Three-coordinate air radar height measurement value correction method based on joint estimation

Abstract

The invention relates to a three-coordinate air radar height measurement value correction method based on joint estimation, and belongs to the technical field of multi-radar data fusion. According to the method, a relative system error thought is adopted, observation data of main and auxiliary station radars on a typical air route target are selected, and a height relative system error joint calculation model derived from radar asynchronous measurement data is established through three-dimensional unified rectangular coordinate conversion, linear parameter estimation, time registration point calculation and the like; and the reliability of an error accumulation estimation result is ensured through operations such as singular value elimination. Experimental results show that the follow-up height measurement value of the auxiliary station radar is corrected according to the cumulative estimation result, the average difference of the height values of the track lines is reduced by one order of magnitude, the error correction effect is very ideal, and the requirements for air radar height estimation and fusion precision in engineering practice are met. The estimation method provided by the invention is scientific, reasonable in scheme implementation steps and very high in operability and practicability.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-radar data fusion, and particularly relates to a method for correcting the altitude measurement value of a three-coordinate air defense radar based on joint estimation. Background Art

[0002] Three-coordinate air defense radars are generally deployed on the ground. By mechanically scanning in the horizontal direction (azimuth angle) and electrically scanning in the vertical direction (elevation angle), they obtain measurement data of the distance, azimuth, and altitude of airborne targets. In practical applications, the altitude measurement values of two radars for the same airborne target often differ by more than a kilometer, seriously affecting the target association recognition and data fusion effect. At the same time, it poses risks to the handling of special situations.

[0003] The systematic errors existing in the elevation angle and distance measurements are the main factors causing inaccurate altitude measurements of three-coordinate air defense radars. Generally, a systematic error refers to the inherent error of a measurement value relative to a certain reference system. If the absolute altitude value of a specified target is used as the reference system, the absolute systematic error is obtained. In the multi-radar networked observation of airborne targets, the absolute altitude value of the target is mostly unknown in most cases. What we can easily obtain are the discrete observation values of different radars for the same airborne moving target. Traditional data calibration methods all attempt to estimate the absolute systematic error existing in the radar altitude measurement through such measurement data. However, simulation experiments show that the altitude of the target after correcting the systematic error in this way depends on the relative altitude of the single-radar measurement values participating in the calculation, and has little correlation with the true altitude of the target. In practical engineering applications, the estimated result of the absolute systematic error of radar A will vary depending on whether the measurement data of radar B or radar C is used. If it is recognized that the altitude systematic error calculated from the data of A and B is the absolute systematic error of radar A, it may lead to a contradiction where the difference between the corrected target altitude values of A and B decreases while the difference between the corrected altitude values of A and C increases. Therefore, the idea of obtaining the absolute altitude systematic error is difficult to grasp in engineering practice.

[0004] For the measurement system of an air surveillance radar network, in most cases, only the observation data of multiple radars on the same target in the same time period can be provided, and usually a set of measurement values (distance, azimuth, altitude) on a typical flight path (the target flies in a straight line at a certain altitude) can be obtained. Based on such a data environment, we propose: ①Relative to other radars in the network, the observation of a certain radar is accurate. At this time, the altitude measurement value of this radar (named the master station) can be used as the true description of the target altitude, and other radars (named slave stations) can use this as a reference to obtain the relative systematic error of the altitude of the slave station radar relative to the master station radar. For a regional radar network, other radars can be corrected based on the master station. In this way, while achieving the consistency of the observation results of each radar, the complexity of the estimation method is simplified, which is convenient for engineering implementation. ②Regarding the range and elevation measurement errors as the main components of the altitude systematic error, a joint solution model for the relative systematic error of altitude derived from asynchronous radar measurement data is established. ③A cumulative estimation method for the relative systematic error of altitude of a three-coordinate air surveillance radar based on the solution results of multiple range and elevation relative systematic errors is proposed, and the influence of abnormal error solution results is shielded by means of historical experience data. ④Based on the cumulative estimation results, the altitude measurement values in the subsequent observations of the slave station radar are corrected. Summary of the Invention

[0005] (1) Technical Problems to be Solved

[0006] The technical problem to be solved by the present invention is how to provide a method for correcting the altitude measurement value of a three-coordinate air surveillance radar based on joint estimation to solve the problem of systematic errors existing in the measurement of the elevation angle and range.

[0007] (2) Technical Solutions

[0008] To solve the above technical problems, the present invention proposes a method for correcting the altitude measurement value of a three-coordinate air surveillance radar based on joint estimation, and the method includes the following steps:

[0009] Step 1: Initialize the range relative systematic error list ER and the elevation relative systematic error list EP of the slave station radar B.

[0010] Step 2: Select the observation data of a straight flight path of the same air target by the master station radar A and the slave station radar B {(t SAi ,R Ai ,θ Ai ,h Ai ), i = 1, 2,... n} and {(t SBj ,R Bj ,θ Bj ,h Bj ), j = 1, 2,... m}, where n represents the number of observation data points of the master station radar A, and m represents the number of observation data points of the slave station radar B; (t SAi, R Ai , θ Ai , h Ai ) represents t SAi The target distance R measured by the master station radar A at time t Ai , azimuth θ Ai and altitude h Ai ; (t SBj , R Bj , θ Bj , h Bj ) represents t SBj The target distance R measured by the slave station radar B at time t Bj , azimuth θ Bj and altitude h Bj .

[0011] Step 3: Perform coordinate transformation on the observation data of the master station radar A to obtain a set of corresponding three-dimensional unified rectangular coordinates {(t SAi , x SAi , y SAi , z SAi ), i = 1, 2, … n}.

[0012] Step 4: Perform coordinate transformation on the observation data of the slave station radar B to obtain a set of corresponding three-dimensional unified rectangular coordinates {(t SBj , x SBj , y SBj , z SBj ), j = 1, 2, … m}.

[0013] Step 5: Use the linear parameter estimation model to estimate the parameters of the altitude observation data of the master station radar A and the three-dimensional observation data of the slave station radar B to obtain the altitude observation track line parameters of the master station radar A and the three-dimensional observation track line parameters of the slave station radar B;

[0014] Step 6: Calculate the altitude time registration point of the master station radar A and the three-dimensional time registration point of the slave station radar B according to the observation point time of the slave station radar B; Calculate the distance between the time registration point of the slave station radar B and the radar station site and the corresponding target altitude value, expressed as {(R′ Bi , h B ′ i ), i = 1, 2, … m};

[0015] Step 7: Set the range and elevation relative system errors of the secondary station radar B as (λ, α). Use the time registration point data of the primary station radar A and the secondary station radar B to construct a joint solution system of equations for the altitude relative system error with (λ, α) as the unknowns, and use the quasi-Newton method for finding a set of real roots of the non-linear equations to solve this system of equations; if the system of equations has no solution, go to Step 2, select the straight track line observation data of the primary station radar A and the secondary station radar B for the same airborne target, and start a new round of altitude system error estimation; if the system of equations has a solution, let the solution of the system of equations be (Dr, Dp).

[0016] Step 8: Respectively perform singular value judgment on Dr and Dp, incorporate the non-singular values into the relative system error lists ER and EP of the secondary station radar B, and organize the error lists.

[0017] Step 9: If the length of the error list is greater than or equal to the basic statistical number PN, calculate the mean value of the list elements and output it as the cumulative estimation result of the altitude relative system error of the secondary station radar B; otherwise, it is considered that the current condition for estimating the altitude relative system error of the secondary station radar B is not yet available.

[0018] Step 10: Go to Step 2, select the straight track line observation data of the primary station radar A and the secondary station radar B for the same airborne target, and start a new round of system error estimation.

[0019] Step 11: Based on the effective cumulative estimation result of the altitude relative system error output in Step 9, correct all subsequent altitude measurement values of the secondary station radar B.

[0020] (III) Beneficial Effects

[0021] The present invention proposes a method for correcting the altitude measurement value of a three-coordinate air surveillance radar based on joint estimation. The present invention adopts the idea of relative system error. By selecting the observation data of the primary and secondary station radars for typical route targets, through three-dimensional unified rectangular coordinate transformation, linear parameter estimation, time registration point calculation, etc., a joint solution model of the altitude relative system error derived from asynchronous radar measurement data is established, and the reliability of the error cumulative estimation result is ensured through operations such as singular value rejection. Experimental results show that by correcting all subsequent altitude measurement values of the secondary station radar with this cumulative estimation result, the average difference of the track line altitude values is reduced by one order of magnitude, and the error correction effect is very ideal, meeting the requirements of air surveillance radar altitude estimation and fusion accuracy in engineering practice. The estimation method provided by the present invention is scientific, the implementation steps of the scheme are reasonable, and the operability and practicability are very strong. Description of the Drawings

[0022] Figure 1 It is the main implementation steps of the method for correcting the altitude measurement value of the air surveillance radar in the technical solution of the present invention.

[0023] Figure 2 It is a comparison chart of the height measurement values of the first simulated observation track line in the embodiment of the present invention;

[0024] Figure 3 It is a function flow chart for solving linear algebraic equations by the full-selection principal element Gaussian elimination method;

[0025] Figure 4 It is the relative systematic error value of the distance of the auxiliary station obtained from 81 valid calculations in 100 consecutive simulations in the embodiment of the present invention;

[0026] Figure 5 It is the relative systematic error value of the pitch of the auxiliary station obtained from 81 valid calculations in 100 consecutive simulations in the embodiment of the present invention;

[0027] Figure 6 It is a schematic diagram of the XY plane projection of the first simulated observation track line in the verification experiment of the embodiment of the present invention;

[0028] Figure 7 It is a comparison chart of the height measurement values of the first simulated main and auxiliary station radar track lines in the verification experiment of the embodiment of the present invention;

[0029] Figure 8 It is a comparison chart of the height measurement values of the first simulated main and auxiliary station track lines and the height correction value of the auxiliary station track line in the verification experiment of the present invention;

[0030] Figure 9 It is the calculation result of the correction rate of the height value of the auxiliary station after measurement correction relative to the simulated true value in the first simulation of the verification experiment of the present invention;

[0031] Figure 10 It is a comparison chart of the average value of the height difference between the main and auxiliary station observation track lines and the average value of the height difference between the main and auxiliary station track lines after correction in the verification experiment of the present invention;

[0032] Figure 11 It is a schematic diagram of the correction rate of the average value of the height difference between the main and auxiliary station track lines after correction compared with that before correction in the verification experiment of the present invention. Specific embodiments

[0033] To make the purpose, content and advantages of the present invention clearer, the following combines the drawings and embodiments to further describe the specific embodiments of the present invention in detail.

[0034] The purpose of the present invention is to propose a method for correcting the height measurement value of a three-coordinate air-defense radar based on joint estimation, which is a normalization method for correcting the height measurement value of a three-coordinate air-defense radar applicable to a multi-radar asynchronous measurement environment, so as to achieve the best superposition of the height observation results of multiple three-coordinate air-defense radars for the same target.

[0035] To achieve the above object, the present invention provides a method for correcting the altitude measurement value of a three-coordinate air radar based on joint estimation, and the method is applied to the pre-data preprocessing process of a multi-radar data fusion system. By applying this method, the altitude system error estimation result is obtained, and the subsequent altitude measurement values of the slave station are corrected, which has an obvious promoting effect on improving the correct rate of multi-radar target association recognition, enhancing the accuracy of target state estimation, and reducing the risk of special situation handling.

[0036] The method includes the following steps:

[0037] Step 1: Initialize the distance relative system error list ER and the pitch relative system error list EP of the slave station radar B.

[0038] Step 2: Select a straight flight track observation data set of the same air target by the master station radar A and the slave station radar B, {{(t SAi , R Ai , θ Ai , h Ai ), i = 1, 2,... n} and {{(t SBj , R Bj , θ Bj , h Bj ), j = 1, 2,... m}, where n represents the number of observation data points of the master station radar A, and m represents the number of observation data points of the slave station radar B; (t SAi , R Ai , θ Ai , h Ai ) represents the target distance R SAi measured by the master station radar A at time t Ai , azimuth θ Ai and altitude h Ai ; (t SBj , R Bj , θ Bj , h Bj ) represents the target distance R SBj measured by the slave station radar B at time t Bj , azimuth θ Bj and altitude h Bj .

[0039] Step 3: Perform coordinate transformation on the observation data of the master station radar A to obtain a set of corresponding three-dimensional unified rectangular coordinates {{(t SAi , x SAi , y SAi , z SAi ), i = 1, 2,... n}.

[0040] Step 4: Perform coordinate transformation on the observation data of the slave station radar B to obtain a set of corresponding three-dimensional unified rectangular coordinates {{(t SBj , x SBj, y SBj , z SBj ), j = 1, 2, … m}.

[0041] Step 5: Use the linear parameter estimation model to estimate the parameters of the height observation data of the master station radar A and the three-dimensional observation data of the slave station radar B, and obtain the parameters of the height observation track line of the master station radar A and the parameters of the three-dimensional observation track line of the slave station radar B.

[0042] Step 6: Calculate the height time registration points of the master station radar A and the three-dimensional time registration points of the slave station radar B according to the observation point time of the slave station radar B. Calculate the distance between the time registration point of the slave station radar B and the radar station site and the corresponding target height value, expressed as {(R′ Bi , h B ′ i ), i = 1, 2, … m}.

[0043] Step 7: Set the distance and pitch relative system errors of the slave station radar B as (λ, θ), use the time registration point data of the master station radar A and the slave station radar B to construct a joint solution system of equations for the relative system error of height with (λ, α) as unknowns, and use the quasi-Newton method for finding a set of real roots of the non-linear equation system to solve this equation system. If the equation system has no solution, go to Step 2, select the straight track line observation data of the master station radar A and the slave station radar B for the same air target, and start a new round of height system error estimation. If the equation system has a solution, assume the solution of the equation system is (Dr, Dp).

[0044] Step 8: Respectively perform singular value judgment on Dr and Dp, incorporate the non-singular values into the relative system error lists ER and EP of the slave station radar B, and sort out the error lists.

[0045] Step 9: If the length of the error list is greater than or equal to the basic statistical number PN, calculate the mean value of the list elements and output it as the cumulative estimation result of the relative system error of the height of the slave station radar B. Otherwise, it is considered that the current condition for estimating the relative system error of the height of the slave station radar B is not yet available.

[0046] Step 10: Go to Step 2, select the straight track line observation data of the master station radar A and the slave station radar B for the same air target, and start a new round of system error estimation.

[0047] Step 11: Based on the effective cumulative estimation result of the relative system error of height output in Step 9, correct all subsequent height measurement values of the slave station radar B.

[0048] The said Step 1 includes the following steps:

[0049] Step 1.1: Create a list ER with the element type of real numbers to store the historical distance relative system error estimates of the slave station radar B.

[0050] Step 1.2: Create a list EP of real number element type to store the historical pitch relative system error estimates of the secondary station radar B.

[0051] The said Step 2 includes the following steps:

[0052] Step 2.1: When an airborne target is on a straight flight path, select the target observation data reported by the master and secondary station radars in the same time period. The number of observation data for each radar is generally not less than 10 points. "Same time period" means that the time difference between the first points of the observation data of the master and secondary station radars is not greater than one radar detection period T (generally 10 or 20 seconds), and the time difference between the last points is also not greater than T.

[0053] The observation data of the selected master station radar A is: {(t SAi ,R Ai ,θ Ai ,h Ai ), i = 1, 2,... n}. Among them, (t SAi ,R Ai ,θ Ai ,h Ai ) represents the target distance R SAi measured by the master station radar A at time t Ai , azimuth θ Ai and altitude h Ai , and n represents the number of observation data points of the master station radar A.

[0054] The observation data of the selected secondary station radar B is: {(t SBj ,R Bj ,θ Bj ,h Bj ), j = 1, 2,... m}. Among them, (t SBj ,R Bj ,θ Bj ,h Bj ) represents the target distance R SBj measured by the secondary station radar B at time t Bj , azimuth θ Bj and altitude h Bj , and m represents the number of observation data points of the secondary station radar B. And |t SB1 - t SA1 | ≤ T, |t SBm - t SAn | ≤ T.

[0055] The said Step 3 includes the following steps:

[0056] Step 3.1: The observation data of the master station radar A {(t SAi ,R Ai ,θAi , h Ai ), i = 1, 2, … n} is converted into three-dimensional rectangular coordinates centered on this station {(t SAi , x Ai , y Ai , z Ai ), i = 1, 2, … n}. Among them:

[0057]

[0058] Step 3.2: Convert {(t SAi , x Ai , y Ai , z Ai ), i = 1, 2, … n} into three-dimensional unified rectangular coordinates {(t SAi , x SAi , y SAi , z SAi ), i = 1, 2, … n}.

[0059] Among them:

[0060]

[0061] (X SA , Y SA , Z SA ) represents the three-dimensional rectangular coordinates of radar A in the unified coordinate system, that is, the site coordinates of the main station radar A.

[0062] Step 4 includes the following steps:

[0063] Step 4.1: Convert the observation data of the auxiliary station radar B {(t SBj , R Bj , θ Bj , h Bj ), j = 1, 2, … m} into three-dimensional rectangular coordinates centered on this station {(t SBj , x Bj , y Bj , z Bj ), j = 1, 2, … m}. Among them:

[0064]

[0065] Step 4.2: Convert {(t SBj , x Bj , y Bj , z Bj ), j = 1, 2, … m} into three-dimensional unified rectangular coordinates {(t SBj , x SBj , y SBj , z SBj), j = 1, 2, … m}. Where:

[0066]

[0067] (X SB , Y SB , Z SB ) represents the three-dimensional rectangular coordinates of radar B in the unified coordinate system, that is, the site coordinates of the auxiliary station radar B.

[0068] The said step 5 includes the following steps:

[0069] Step 5.1: Use the linear parameter estimation model to estimate the parameters of the altitude observation data of the master station radar A, and obtain the parameters (k AZ , d AZ ) of the altitude observation track line of the master station radar A, including the following steps:

[0070] Step 5.1.1: Abbreviate the Z-axis observation data {(t SAi , z SAi ), i = 1, 2, … n} of the master station radar A as: {(x i , y i ), i = 1, 2, … n}. Assign {(x i , y i ) to the structure array XY, the length of the array is n, and the array elements are structures, and the structure members are (x, y). Call the linear parameter estimation function XYT_TO_kb(n, XY, k, d) to obtain the best straight track line parameters (k AZ , d AZ ) = (k, d) of the Z-axis measurement of the master station radar A. Where the implementation process of the function XYT_TO_kb(n, XY, k, d) includes the following steps:

[0071] Step X.1: Initialize the function, define variables tx = 0, tx2 = 0, ty = 0, ty2 = 0, txy = 0, ii = 0.

[0072] Step X.2: Accumulate the x member value of the element with subscript ii in the array XY to the variable tx; accumulate the square of the x member value of the element with subscript ii in the array XY to the variable tx2; accumulate the y member value of the element with subscript ii in the array XY to the variable ty; accumulate the square of the y member value of the element with subscript ii in the array XY to the variable ty2; accumulate the product of the x and y member values of the element with subscript ii in the array XY to the variable txy.

[0073] Step X.3: Let ii = ii + 1. If ii < n, then go to step X.2, otherwise, go to step X.4.

[0074] Step X.4: Let: a1 = tx / n, a2 = tx2 / n, b1 = ty / n, b2 = ty2 / n, c0 = txy / n.

[0075] Step X.5: Let: aa = c0 - a1*b1, bb = a2 - b2 - a1*a1 + b1*b1, cc = a1*b1 - c0.

[0076] Step X.6: Let:

[0077] d1 = b1 - a1*k1; d2 = b1 - a1*k2.

[0078] Step X.7: Let:

[0079]

[0080] Where XY[0].x represents the x member value of the element with subscript 0 in the array XY, XY[0].y represents the y member value of the element with subscript 0 in the array XY, and |...| represents taking the absolute value.

[0081] Step X.8: If L1 > L2, take k = k2, d = d2; otherwise take k = k1, d = d1. Output k and d as parameters, and the function runs to completion.

[0082] Step 5.2: Perform three-dimensional linear parameter estimation on the observation data of the secondary station radar B using a linear parameter estimation model to obtain the observation track line parameters (k BX , d BX )(k BY , d BY )(k BZ , d BZ ), including the following steps:

[0084] Step 5.2.1: Abbreviate the X-axis observation data {(t SBj , x SBj ), j = 1, 2,... m} of the secondary station radar B as: {(x j , y j ), j = 1, 2,... m}. Assign {(x j , y j ), j = 1, 2,... m} to the structure array XY, the length of the array is m, the array elements are structures, and the structure members are (x, y). Call the linear parameter estimation function XYT_TO_kb(m, XY, k, d) to obtain the best straight track line parameters (k BX , d BX ) = (k, d) for the X-axis measurement of the secondary station radar B.

[0085] Step 5.2.2: Abbreviate the Y-axis observation data \(\{(t SBj , y SBj ), j = 1, 2, \ldots m\}\) of the secondary station radar B as: \(\{(x j , y j ), j = 1, 2, \ldots m\}\). Assign \(\{(x j , y j ), j = 1, 2, \ldots m\}\) to the structure array XY. The length of the array is m, and the array elements are structures. The structure members are (x, y). Call the linear parameter estimation function XYT_TO_kb(m, XY, k, d) to obtain the optimal straight-line track parameters \((k BY , d BY ) = (k, d)\) of the Y-axis measurement of the secondary station radar B.

[0086] Step 5.2.3: Abbreviate the Z-axis observation data \(\{(t SBj , z SBj ), j = 1, 2, \ldots m\}\) of the secondary station radar B as: \(\{(x j , y j ), j = 1, 2, \ldots m\}\). Assign \(\{(x j , y j ), j = 1, 2, \ldots m\}\) to the structure array XY. The length of the array is m, and the array elements are structures. The structure members are (x, y). Call the linear parameter estimation function XYT_TO_kb(m, XY, k, d) to obtain the optimal straight-line track parameters \((k BZ , d BZ ) = (k, d)\) of the Z-axis measurement of the secondary station radar B.

[0087] Step 6 includes the following steps:

[0088] Step 6.1: Calculate the height time registration point coordinates \(\{z' SAi , i = 1, 2, \ldots m\}\) of the master station radar A according to the observation point time of the secondary station radar B. Where: \(z' SAi = k AZ * t SBi + d AZ .

[0089] Step 6.2: Calculate the three-dimensional rectangular coordinates \(\{(x' SBi , y' SBi , z' SBi ), i = 1, 2, \ldots m\}\) of the time registration point of the secondary station radar B according to the observation point time of the secondary station radar B. Where:

[0090] x' SBi = k BX * t SBi + dBX , y' SBi = k BY * t SBi + d BY , z' SBi = k BZ * t SBi + d BZ .

[0091] Step 6.3: Calculate the distances between each of {(x', SBi , y' SBi , z' SBi ), i = 1, 2, … m} and the site location of the secondary radar B, and the corresponding target height values {(R', Bi , h B ' i ), i = 1, 2, … m}. The method is as follows: Assign {(x', SBi , y' SBi , z' SBi ), i = 1, 2, … m} to the structure array XYZ with a length of m, where the array elements are structures and the structure members are (x, y, z); Assign the three-dimensional rectangular coordinates of the site location of the secondary radar B represented by (X SB , Y SB , Z SB ) to (XO, YO, ZO). Call the function XYZ_TO_RAh(m, XYZ, XO, YO, ZO, RAh) for converting rectangular coordinates to polar coordinates to obtain a two-dimensional polar coordinate array RAh centered on the secondary radar B. Then, assign the members (RR, hh) of the element with index i - 1 in the array RAh to (R', Bi , h B ' i ) one by one.

[0092] Among them: The length of the RAh array is m, the array elements are structures, and the structure members are (RR, hh), representing the distance and altitude values. The implementation process of the function XYZ_TO_RAh(m, XYZ, XO, YO, ZO, RAh) includes the following steps:

[0093] Step Z.1: Let: ii = 0;

[0094] Step Z.2: Let: xx = XYZ[ii].x – XO,

[0095] yy = XYZ[ii].y – YO,

[0096] zz = XYZ[ii].z – ZO,

[0097] Among them, XYZ[ii].x represents the value of member x of the element with subscript ii in the structure array XYZ; XYZ[ii].y represents the value of member y of the element with subscript ii in the structure array XYZ; XYZ[ii].z represents the value of member z of the element with subscript ii in the structure array XYZ.

[0098] Step Z.3 assigns RAh[ii].RR to

[0099] Step Z.4 assigns RAh[ii].hh to XYZ[ii].z.

[0100] Step Z.5 sets ii = ii + 1. If ii < m, go to Step Z.2. Otherwise, output the structure array RAh as a parameter and the function runs to completion.

[0101] The said Step 7 includes the following steps:

[0102] Step 7.1: Let:

[0103] A z1i = R′ Bi sinα′ Bi A z2i = -sinα′ Bi A z3i = -R′ Bi cosα′ Bi A z4i = cosα′ Bi .

[0104] Step 7.2: Set the distance and pitch relative system errors of the secondary station radar B to be (λ, α), and construct the following joint solution equations for the height relative system error with (λ, α) as unknowns:

[0105]

[0106] Where:

[0107] Step 7.3: Use the quasi-Newton method for finding a set of real roots of the non-linear equations to solve the equations (1). If the equations have no solution, go to Step 2, select the observation data of the straight flight track lines of the main station radar A and the secondary station radar B for the same airborne target, and start a new round of system error estimation. If the equations have a solution, let the solution of the equations be (Dr, Dp).

[0108] The said Step 8 includes the following steps:

[0109] Step 8.1: Determine the singular values of Dr, incorporate the non-singular values into the range relative systematic error list ER of the auxiliary station radar B, and organize the error list ER. The steps are as follows:

[0110] Step 8.1.1: If the length of the list ER is less than the basic statistical number PN, add Dr to the end of the list ER and go to Step 8.2. Otherwise, go to Step 8.1.2. Here, the basic statistical number PN represents the minimum number of times to obtain the systematic error estimate, which is set by the user. Generally, PN≥10.

[0111] Step 8.1.2: Calculate the sample standard deviation DevR and the mean AveR of the elements in the list ER. If the absolute value of the difference between Dr and the mean AveR is less than MU times the sample standard deviation DevR, add Dr to the end of the list ER. Otherwise, go to Step 8.2. Here, MU is set by the user. Generally, 2≥MU≥3.

[0112] Step 8.1.3: If the length of the list ER is greater than the maximum retention number PM, recalculate the mean AveR of the elements in the list ER and delete the element with the largest absolute value of the difference from the mean AveR in the list ER. Here, the maximum retention number PM represents the maximum number of times to store the systematic error estimate, which is set by the user. Generally, PM≥30 and PM>PN.

[0113] Step 8.2: Determine the singular values of Dp, incorporate the non-singular values into the elevation relative systematic error list EP of the auxiliary station radar B, and organize the error list EP. The steps are as follows:

[0114] Step 8.2.1: If the length of the list EP is less than the basic statistical number PN, add Dp to the end of the list EP and go to Step 9. Otherwise, go to Step 8.2.2.

[0115] Step 8.2.2: Calculate the sample standard deviation DevP and the mean AveP of the elements in the list EP. If the absolute value of the difference between Dp and the mean AveP is less than MU times the sample standard deviation DevP, add Dp to the end of the list EP. Otherwise, go to Step 9.

[0116] Step 8.2.3: If the length of the list EP is greater than the maximum retention number PM, recalculate the mean AveP of the elements in the list EP and delete the element with the largest absolute value of the difference from the mean AveP in the list EP.

[0117] The said Step 9 includes the following steps:

[0118] Step 9.1: If the length of the range relative systematic error list ER is greater than or equal to the basic statistical number PN, calculate the mean of the elements in the list ER Output the cumulative estimation result of the relative systematic error of the distance of the secondary station radar B. Otherwise, it is considered that the current condition for estimating the relative systematic error of the distance of the secondary station radar B is not yet met.

[0119] Step 9.2: If the length of the list EP of the relative systematic error in pitch is greater than or equal to the basic statistical number PN, calculate the element mean β of the list EP, and output it as the cumulative estimation result of the relative systematic error in pitch of the secondary station radar B. Otherwise, it is considered that the current condition for estimating the relative systematic error in pitch of the secondary station radar B is not yet met.

[0120] Step 9.3: When both the cumulative estimation result of the relative systematic error in distance and the cumulative estimation result β of the relative systematic error in pitch are valid values, it is considered that the estimation result of the relative systematic error in height of the secondary station radar B is valid. The judgment criteria for and β being valid values are less than a certain fixed value ME.

[0121] The said step 11 includes the following steps:

[0122] Step 11.1: Assume that a random subsequent observation point data of the secondary station radar B is obtained as: (t SB , R B , θ B , h B ), which represents the target distance R SB measured by the secondary station radar B at time t B , azimuth θ B and altitude h B .

[0123] Step 11.2: The correction value h′ B of the target height measurement value is calculated by the formula:

[0124]

[0125] where Z SB represents the Z coordinate of the radar B station site in the unified coordinate system, that is, the altitude; is the effective cumulative estimation result of the relative systematic error in height of the secondary station radar B obtained through step 9.

[0126] Example 1:

[0127] This example describes a method for correcting the height measurement value of a three-coordinate air defense radar based on joint estimation. The simulation calculation process in this example is implemented based on the C# language and can be applied to the preprocessing process of multi-radar networking systems, including the following steps:

[0128] Step 1: Initialize the distance relative system error list ER and the pitch relative system error list EP of the secondary station radar B. That is: create lists ER and EP of the element type of real numbers to store the historical distance and pitch relative system error estimates of the secondary station radar B. The C# code is as follows:

[0129] List <double>ER = newList <double>();

[0130] List <double>EP = newList <double>();

[0131] Step 2: Simulate the observation data of a straight-line track of the same airborne target by the master station radar A and the slave station radar B, which are \(\{(t SAi , R Ai , \theta Ai , h Ai ), i = 1, 2, \ldots, n\}\) and \(\{(t SBj , R Bj , \theta Bj , h Bj ), j = 1, 2, \ldots, m\}\), where \(n\) represents the number of observation data points of the master station radar A, and \(m\) represents the number of observation data points of the slave station radar B. The positioning and error parameters of radar A and radar B are shown in Table 1; the parameters of a straight-line track of the airborne target are shown in Table 2; the first simulated observation data of radar A and radar B are shown in Tables 3 and 4, respectively, and \(n = m = 25\).

[0132] Table 1: Basic parameters of the radar

[0133] Parameter Master Station Radar A Slave Station Radar B X-axis Coordinate 1580 km 1500 km Y-axis Coordinate 2680 km 2550 km Altitude h 500m 200m Range Systematic Error 0.01 km -0.2 km Azimuth Systematic Error 0.002 degrees 1.8 degrees Elevation Systematic Error 0.001 degrees 0.5 degrees Range Random Error 0.08 km 0.1 km Azimuth Random Error 0.08 degrees 0.1 degrees Elevation Random Error 0.008 degrees 0.01 degrees Time Stamp Random Error 0.03 seconds 0.05 seconds Measurement Period 10 seconds 10 seconds Antenna Initial Phase 260 degrees 50 degrees

[0134] Table 2: Track line parameters

[0135] Parameter Single Value Start Time (seconds) 50 seconds Target Starting Point X-axis Coordinate (km) Uniformly Distributed within 1700 ± 3% Target Starting Point Y-axis Coordinate (km) Uniformly Distributed within 2540 ± 3% Flight Altitude (Remains Unchanged, m) Uniformly Distributed within 1500 ± 10% Course (North is 0 degrees) Uniformly Distributed within 300 ± 30% Target Speed (km / hour) Uniformly Distributed within 1200 ± 5% Number of Track Points 25

[0136] Table 3: Observation data of the master station radar A

[0137]

[0138]

[0139] Table 4: Observation data of the slave station radar B

[0140]

[0141]

[0142] Step 3: Perform coordinate transformation on the observation data of the master station radar A to obtain a set of corresponding three-dimensional unified rectangular coordinates

[0143] \{(t SAi , x SAi , y SAi , z SAi ), i = 1, 2, \ldots, n\}\), and the calculation results of the first simulated observation data are shown in Table 5. It includes the following steps:

[0144] Step 3.1: The observation data of the master station radar A \(\{(t SAi , R Ai , \theta Ai , h Ai ), i = 1, 2, … n} is converted into a three-dimensional rectangular coordinate system centered at this station {(t SAi , x Ai , y Ai , z Ai ), i = 1, 2, … n}. Among them:

[0145]

[0146] Step 3.2: Convert {(t SAi , x Ai , y Ai , z Ai ), i = 1, 2, … n} into a three-dimensional unified rectangular coordinate system {(t SAi , x SAi , y SAi , z SAi ), i = 1, 2, … n}.

[0147] Among them:

[0148]

[0149] (X SA , Y SA , Z SA ) represents the three-dimensional rectangular coordinates of radar A in the unified coordinate system, that is, the site coordinates of the main station radar A. In this embodiment, the value is (1580 km, 2680 km, 0.5 km).

[0150] Table 5: Three-dimensional unified rectangular coordinates of the observation data of the main station radar A

[0151]

[0152]

[0153] Step 4: Perform coordinate transformation on the observation data of the secondary station radar B to obtain a set of corresponding three-dimensional unified rectangular coordinates {(t SBj , x SBj , y SBj , z SBj ), j = 1, 2, … m}. The calculation results of the first simulated observation data are shown in Table 6. The steps include:

[0154] Step 4.1: Convert the observation data of the secondary station radar B {(t SBj , R Bj , θ Bj , h Bj ), j = 1, 2, … m} into a three-dimensional rectangular coordinate system centered at this station {(t SBj , x Bj , y Bj , z Bj ), j = 1, 2, … m}. Where:

[0155]

[0156] Step 4.2: Convert {(t SBj , x Bj , y Bj , z Bj ), j = 1, 2, … m} into three-dimensional unified rectangular coordinates {(t SBj , x SBj , y SBj , z SBj ), j = 1, 2, … m}. Where:

[0157]

[0158] (X SB , Y SB , Z SB ) represents the three-dimensional rectangular coordinates of radar B in the unified coordinate system, that is, the site coordinates of the secondary station radar B. In this embodiment, the value is (1500 km, 2550 km, 0.2 km).

[0159] Table 6: Three-dimensional unified rectangular coordinates of the observation data of the secondary station radar B

[0160]

[0161]

[0162] Figure 2 Figure 6 gives a comparison diagram of the height measurement values of the first simulated track lines of radars A and B drawn according to Table 5 and Table 6. It can be seen from the figure that due to the range and elevation systematic errors in the measurements of radars A and B, the heights of the two observation track lines for the same target are split by 800 m to 1450 m; at the same time, the random errors in the measurements make the single height track line show serrations to varying degrees.

[0163] Step 5: Use the linear parameter estimation model to estimate the parameters of the height observation data of the master station radar A and the three-dimensional observation data of the secondary station radar, and obtain the parameters of the height observation track line of the master station radar and the parameters of the three-dimensional observation track line of the secondary station radar. The steps are as follows:

[0164] Step 5.1: Adopt the linear parameter estimation model to estimate the parameters of the height observation data of the master station radar A, and obtain the parameters of the height observation track line of the master station radar (k AZ , d AZ ), including the following steps:

[0165] Step 5.1.1: Denote the Z-axis observation data \(\{(t SAi , z SAi ), i = 1, 2, \ldots n\}\) of the master station radar A as: \(\{(x i , y i ), i = 1, 2, \ldots n\}\). Assign \(\{(x i , y i ), i = 1, 2, \ldots n\}\) to the structure array XY with the array length of n, and the array elements are structures with structure members (x, y). Call the linear parameter estimation function XYT_TO_kb(n, XY, k, d) to obtain the optimal observation track line parameters \((k AZ , d AZ )=(k, d)\) of the Z-axis measurement of the master station A. Among them, the C# implementation code of the function XYT_TO_kb(n, XY, k, d) is as follows:

[0166]

[0167]

[0168] According to Step 5.1, obtain the altitude observation track line parameters \((k AZ , d AZ )=(0.0001, 1.5948)\) of the first simulated observation data of the master station radar A.

[0169] Step 5.2: Use the linear parameter estimation model to perform three-dimensional straight line parameter estimation on the observation data of the slave station radar B to obtain the observation track line parameters \((k BX , d BX )(k BY , d BY )(k BZ , d BZ ), including the following steps:

[0171] Step 5.2.1: Denote the X-axis observation data \(\{(t SBj , x SBj ), j = 1, 2, \ldots m\}\) of the slave station radar B as: \(\{(x j , y j ), j = 1, 2, \ldots m\}\). Assign \(\{(x j , y j ), j = 1, 2, \ldots m\}\) to the structure array XY with the array length of m, and the array elements are structures with structure members (x, y). Call the linear parameter estimation function XYT_TO_kb(m, XY, k, d) to obtain the optimal straight line track line parameters \((k BX , d BX )=(k, d)\).

[0172] Step 5.2.2: Abbreviate the Y-axis observation data of the secondary station radar B, \(\{(t SBj , y SBj ), j = 1, 2, \ldots m\}\) as: \(\{(x j , y j ), j = 1, 2, \ldots m\}\). Assign \(\{(x j , y j ), j = 1, 2, \ldots m\}\) to the structure array XY. The length of the array is m, and the array elements are structures. The structure members are (x, y). Call the linear parameter estimation function XYT_TO_kb(m, XY, k, d) to obtain the best straight-line track parameter \((k BY , d BY )=(k, d)\) for the Y-axis measurement of the secondary station radar B.

[0173] Step 5.2.3: Abbreviate the Z-axis observation data of the secondary station radar B, \(\{(t SBj , z SBj ), j = 1, 2, \ldots m\}\) as: \(\{(x j , y j ), j = 1, 2, \ldots m\}\). Assign \(\{(x j , y j ), j = 1, 2, \ldots m\}\) to the structure array XY. The length of the array is m, and the array elements are structures. The structure members are (x, y). Call the linear parameter estimation function XYT_TO_kb(m, XY, k, d) to obtain the best straight-line track parameter \((k BZ , d BZ )=(k, d)\) for the Z-axis measurement of the secondary station radar B.

[0174] According to Step 5.2, obtain the observed track parameters of the first simulated observation data of the secondary station radar B: \((k BX , d BX ) = (-0.3286, 1686.5839)\), \((k BY , d BY ) = (0.0034, 2551.3949)\), \((k BZ , d BZ ) = (-0.0028, 3.2313)\).

[0175] Step 6: Calculate the main station radar altitude time registration point and the secondary station radar three-dimensional time registration point according to the secondary station radar observation point time. Calculate the distance between the secondary station radar time registration point and the radar station site and the corresponding target altitude value, expressed as \(\{(R' Bi , h B ' i ), i = 1, 2, \ldots m\}\).

[0176] Step 6.1: Calculate the height-time registration point coordinates {z′ SAi , i = 1, 2, … m} of the master radar A according to the observation point time of the slave radar B. Among them: z′ SAi = k AZ * t SBi + d AZ .

[0177] The calculation results of the height-time registration point coordinates {z′ SAi , i = 1, 2, … m} of the first simulated observation track line of the master radar A are shown in Table 7.

[0178] Table 7: Height-time registration point coordinates of the master radar A

[0179]

[0180]

[0181] Step 6.2: Calculate the three-dimensional rectangular coordinates {(x′ SBi , y′ SBi , z′ SBi ), i = 1, 2, … m} of the time registration point of the slave radar B according to the observation point time of the slave radar B. Among them:

[0182] x′ SBi = k BX * t SBi + d BX , y′ SBi = k BY * t SBi + d BY , z′ SBi = k BZ * t SBi + d BZ .

[0183] The calculation results of the three-dimensional rectangular coordinates {(x′ SBi , y′ SBi , z′ SBi ), i = 1, 2, … m} of the first simulated observation track line of the slave radar B are shown in Table 8.

[0184] Table 8: Three-dimensional rectangular coordinates of the time registration point of the slave radar B

[0185]

[0186]

[0187] Step 6.3: Calculate {(x′ SBi , y′ SBi , z' SBi ), i = 1, 2, … m} and the distances and corresponding target height values {(R' Bi , h B ' i ), i = 1, 2, … m}. The method is as follows: Assign {(x' SBi , y' SBi , z' SBi ), i = 1, 2, … m} to the structure array XYZ. The length of the array is m, and the array elements are structures. The structure members are (x, y, z); Assign the three-dimensional rectangular coordinates of the site of the secondary radar B represented by (X SB , Y SB , Z SB ) to (XO, YO, ZO). Call the function XYZ_TO_RAh(m, XYZ, XO, YO, ZO, RAh) to obtain the two-dimensional polar coordinate array RAh centered on the secondary radar B. Then, assign the members (RR, hh) of the element with index i - 1 in the array RAh to (R' Bi , h B ' i ) one by one.

[0188] Among them: The length of the RAh array is m, and the array elements are structures. The structure members are (RR, hh), representing the distance and altitude value. The C# implementation code of the function XYZ_TO_RAh(m, XYZ, XO, YO, ZO, RAh) is as follows:

[0189]

[0190] The distances and corresponding target height values {(R' Bi , h B ' i ), i = 1, 2, … m} of the time registration points of the first simulated observation track line of the secondary radar B and the site of the secondary radar B are shown in Table 9.

[0191] Table 9: Three-dimensional polar coordinates of the time registration points of the secondary radar B

[0192]

[0193]

[0194] Step 7: Set the distance and pitch relative system errors of the secondary station radar B as (λ, α), construct a joint solution system of equations for the height relative system error with (λ, α) as the unknowns using the time registration point data of the primary station and the secondary station, and solve this system of equations using the quasi-Newton method for finding a set of real roots of the non-linear system of equations. If the system of equations has no solution, go to Step 2, select the straight track line observation data of the primary station A and the secondary station radar B for the same airborne target, and start a new round of height system error estimation. If the system of equations has a solution, let the solution of the system of equations be (Dr, Dp). It includes the following steps:

[0195] Step 7.1: Let:

[0196]

[0197] A z1i = R′ Bi sinα′ Bi ,A z2i =-sinα′ Bi ,A z3i =-R′ Bi cosα′ Bi ,A z4i =cosα′ Bi 。

[0198] Calculate the parameter values of A z1 、A z2 、A z3 、A z4 according to the first simulated observation data of the secondary station radar B (see Table 9), and the values are shown in Table 10.

[0199] Table 10: Parameter A calculated from the first simulated observation data of the secondary station radar B z value

[0200]

[0201]

[0202] Step 7.2: Set the distance and pitch relative system errors of the secondary station radar B as (λ, α), and construct the following system of equations for solving the height relative system error with (λ, α) as the unknowns:

[0203]

[0204] Where:

[0205] In this embodiment, use the dnetnfun_RP(rap,ff,m) function to calculate the function value f 1 (λ, α) and f 2 (λ, α). rap is a one-dimensional array of length 2 that stores the values of the unknowns (λ, α); m = 25, representing the number of observation data points of the secondary station radar B, that is, the number of time registration points; ff is a one-dimensional array of length 2 that returns the function values on the left side of the system of equations (1). The C# implementation code of the dnetnfun_RP() function is as follows:

[0206]

[0207]

[0208] Step 7.3: Use the quasi-Newton method for finding a set of real roots of a nonlinear system of equations to solve the system of equations (1). If the system of equations has no solution, go to Step 2, select the straight-line track observation data of the main station A and the secondary station radar B for another same airborne target, and start a new round of systematic error estimation. If the system of equations has a solution, let the solution of the system of equations be (Dr, Dp).

[0209] Among them, the implementation function of the quasi-Newton method for finding a set of real roots of a nonlinear system of equations in this embodiment is named

[0210] dnetn_RP(nn, eps, tt, hhh, rap, kk, m). In this embodiment, nn = 2, indicating that there are 2 unknowns in the system of equations (1); eps = 0.0000001, indicating the control accuracy requirement; tt = 0.2, which is a variable for controlling the change of hhh; hhh = 1.0, indicating the initial value of the increment; kk = 3000, indicating the maximum number of allowed iterations; m = 25, representing the number of observation data points of the secondary station radar B, that is, the number of time registration points; rap is a one-dimensional array of length nn that stores the initial values (0.0, 0.0) of the unknowns (λ, α). The function return value is the actual number of iterations, and a set of real solutions of the system of equations is stored in rap. The C# implementation code of the dnetn_RP() function is as follows:

[0211] int dnetn_RP(int nn, double eps, double tt, double hhh, double[] rap, int kk, int m) / / Find a set of real roots of a nonlinear system of equations

[0212]

[0213]

[0214] Among them, agaus() is a function for solving a system of linear algebraic equations by the full pivoting Gaussian elimination method. The function implementation flow chart is as Figure 3 shown.

[0215] In this embodiment, according to the first simulated observation data, the dnetn_RP() function actually iterates 11 times. The solution of the system of equations is (-1.413106, 0.008815), which is assigned to the variables (Dr, Dp), indicating that the relative systematic errors of distance and pitch obtained in this round of calculation are -1.413106 km and 0.505070 degrees respectively. In this embodiment, a flight path is randomly generated according to the parameters in Table 2, and the dnetn_RP() function is calculated for 100 consecutive simulated observation data. The dnetn_RP() function returns 81 valid calculation results, and the actual number of iterations for each calculation does not exceed 18 times. Figure 4 , Figure 5 The relative systematic error values of distance and pitch obtained from these 81 valid calculations are given.

[0216] Step 8: Perform singular value judgment on Dr and Dp respectively, incorporate the non-singular values into the relative systematic error lists ER and EP of the secondary radar B, and organize the error lists. The steps are as follows:

[0217] Step 8.1: Perform singular value judgment on Dr, incorporate the non-singular values into the distance relative systematic error list ER of the secondary radar B, and organize the error list ER. The steps are as follows:

[0218] Step 8.1.1: If the length of the list ER is less than the basic statistical number PN, add Dr to the end of the list ER and go to Step 8.2. Otherwise, go to Step 8.1.2. Here, the basic statistical number PN represents the minimum number of times to obtain the systematic error estimate, which is set by the user. Generally, PN ≥ 10. In this embodiment, PN is set to 10.

[0219] Step 8.1.2: Calculate the sample standard deviation DevR and the mean AveR of the elements in the list ER. If the absolute value of the difference between Dr and the mean AveR is less than MU times the sample standard deviation DevR, add Dr to the end of the list ER. Otherwise, go to Step 8.2. Here, MU is set by the user. Generally, 2 ≥ MU ≥ 3. In this embodiment, MU is set to 2.5.

[0220] Step 8.1.3: If the length of the list ER is greater than the maximum retention number PM, recalculate the mean AveR of the elements in the list ER, and delete the element with the largest absolute value of the difference from the mean AveR in the list ER. Here, the maximum retention number PM represents the maximum number of times to store the systematic error estimate, which is set by the user. Generally, PM ≥ 30 and PM > PN. In this embodiment, PM is set to 45.

[0221] The C# implementation code for Step 8.1 is as follows:

[0222] / / Step 8.1.1

[0223] if (ER.Count < PN) ER.Add(Dr);

[0224] else

[0225] Del3Dev_one(Dr, ER);

[0226] Among them, the implementation code of the Del3Dev_one() function is as follows:

[0227]

[0228] Among them, the implementation code of the function CalSTDev() for calculating the sample standard deviation of a list is as follows:

[0229]

[0230]

[0231] Step 8.2: Perform singular value judgment on Dp, include the non-singular values in the pitch relative system error list EP of the auxiliary station radar B, and sort out the error list EP. The steps are as follows:

[0232] Step 8.2.1: If the length of the list EP is less than the basic statistical times PN, add Dp to the end of the list EP, and go to Step 9. Otherwise, go to Step 8.2.2.

[0233] Step 8.2.2: Calculate the sample standard deviation DevP and the mean AveP of the elements in the list EP. If the absolute value of the difference between Dp and the mean AveP is less than MU times the sample standard deviation DevP, add Dp to the end of the list EP. Otherwise, go to Step 9.

[0234] Step 8.2.3: If the length of the list EP is greater than the maximum retention times PM, recalculate the mean AveP of the elements in the list EP, and delete the element with the largest absolute value of the difference from the mean AveP in the list EP.

[0235] The C# implementation code of Step 8.2 is as follows:

[0236] / / Step 8.2.1.

[0237] if (EP.Count < PN) EP.Add(Dp);

[0238] else

[0239] Del3Dev_one(Dp, EP); / / The function implementation code is the same as 8.1

[0240] Step 9: If the length of the error list is greater than or equal to the basic statistical count PN, calculate the mean value of the list elements and output it as the cumulative estimation result of the relative systematic error of the height of the secondary station radar B. Otherwise, it is considered that the current condition for estimating the relative systematic error of the height of the secondary station radar B is not yet met. It includes the following steps:

[0241] Step 9.1: If the length of the relative systematic error list ER of distance is greater than or equal to the basic statistical count PN, calculate the mean value of the elements of the list ER and output it as the cumulative estimation result of the relative systematic error of the distance of the secondary station radar B. Otherwise, it is considered that the current condition for estimating the relative systematic error of the distance of the secondary station radar B is not yet met.

[0242] Step 9.2: If the length of the relative systematic error list EP of pitch is greater than or equal to the basic statistical count PN, calculate the mean value β of the elements of the list EP and output it as the cumulative estimation result of the relative systematic error of the pitch of the secondary station radar B. Otherwise, it is considered that the current condition for estimating the relative systematic error of the pitch of the secondary station radar B is not yet met.

[0243] Step 9.3: When both the cumulative estimation result of the relative systematic error of distance and the cumulative estimation result β of the relative systematic error of pitch are valid values, it is considered that the estimation result of the relative systematic error of the height of the secondary station radar B is valid. The judgment criteria for and β being valid values are less than a certain fixed value ME. In this embodiment, ME is set to 10000.

[0244] Step 10: Go to Step 2, select the observation data of the other straight track lines of the same airborne target by the master station A and the secondary station radar B, and start a new round of systematic error estimation.

[0245] In this embodiment, 100 different straight track line observation results of the same airborne target by the master station radar A and the secondary station radar B are simulated according to Step 2. After being processed by Steps 3 to 7, the calculation results of the relative systematic errors of 81 heights (distance, pitch) are successfully solved. Finally, through Steps 8 and 9 for singular value rejection, error list sorting and discrimination, the lengths of the relative systematic error lists EP and ER of distance and pitch are 45, which is greater than the specified basic statistical count PN = 10. The mean value of the output list is used as the cumulative estimation result of the relative systematic error of height (distance, pitch) as follows: β = 0.008731 radians, that is, 0.5003 degrees.

[0246] Step 11: Based on the valid cumulative estimation result of the relative systematic error of height output in Step 9, correct all subsequent height measurement values of the secondary station radar B. It includes the following steps:

[0247] Step 11.1: Assume that an arbitrary subsequent observation point data of the slave station radar B is: (t SB , R B , θ B , h B ), which represents the target distance R SB measured by the slave station radar B at time t B , azimuth θ B and altitude h B .

[0248] Step 11.2: The correction value h′ B of the target height measurement value is calculated by the formula:

[0249]

[0250] where Z SB represents the Z coordinate of the radar B station site in the unified coordinate system, that is, the altitude; ( β = 0.008731) is the cumulative estimation result of the relative systematic error of the effective height (distance, pitch) of the slave station radar B obtained through Step 9.

[0251] Step 12: Verification experiment. In order to further verify the effectiveness of the error estimation, we use the cumulative estimation result of the relative systematic error of the height of the slave station radar B obtained in Step 9 ( β = 0.008731) and the correction formula in Step 11.2 to correct the multi-point height measurement data on other track lines of the slave station radar B. By comparing the change in the average difference between the height values of the track line before and after correction and the height measurement value of the master station radar A, the effectiveness of the error estimation and correction method of the present invention is verified. The verification experiment includes the following steps:

[0252] Step 12.1: Keep the basic parameters of the master station radar A and the slave station radar B set in Table 1 unchanged, and simulate the track line observation data of the master and slave station radars for the same air target according to a set of composite (straight line + arc) track line parameters of the air target set in Table 11.

[0253] Table 11: Composite track line parameters

[0254]

[0255]

[0256]

[0257] Simulate the observation data according to Table 1 and Table 11. In the first simulation, the master and slave station radars each obtain 111 measurement points. The projections of the observation track lines of the master and slave station radars on the XY plane are as Figure 6 , and the comparison of the height measurement values of the track lines of the master and slave station radars is as Figure 7 After calculation, the minimum value of the height difference between the main and auxiliary station radar observation track lines is 866.31 m, the maximum value is 2006.79 m, and the average value is 1332.84 m.

[0258] Step 12.2: According to the relative systematic error cumulative estimation result of the height (distance, pitch) of the auxiliary station radar B ( β = 0.008731), adopt the correction formula in Step 11.2 to correct the height measurement value of the track points of the auxiliary station radar B generated by simulation in Step 12.1.

[0259] After correction, the comparison between the height measurement values of the main and auxiliary station track lines generated by the first simulation and the corrected height values of the auxiliary station track line is as Figure 8 shown. The corrected height value is very close to the main station measurement and is almost indistinguishable. After calculation, the minimum value of the height difference between the main and auxiliary station radar observation track lines after correction is 1.19 m, the maximum value is 77.96 m, and the average value of the height difference is 22.37 m. Compared with the average value of 1332.84 m before correction, the correction rate is 98.32%. The correction rate of the corrected track line height of the auxiliary station radar B compared with the true value of the simulated track line height is as Figure 9 shown. When the target is flying at a normal height, the correction rate remains above 95%. When the target is taking off or landing and the flight height is relatively low (200 m - 500 m), the height correction rate is about 80%.

[0260] Step 12.3: Repeat Step 12.1 and Step 12.2 100 times. After calculation, the average value of the height difference between the main and auxiliary station observation track lines and the average value of the height difference between the main and auxiliary station track lines after correction are as Figure 10 shown, and the correction rate of the average value of the height difference is as Figure 11 shown. After statistics, the minimum value of the correction rate is 87.49%, the maximum value is 98.52%, and the average value is 96.51%. Among the 100 corrections, the correction rate remains above 90% in 86 times, and the average difference between the height values of the main and auxiliary station track lines has decreased by one order of magnitude, and the correction effect is very ideal. Thus, the effectiveness of using the method described in the present invention for height systematic error estimation and correction is further verified.

[0261] On the premise of not departing from the technical principle of the present invention, several improvements and deformations can be made to the present invention, and these improvements and deformations should also be regarded as the protection scope of the present invention. For example but not limited to the following points:

[0262] (1)Regarding the use of lists. The list in the present invention is a data set with a specific structure as the data type. The number of set elements can change dynamically. The elements are connected by pointers, and elements can be easily inserted and deleted, and the capacity can be automatically changed. For example, in C and C++, the list in the present invention can be expressed in the form of a singly linked list, and in C#, it can be expressed by a generic List.

[0263] (2)Regarding the selection of the main station radar. The present invention designates the measurement value of the most accurate air surveillance radar in the radar network as the true description of the target height, and names it the main station. In engineering practice, higher-precision and higher-data-rate target height measurement values can be obtained through air traffic control radars, flight inspection equipment, ADS-B equipment, etc., and these can be used as the true target height. Selecting a measurement device with higher precision and data rate as the main station will help improve the error estimation and track correction effects of the present invention. Such improvements and variations should also be regarded as within the protection scope of the present invention.

[0264] (3)Regarding the solution of the system of equations for jointly solving the relative systematic errors of height (distance, pitch). In step 7 of the present invention, the quasi-Newton method for finding a set of real roots of a nonlinear system of equations is used to solve the system of equations (1). Simulation experiments prove that this method is time-saving and reliable. Exploring the use of other numerical calculation methods to solve the system of equations (1) should be regarded as an improvement and variation of step 7.

[0265] (4)In the present invention, the cumulative estimation of the relative systematic error is an offline and post-event process. Compared with the time complexity of program implementation, we are more concerned about the accuracy of the estimation result and the online and post-event track correction effect. Therefore, the improvement and enhancement of the execution efficiency of the method or embodiment program of the present invention should also be regarded as within the protection scope of the present invention.

[0266] The present invention adopts the idea of relative systematic error. By selecting the observation data of the main and auxiliary station radars for typical route targets, through three-dimensional unified rectangular coordinate transformation, linear parameter estimation, time registration point calculation, etc., a joint solution model for the relative systematic error of height derived from asynchronous radar measurement data is established, and operations such as singular value rejection are performed to ensure the reliability of the error cumulative estimation result. The experimental results show that by correcting the subsequent height measurement values of the auxiliary station radar with this cumulative estimation result, the average difference of the height values of the track line is reduced by an order of magnitude, and the error correction effect is very ideal, meeting the requirements for air surveillance radar height estimation and fusion accuracy in engineering practice. The estimation method provided by the present invention is scientific, the implementation steps of the scheme are reasonable, and the operability and practicability are very strong.

[0267] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention.< / double> < / double> < / double> < / double>

Claims

1. A three-coordinate air radar altitude measurement value correction method based on joint estimation, characterized in that: The method comprises the following steps: Step 1: Initialize the distance relative system error list ER and the elevation relative system error list EP of the auxiliary station radar B; Step 2: Select the observation data of a straight line track of the main radar A and the auxiliary radar B on the same aerial target {(t SAi ,R Ai ,θ Ai ,h Ai ), i=1,2,…n} and {(t SBj ,R Bj ,θ Bj ,h Bj ), j = 1, 2, ... m}, n represents the number of observation data points of the main station radar A, and m represents the number of observation data points of the auxiliary station radar B; (t SAi ,R Ai ,θ Ai ,h Ai ) indicates t SAi The target distance R measured by the master radar A at the moment Ai 、Directionθ Ai and altitude h Ai ;(t SBj ,R Bj ,θ Bj ,h Bj ) indicates t SBj The target distance R measured by the auxiliary station radar B at the moment Bj 、Directionθ Bj and altitude h Bj ; Step 3: Perform coordinate transformation on the observation data of the master radar A to obtain a set of corresponding three-dimensional unified rectangular coordinates {(t SAi ,x SAi ,y SAi ,z SAi ), i=1,2,…n}; Step 4: Perform coordinate transformation on the observation data of the auxiliary radar B to obtain a set of corresponding three-dimensional unified rectangular coordinates {(t SBj ,x SBj ,y SBj ,z SBj ), j = 1, 2, ... m}; Step 5: Use the linear parameter estimation model to estimate the parameters of the main station radar A altitude observation data and the auxiliary station radar B three-dimensional observation data to obtain the main station radar A altitude observation track parameters and the auxiliary station radar B three-dimensional observation track parameters; Step 6: According to the observation point time of the auxiliary station radar B, calculate the height time registration point of the main station radar A and the three-dimensional time registration point of the auxiliary station radar B; Calculate the distance between the auxiliary radar B time registration point and the radar station site and the corresponding target height value, expressed as {(R′ Bi ,h′ Bi ), i=1,2,…m}; Step 7: Set the relative systematic errors of range and elevation of the auxiliary radar B as (λ, α), use the time registration point data of the main radar A and the auxiliary radar B to construct a joint solution equation group of the relative systematic error of altitude with (λ, α) as the unknown variable, and use the quasi-Newton method for finding a set of real roots of the nonlinear equation group to solve the equation group; If the equations have no solution, go to step 2, select the other straight track observation data of the main radar A and the auxiliary radar B on the same air target, and start a new round of altitude system error estimation; if the equations have a solution, set the solution of the equations to (Dr, Dp); Step 8: Perform singular value judgment on Dr and Dp respectively, include the non-singular values ​​into the relative system error list ER and EP of the auxiliary station radar B, and sort out the error list; Step 9: If the length of the error list is greater than or equal to the basic statistical number PN, the mean of the list elements is calculated and output as the cumulative estimation result of the relative system error of the height of the auxiliary station radar B; Otherwise, it is considered that the relative system error estimation condition of the height of the auxiliary station radar B is not met at present; Step 10: Go to step 2, select the other straight track observation data of the main radar A and the auxiliary radar B on the same air target, and start a new round of system error estimation; Step 11: Based on the effective relative height system error cumulative estimation result output from step 9, correct all subsequent height measurement values ​​of auxiliary station radar B.

2. The three-coordinate air radar altitude measurement value correction method based on joint estimation as claimed in claim 1, characterized in that: The step 1 comprises the following steps: Step 1.1: Create a list ER with real number element type to store the relative system error estimates of the auxiliary radar B. Step 1.2: Create a list EP with real number element type to store the relative system error estimates of the auxiliary station radar B; The step 2 comprises the following steps: Step 2.1: Select the target observation data reported by the primary and secondary radars at the same time when the aerial target is on a straight track; the number of observation data of each radar is not less than 10 points; "same time" means that the time difference of the first point of the primary and secondary radar observation data is not greater than 1 radar detection cycle T, and the time difference of the last point is not greater than T; Step 2.2: The observation data of the selected master radar A is: {(t SAi , R Ai ,θ Ai ,h Ai ), i = 1, 2, ... n}; where (t SAi , R Ai ,θ Ai ,h Ai ) indicates t SAi The target distance R measured by the master radar A at the moment Ai 、Directionθ Ai and altitude h Ai , n represents the number of observation data points of the master radar A; Step 2.3: The observation data of the selected auxiliary station radar B is: {(t SBj , R Bj ,θ Bj ,h Bj ), j = 1, 2, ... m}; where (t SBj , R Bj ,θ Bj ,h Bj ) indicates t SBj The target distance R measured by the auxiliary station radar B at the moment Bj 、Directionθ Bj and altitude h Bj , m represents the number of observation data points of the auxiliary radar B, and |t SB1 -t SA1 |≤T,|t SBm -t SAn |≤T.

3. The three-coordinate air radar altitude measurement value correction method based on joint estimation as claimed in claim 2, characterized in that: The step 3 comprises the following steps: Step 3.1: The observation data {(t SAi , R Ai ,θ Ai ,h Ai ), i = 1, 2, ... n} into a three-dimensional rectangular coordinate {(t SAi , x Ai ,y Ai , z Ai ), i=1, 2, ... n}; wherein: Step 3.2: Replace {(t SAi , x Ai ,y Ai , z Ai ), i = 1, 2, ... n} into three-dimensional unified rectangular coordinates {(t SAi , x SAi ,y SAi , z SAi ), i=1, 2, ... n}; wherein: (X SA , Y SA , Z SA ) represents the three-dimensional rectangular coordinates of radar A in the unified coordinate system, that is, the site coordinates of the master radar A.

4. The three-coordinate air radar altitude measurement value correction method based on joint estimation as claimed in claim 3, characterized in that: The step 4 comprises the following steps: Step 4.1: The observation data {(t SBj , R Bj ,θ Bj ,h Bj ), j = 1, 2, ... m} into a three-dimensional rectangular coordinate {(t SBj , x Bj ,y Bj , z Bj ), j = 1, 2, ... m}; in: Step 4.2: Replace {(t SBj , x Bj ,y Bj , z Bj ), j = 1, 2, ... m} into three-dimensional unified rectangular coordinates {(t SBj , x SBj ,y SBj , z SBj ), j = 1, 2, ... m}; wherein: (X SB , Y SB , Z SB ) represents the three-dimensional rectangular coordinates of radar B in the unified coordinate system, that is, the site coordinates of auxiliary radar B.

5. The three-coordinate air radar altitude measurement value correction method based on joint estimation as claimed in claim 4, characterized in that: The step 5 comprises the following steps: Step 5.1: Use the linear parameter estimation model to estimate the parameters of the height observation data of the master radar A and obtain the height observation track parameters of the master radar A (k AZ , d AZ ), comprising the following steps: Step 5.1.1: Transform the Z-axis observation data {(t SAi , z SAi ), i = 1, 2, ... n} is abbreviated as: {(x i ,y i ), i = 1, 2, ... n}; {(x i ,y i ), i = 1, 2, ... n} are assigned to the structure array XY, the array length is n, the array element is a structure, and the structure member is (x, y); call the linear parameter estimation function XYT_TO_kb(n, XY, k, d) to obtain the optimal straight line track parameters (k AZ , d AZ ) = (k, d); Step 5.2: Use the linear parameter estimation model to perform three-dimensional linear parameter estimation on the observation data of the auxiliary station radar B, and obtain the observation track parameters (k BX , d BX )、(k BY , d BY )、(k BZ , d BZ ), comprising the following steps: Step 5.2.1: Substitute the X-axis observation data {(t SBj , x SBj ), j = 1, 2, ... m} is abbreviated as: {(x j ,y j ), j = 1, 2, ... m}; {(x j ,y j ), j = 1, 2, ... m} is assigned to the structure array XY, the array length is m, the array element is a structure, and the structure member is (x, y); call the linear parameter estimation function XYT_TO_kb(m, XY, k, d) to obtain the optimal straight track line parameters (k BX , d BX ) = (k, d); Step 5.2.2: Substitute the Y-axis observation data {(t SBj ,y SBj ), j = 1, 2, ... m} is abbreviated as: {(x j ,y j ), j = 1, 2, ... m}; {(x j ,y j ), j = 1, 2, ... m} is assigned to the structure array XY, the array length is m, the array element is a structure, and the structure member is (x, y); call the linear parameter estimation function XYT_TO_kb(m, XY, k, d) to obtain the optimal straight track line parameters (k BY , d BY ) = (k, d); Step 5.2.3: Submit the Z-axis observation data {(t SBj , z SBj ), j = 1, 2, ... m} is abbreviated as: {(x j ,y j ), j = 1, 2, ... m}; {(x j ,y j ), j = 1, 2, ... m} is assigned to the structure array XY, the array length is m, the array element is a structure, and the structure member is (x, y); call the linear parameter estimation function XYT_TO_kb (m, XY, k, d) to obtain the optimal straight line track parameters (k BZ , d BZ )=(k,d).

6. The three-coordinate air radar altitude measurement value correction method based on joint estimation as claimed in claim 5, characterized in that: The implementation process of the function XYT_TO_kb(n, XY, k, d) includes the following steps: Step X.1: Initialize the function, define variables tx=0, tx2=0, ty=0, ty2=0, txy=0, ii=0; Step X.2: Accumulate the x - member value of the element with subscript ii in the XY array into the variable tx; square the x - member value of the element with subscript ii in the XY array and accumulate it into the variable tx2; accumulate the y - member value of the element with subscript ii in the XY array into the variable ty; square the y - member value of the element with subscript ii in the XY array and accumulate it into the variable ty2; multiply the x and y - member values of the element with subscript ii in the XY array and accumulate it into the variable txy; Step X.3: Let ii = ii + 1. If ii < n, go to Step X.2; otherwise, go to Step X.4; Step X.4: Let: a1 = tx / n, a2 = tx2 / n, b1 = ty / n, b2 = ty2 / n, c0 = txy / n; Step X.5: Let: aa = c0 - a1 * b1, bb = a2 - b2 - a1 * a1 + b1 * b1, cc = a1 * b1 - c0; Step X.6: Order: d1 = b1 - a1 * k1; d2 = b1 - a1 * k2; Step X.7: Let: where XY[0].x represents the x - member value of the element with subscript 0 in the XY array, XY[0].y represents the y - member value of the element with subscript 0 in the XY array, and |...| represents taking the absolute value; Step X.8: If L1 > L2, take k = k2, d = d2; otherwise take k = k1, d = d1; Output k and d as parameters, and the function runs to completion.

7. The three-coordinate air radar altitude measurement value correction method based on joint estimation as claimed in claim 5 or 6, characterized in that: The said Step 6 includes the following steps: Step 6.1: Calculate the coordinates of the height time registration point {z′ SAi , i = 1, 2, ... m}; where: z′ SAi =k AZ *t SBi +d AZ ; Step 6.2: According to the observation point time of the auxiliary radar B, calculate the three-dimensional rectangular coordinates {(x′ SBi , y′ SBi , z′ SBi ), i=1, 2, ...m}; wherein: x′ SBi =k BX *t SBi +d BX ,y′ SBi =k BY *t SBi +d BY ,z′ SBi =k BZ *t SBi +d BZ ; Step 6.3: Calculate {(x′ SBi , y′ SBi , z′ SBi ), i = 1, 2, ... m} and the distance from the auxiliary radar station B and the corresponding target height value {(R′ Bi , h′ Bi ), i = 1, 2, ... m}; the method is: {(x′ SBi , y′ SBi , z′ SBi ), i = 1, 2, ... m} is assigned to the structure array XYZ, the array length is m, the array element is a structure, and the structure member is (x, y, z); (X SB , Y SB , Z SB ) is assigned to (XO, YO, ZO); the function XYZ_TO_RAh(m, XYZ, XO, YO, ZO, RAh) is called to convert the rectangular coordinates to polar coordinates to obtain the two-dimensional polar coordinate array RAh centered on the auxiliary radar B; then the members (RR, hh) of the array RAh with the element subscript i-1 are assigned to (R′ Bi , h′ Bi ), where: RAh array length is m, array elements are structures, and structure members are (RR, hh), representing distance and altitude values.

8. The three-coordinate air radar altitude measurement value correction method based on joint estimation as claimed in claim 7, characterized in that: The implementation process of the function XYZ_TO_RAh(m, XYZ, XO, YO, ZO, RAh) includes the following steps: Step Z.1: Let: ii = 0; Step Z.2: Let: xx = XYZ[ii].x - XO, yy = XYZ[ii].y - YO, zz = XYZ[ii].z - ZO, where XYZ[ii].x represents the value of member x of the element with subscript ii in the structure array XYZ; XYZ[ii].y represents the value of member y of the element with subscript ii in the structure array XYZ; XYZ[ii].z represents the value of member z of the element with subscript ii in the structure array XYZ; Step Z.3 Assign RAh[ii].RR to Step Z.4 Assign RAh[ii].hh with XYZ[ii].z; Step Z.5 Let ii = ii + 1; If ii < m, go to Step Z.2; otherwise, output the structure array RAh as a parameter, and the function runs to completion.

9. The three-coordinate air radar altitude measurement value correction method based on joint estimation as claimed in claim 8, characterized in that: The said Step 7 includes the following steps: Step 7.1: Order: A z1i =R′ Bi sinα′ Bi ,A z2i =-sinα′ Bi ,A z3i =-R′ Bi cosα′ Bi ,A z4i =cosα′ Bi ; Step 7.2: Set the distance and pitch relative system errors of the secondary station radar B as (λ, α), and construct the following joint solution equations for the height relative system error with (λ, α) as unknowns: where: Step 7.3: Use the quasi - Newton method for finding a set of real roots of the non - linear equations to solve the equations (1); If the equations have no solution, go to Step 2, select the straight - line track observation data of the main station radar A and the secondary station radar B for the same airborne target, and start a new round of system error estimation; If the equations have a solution, assume the solution of the equations is (Dr, Dp).

10. The three-coordinate air radar altitude measurement value correction method based on joint estimation as claimed in claim 9, characterized in that: The said Step 8 includes the following steps: Step 8.1: Perform singular value judgment on Dr, incorporate non-singular values ​​into the distance relative system error list ER of the auxiliary station radar B, and organize the error list ER; including the following steps: Step 8.1.1: If the length of the list ER is less than the basic statistical number PN, add Dr to the end of the list ER and go to step 8.2; otherwise, go to step 8.1.2; where the basic statistical number PN represents the minimum number of times to obtain the system error estimate, which is set by the user; Step 8.1.2: Calculate the sample standard deviation DevR and mean AveR of the elements in the list ER. If the absolute value of the difference between Dr and mean AveR is less than MU times the sample standard deviation DevR, add Dr to the end of the list ER; otherwise, go to step 8.2; MU is set by the user. Step 8.1.3: If the length of the list ER is greater than the maximum number of retention times PM, recalculate the mean AveR of the elements in the list ER and delete the element in the list ER whose absolute difference with the mean AveR is the largest; wherein the maximum number of retention times PM represents the maximum number of stored system error estimates, which is set by the user, and PM>PN; Step 8.2: Perform singular value judgment on Dp, incorporate non-singular values ​​into the elevation relative system error list EP of the auxiliary station radar B, and organize the error list EP; including the following steps: Step 8.2.1: If the length of the list EP is less than the basic statistical number PN, add Dp to the end of the list EP and go to step 9; otherwise, go to step 8.2.2; Step 8.2.2: Calculate the sample standard deviation DevP and mean AveP of the elements in the list EP. If the absolute value of the difference between Dp and mean AveP is less than MU times the sample standard deviation DevP, add Dp to the end of the list EP; otherwise, go to step 9; Step 8.2.3: If the length of the list EP is greater than the maximum retention number PM, recalculate the mean AveP of the elements in the list EP and delete the element in the list EP with the largest absolute value of the difference with the mean AveP.

11. The three-coordinate air radar altitude measurement value correction method based on joint estimation as claimed in claim 10, characterized in that: The step 9 comprises the following steps: Step 9.1: If the length of the distance relative systematic error list ER is greater than or equal to the basic statistical number PN, calculate the mean of the elements of the list ER Output as the cumulative estimation result of the relative system error of the distance of the auxiliary station radar B; Otherwise, it is considered that the distance relative system error estimation condition of auxiliary station radar B is not met at present; Step 9.2: If the length of the elevation relative system error list EP is greater than or equal to the basic statistical number PN, the element mean β of the list EP is calculated and output as the cumulative estimation result of the elevation relative system error of the auxiliary station radar B; Otherwise, it is considered that the relative system error estimation condition of the auxiliary station radar B is not met at present; Step 9.3: When the distance relative system error is accumulated, the estimated result When the cumulative estimation result of the relative system error in pitch and elevation β are both valid values, the relative system error estimation result of the height of the auxiliary station radar B is considered valid; The criterion for the validity of β and β is that they are less than a certain fixed value ME.

12. The three-coordinate air radar altitude measurement value correction method based on joint estimation as claimed in claim 11, characterized in that: The step 11 comprises the following steps: Step 11.1: Assume that the data of an arbitrary subsequent observation point of the auxiliary station radar B is: (t SB ,R B ,θ B ,h B ), indicating t SB The target distance R measured by the auxiliary station radar B at the moment B 、Directionθ B and altitude h B ; Step 11.2: Correction value h′ of target height measurement B The calculation formula is: Among them, Z SB It represents the Z coordinate of radar station B in the unified coordinate system, i.e. the altitude; It is the cumulative estimation result of the relative system error of the effective height of the auxiliary station radar B obtained in step 9.

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