Antenna phase center calibration method and system based on minimum PCV deviation constraint

Abstract

The application relates to an antenna phase center calibration method and system based on minimum PCV deviation constraints, which comprises the following steps: determining the equivalent conversion relationship of a phase model according to the coupling of PCO and PCV; determining the optimal constraint condition; converting the original model into an equivalent phase model according to the optimal constraint condition; constructing virtual observation values for simulation positioning test, which comprises the following steps: constructing virtual observation values by using a first model in a virtual coordinate system, correcting by using another model, then using a least square method for single point positioning calculation to calculate the positioning error in the north-east-high direction; verifying the coordinate estimation of the simulation positioning test and the difference between the converted phase model PCO with the constraint condition, and outputting the antenna phase center calibration result. The application has the advantages that on the basis of considering the PCO / PCV coupling, additional constraint conditions are added to convert the compared phase models, the workload of phase model comparison is reduced, and the influence of the phase model difference on positioning is more directly reflected.

Description

Technical Field

[0001] This invention belongs to the field of antenna measurement technology and satellite navigation and positioning, and specifically relates to a method for calibrating the absolute phase center of a ground receiver antenna by evaluating the consistency of the antenna phase model based on the minimum PCV deviation constraint. Background Technology

[0002] In the calibration of the absolute phase center of a ground receiver antenna, it is necessary to compare calibrations from different methods or institutions. Due to the correlation between PCO (Antenna Phase Center Offset) and PCV (Antenna Phase Center Variation) in the phase model, the calibration results must be merged into the same PCO before comparing PCV differences. In actual data processing, calibration results from different methods or institutions vary, requiring conversion for each comparison. Moreover, this method can only assess differences in the observed value domain and is not intuitive. Therefore, it is necessary to try different evaluation methods for a fast, convenient, and accurate assessment of model differences and consistency. This invention proposes an equivalent phase model conversion method with an additional minimum PCV constraint based on the PCO / PCV correlation in the antenna phase model, to achieve more accurate and efficient calibration of the absolute phase center of a ground receiver antenna. Summary of the Invention

[0003] The technical problem this invention aims to solve is that, in common ground receiver antenna absolute phase center calibration methods, the antenna phase comparison process requires PCO alignment due to correlation, and comparisons can only be made in the observation domain. This results in complex data processing, unintuitive comparison results, and difficulty in assessing the impact of model differences on positioning.

[0004] The technical solution adopted in this invention is an antenna phase center calibration method based on minimum PCV deviation constraint, which includes the following steps:

[0005] Step 1: Determine the equivalent transformation relationship of the phase model based on the coupling between PCO and PCV;

[0006] Step 2: Determine the optimal constraints and perform an equivalent phase model transformation on the original model according to the optimal constraints;

[0007] Step 3: Construct virtual observations for simulation positioning test. This includes constructing virtual observations in a virtual coordinate system using the first model, correcting them with another model, and then using the least squares method to perform single-point positioning calculation and calculate the positioning error in the northeast-northeast direction.

[0008] Step 4: Verify the difference between the coordinate estimate from the simulation positioning test and the phase model PCO after transformation with constraints, and output the antenna phase center calibration result.

[0009] Furthermore, in step 1, when model A1 is known, to equivalently transform A1 to model A2, the PCC calculated by A1 and A2 according to the definition of antenna phase error must be equal or the PCC in each direction must differ by a constant, thus determining the equivalent transformation relationship of the phase model.

[0010] Furthermore, step 2 is implemented by including the following sub-steps:

[0011] Step 2.1, based on the target of minimizing PCV, establish the antenna phase constraint conditions as follows:

[0012]

[0013] Where PCO0 / PCV0 are the model values ​​after constraints on the original antenna model PCO1 / PCV1, α represents the azimuth angle, and z represents the nadir angle. This represents the row vector consisting of all grid points PCV0, where PCV0 is the corresponding column vector, n represents the number of grid points, (α1, z1) represents the azimuth angle α1 and zenith distance z1 corresponding to the first grid point, ... (α n ,z n ) represents the azimuth angle α corresponding to the nth grid point. n and zenith distance z n PCV0(α,z) represents the value corresponding to a grid point; represents the sum of squares of PCV0 over all grid points, and min indicates that the left side of the equation reaches its minimum value;

[0014] Step 2.2, let d pco =(d N ,d E ,d U ), representing the difference in PCO between the two models, d N d E d U It is d pco The projection of d in the N, E, U directions of the antenna coordinate system D Represent the model baseline error; solve for the parameter X = (d) based on the constraints. pco ,d D This allows the equivalent transformation model to satisfy the constraints. The solution method is as follows:

[0015] Taking the derivative with respect to X and setting it to 0, we get:

[0016]

[0017] Right now

[0018]

[0019] Where N and V represent the normal equation and error vector, respectively, H = (e, -1) represents the coefficient matrix corresponding to all grid points, e represents the direction vector from the station to the satellite, PCV1 represents the vector composed of the PCV values ​​of all grid points in the original model, and N -1 H represents the inverse matrix of the normal equation. T This indicates the transpose of the coefficient matrix;

[0020] After calculating X, the given phase is transformed to satisfy the minimum PCV constraint condition according to the equivalent transformation relationship of the phase model determined in step 1.

[0021] Furthermore, step 3 is implemented by including the following sub-steps:

[0022] Step 3.1: Construct virtual positioning simulation observations using the antenna phase model. Assume an antenna is placed in the NEU coordinate system, and the phase model of this antenna is PCC1(PCO1 / PCV1). Then, observe the virtual satellite, and the observation value is PCC0(PCO0 / PCV0). Divide the upper hemisphere of the antenna into grid points, ensuring the grid division is consistent with that of PCV. The virtual satellite is located on these grid points. The virtual ranging observation equation is as follows:

[0023]

[0024] Where, d T Represents the clock bias parameter, where i identifies the i-th virtual satellite, and V i This represents the residual of the corresponding virtual observation equation. Indicates virtual observations. This represents the phase center correction value of the antenna, e represents the direction vector, and dn, de, and du represent the N, E, and U deviations of the observation value in the NEU coordinate system, respectively.

[0025] Step 3.2: Solve the coordinate deviation of the simulated single-point positioning using least squares. This includes adjusting the coordinate deviation for all the virtual ranging observations of the grid points mentioned above, according to the least squares principle. The parameter to be estimated is X = (dn, de, du, dt), where dt represents the common ranging deviation of all virtual observations in different orientations. The coefficient vector corresponding to the i-th virtual observation is H. i =(- i ,1),e i Let i represent the direction vector of satellite i, and let the design matrix corresponding to all observations be denoted as . The error vector is denoted as V = (V 1 ,…, n ) T The formula for least squares estimation of the parameters to be estimated is as follows:

[0026] X=(H T×H) -1 ×(G T ×V)

[0027] in, V represents the transpose of the coefficient vectors of the 1st to nth virtual satellites, respectively. 1 ,…, n The residuals of the virtual observation equations for the 1st to nth satellites, as represented by equation (11), are respectively expressed.

[0028] Furthermore, the implementation of step 4 includes the following sub-steps:

[0029] Step 4.1: For the two given antenna phase models A1 and A2, perform constrained phase model equivalent transformations to obtain B1 and B2. Then, calculate the PCO difference between the transformed B1 and B2, denoted as d. pco ;

[0030] Step 4.2: Perform virtual positioning on the pre-conversion phase models A1 and A2 according to Step 3, and calculate the positioning error, denoted as d. a Then, virtual positioning is performed on the transformed phase models B1 and B2 in the same way, and the positioning error is denoted as d. b Compare the d obtained in step 4.1 pco With d a d b ;

[0031] Step 4.3: In actual antenna phase calibration, the data is divided into multiple time periods. The calibration results of different time periods are converted according to the minimum PCV mentioned above. If the difference in PCO between different time periods after conversion is less than the calibration accuracy requirement, the phase center calibration result is considered to have converged and the repeatability accuracy meets the requirements.

[0032] On the other hand, the present invention also provides an antenna phase center calibration system based on minimum PCV deviation constraint, for implementing the antenna phase center calibration method based on minimum PCV deviation constraint as described above.

[0033] Moreover, it includes the following modules,

[0034] The first module is used to determine the equivalent transformation relationship of the phase model based on the coupling between PCO and PCV.

[0035] The second module is used to determine the optimal constraints and perform equivalent phase model transformation on the original model according to the optimal constraints.

[0036] The third module is used to construct virtual observations for simulation positioning tests. This includes constructing virtual observations in a virtual coordinate system using the first model, correcting them with another model, and then using the least squares method to perform single-point positioning calculations and calculate the positioning error in the northeast-high direction.

[0037] The fourth module is used to verify the difference between the coordinate estimate from the simulation positioning test and the phase model PCO after transformation with constraints, and outputs the antenna phase center calibration result.

[0038] Alternatively, it may include a processor and a memory, the memory being used to store program instructions, and the processor being used to call the stored instructions in the memory to execute an antenna phase center calibration method based on minimum PCV deviation constraints as described above.

[0039] Alternatively, it may include a readable storage medium storing a computer program that, when executed, implements an antenna phase center calibration method based on minimum PCV deviation constraints as described above.

[0040] This invention proposes a novel antenna phase center calibration scheme based on minimum PCV deviation constraints, which can evaluate model differences in the positioning domain, reduce the data processing process during antenna phase model evaluation, and improve the accuracy of phase model comparison.

[0041] The present invention is simple and convenient to implement, highly practical, and solves the problems of low practicality and inconvenience in actual application of related technologies, thus having significant market value. Attached Figure Description

[0042] Figure 1 This is a diagram showing the PCV changes of the TRM57971 antenna before and after the equivalent conversion in this embodiment of the invention.

[0043] Figure 2 This is a graph showing the change in PCV before and after constraints in an embodiment of the present invention. Detailed Implementation

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

[0045] This invention addresses the issue of outdoor absolute calibration results for receiver antennas. When comparing and evaluating phase models, it's necessary to align the average phase center offset (PCO) of the reference model and the model to be evaluated to the same baseline, and then compare the difference in phase center variation (PCV). This invention innovatively proposes a new antenna phase model positioning domain consistency evaluation method based on PCO / PCV coupling. The advantage of this invention is that, considering PCO / PCV coupling, it adds additional constraints to the compared phase models for equivalent transformation. This ensures that the equivalent single-point positioning difference between the models equals the difference in PCO after transformation, transforming the phase model evaluation from the observation domain to the positioning domain. This reduces the amount of repetitive calculations during phase model comparison and more intuitively reflects the impact of phase model differences on positioning.

[0046] This invention provides an antenna phase center calibration method based on minimum PCV deviation constraints. By applying minimum PCV constraints to an equivalent phase model transformation, it achieves fast, convenient, and accurate antenna phase model consistency evaluation. The implementation process includes the following steps:

[0047] Step 1: Determine the equivalent transformation method of the phase model based on the coupling between PCO and PCV.

[0048] Furthermore, for ease of implementation and reference, the preferred implementation method for step 1 of the embodiment is provided as follows:

[0049] Step 1.1: Determine the basic method for equivalent transformation of the phase model PCO / PCV based on the formula for calculating phase error. In the GNSS field, the phase center correction (PCC) error introduced by the transmitting or receiving antenna is generally decomposed into antenna phase offset (PCO) and antenna phase variation (PCV) relative to PCO.

[0050] According to the definition, the formula for calculating antenna phase error PCC is as follows:

[0051] PCC(α,z)=-e·PCO+PCV(α,z)+D (5)

[0052] Where α and z represent the azimuth and zenith distance of the satellite, PCC(α,z) represents the corresponding antenna phase error, PCV(α,z) represents the corresponding antenna phase change, e represents the direction vector of the station pointing to the satellite, PCO represents the antenna phase center deviation, and D represents the common part of the phase ranging deviation of each azimuth. Since D has a similar effect to the receiver clock error, D cannot be accurately calibrated, that is, any value of D will not affect the correction effect of the phase model. Therefore, when the model A1(PCO1 / PCV1(α,z) / D1) is known, A1 should be equivalently transformed into model A2(PCO2 / PCV2(α,z) / D2). The PCC calculated by A1 and A2 according to equation (5) must be equal (or the PCC of each direction differs by a constant).

[0053] Step 1.2: Based on the principles in Step 1.1, derive the equivalent transformation formula, that is:

[0054] PCC=-e·PCO1+PCV1(α,z)+D1=-e·PCO2+PCV2(α,z)+D2 (6)

[0055] PCV2(α,z)=PCV1(α,z)+e·d pco -d D (7)

[0056] Where, d pco =(PCO2-PCO1)=(d N ,d E ,d U ), representing the difference in PCO between the two models, d N d E d U It is d pco The projection of d in the N, E, U directions of the antenna coordinate system D =D2-D1 represents the model reference difference; PCO1 / PCV1(α,z) / D1 represent the antenna phase offset, change and reference of the original phase model A1, respectively, while PCO2 / PCV2(α,z) / D2 represent the corresponding antenna phase offset, change and reference of the transformed model A2, respectively.

[0057] There is a coupling relationship between PCO, PCV and D, which also indicates that PCC can be decomposed into different PCO / PCV combinations. For the two sets of values ​​of the same antenna phase model: PCO1 / PCV1 and PCO2 / PCV2, they satisfy the relationship (7).

[0058] Therefore, given any set of d pco Then, according to equation (7), model A1 can be transformed to be related to d. pcoThe corresponding model is A2. In this embodiment, the antenna phase data igs05.atx and igs14.atx released by igs are selected respectively. For the phase model of the L1 frequency point of the TRM57971 antenna, the differences of different versions of PCO are shown in Table 1. In this embodiment, the model of igs05.atx is aligned to igs14.atx, and d is selected. D =-d U This allows the PCV in the zenith direction to be 0 before and after the transformation. The PCV changes before and after the equivalent transformation are as follows: Figure 1 As shown.

[0059] Table 1. PCO differences between different IGS versions of the TRM57971 antenna.

[0060]

[0061] Step 2: Determine the optimal constraints and perform an equivalent phase model transformation on the original model according to the optimal constraints.

[0062] Furthermore, for ease of implementation and reference, the preferred implementation method for step 2 of the embodiment is provided as follows:

[0063] Step 2.1: Establish antenna phase constraints. Since PCO is represented as a three-dimensional vector in the antenna coordinate system, its effect on positioning is equivalent to a translation transformation. The relative change of PCV is complex and is given in the form of grid point correction values. Therefore, if the change of PCV at different grid points of the constrained antenna phase model is as small as possible, the interpolation error can be reduced.

[0064] When given a set of original models A1, model A1(PCO1 / PCV1(α,z) / D1) can be transformed by formula (7) to obtain the transformed model A2(PCO2 / PCV2(α,z) / D2). As can be seen from step 1.2, PCC can be decomposed into an infinite number of equivalent (PCO / PCV / D) combinations. Therefore, there are an infinite number of transformation relationships, and thus there are multiple models A2. Let the model in model A2 that satisfies the constraint condition (8) be A0(PCO0 / PCV0(α,z) / D0). Therefore, in this step, determining the optimal constraint condition means giving the constraint condition of A0. PCO is generally given in the form of a three-dimensional vector and then projected onto the satellite direction, while PCV divides the upper hemisphere of the antenna into equal intervals and directly gives the ranging deviation at the corresponding grid point azimuth. Based on the goal of minimizing the sum of the squares of PCV, the constraint condition is given. Model A0 satisfies the following antenna phase model constraint, namely:

[0065]

[0066] Where PCO0 / PCV0 is the optimal phase model value that satisfies the above conditions, α represents the azimuth angle, and z represents the nadir angle. This represents the row vector consisting of all grid points PCV0 of the optimal phase model A0, where PCV0 is the corresponding column vector, n represents the number of grid points, (α1, z1) represents the azimuth angle α1 and zenith distance z1 corresponding to the first grid point, ... (α n ,z n ) represents the azimuth angle α corresponding to the nth grid point. n and zenith distance z n PCV0(α,z) represents the value corresponding to a grid point; Let represent the sum of the squares of PCV0 at all grid points, and let represent the minimum value obtained on the left side of equation (8).

[0067] Step 2.2: Solve for the parameter X = (d) based on the constraints. pco ,d D This ensures that the equivalent transformation model satisfies the constraints. In equation (8), taking the derivative with respect to X and setting the derivative to 0 yields:

[0068]

[0069] Right now

[0070]

[0071] Where N and V represent the normal equation and error vector, respectively, and H = (e, -1) represents the coefficient matrix corresponding to all grid points. N represents the row vector consisting of all grid points PCV1 of a given or known model A1, where PCV1 is the corresponding column vector. -1 H represents the inverse matrix of the normal equation. T This represents the transpose of the coefficient matrix. The parameter X to be estimated can be calculated using equation (10), and then the given phase is transformed to satisfy the minimum PCV constraint condition according to the method in step 1.

[0072] In this embodiment, the TRM57971 antenna L1 frequency phase model published in the igs14.atx file is also selected. Then, the minimum PCV constraint mentioned above is applied, with a grid spacing of 5°, consistent with the PCV grid spacing in the phase model. According to formula (10), X = (0.022, -0.014, 3.464, 1.596) mm can be obtained. Then, the equivalent transformation is performed according to step 1, and the changes before and after are as follows. Figure 2 As shown.

[0073] Step 3: Construct virtual observations for simulation positioning tests.

[0074] The positioning difference between the two models was calculated through a virtual simulation positioning experiment. In a virtual coordinate system, virtual observations were constructed using the first model, corrected using the other model, and then the least squares method was used to perform single-point positioning calculations to determine the positioning error in the northeast (NEU) direction.

[0075] Furthermore, for ease of implementation and reference, the preferred implementation method for step 3 of the embodiment is provided as follows:

[0076] Step 3.1: Construct virtual positioning simulation observations using the antenna phase model. In the simulation positioning experiment, an antenna is placed in the NEU coordinate system. The phase model of this antenna is PCC1(PCO1 / PCV1). Then, the virtual satellite is observed, and the observation value is PCC0(PCO0 / PCV0). The upper hemisphere of the antenna is divided into grid points, and the grid points are consistent with the grid division of PCV. The virtual satellite is located on these grid points. The virtual ranging observation equation is as follows:

[0077]

[0078] Where, d T Represents the clock bias parameter, where i identifies the i-th virtual satellite, and V i This represents the residual of the corresponding virtual observation equation.

[0079] Indicates virtual observations. The value represents the phase center correction of the antenna, e represents the direction vector, and dn, de, and du represent the N, E, and U deviations of the observation in the NEU coordinate system, respectively.

[0080] Step 3.2: Solve for the coordinate deviation of the simulated single-point positioning using least squares. For the virtual ranging observations of all the grid points mentioned above, calculate the coordinate deviation by adjustment according to the least squares principle. The parameter to be estimated is X = (dn, de, du, dt), where dt represents the common ranging deviation of all virtual observations in different orientations, and the coefficient vector corresponding to the i-th virtual observation is H. i =(- i ,1),e i Let i represent the direction vector of satellite i, and let the design matrix corresponding to all observations be denoted as . The error vector is denoted as V = (V 1 ,…, n ) T The formula for least squares estimation of the parameters to be estimated is as follows:

[0081] X=(H T ×H) -1 ×(H T ×V) (12)

[0082] in, V represents the transpose of the coefficient vectors of the 1st to nth virtual satellites, respectively. 1 ,…, n The residuals of the virtual observation equations for the 1st to nth satellites, as represented by equation (11), are respectively expressed.

[0083] In this example, the TRM57971 antenna models released in igs05.atx and igs14.atx were also selected for virtual positioning tests. The virtual satellites were evenly distributed on a 5° grid. The virtual positioning result was X = (0.062, -0.2743, 1.5431) mm, which also shows that the difference between the TRM57971 antennas released in igs05.atx and igs14.atx in the positioning domain exceeds 1 mm.

[0084] Step 4: Verify the difference between the coordinate estimate obtained from the simulation positioning test and the phase model PCO after transformation with constraints. Based on the obtained difference, further realize the absolute phase center calibration of the ground receiver antenna and output the antenna phase center calibration result.

[0085] This invention performs a constrained phase model equivalent transformation on two given models A1 and A2 to obtain B1 and B2, compares the virtual positioning differences between A1 / A2 and B1 / B2, and the changes in PCO differences between A1 / A2 and B1 / B2 before and after the transformation.

[0086] Furthermore, for ease of implementation and reference, the preferred implementation method for step 4 of the embodiment is provided as follows:

[0087] Step 4.1: For two given antenna phase models A1 and A2, perform constrained phase model equivalent transformations to obtain B1 and B2. Then calculate the PCO difference between B1 and B2 after the transformation, denoted as d. pco .

[0088] Step 4.2: Perform virtual positioning on the pre-conversion phase models A1 and A2 according to Step 3, and calculate the positioning error, denoted as d. a Then, virtual positioning is performed on the transformed phase models B1 and B2 in the same way, and the positioning error is denoted as d. b Compare d in step 4.1 pco With d a d b Quantitative relationships.

[0089] In this example, the aforementioned case was also selected, and the comparison results are shown in Table 2:

[0090] Table 2 Comparison of virtual positioning results and PCO differences before and after constraints.

[0091]

[0092] As can be seen from the table, the virtual positioning result remains unchanged before and after the equivalent phase model conversion. Secondly, the PCO difference of the phase models that meet the constraints is equal to the virtual positioning result. Therefore, if different institutions publish antenna phase models that meet the minimum PCV, the PCO results of different models can be directly compared. The difference in PCO is the difference between these models in the positioning domain, which eliminates the need for data processing in virtual positioning experiments.

[0093] Step 4.3: In actual antenna phase calibration, the data can be divided into multiple time periods. The calibration results of different time periods are converted according to the minimum PCV mentioned above. If the difference in PCO between different time periods after conversion is less than the calibration accuracy requirement (e.g., 1 mm), then the phase center calibration result can be considered to have converged and the repeatability accuracy meets the requirements.

[0094] In this example, the phase center of the TRM59800 antenna was calibrated. The collected data was divided into four consecutive time periods (1-4), each lasting 4 hours. Three-difference observations were used for phase center calibration in a two-step method. The calibration results were then equivalently transformed according to step 2. The PCO estimation results and the differences between the time periods are shown in Table 3. It can be seen that the original PCO estimates may have significant differences of several millimeters between the time periods, but after the equivalent transformation, the PCO differences are all less than 1 mm. Therefore, the current calibration results can be considered convergent, achieving an accuracy of 1 mm.

[0095] Table 3. PCO Differences After Equivalent Transformation of TRM59800 Antenna Continuous Time Calibration Results

[0096]

[0097] The antenna phase model consistency evaluation method in this invention can be used to compare the differences between antenna phase models published by different organizations. It transforms the model differences from the observation domain to the positioning domain, making the model differences more intuitive, simplifying the evaluation process, and improving the accuracy of the absolute phase center calibration of the ground receiver antenna.

[0098] In specific implementation, the method proposed in the technical solution of this invention can be automatically executed by those skilled in the art using computer software technology. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of this invention and computer equipment including the computer program running the corresponding computer program, should also be within the protection scope of this invention.

[0099] In some possible embodiments, an antenna phase center calibration system based on minimum PCV deviation constraints is provided, including the following modules:

[0100] The first module is used to determine the equivalent transformation relationship of the phase model based on the coupling between PCO and PCV.

[0101] The second module is used to determine the optimal constraints and perform equivalent phase model transformation on the original model according to the optimal constraints.

[0102] The third module is used to construct virtual observations for simulation positioning tests. This includes constructing virtual observations in a virtual coordinate system using the first model, correcting them with another model, and then using the least squares method to perform single-point positioning calculations and calculate the positioning error in the northeast-high direction.

[0103] The fourth module is used to verify the difference between the coordinate estimate from the simulation positioning test and the phase model PCO after transformation with constraints, and outputs the antenna phase center calibration result.

[0104] In some possible embodiments, an antenna phase center calibration system based on minimum PCV deviation constraint is provided, including a processor and a memory. The memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute the antenna phase center calibration method based on minimum PCV deviation constraint as described above.

[0105] In some possible embodiments, an antenna phase center calibration system based on minimum PCV deviation constraint is provided, including a readable storage medium on which a computer program is stored. When the computer program is executed, it implements the antenna phase center calibration method based on minimum PCV deviation constraint as described above.

[0106] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A method for antenna phase center calibration based on minimum PCV deviation constraint, characterized in that, Performing an equivalent phase model transformation with additional minimum PCV constraints includes the following steps: Step 1: Determine the equivalent transformation relationship of the phase model based on the coupling between PCO and PCV; Step 2: Determine the optimal constraints and perform an equivalent phase model transformation on the original model according to the optimal constraints; the optimal constraints are established based on the objective of minimizing PCV, specifically as follows: in, PCO 0 / PCV 0 represents the original antenna model. PCO 1 / PCV The model values ​​after constraint 1 Indicates azimuth. Indicates the nadir angle. Indicates all grid points PCV A row vector consisting of 0s For the corresponding column vectors; This represents the value corresponding to a grid point. Indicates all grid points PCV 0 sum of squares, This indicates that the left side of the equation has reached its minimum value; set up , representing the difference in PCO between the two models. d N , d E , d U yes d pco Projection in the N, E, U directions of the antenna coordinate system Represent the model baseline error; solve for the parameters based on the constraints. X =( d pco , d D ), Right now in, N and V Let the normal equation and error vector be represented respectively. H =( e (-1) represents the coefficient matrix corresponding to all grid points. This represents the direction vector from the station to the satellite. This represents a vector consisting of the PCV values ​​of all grid points in the original model. The inverse matrix of the normal equation, This indicates the transpose of the coefficient matrix; According to the equivalent transformation relationship of the phase model determined in step 1, the given phase is transformed to satisfy the minimum PCV constraint condition; Step 3: Construct virtual observations for simulation positioning test. This includes constructing virtual observations in a virtual coordinate system using the first model, correcting them with another model, and then using the least squares method to perform single-point positioning calculation and calculate the positioning error in the northeast-northeast direction. Step 4: Verify the difference between the coordinate estimate from the simulation positioning test and the transformed phase model PCO with constraints, and output the antenna phase center calibration result; implemented as follows. For two given antenna phase models A1 and A2, perform constrained phase model equivalent transformations to obtain B1 and B2. Then, calculate the PCO difference between the transformed B1 and B2, denoted as d. pco ; The PCO difference of the phase model that satisfies the constraints is equal to the virtual positioning result. The PCO difference is the difference of the model in the positioning domain. In the actual antenna phase calibration, the data is divided into multiple time periods. The calibration results of different time periods are transformed according to step 2 with minimum PCV constraints. If the PCO difference of different time periods after the transformation is less than the preset calibration accuracy requirement, it is determined that the phase center calibration result has converged and the repeatability accuracy meets the requirements.

2. The antenna phase center calibration method based on minimum PCV deviation constraint according to claim 1, characterized in that: In step 1, based on the known model A At 1 o'clock, it is necessary to A 1. Equivalent transformation to model A 2, A 1 and A 2. The PCC calculated according to the definition of antenna phase error must be equal or the PCC in each direction must differ by a constant, and the equivalent transformation relationship of the phase model must be determined.

3. The antenna phase center calibration method based on minimum PCV deviation constraint according to claim 1, characterized in that: In step 2, ={ PCV 0 (α 1 ,z 1 ) ,…, PCV 0 (α n ,z n ) } represents all grid points PCV A row vector consisting of 0s n represents the number of grid points. (α 1 ,z 1 ) This indicates the azimuth angle corresponding to the first grid point. α 1 and zenith distance z 1,… (α n ,z n ) This represents the azimuth angle corresponding to the nth grid point. α n and zenith distance z n .

4. The antenna phase center calibration method based on minimum PCV deviation constraint according to claim 1, characterized in that: Step 3 is implemented by including the following sub-steps: Step 3.1: Construct virtual positioning simulation observations using the antenna phase model. Assume an antenna is placed in the NEU coordinate system, and the phase model of this antenna is PCC1(PCO1 / PCV1). Then, observe the virtual satellite, and the observation value is PCC0(PCO0 / PCV0). Divide the upper hemisphere of the antenna into grid points, ensuring the grid division is consistent with that of PCV. The virtual satellite is located on these grid points. The virtual ranging observation equation is as follows: in, Represents the clock difference parameter. i Used to identify the first i A virtual satellite, This represents the residual of the corresponding virtual observation equation. Indicates virtual observations. This indicates the phase center correction value of the antenna. Represents the direction vector. These represent the N, E, and U deviations of the observed value in the NEU coordinate system, respectively. Step 3.2: Solve for the coordinate deviation of the simulated single-point positioning using least squares, including the virtual distance measurement observations for all the grid points mentioned above. Adjust the coordinate deviation according to the least squares principle. The parameter to be estimated is... , This represents the common distance measurement bias across all virtual observations in different orientations. i The coefficient vector corresponding to each virtual observation is , Indicates satellite i The direction vector, and the design matrix corresponding to all observations, are denoted as . The error vector is denoted as The formula for least squares estimation of the parameters to be estimated is as follows: in, These represent the transposes of the coefficient vectors of the 1st to nth virtual satellites, respectively. The residuals of the virtual observation equations for the 1st to nth satellites, as represented by equation (11), are respectively expressed.

5. The antenna phase center calibration method based on minimum PCV deviation constraint according to claim 1, characterized in that: The implementation of step 4 further includes, Virtual positioning was performed on phase models A1 and A2 before the conversion according to step 3, and the positioning error was calculated and denoted as d. a Then, virtual positioning is performed on the transformed phase models B1 and B2 in the same way, and the positioning error is denoted as d. b The obtained d pco With d a d b .

6. An antenna phase center calibration system based on minimum PCV deviation constraint, characterized in that: This method is used to implement an antenna phase center calibration method based on minimum PCV deviation constraint as described in any one of claims 1-5.

7. The antenna phase center calibration system based on minimum PCV deviation constraint according to claim 6, characterized in that: Includes the following modules, The first module is used to determine the equivalent transformation relationship of the phase model based on the coupling between PCO and PCV. The second module is used to determine the optimal constraints and perform equivalent phase model transformation on the original model according to the optimal constraints. The third module is used to construct virtual observations for simulation positioning tests. This includes constructing virtual observations in a virtual coordinate system using the first model, correcting them with another model, and then using the least squares method to perform single-point positioning calculations and calculate the positioning error in the northeast-high direction. The fourth module is used to verify the difference between the coordinate estimate from the simulation positioning test and the phase model PCO after transformation with constraints, and outputs the antenna phase center calibration result.

8. The antenna phase center calibration system based on minimum PCV deviation constraint according to claim 6, characterized in that: It includes a processor and a memory, the memory being used to store program instructions, and the processor being used to call the stored instructions in the memory to execute the antenna phase center calibration method based on the minimum PCV deviation constraint as described in any one of claims 1-5.

9. The antenna phase center calibration system based on minimum PCV deviation constraint according to claim 6, characterized in that: The device includes a readable storage medium on which a computer program is stored, and when the computer program is executed, it implements an antenna phase center calibration method based on minimum PCV deviation constraints as described in any one of claims 1-5.

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