A method for estimating the altitude of aerial targets based on spaceborne radar networking

Abstract

The invention discloses an aerial target height estimation method based on satellite-borne radar networking. The radar networking is composed of a radar group consisting of two or more satellite-borne radars. The aerial target height estimation method comprises the following steps: step S1: using the radar group to respectively measure the radial distance and azimuth of the aerial target; step S2: using a position calculation model of the aerial target in the radar array coordinate system to calculate the position of the aerial target in the radar array coordinate system by using the least squares method; step S3: calculating the position of the aerial target in the satellite orbit coordinate system according to the position of the aerial target in the radar array coordinate system; step S4: calculating the altitude of the aerial target according to the position of the aerial target in the satellite orbit coordinate system and the radius of the earth where the aerial target is located. The invention establishes an equation group containing unknown variables such as the target altitude, thereby solving the problem that a single satellite-borne detection radar has a large target tracking pitch angle error and is unable to estimate the altitude of the aerial target.

Description

Technical Field

[0001] The present invention belongs to the field of satellite-borne radar target tracking, and in particular relates to an aerial target height estimation method based on satellite-borne radar networking. Background Art

[0002] Spaceborne radars offer all-weather, all-day strategic and tactical early warning capabilities, are unrestricted by the Earth's curvature, and are less vulnerable to attack. They play a crucial role in early warning and defense systems. Spaceborne radar target tracking utilizes nonlinear filtering algorithms based on the target's motion model and radar measurements to achieve high-precision tracking. However, there are two main errors associated with target observation: measurement error and positioning error within the detection platform itself. Both errors impact target tracking.

[0003] When a single spaceborne radar tracks and locates an aerial target, the target pitch angle measurement error is generally larger than the target radial distance and azimuth measurement errors, resulting in the inability to estimate the altitude of the aerial target. The lack of aerial target altitude information seriously amplifies the target positioning error on the one hand, and is not conducive to target attribute discrimination and threat estimation on the other. Summary of the Invention

[0004] The purpose of the present invention is to provide an aerial target altitude estimation method based on satellite-borne radar networking to solve the problem that the pitch angle error of target tracking by a single satellite-borne detection radar is too large and the method is incapable of estimating the altitude of aerial targets.

[0005] The present invention adopts the following technical solution: a method for estimating the height of an aerial target based on a spaceborne radar network, wherein the radar network comprises a radar group consisting of two or more spaceborne radars, and the method for estimating the height of an aerial target comprises the following steps:

[0006] Step S1: using a radar group to measure the radial distance and azimuth of the aerial target respectively;

[0007] Step S2: Calculate the position of the aerial target in the radar array coordinate system using the least squares method through the position calculation model of the aerial target in the radar array coordinate system;

[0008] Step S3: Calculate the position of the aerial target in the satellite orbit coordinate system based on the position of the aerial target in the radar array coordinate system;

[0009] Step S4: Calculate the altitude of the aerial target based on the position of the aerial target in the satellite orbit coordinate system and the radius of the earth where the aerial target is located.

[0010] Furthermore, when the radar group consists of a first radar of a first satellite and a second radar of a second satellite, the position calculation model of the aerial target in the radar array coordinate system in step S2 is composed of the following steps:

[0011] Establish a position calculation model for aerial targets in the satellite orbit coordinate system;

[0012] The position of the aerial target in the first satellite orbit coordinate system is transformed into the position in the first radar array coordinate system, and the position of the aerial target in the second satellite orbit coordinate system is transformed into the position in the second radar array coordinate system, so as to obtain the position calculation model of the aerial target in the radar array coordinate system.

[0013] Furthermore, the position calculation model of the aerial target in the satellite orbit coordinate system is:

[0014]

[0015] in,

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] a 36 =cosθ2·C2A2+sinθ2·C2B2

[0022]

[0023]

[0024]

[0025] a 44 =A2C2

[0026] a 45 =B2C2

[0027]

[0028] Wherein, (A1, B1, C1) is the unit normal vector of the plane OS1S2 in the first satellite orbit coordinate system, (A2, B2, C2) is the unit normal vector of the plane OS1S2 in the second satellite orbit coordinate system, (X1, Y1, Z1) is the position of the aerial target in the first satellite orbit coordinate system, (X2, Y2, Z2) is the position of the aerial target in the second satellite orbit coordinate system, is the distance from the first radar to the center of the earth, is the distance from the second radar to the center of the earth, θ1 is the angle at which the XOZ plane of the first satellite orbit coordinate system coincides with the plane where the first radar, the second radar, and the center of the earth are located after the XOZ plane of the first satellite orbit coordinate system is rotated counterclockwise around the Z axis by an angle θ1, and θ2 is the angle at which the XOZ plane of the second satellite orbit coordinate system coincides with the plane where the first radar, the second radar, and the center of the earth are located after the XOZ plane of the second satellite orbit coordinate system is rotated counterclockwise around the Z axis by an angle θ2.

[0029] Furthermore, the position calculation model of the aerial target in the radar array coordinate system is:

[0030]

[0031] in, is the radial distance and azimuth of the air target measured by the first radar, are the radial distance and azimuth of the air target measured by the second radar, (x1, y1, z1) are the coordinates of the air target in the first radar array coordinate system, and (x2, y2, z2) are the coordinates of the air target in the second radar array coordinate system.

[0032] Where,

[0033]

[0034]

[0035] in, is the antenna array attitude angle of the first radar, is the antenna array attitude angle of the second radar, is the attitude angle of the first satellite, is the attitude angle of the second satellite.

[0036] Furthermore, in step S3, the position formula of the aerial target in the satellite orbit coordinate system is calculated as:

[0037]

[0038] Furthermore, in step S4, the formula for calculating the height of the aerial target is:

[0039]

[0040] Where h is the height of the aerial target, r e is the radius of the earth where the aerial target is located,

[0041] in,

[0042] Where a is the equatorial radius of the Earth, b is the polar radius of the Earth, and L at is the estimated latitude of the aerial target.

[0043] Furthermore, when the radar group consists of a first radar of a first satellite and a second radar of a second satellite, and the XOZ plane of the first satellite orbital coordinate system coincides with the plane of the second satellite orbital coordinate system, that is, the XOZ plane of the first satellite orbital coordinate system rotates counterclockwise around the Z axis to a rotation angle θ1=0° of the plane where the first radar, the second radar, and the center of the earth are located, and the XOZ plane of the second satellite orbital coordinate system rotates counterclockwise around the Z axis to a rotation angle θ2=0° of the plane where the first radar, the second radar, and the center of the earth are located,

[0044] The coordinates (x1, y1, z1) of the aerial target in the first radar array coordinate system in step S2 are corrected to obtain the corrected coordinates (x′1, y′1, z′1) of the aerial target in the first radar array coordinate system, and the coordinates (x2, y2, z2) of the aerial target in the second radar array coordinate system are corrected to obtain the corrected coordinates (x′2, y′2, z′2) of the aerial target in the second radar array coordinate system. After correction, a position calculation model of the aerial target in the radar array coordinate system is obtained according to (x′1, y′1, z′1) and (x′2, y′2, z′2). The correction method is:

[0045]

[0046] Furthermore, when the antenna array attitude angle of the first radar, the antenna array attitude angle of the second radar, the attitude angle of the first satellite, and the attitude angle of the second satellite are equal to 0°, in step S2: the position calculation model of the aerial target in the radar array coordinate system is:

[0047]

[0048] Where (x1, y1, z1) is the coordinate of the air target in the first radar array coordinate system, (x2, y2, z2) is the coordinate of the air target in the second radar array coordinate system, is the distance from the first radar to the center of the earth, is the distance from the second radar to the center of the earth, are the radial distance and azimuth of the air target measured by the first radar, The radial distance and azimuth of the air target measured by the first radar.

[0049] Furthermore, when the radar group consists of a first radar of a first satellite, a second radar of a second satellite, a third radar of a third satellite, and so on, an nth radar of an nth satellite, then in step S2, the position calculation model of the aerial target in the radar array coordinate system is:

[0050]

[0051] in,

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] b 33 =cosθ2·C2A2+sinθ2·C2B2

[0063] b 41 =A2C2

[0064] b 42 =B2C2

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074] d 33 =cosθ n ·C n A n +sinθ n ·C n Bn

[0075] d 41 =A n C n

[0076] d 42 =B n C n

[0077]

[0078]

[0079] Where, α n is the angle between the first radar and the nth radar and the center of the earth, θ n The XOZ plane of the nth satellite orbital coordinate system rotates counterclockwise around the Z axis by an angle θ n The rotation angle of the plane with the first radar, the second radar and the center of the earth, θ 1n is the angle between the XOZ plane of the first satellite orbit coordinate system and the planes of the first radar, the nth radar and the center of the earth, (A 1n ,B 1n ,C 1n ) is the unit normal vector of the plane where the first radar, the nth radar and the center of the earth are located in the first satellite orbit coordinate system, (A n ,B n ,C n ) is the unit normal vector of the plane where the first radar, the nth radar and the center of the earth are located in the nth satellite orbit coordinate system, is the attitude angle of the nth satellite, is the antenna array attitude angle of the nth radar, and are the azimuth and radial distance of the air target measured by the nth radar, is the distance from the nth radar to the center of the earth, (x n ,y n ,z n ) is the coordinate of the aerial target in the nth radar array coordinate system.

[0080] Furthermore, in step S2, the position of the aerial target in the radar array coordinate system is calculated as follows:

[0081]

[0082] Where X=[x1,y1,z1,…,x n ,y n ,z n ] T , H, K are coefficient matrices, and

[0083]

[0084] in,

[0085]

[0086]

[0087]

[0088]

[0089]

[0090] The above formula for calculating the position of the aerial target in the radar array coordinate system is regarded as a weighted least squares problem with constraints, that is,

[0091]

[0092] Where W = diag(w1,w2,…w 2n-1 )>0 is the weight matrix, which is determined by the measurement error, and the minimum norm least squares solution X is obtained by QR decomposition.

[0093] The beneficial effects of the present invention are as follows: the present invention utilizes the measurement of the target by two radars at the same time, and combines the spatial positions of the radars themselves to derive a group of linear equations about the position vectors of the target in the two radar array coordinate systems, and generalizes it to multiple radars to derive a group of linear equations about the position vectors of the target in the multiple radar array coordinate systems. Taking into account the difference in measurement errors of each radar in practice, the linear equations are solved using a constrained weighted least squares method to ultimately obtain the distance from the target to the center of the earth, and the height of the target is calculated taking into account the influence of the earth's curvature; the present invention establishes a group of equations including unknown variables such as the target height by constructing a geometric relationship between the radar and the target, thereby solving the problem that the pitch angle error of the target tracking of a single satellite-borne detection radar is too large and the altitude estimation capability of the aerial target is not available. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] FIG1( a ) is a schematic diagram of the spatial position of the radar and the target in the present invention;

[0095] FIG1( b ) is a schematic diagram of a plane where the first radar, the second radar and the center of the earth are located in the present invention;

[0096] Figure 2(a) shows the STK spatial position diagram of four different radars and a single target;

[0097] Figure 2(b) shows the STK spatial position diagram of two radars and five different targets;

[0098] Figure 3(a) shows the aerial target height estimation results based on different radar measurement fusion under different measurement errors;

[0099] Figure 3(b) shows the aerial target height estimation results based on different radar measurement fusion under different measurement errors;

[0100] Figure 4 This is the height estimation result diagram of targets at different positions in the joint detection area of ​​two radars. DETAILED DESCRIPTION

[0101] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0102] The present invention discloses a method for estimating the altitude of an aerial target based on a satellite-borne radar network. To address the problem of excessive pitch angle error, the method utilizes multiple satellites to jointly calculate the target altitude. The radar network is composed of two or more satellite-borne radars forming a radar group. The method for estimating the altitude of an aerial target comprises the following steps:

[0103] Step S1: using a radar group to measure the radial distance and azimuth of the aerial target respectively;

[0104] Step S2: Calculate the position of the aerial target in the radar array coordinate system using the least squares method through the position calculation model of the aerial target in the radar array coordinate system;

[0105] Step S3: Calculate the position of the aerial target in the satellite orbit coordinate system based on the position of the aerial target in the radar array coordinate system;

[0106] Step S4: Calculate the altitude of the aerial target based on the position of the aerial target in the satellite orbit coordinate system and the radius of the earth where the aerial target is located.

[0107] When the radar group consists of a first radar of a first satellite and a second radar of a second satellite, the position calculation model of the aerial target in the radar array coordinate system in step S2 is composed of the following steps:

[0108] Establish a position calculation model for aerial targets in the satellite orbit coordinate system;

[0109] The position of the aerial target in the first satellite orbit coordinate system is transformed into the position in the first radar array coordinate system, and the position of the aerial target in the second satellite orbit coordinate system is transformed into the position in the second radar array coordinate system, so as to obtain the position calculation model of the aerial target in the radar array coordinate system.

[0110] Among them, the position calculation model of the aerial target in the satellite orbit coordinates is:

[0111]

[0112] in,

[0113]

[0114]

[0115]

[0116]

[0117]

[0118] a 36 =cosθ2·C2A2+sinθ2·C2B2

[0119]

[0120]

[0121]

[0122] a 44 =A2C2

[0123] a 45 =B2C2

[0124]

[0125] Wherein, (A1, B1, C1) is the unit normal vector of the plane OS1S2 in the first satellite orbit coordinate system, (A2, B2, C2) is the unit normal vector of the plane OS1S2 in the second satellite orbit coordinate system, (X1, Y1, Z1) is the position of the aerial target in the first satellite orbit coordinate system, (X2, Y2, Z2) is the position of the aerial target in the second satellite orbit coordinate system, is the distance from the first radar to the center of the earth, is the distance from the second radar to the center of the earth, θ1 is the angle at which the XOZ plane of the first satellite orbit coordinate system coincides with the plane where the first radar, the second radar, and the center of the earth are located after the XOZ plane of the first satellite orbit coordinate system is rotated counterclockwise around the Z axis by an angle θ1, and θ2 is the angle at which the XOZ plane of the second satellite orbit coordinate system coincides with the plane where the first radar, the second radar, and the center of the earth are located after the XOZ plane of the second satellite orbit coordinate system is rotated counterclockwise around the Z axis by an angle θ2.

[0126] The establishment of the position calculation model of the aerial target in the satellite orbit coordinates consists of the following steps:

[0127] As shown in Figure 1(a), assume that the first radar is located at S1, the second radar is located at S2, the position information is accurately known, and the aerial target is located at point P. Connect the first radar, the second radar and the center of the earth O to form a plane OS1S2, and H is the projection of the target P on the plane OS1S2. Let the coordinates of the target P in the first satellite orbit coordinate system be P1(X1, Y1, Z1), let the coordinates of the target P in the second satellite orbit coordinate system be P2(X2, Y2, Z2), and the distance from the first radar to the center of the earth be The distance from the second radar to the center of the earth is The distance from the target to the center of the Earth is |OP|.

[0128] From the geometric relationship, we can get

[0129] P1H=P2H

[0130]

[0131]

[0132] Among them, P1H is the distance from the target P to the plane OS1S2 in the first satellite orbit coordinate system, and P2H is the distance from the target P to the plane OS1S2 in the second satellite orbit coordinate system, that is,

[0133] |P1H|=|A1X1+B1Y1+C1Z1|

[0134] |P2H|=|A2X2+B2Y2+C2Z2|

[0135] Among them, (A1, B1, C1) is the unit normal vector of the plane OS1S2 in the first satellite orbit coordinate system, and (A2, B2, C2) is the unit normal vector of the plane OS1S2 in the second satellite orbit coordinate system. The coordinates of the projection point H in the first satellite orbit coordinate system and the second satellite orbit coordinate system are respectively expressed as

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142] As shown in Figure 1-(b), in plane OS1S2, according to the geometric properties, we have

[0143] sin A1=|HH1| / |OP|

[0144] cos A1=(r s -|S1H1|) / |OP|

[0145] sin A2=|HH2| / |OP|

[0146] cos A2=(r s -|S2H2|) / |OP|

[0147] When the projection point H falls on the left side of triangle OS1S2,

[0148]

[0149]

[0150] Then there is,

[0151]

[0152]

[0153] When the projection point H falls within the triangle OS1S2,

[0154]

[0155]

[0156] Then there is,

[0157]

[0158]

[0159] When the projection point H falls on the right side of triangle OS1S2,

[0160]

[0161]

[0162] Then there is,

[0163]

[0164]

[0165] Let θ1 be the angle corresponding to the XOZ plane of the first satellite orbit coordinate system rotating counterclockwise around the Z axis by an angle θ1 and coinciding with the plane OS1S2, and θ2 be the angle corresponding to the XOZ plane of the second satellite orbit coordinate system rotating counterclockwise around the Z axis by an angle θ2 and coinciding with the plane OS1S2; then when the projection point H falls on the left side of the triangle OS1S2,

[0166]

[0167]

[0168]

[0169]

[0170] Then, when the projection point H falls within the triangle OS1S2,

[0171]

[0172]

[0173]

[0174]

[0175] Then, when the projection point H falls on the right side of triangle OS1S2,

[0176]

[0177]

[0178]

[0179]

[0180] Therefore, let

[0181]

[0182]

[0183] Then no matter where the projection point falls, it can be written as

[0184]

[0185]

[0186] Combining the linear equations

[0187]

[0188] The position of the aerial target in the first satellite orbit coordinate system is transformed into the position in the first radar array coordinate system, and the position of the aerial target in the second satellite orbit coordinate system is transformed into the position in the second radar array coordinate system. Finally, the position calculation model of the aerial target in the radar array coordinate system is obtained. The transformation method consists of the following steps:

[0189] Transform the radar measurement coordinate system to the antenna array coordinate system

[0190] x=r z cos E sin A z

[0191] y=r z sin E

[0192] z=r z cos E cos A z

[0193] Among them, r z 、A z and E are the radial distance, azimuth, and elevation angle of the aerial target measured by the radar; x, y, and z are the positions of the aerial target in the antenna array coordinate system.

[0194] Transform the antenna array coordinate system to the satellite body coordinate system

[0195]

[0196] Among them, γ c 、 and ψ c They are the roll angle, pitch angle and yaw angle of the radar antenna array respectively; M1, M2, M3 are the rotation matrices that rotate counterclockwise around the x-axis, y-axis and z-axis by a certain angle according to the right-hand rule, x b ,y b , z b is the position of the aerial target in the satellite's coordinate system.

[0197] Transform the satellite body coordinate system to the satellite orbit coordinate system

[0198]

[0199] Among them, γ s 、 and ψ s are the roll angle, pitch angle and yaw angle of the satellite attitude respectively; X, Y, Z are the positions of the aerial target in the satellite orbit coordinate system.

[0200] Let (x1, y1, z1) be the coordinates of the air target in the first radar array coordinate system, and (x2, y2, z2) be the coordinates of the air target in the second radar array coordinate system. is the antenna array attitude angle of the first radar, is the antenna array attitude angle of the second radar, is the attitude angle of the first satellite, is the attitude angle of the second satellite; then we can get:

[0201]

[0202] Where,

[0203]

[0204]

[0205] If the radial distance and azimuth angle of the aerial target are measured as but

[0206]

[0207] Then the position calculation model of the aerial target in the radar array coordinate system is:

[0208]

[0209] in, is the radial distance and azimuth of the air target measured by the first radar, are the radial distance and azimuth of the aerial target measured by the second radar. The above formula is a system of linear equations about the variables (x1, y1, z1, x2, y2, z2). There are 6 linear equations in total, and there is a unique solution.

[0210] When the XOZ plane of the first satellite orbital coordinate system of the radar group coincides with the plane of the second satellite orbital coordinate system, that is, the XOZ plane of the first satellite orbital coordinate system rotates counterclockwise around the Z axis to the rotation angle θ1 = 0° of the plane where the first radar, the second radar and the center of the earth are located, and the XOZ plane of the second satellite orbital coordinate system rotates counterclockwise around the Z axis to the rotation angle θ2 = 0° of the plane where the first radar, the second radar and the center of the earth are located, the required variables (x1, y1, z1, x2, y2, z2) deviate greatly from the true values. Therefore, it is necessary to calculate the value of the air target in step S2 in the first step. The coordinates (x1, y1, z1) in the first radar array coordinate system are corrected to obtain the corrected coordinates (x′1, y′1, z′1) of the air target in the first radar array coordinate system. The coordinates (x2, y2, z2) of the air target in the second radar array coordinate system are corrected to obtain the corrected coordinates (x′2, y′2, z′2) of the air target in the second radar array coordinate system. After correction, the position calculation model of the air target in the radar array coordinate system is obtained according to (x′1, y′1, z′1) and (x′2, y′2, z′2). The correction method is:

[0211]

[0212] When the antenna array attitude angle of the first radar, the antenna array attitude angle of the second radar, the attitude angle of the first satellite, and the attitude angle of the second satellite are equal to 0°, in step S2: the coefficient matrix of the position calculation model of the aerial target in the radar array coordinate system is irreversible and the solution does not exist, it is simplified to:

[0213]

[0214] The above formula can be used to solve the variables (x1, z1, x2, z2), and then find the variables (y1, y2).

[0215] When the radar group consists of the first radar of the first satellite, the second radar of the second satellite, the third radar of the third satellite, and so on, the nth radar of the nth satellite, step S2: the position calculation model of the aerial target in the radar array coordinate system consists of the following steps:

[0216] Assume that there are n (n≥3) radars measuring the target, and the coordinates of the target in the n radar array coordinate system are (x1, y1, z1), (x2, y2, z2)…, (x n ,y n ,z n ), the radial distance and azimuth of the target are measured as A system of linear equations can be obtained.

[0217]

[0218] in,

[0219]

[0220]

[0221]

[0222]

[0223]

[0224]

[0225]

[0226]

[0227]

[0228]

[0229] b 33 =cosθ2·C2A2+sinθ2·C2B2

[0230] b 41 =A2C2

[0231] b 42 =B2C2

[0232]

[0233]

[0234]

[0235]

[0236]

[0237]

[0238]

[0239]

[0240]

[0241] d 33 =cosθ n ·C n A n +sinθ n ·C n B n

[0242] d 41 =A n C n

[0243] d 42 =B n C n

[0244]

[0245]

[0246] Where, α n is the angle between the first radar and the nth radar and the center of the earth, θ n The XOZ plane of the nth satellite orbital coordinate system rotates counterclockwise around the Z axis by an angle θ n The rotation angle of the plane with the first radar, the second radar and the center of the earth, θ 1n is the angle between the XOZ plane of the first satellite orbit coordinate system and the planes of the first radar, the nth radar and the center of the earth, (A 1n ,B 1n,C 1n ) is the unit normal vector of the plane where the first radar, the nth radar and the center of the earth are located in the first satellite orbit coordinate system, (A n ,B n ,C n ) is the unit normal vector of the plane where the first radar, the nth radar and the center of the earth are located in the nth satellite orbit coordinate system, is the attitude angle of the nth satellite, is the antenna array attitude angle of the nth radar, and are the azimuth and radial distance of the air target measured by the nth radar, is the distance from the nth radar to the center of the earth, (x n ,y n ,z n ) is the coordinate of the aerial target in the nth radar array coordinate system.

[0247] Considering the different measurement errors of each radar, the constrained weighted least square method is used to solve the linear equations to obtain the target height: the obtained 5n-4 equations constitute a linear equation system, which can theoretically solve the variables (x1, y1, z1, ..., x n ,y n ,z n ).

[0248] Considering the error in radar measurement, the obtained equations are overdetermined and have no solution in the usual sense. Therefore, the least squares method is used to solve the equations. The position calculation model of the aerial target in the radar array coordinate system can be written as

[0249]

[0250] Where X=[x1,y1,z1,…,x n ,y n ,z n ] T , H, K are coefficient matrices, and

[0251]

[0252]

[0253] in,

[0254]

[0255]

[0256]

[0257]

[0258]

[0259] The above formula for calculating the position of the aerial target in the radar array coordinate system is regarded as a weighted least squares problem with constraints, that is,

[0260]

[0261] Where W = diag(w1,w2,…w 2n-1 )>0 is the weight matrix, which is determined by the measurement error, and the QR decomposition is used to find the minimum norm least squares order

[0262]

[0263] Its QR decomposition is

[0264]

[0265] Among them, Q satisfies Q T Q=I m . Then the minimum norm least squares solution of X is

[0266]

[0267] In step S3, the position formula of the aerial target in the satellite orbit coordinate system is calculated as:

[0268]

[0269] In step S4, the formula for calculating the height of the aerial target is:

[0270]

[0271] Where h is the height of the aerial target, r e is the radius of the earth where the aerial target is located,

[0272] in,

[0273] Where a is the equatorial radius of the Earth, b is the polar radius of the Earth, and L at is the estimated latitude of the aerial target.

[0274] Example 1

[0275] Four satellites are set up and carry four radars to form a radar group, named satellite 1, satellite 2, satellite 3, and satellite 4 respectively. Satellite 1 corresponds to radar 1, satellite 2 corresponds to radar 2, satellite 3 corresponds to radar 3, and satellite 4 corresponds to radar 4. The specific orbital parameters of the onboard detection radar satellites are shown in Table 1. The radar antenna array attitude angles are: roll angle r c=30°, pitch angle Yaw angle ψ c = 0°, and the satellite attitude angles are all 0°. Satellites 1 and 4 are in the same orbital plane. Assume that the aerial target is flying in a straight line at a constant speed and an altitude of 9 km. Figure 2-(a) shows the 2D true trajectory of a single aerial target tracked by four satellite-borne detection radars at 1300s in the STK range scenario. In this embodiment, the radar measurements are identical, with standard deviations of 0.9 km in radial range and 0.03° in azimuth for all four radars.

[0276] Table 1 The number of orbital elements of the four satellites

[0277]

[0278] Figure 3-(a) shows the simulation results for aerial target altitude estimation using two and three radars, respectively. As shown in Figure 3-(a), the altitude estimation accuracy using the fusion of Radar 1 and Radar 2 is between 3.5 km and 8 km, while the altitude estimation accuracy using the fusion of Radar 2 and Radar 3 is between 2.5 km and 3.5 km. This indicates that when the number of radars is the same, the positional relationship between the target and the radars affects the accuracy of target altitude estimation. The specific impact of this relationship will be detailed in Case 3.

[0279] The altitude estimation accuracy of aerial targets based on the fusion of target measurements from Radar 1, Radar 2, and Radar 3 is between 1.5 km and 2 km. This shows that the more radars there are, the higher the altitude estimation accuracy.

[0280] Since radar 1 and radar 4 have the same orbital inclination, simulation shows that the altitude estimation accuracy of the fusion of radar 1 and radar 4 measurements is between 7km and 9km. This shows that the altitude estimation accuracy is worse when the radar satellites are on the same orbit than when they are on different orbits.

[0281] Example 2

[0282] Four satellites are set up and carry four radars to form a radar group, named satellite 1, satellite 2, satellite 3, and satellite 4 respectively. Satellite 1 corresponds to radar 1, satellite 2 corresponds to radar 2, satellite 3 corresponds to radar 3, and satellite 4 corresponds to radar 4. The specific orbital parameters of the onboard detection radar satellites are shown in Table 1. The radar antenna array attitude angles are: roll angle r c =30°, pitch angle Yaw angle ψ c= 0°, and the satellite attitude angles are all 0°. Satellites 1 and 4 are in the same orbital plane. Assume that the aerial target is flying in a straight line at a constant speed and an altitude of 9 km. In this embodiment, the radar measurements are different, and the standard deviations of the four radars are: Radar 1, 0.9 km radial range, 0.03° azimuth; Radar 2, 0.7 km radial range, 0.02° azimuth; Radar 3, 0.5 km radial range, 0.01° azimuth; Radar 4, 0.8 km radial range, 0.025° azimuth.

[0283] Table 1 The number of orbital elements of the four satellites

[0284]

[0285] The simulation results are shown in Figure 3-(b). Assuming the measurement error of Radar 1 remains unchanged, when the measurement errors of Radars 2 and 3 decrease, the altitude estimation accuracy using the fusion of Radars 1 and 2 improves to 3km-7km, the accuracy using the fusion of Radars 2 and 3 improves to 1.5km-2km, and the accuracy using the fusion of Radars 1, 2, and 3 improves to 1km-1.5km. This shows that when the measurement error of one radar among multiple radars is reduced, the final altitude estimation result will be improved. Comparing the target altitude estimation results of Radars 1 and 2 with those of Radars 2 and 3, it can be seen that the difference in target and radar position has a certain impact on altitude estimation accuracy, which will be analyzed in detail in Case 3.

[0286] Example 3

[0287] Set up two satellites and carry two radars to form a radar group, and estimate the different positions and heights of multiple space targets. The number of six orbits of the carrier satellite is set as:

[0288] Satellite 1's orbit has a semi-major axis of 6978.14 km, an eccentricity of 1.369e-15, an orbital inclination of 20°, an argument of perigee of 0°, a right ascension of the ascending node of 0°, and a mean anomaly of 50°.

[0289] Satellite 2's orbit has a semi-major axis of 6978.14 km, an eccentricity of 1.369e-15, an orbital inclination of 25°, an argument of perigee of 0°, a right ascension of the ascending node of 0°, and a mean anomaly of 60°.

[0290] Five aerial targets were set up at five different locations within the common detection area, all moving in a uniform linear motion at an altitude of 9 km. The altitude estimation results for the targets at different locations were compared. Figure 2(b) shows the 2D true trajectories of the five aerial targets tracked by two spaceborne detection radars at 1500 seconds from the start of the STK medium-range scenario. For ease of observation, the antenna attitude angles of both radars and the satellite attitude angle were set to 0°. The standard deviations of the measurement errors of both radars for the aerial targets were 0.9 km in radial range and 0.03° in azimuth.

[0291] like Figure 4 As shown in the figure, comparing the altitude estimation accuracy of five targets at different locations, the altitude estimation accuracy of Targets 1 (Aircraft 1) and 3 (Aircraft 3), located at the lower right edge of the radar's common detection area, is between 2km and 2.5km. The altitude estimation accuracy of Targets 2 (Aircraft 2) and 5 (Aircraft 5), located at the upper left edge of the detection area, is between 3.5km and 6km. The altitude estimation accuracy of Target 4 (Aircraft 4), located at the center of the detection area, is within 1km. This shows that within the radar detection area, the closer to the center, the higher the altitude estimation accuracy; the farther away from the center, the lower the altitude estimation accuracy.

[0292] The present invention solves the problem in the prior art of large measurement errors caused by excessive pitch angle errors in target tracking by a single satellite-borne detection radar. By constructing a geometric relationship between the radar and the target, the present invention establishes a set of equations containing unknown variables such as the target height. Taking into account the radar measurement error, the equation is described as a weighted least squares problem with equality constraints, and QR decomposition is used to obtain the minimum norm least squares solution.

[0293] The simulation verification results show that the networked measurement fusion of spaceborne detection radars has the ability to estimate the altitude of aerial targets. Different numbers of spaceborne detection radars and different orbit combinations will affect the accuracy of target altitude estimation. Generally speaking, the more fused radars there are, the higher the accuracy of aerial target altitude estimation; the target altitude estimation accuracy is higher when satellites are in different orbits than when satellites are in the same orbit; at the same time, the accuracy of aerial target altitude estimation is related to the location of the target. In the detection area of ​​multiple radars, the closer the target is to the center area, the higher the altitude estimation accuracy.

[0294] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for estimating the height of an aerial target based on a spaceborne radar network, characterized in that: The radar network is composed of two or more spaceborne radars forming a radar group, and the method for estimating the height of an aerial target is composed of the following steps: Step S1: using a radar group to measure the radial distance and azimuth of the aerial target respectively; Step S2: Calculate the position of the aerial target in the radar array coordinate system using the least squares method through the position calculation model of the aerial target in the radar array coordinate system; Step S3: Calculate the position of the aerial target in the satellite orbit coordinate system based on the position of the aerial target in the radar array coordinate system; Step S4: Calculate the altitude of the aerial target based on the position of the aerial target in the satellite orbit coordinate system and the radius of the earth where the aerial target is located; When the radar group consists of a first radar of a first satellite and a second radar of a second satellite, the position calculation model of the aerial target in the radar array coordinate system in step S2 is composed of the following steps: Establish a position calculation model for aerial targets in the satellite orbit coordinate system; The position of the aerial target in the first satellite orbit coordinate system is transformed into the position in the first radar array coordinate system, and the position of the aerial target in the second satellite orbit coordinate system is transformed into the position in the second radar array coordinate system, thereby obtaining a position calculation model of the aerial target in the radar array coordinate system; The position calculation model of the aerial target in the satellite orbit coordinate system is: in, a 36 =cosθ2·C2A2+sinθ2·C2B2 <h2 style=";text-align:left;direction:ltr">a<h2 style=";text-align:left;direction:ltr"> 44 <h2 style=";text-align:left;direction:ltr"> =A2C2 a 45 =B2C2 Wherein, (A1, B1, C1) is the unit normal vector of the plane OS1S2 in the first satellite orbit coordinate system, (A2, B2, C2) is the unit normal vector of the plane OS1S2 in the second satellite orbit coordinate system, (X1, Y1, Z1) is the position of the aerial target in the first satellite orbit coordinate system, (X2, Y2, Z2) is the position of the aerial target in the second satellite orbit coordinate system, is the distance from the first radar to the center of the earth, is the distance from the second radar to the center of the earth, θ1 is the angle corresponding to the coincidence of the XOZ plane of the first satellite orbit coordinate system with the plane of the line connecting the first radar, the second radar and the center of the earth after the XOZ plane of the first satellite orbit coordinate system is rotated counterclockwise around the Z axis by an angle θ1, and θ2 is the angle corresponding to the coincidence of the XOZ plane of the second satellite orbit coordinate system with the plane of the line connecting the first radar, the second radar and the center of the earth after the XOZ plane of the second satellite orbit coordinate system is rotated counterclockwise around the Z axis by an angle θ2; is the radial distance of the air target measured by the first radar, is the radial distance of the aerial target measured by the second radar, and α2 is the angle between the first radar, the second radar and the center of the earth; Among them, the first radar is located at S1, the second radar is located at S2, and the first radar, the second radar and the center of the earth O are connected to form a plane OS1S2.

2. The method for estimating the height of an aerial target based on a spaceborne radar network according to claim 1, wherein: The position calculation model of the aerial target in the radar array coordinate system is: in, is the radial distance and azimuth of the air target measured by the first radar, are the radial distance and azimuth of the air target measured by the second radar, (x1, y1, z1) are the coordinates of the air target in the first radar array coordinate system, and (x2, y2, z2) are the coordinates of the air target in the second radar array coordinate system. Where, in, is the antenna array attitude angle of the first radar, is the antenna array attitude angle of the second radar, is the attitude angle of the first satellite, is the attitude angle of the second satellite.

3. A method for estimating the height of an aerial target based on a spaceborne radar network according to claim 2, characterized in that: In step S3, the position formula of the aerial target in the satellite orbit coordinate system is calculated as:

4. The method for estimating the height of an aerial target based on a spaceborne radar network according to claim 3, wherein: In step S4, the formula for calculating the height of the aerial target is: Where h is the height of the aerial target, r e is the radius of the earth where the aerial target is located, in, Where a is the equatorial radius of the Earth, b is the polar radius of the Earth, and L at is the estimated latitude of the aerial target.

5. The method for estimating the height of an aerial target based on a spaceborne radar network according to claim 2, wherein: When the radar group consists of a first radar of a first satellite and a second radar of a second satellite, and the XOZ plane of the first satellite orbital coordinate system coincides with the plane of the second satellite orbital coordinate system, that is, the XOZ plane of the first satellite orbital coordinate system rotates counterclockwise around the Z axis to a rotation angle θ1=0° of the plane where the first radar, the second radar, and the center of the earth are located, and the XOZ plane of the second satellite orbital coordinate system rotates counterclockwise around the Z axis to a rotation angle θ2=0° of the plane where the first radar, the second radar, and the center of the earth are located, The coordinates (x1, y1, z1) of the aerial target in the first radar array coordinate system in step S2 are corrected to obtain the corrected coordinates (x1′, y1′, z1′) of the aerial target in the first radar array coordinate system, and the coordinates (x2, y2, z2) of the aerial target in the second radar array coordinate system are corrected to obtain the corrected coordinates (x′2, y′2, z′2) of the aerial target in the second radar array coordinate system. After correction, a position calculation model of the aerial target in the radar array coordinate system is obtained according to (x1′, y1′, z1′) and (x′2, y′2, z′2). The correction method is:

6. The method for estimating the height of an aerial target based on a spaceborne radar network according to claim 2, wherein: When the antenna array attitude angle of the first radar, the antenna array attitude angle of the second radar, the attitude angle of the first satellite, and the attitude angle of the second satellite are equal to 0°, in step S2: the position calculation model of the aerial target in the radar array coordinate system is: Where (x1, y1, z1) is the coordinate of the aerial target in the first radar array coordinate system, (x2, y2, z2) is the coordinate of the aerial target in the second radar array coordinate system, is the distance from the first radar to the center of the earth, is the distance from the second radar to the center of the earth, are the radial distance and azimuth of the air target measured by the first radar, The radial distance and azimuth of the air target measured by the second radar.

7. The method for estimating the height of an aerial target based on a spaceborne radar network according to claim 1, wherein: When the radar group consists of a first radar of a first satellite, a second radar of a second satellite, a third radar of a third satellite, and so on, an nth radar of an nth satellite, then in step S2, the position calculation model of the aerial target in the radar array coordinate system is: in, b 33 =cosθ2·C2A2+sinθ2·C2B2b 34 =A2C2 b 35 =B2C2 d 33 =cosθ n ·C n A n +sinθ n ·C n B n d 41 =A n C n d 42 =B n C n Where, α n is the angle between the first radar and the nth radar and the center of the earth, θ n The XOZ plane of the nth satellite orbital coordinate system rotates counterclockwise around the Z axis by an angle θ n The rotation angle of the plane with the first radar, the second radar and the center of the earth, θ 1n is the angle between the XOZ plane of the first satellite orbit coordinate system and the planes of the first radar, the nth radar and the center of the earth, (A 1n ,B 1n ,C 1n ) is the unit normal vector of the plane where the first radar, the nth radar and the center of the earth are located in the first satellite orbit coordinate system, (A n ,B n ,C n ) is the unit normal vector of the plane where the first radar, the nth radar and the center of the earth are located in the nth satellite orbit coordinate system, is the attitude angle of the nth satellite, is the antenna array attitude angle of the nth radar, and are the azimuth and radial distance of the air target measured by the nth radar, is the distance from the nth radar to the center of the earth, (x n ,y n ,z n ) is the coordinate of the aerial target in the nth radar array coordinate system.

8. The method for estimating the height of an aerial target based on a spaceborne radar network according to claim 7, wherein: In step S2, the formula for calculating the position of the aerial target in the radar array coordinate system is: Where X=[x1,y1,z1,…,x n ,y n ,z n ] T , H, K are coefficient matrices, and in, The above formula for calculating the position of the aerial target in the radar array coordinate system is regarded as a weighted least squares problem with constraints, that is, Where W = diag(w1,w2,…w 2n-1 )>0 is the weight matrix, which is determined by the measurement error, and the QR decomposition is used to find the minimum norm least squares solution X.

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