18), and the phase pattern is obtained. This completes the calibration of the antenna phase center error.

[0202] This invention presents a simple and easy-to-implement antenna calibration method. This method is suitable for large-scale calibration of low-cost antennas and can facilitate the promotion of high-precision applications of low-cost antennas. Specifically:

[0203] In the process of constructing the phase center error measurement value, the carrier phase ambiguity is directly eliminated by using the three-difference combination, avoiding the complex ambiguity resolution and verification process, and reducing the complexity of phase center error calibration.

[0204] During the phase pattern fitting process, a weight matrix for the triple-difference phase center error measurement values ​​was constructed using the area of ​​a spherical quadrilateral, which reduced the impact of triple-difference noise on the phase pattern fitting accuracy and improved the accuracy of the antenna calibration results.

[0205] The following will be combined with the appendix Figure 5 This invention provides a detailed description of an antenna calibration device according to an embodiment of the invention, specifically including:

[0206] The first calculation module is used to obtain the carrier phase observation of the antenna to be calibrated to the GNSS satellite and the carrier phase observation of the reference antenna to the GNSS satellite within a preset time period.

[0207] The second calculation module is used to select visible satellites that meet preset conditions from the GNSS satellites within the preset time period based on the carrier phase observations of the GNSS satellites by the antenna to be calibrated and the carrier phase observations of the GNSS satellites by the reference antenna, calculate the unit observation vector of the visible satellites, determine the reference satellite for each epoch based on the unit observation vectors of all the visible satellites, and construct the three-difference phase center error measurement values ​​for all epochs based on the carrier phase observations of the reference satellites by the antenna to be calibrated and the carrier phase observations of the reference satellites by the reference antenna for each epoch.

[0208] The third calculation module is used to construct a spherical quadrilateral based on the satellite unit observation vector of the observations constituting the three-difference phase center error measurement value, set the weight of each three-difference phase center error measurement value according to the area of ​​the spherical quadrilateral, construct a spherical harmonic function weighted fitting model according to the weight of the three-difference phase center error measurement value, and solve the spherical harmonic fitting function weighted model to obtain the phase pattern of the antenna to be calibrated.

[0209] Based on the above technical solution, further, the first calculation module is specifically used to acquire the carrier phase observations of the antenna to be calibrated for the GNSS satellite. and the carrier phase observations of the GNSS satellite by the reference antenna.

[0210]

[0211] Among them, r1 s The geometric distance from the antenna to be calibrated to the GNSS satellite is... Let be the geometric distance from the reference antenna to the GNSS satellite, c be the speed of light, and δt1, δt2, and δt be the distances from the reference antenna to the GNSS satellite. s denoted as clock errors of the first receiver, the second receiver, and the GNSS satellite, respectively; I as ionospheric error; T as tropospheric error; λ as carrier wavelength; N as carrier phase integer ambiguity; ξ(azi,ele) as phase center error; azi as satellite azi in the antenna body coordinate system; ele as satellite elevation in the antenna body coordinate system; and ε as carrier phase measurement noise.

[0212] Based on the above technical solution, the second computing module further includes:

[0213] The first submodule is used to mark the carrier phase observations of the GNSS satellite by the antenna to be calibrated and the carrier phase observations of the GNSS satellite by the reference antenna that contain cycle slips.

[0214] The second submodule is used to select visible satellites without cycle slips in the current time difference interval from the GNSS satellites;

[0215] The third submodule is used to calculate the coordinates of the visible satellites and derive the geometric distance from the antenna to the visible satellites and the unit observation vector of the visible satellites when the number of visible satellites is greater than a preset number.

[0216] Otherwise, continue processing the next epoch, repeating the second submodule until all epochs have been processed;

[0217] The fourth submodule is used to perform time difference interval T based on the unit observation vector of each of the visible satellites. diffFor the varying angular distance within the range, select a reference satellite.

[0218] Based on the above technical solution, the fourth submodule is further configured to:

[0219] Calculate epoch tT diff The angular distance Δθ of the motion of the visible satellite s is obtained by taking the dot product of the unit observation vector of the visible satellite at epoch t. s (t):

[0220] Δθ s (t)=e s (t)e s (tT diff )

[0221] Where: e s Let be the unit observation vector from the antenna to the visible satellite s. [x s y s z s [x1y1z1] represents the precise coordinates of the visible satellite s, and [x1y1z1] represents the coordinates of the antenna to be calibrated.

[0222] Comparison at time difference interval T diff The reference satellite is determined by the angular distances of all visible satellites within the range; the reference satellite r is...

[0223] Based on the above technical solution, the third computing module is further configured to:

[0224] The carrier phase observations of the antenna to be calibrated and the reference antenna relative to the visible satellite s are subtracted to obtain the single-difference carrier phase observation.

[0225] Based on the single-difference carrier phase observation The relative phase center error Ξ of the visible satellite s along the incident direction is obtained. s ;

[0226] For the antenna to be calibrated and the reference antenna at epoch tT diff The first relative phase center error Ξ is obtained by subtracting the carrier phase observations of the visible satellite s and the reference satellite r from the epoch t. s (t), Second relative phase center error Ξ r (t), Third relative phase center error Ξ s (tT diff ) and the fourth relative phase center error Ξ r (tT diff ), where the first relative phase center error Ξ s(t) is the relative phase center error of the visible satellite s at epoch t, ​​and the second relative phase center error Ξ r (t) is the relative phase center error of the reference satellite r at epoch t, ​​and the third relative phase center error Ξ s (tT diff ) is a visible satellite s in epoch tT diff The relative phase center error, the fourth relative phase center error Ξ r (tT diff () is the reference satellite r at epoch tT diff The relative phase center error;

[0227] The difference between the first relative phase center error and the second relative phase center error is used to obtain the first double-difference phase center error measurement value Ξ. sr (t), the difference between the third relative phase center error and the fourth relative phase center error is used to obtain the second double-difference phase center error measurement value Ξ. sr (tT diff ):

[0228] The first double-difference phase center error measurement value Ξ sr (t) and the second double-difference phase center error measurement value Ξ sr (tT diff By performing a difference operation, the measured value of the three-difference phase center error Ξ is obtained. sr (t,tT diff ),Right now

[0229] in, For triple-difference carrier phase observations, It is a triple-difference noise component. It is the tri-difference antenna-satellite geometric distance;

[0230] After processing all the observations for all epochs, the set of three-difference phase center error measurements Ω is obtained. Ξ ,

[0231] Ω Ξ ={Ξ sr (t,tT diff )|s=1,2,...,r-1,r+1,...;t=T diff +1,T diff +2,...}.

[0232] Based on the above technical solution, the fourth calculation module is further configured to:

[0233] The measured values ​​of the three-difference phase center error are expanded using spherical harmonic functions to form a weighted fitting model of the spherical harmonic function. The formula for the expansion of the spherical harmonic function is as follows:

[0234]

[0235] Where: n max Let m′ be the highest order of the spherical harmonic function, and m′ = max(m max ,n),m max Let m be the highest degree of the spherical harmonic function. max ≤n max , For a normalized adjoint Legendre polynomial of degree m, a nm and b nm Let be the spherical harmonic coefficients to be determined;

[0236] Calculate the area of ​​the spherical quadrilateral formed by the unit observation vectors corresponding to the relative phase center error measurements that constitute the three-difference phase center error measurements;

[0237] Based on the area of ​​the spherical quadrilateral corresponding to each of the three-difference phase center error measurements, determine the weight matrix W of the three-difference phase center error measurements. Ξ ;

[0238] The set of three-difference phase center error measurements Ω Ξ As input data, the least squares method is used, based on the weight matrix W of the three-difference phase center error measurements. Ξ Solve for the spherical harmonic coefficients a nm and b nm The model for the phase center error is obtained as follows:

[0239]

[0240] The phase center error at the grid points in the model is calculated to obtain the phase pattern, which is the calibration result of the phase center error of the antenna to be calibrated.

[0241] This invention provides an antenna calibration device suitable for large-scale calibration of low-cost antennas, which can help promote the high-precision application of low-cost antennas. In constructing the phase center error measurement value, the carrier phase ambiguity is directly eliminated by using a triple-difference combination, avoiding complex ambiguity resolution and verification processes, and reducing the complexity of phase center error calibration. In the phase pattern fitting process, the weight matrix of the triple-difference phase center error measurement value is constructed using the area of ​​a spherical quadrilateral, reducing the impact of triple-difference noise on the phase pattern fitting accuracy and improving the accuracy of the antenna calibration results.

[0242] Furthermore, embodiments of the present invention include a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement an antenna calibration method as described in any of the above technical solutions.

[0243] This invention also includes a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements an antenna calibration method as described in any of the above technical solutions.

[0244] The above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. An antenna calibration method, characterized in that, The method includes: Acquire the carrier phase observations of the antenna to be calibrated and the carrier phase observations of the reference antenna on the GNSS satellite within a preset time period; Based on the carrier phase observations of the GNSS satellite by the antenna to be calibrated and the carrier phase observations of the GNSS satellite by the reference antenna, visible satellites that meet the preset conditions are selected from the GNSS satellites within each epoch of the preset time period. The unit observation vector of the visible satellite is calculated, and the reference satellite for each epoch is determined based on the unit observation vectors of all the visible satellites. Based on the carrier phase observations of the reference satellite for each epoch by the antenna to be calibrated and the carrier phase observations of the reference satellite for each epoch by the reference antenna, the three-difference phase center error measurement values ​​for all epochs are constructed. Based on the satellite unit observation vectors that constitute the three-difference phase center error measurements, a spherical quadrilateral is constructed. The weight of each three-difference phase center error measurement is set according to the area of ​​the spherical quadrilateral. A spherical harmonic function weighted fitting model is constructed based on the weights of the three-difference phase center error measurements, and the spherical harmonic fitting function weighted model is solved to obtain the phase pattern of the antenna to be calibrated.

2. The method according to claim 1, characterized in that, The acquisition of carrier phase observations of the GNSS satellite from the antenna to be calibrated and from the reference antenna within a preset time period specifically includes: Acquire the carrier phase observations of the antenna to be calibrated for the GNSS satellite. and the carrier phase observations of the GNSS satellite by the reference antenna. in, The geometric distance from the antenna to be calibrated to the GNSS satellite is... Let be the geometric distance from the reference antenna to the GNSS satellite, c be the speed of light, and δt1, δt2, and δt be the distances from the reference antenna to the GNSS satellite. s denoted as clock errors of the first receiver, the second receiver, and the GNSS satellite, respectively; I as ionospheric error; T as tropospheric error; λ as carrier wavelength; N as carrier phase integer ambiguity; ξ(azi,ele) as phase center error; azi as satellite azi in the antenna body coordinate system; ele as satellite elevation in the antenna body coordinate system; and ε as carrier phase measurement noise.

3. The method according to claim 1, characterized in that, The process, based on the carrier phase observations of the GNSS satellite from the antenna to be calibrated and the carrier phase observations of the GNSS satellite from the reference antenna, involves selecting visible satellites that meet preset conditions from the GNSS satellites within each epoch of the preset time period, calculating the unit observation vector of the visible satellites, and determining the reference satellite for each epoch based on the unit observation vectors of all the visible satellites. Specifically, this includes: S21. Mark the carrier phase observations of the GNSS satellite by the antenna to be calibrated and the carrier phase observations of the GNSS satellite by the reference antenna that contain cycle slips; S22. Select visible satellites from the GNSS satellites that have no cycle slip in the current time difference interval; S23. If the number of visible satellites is greater than the preset number, calculate the coordinates of the visible satellites, and derive the geometric distance from the antenna to the visible satellites and the unit observation vector of the visible satellites. Otherwise, continue processing the next epoch and repeat step S22 until all epochs have been processed; S24. Based on the unit observation vector of each of the visible satellites at the time difference interval T diff For the varying angular distance within the range, select a reference satellite.

4. The method according to claim 3, characterized in that, Step S24 specifically includes: Calculate epoch tT diff The angular distance Δθ of the motion of the visible satellite s is obtained by taking the dot product of the unit observation vector of the visible satellite at epoch t. s (t): Δθ s (t)=e s (t)e s (t-T diff ) Where: e s Let be the unit observation vector from the antenna to the visible satellite s. [x s y s z s [x1 y1 z1] represents the precise coordinates of the visible satellite s, and [x1 y1 z1] represents the coordinates of the antenna to be calibrated. Comparison at time difference interval T diff The reference satellite is determined by the angular distances of all visible satellites within the range. The reference satellite r is 5. The method according to claim 4, characterized in that, The method of constructing the three-difference phase center error measurement values ​​for all epochs based on the carrier phase observations of the reference satellite at each epoch by the antenna to be calibrated and the carrier phase observations of the reference satellite at each epoch by the reference antenna specifically includes: The carrier phase observations of the antenna to be calibrated and the reference antenna relative to the visible satellite s are subtracted to obtain the single-difference carrier phase observation. Based on the single-difference carrier phase observation The relative phase center error Ξ of the visible satellite s along the incident direction is obtained. s ; For the antenna to be calibrated and the reference antenna at epoch tT diff The first relative phase center error Ξ is obtained by subtracting the carrier phase observations of the visible satellite s and the reference satellite r from the epoch t. s (t), Second relative phase center error Ξ r (t), Third relative phase center error Ξ s (tT diff ) and the fourth relative phase center error Ξ r (tT diff ), where the first relative phase center error Ξ s (t) is the relative phase center error of the visible satellite s at epoch t, ​​and the second relative phase center error Ξ r (t) is the relative phase center error of the reference satellite r at epoch t, ​​and the third relative phase center error Ξ s (tT diff The fourth relative phase center error (Ξ) is the relative phase center error of the visible satellite s at epoch t-Tdiff. r (tT diff ) is the relative phase center error of the reference satellite r at epoch t-Tdiff; The difference between the first relative phase center error and the second relative phase center error is used to obtain the first double-difference phase center error measurement value Ξ. sr (t), the difference between the third relative phase center error and the fourth relative phase center error is used to obtain the second double-difference phase center error measurement value Ξ. sr (tT diff ): The first double-difference phase center error measurement value Ξ sr (t) and the second double-difference phase center error measurement value Ξ sr (tT diff By performing a difference operation, the measured value of the three-difference phase center error Ξ is obtained. sr (t,tT diff ),Right now in, For triple-difference carrier phase observations, It is a triple-difference noise component. It is the tri-difference antenna-satellite geometric distance; After processing all the observations for all epochs, the set of three-difference phase center error measurements Ω is obtained. Ξ , Ω Ξ ={Ξ sr (t,t-T diff )|s=1,2,...,r-1,r+1,...;t=T diff +1,T diff +2,...}。 6. The method according to claim 5, characterized in that, The step of constructing a weighted fitting model of the spherical harmonic function based on the weights of the measured values ​​of the three-difference phase center error, and solving the weighted fitting model of the spherical harmonic function to obtain the phase pattern of the antenna to be calibrated, specifically includes: The measured values ​​of the three-difference phase center error are expanded using spherical harmonic functions to form a weighted fitting model of the spherical harmonic function. The formula for the expansion of the spherical harmonic function is as follows: Where: n max Let m′ be the highest order of the spherical harmonic function, and m′ = max(m max ,n),m max Let m be the highest degree of the spherical harmonic function. max ≤n max , For a normalized adjoint Legendre polynomial of degree m, a nm and b nm Let be the spherical harmonic coefficients to be determined; Calculate the area of ​​the spherical quadrilateral formed by the unit observation vectors corresponding to the relative phase center error measurements that constitute the three-difference phase center error measurements; Based on the area of ​​the spherical quadrilateral corresponding to each of the three-difference phase center error measurements, determine the weight matrix W of the three-difference phase center error measurements. Ξ ; The set of three-difference phase center error measurements Ω Ξ As input data, the least squares method is used, based on the weight matrix W of the three-difference phase center error measurements. Ξ Solve for the spherical harmonic coefficients a nm and b nm The model for the phase center error is obtained as follows: The phase center error at the grid points in the model is calculated to obtain the phase pattern, which is the calibration result of the phase center error of the antenna to be calibrated.

7. An antenna calibration device, characterized in that, The device includes: The first calculation module is used to obtain the carrier phase observation of the antenna to be calibrated to the GNSS satellite and the carrier phase observation of the reference antenna to the GNSS satellite within a preset time period. The second calculation module is used to select visible satellites that meet preset conditions from the GNSS satellites within the preset time period based on the carrier phase observations of the GNSS satellites by the antenna to be calibrated and the carrier phase observations of the GNSS satellites by the reference antenna, calculate the unit observation vector of the visible satellites, determine the reference satellite for each epoch based on the unit observation vectors of all the visible satellites, and construct the three-difference phase center error measurement values ​​for all epochs based on the carrier phase observations of the reference satellites by the antenna to be calibrated and the carrier phase observations of the reference satellites by the reference antenna for each epoch. The third calculation module is used to construct a spherical quadrilateral based on the satellite unit observation vector of the observations constituting the three-difference phase center error measurement value, set the weight of each three-difference phase center error measurement value according to the area of ​​the spherical quadrilateral, construct a spherical harmonic function weighted fitting model according to the weight of the three-difference phase center error measurement value, and solve the spherical harmonic fitting function weighted model to obtain the phase pattern of the antenna to be calibrated.

8. The apparatus according to claim 7, characterized in that, The first calculation module is specifically used to acquire the carrier phase observations of the antenna to be calibrated for the GNSS satellite. and the carrier phase observations of the GNSS satellite by the reference antenna. in, The geometric distance from the antenna to be calibrated to the GNSS satellite is... Let be the geometric distance from the reference antenna to the GNSS satellite, c be the speed of light, and δt1, δt2, and δt be the distances from the reference antenna to the GNSS satellite. s denoted as clock errors of the first receiver, the second receiver, and the GNSS satellite, respectively; I as ionospheric error; T as tropospheric error; λ as carrier wavelength; N as carrier phase integer ambiguity; ξ(azi,ele) as phase center error; azi as satellite azi in the antenna body coordinate system; ele as satellite elevation in the antenna body coordinate system; and ε as carrier phase measurement noise.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the antenna calibration method according to any one of claims 1 to 6.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the antenna calibration method according to any one of claims 1 to 6.

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