Coordinate aided track quality assessment method

Abstract

In view of the military demand of the coordinate support combat method application, the application provides a coordinate support predicted track quality evaluation method for intercepting aircraft targets, target track information provided by a support station radar is used to predict the instantaneous encounter point of an intercepted missile of a supported station, the target track information of the support station radar is predicted to the predicted encounter point, the error of the target track in the north-sky-east coordinate system of the support station radar is calculated, and then the error of the target in the north-sky-east coordinate system of the support station radar is transferred to the north-sky-east coordinate system of the supported station, the random error mean square deviation and the system error of the slant distance, the elevation angle and the azimuth angle of the target predicted track relative to the supported station are evaluated, and decision support is provided for the supported station to adopt the target coordinates provided by the support station radar to carry out the external information guidance interception combat.

Description

TECHNICAL FIELD

[0001] The present application relates to radar engineering technology, in particular to a predicted track quality evaluation method for coordinate support. BACKGROUND

[0002] Coordinate support is a typical mode in the application of air defense and anti-missile networked operations, and its basic idea is that a fire unit with good shooting conditions cannot track an air target due to some reasons (such as the assigned radar being disturbed or malfunctioning), at which time the target track information sent by an external radar can be used for interception calculation, parameter binding and missile guidance to realize interception operations under the condition of external radar coordinate support, and this combat mode is also called external information guidance. When using external radar track information to conduct interception operations, it is first necessary to judge whether the target track quality provided by the external radar can meet the guidance requirements, that is, whether it can meet the precision requirements of the midcourse guidance handover of the interceptor missile. If the target coordinate information provided by the external radar is poor in precision and cannot meet the precision requirements of the target interception by the interceptor missile seeker, there will be a high risk of failure in launching the missile to intercept the target. Therefore, the adoption of the coordinate support method for interception operations requires prediction of the target track provided by the external radar, prediction of the track quality distribution after the launch of the interceptor missile, and provision of a scientific basis for launch decision-making. SUMMARY

[0003] In view of the military needs of the coordinate support combat method, the present application proposes a coordinate support predicted track quality evaluation method, and the specific steps are as follows:

[0004] Step 1: Convert the target three-dimensional track tracked by the support station in the north-east coordinate system to the north-east coordinate system of the supported station.

[0005] (1) Definition of radar measurement coordinate system

[0006] The radar measurement coordinate system is a ground rectangular coordinate system with the radar station deployment point as the center;

[0007] o s - Coordinate origin, radar vehicle deployment point;

[0008] o s x s axis - the intersection line of the terrestrial meridian plane of the o s point and the plane containing the o s point and perpendicular to the normal line, pointing to the northern direction of the earth;

[0009] o s y s axis - coincides with the normal line of the earth ellipsoid surface of the o s point, pointing outward of the earth ellipsoid surface;

[0010] o s zs axis and o s x s , o s y s The axes constitute a right-handed rectangular coordinate system, i.e. pointing to the east of the earth;

[0011] The direct observation value of the target obtained by the radar adopts the ground spherical coordinate:

[0012] R——slant range, the distance from the coordinate origin o s to the observation point;

[0013] ε——elevation angle, the angle between the target line of sight and the horizontal plane, with the horizontal plane as the reference, the upward angle is positive, and the change range is-90°-90°;

[0014] β——azimuth angle, the angle between the projection of the target line of sight on the horizontal plane and the north direction, with the north direction as the reference, the clockwise angle is positive when viewed from top to bottom, and the change range is 0°-360°;

[0015] (2) Target position and velocity conversion

[0016] Convert the target position and velocity tracked by the supporting station radar in the north-sky-east coordinate system to the north-sky-east coordinate system of the aided station, and the formula is as follows:

[0017]

[0018]

[0019]

[0020]

[0021]

[0022] In the formula, M1 and M2 are coordinate conversion matrices;

[0023] m ij is an element in the coordinate conversion matrix M1, i, j=1, 2, 3;

[0024] (L1, B1, H1) are the longitude, latitude and geodetic height of the site of the supporting station radar, respectively;

[0025] (X1, Y1, Z1) are the geocentric rectangular coordinates of the site of the supporting station radar in the CGCS2000 national geodetic coordinate system;

[0026] (L2, B2, H2) are the longitude, latitude and geodetic height of the site of the aided station, respectively;

[0027] (X2, Y2, Z2) is the geocentric rectangular coordinate of the aided station in CGCS2000 national geodetic coordinate system;

[0028] (x1, y1, z1) are the coordinates of the target on the x, y, z axes of the north-sky-east coordinate system of the aided station respectively, and x, y, z are north, sky, and east respectively;

[0029] are the velocities of the target on the x, y, z axes of the north-sky-east coordinate system of the aided station respectively;

[0030] (x2, y2, z2) are the coordinates of the target on the x, y, z axes of the north-sky-east coordinate system of the aided station respectively;

[0031] are the velocities of the target on the x, y, z axes of the north-sky-east coordinate system of the aided station respectively;

[0032] Step 2: Predict the instantaneous encounter point of the aided station to the target at the current moment, and calculate the time T z that the target flies to the encounter point;

[0033] The target keeps its heading unchanged and flies at a constant speed in a straight line from the current position. If a missile is launched at the aided station at this moment, the encounter condition between the missile and the target is that the target flies to the T' point after T tz , the slant distance of the T' point from the aided station is R z , the height is h z , and the time for the missile to fly to the T' point is T mz . If |T mz -T tz |≤ε, where ε is a threshold parameter of the subscription, then the missile encounters the target.

[0034] The following gives the steps of the iterative algorithm for predicting the instantaneous encounter point:

[0035] (1) Extrapolate the target from the current position to the nearest point from the radar station, and the extrapolation time is T tz0

[0036]

[0037] In the formula, S t is the heading distance of the target relative to the aided station;

[0038] V t is the target speed;

[0039] (2) Calculate the slant distance R z and the height h z of the target after extrapolation T tz0

[0040]

[0041] (3) Calculate the average flight speed of the missile

[0042] missile average flight speed V ave R is the slant distance R from point T′ to the aid station. z And the altitude h of the encounter point T′ from the rescue station z The fitting function, i.e.

[0043] V ave =f(R) z h z )

[0044] (4) Calculate the time T for the missile to reach the target extrapolation point. mz

[0045]

[0046] (5) If T mz >T tz or T mz >T m_max T m_max If the maximum flight time of the interceptor missile is given, and the initial parameters are given, then it cannot be intercepted, there is no encounter point, and it returns; otherwise, proceed to step (6).

[0047] (6) If |T mz -T tz If |≤ε, then stop the calculation and let T be the time it takes for the target to reach the instantaneous encounter point. z =T tz0 Proceed to step (15) to make a final judgment on whether an encounter point exists; otherwise, proceed to step (7).

[0048] (7) The time T for the target to be shifted backward from the current point tz =T tz0 ×k, where k is the calculation coefficient for extrapolation time;

[0049] (8) Calculate the target extrapolation T according to steps (1) and (2). tz The slant distance R afterward z and height h z ;

[0050] (9) Calculate the missile's average flight speed V according to the method in step (3). ave ;

[0051] (10) Calculate the time T for the missile to reach the target extrapolation point according to the method in step (4). mz ;

[0052] (11) If |T mz -T tz|≤ε, stop calculation, let the target fly to the time T of the instantaneous encounter point z = T tz , go to step (15) to make the final judgment of whether there is an encounter point; otherwise, go to step (12);

[0053] (12) If T mz >T tz , let the target be extrapolated forward from the current point for a time T tz = T tz + (T tz0 -T tz) ) x k, repeat steps (8)-(11); otherwise, go to step (13);

[0054] (13) If T mz >T m_max , it is impossible to intercept, there is no encounter point, return; otherwise, go to step (14);

[0055] (14) Let the target be extrapolated forward from the current point for a time T tz = T tz -T tz x k, repeat steps (8)-(11);

[0056] (15) If T z T m_min , T m_min is the minimum flight time of the interceptor missile, and is the initial subscription parameter, it is impossible to intercept, there is no encounter point, return; otherwise, there is an encounter point, continue to step 3 calculation;

[0057] Step 3: In the north-east sky coordinate system of the support station, the target is extrapolated from the current position at a constant speed in a straight line with a step size of ΔT, and the length of ΔT is the guidance period of the missile. The formula is

[0058]

[0059] Step 4: Convert the extrapolated rectangular coordinates of the target in the north-east sky coordinate system of the support station into polar coordinates. The formula is

[0060]

[0061]

[0062] In the formula, (x1, y1, z1) are the rectangular coordinates of the target in the north-east sky coordinate system of the support station after extrapolation in step 3;

[0063] (R1, ε1, β1) are the slant distance, elevation angle and azimuth angle of the target relative to the support station after extrapolation in step 3, respectively;

[0064] Step 5: Calculate the rectangular coordinate error of the target in the north-sky east coordinate system of the support station;

[0065] (1) Random error

[0066] The rectangular coordinate covariance matrix D1 of the target in the north-sky east coordinate system of the support station is

[0067]

[0068]

[0069]

[0070]

[0071] wherein, are the prior random error variances of the slant range, the elevation angle and the azimuth angle of the target measured by the radar of the support station, respectively, and are the initial setting parameters;

[0072] are the variances of the x, y, z coordinates of the target in the north-sky east coordinate system of the support station, respectively;

[0073] are the covariances of the x, y coordinates of the target in the north-sky east coordinate system of the support station;

[0074] are the covariances of the x, z coordinates of the target in the north-sky east coordinate system of the support station;

[0075] are the covariances of the y, z coordinates of the target in the north-sky east coordinate system of the support station;

[0076] (2) System error

[0077] The rectangular coordinate system error of the target in the north-sky east coordinate system of the support station is

[0078]

[0079] wherein, are the prior system error components of the position coordinates of the target on the x, y, z axes in the north-sky east coordinate system of the support station, respectively; are the prior system errors of the slant range, the elevation angle and the azimuth angle of the support station, respectively.

[0080] The maximum value of the system error is

[0081]

[0082] Step 6: Transfer the rectangular coordinate error of the target in the north-sky east coordinate system of the support station to the north-sky east coordinate system of the supported station;

[0083] (1) The random error covariance of the rectangular coordinates of the target in the north-east coordinate system of the aided station

[0084] The random error covariance matrix D2 of the rectangular coordinates of the target in the north-east coordinate system of the aided station is

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095] wherein, are the prior fluctuation error variances of the longitude, latitude and geodetic height station positioning of the aided station radar respectively;

[0096] are the prior fluctuation error variances of the longitude, latitude and geodetic height station positioning of the aided station radar respectively;

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124] In the formula, x tr , y tr , z tr are the coordinate translation amounts of the x, y, z axes of the north-sky-east coordinates of the support station converted into the north-sky-east rectangular coordinates of the supported station, respectively.

[0125]

[0126]

[0127] z tr = -(N1+H1)cosB1sin(L2-L1)

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139]

[0140]

[0141] In the formula, N1 and N2 are the radii of curvature of the prime vertical at the station sites of the supporting station and the supported station respectively;

[0142]

[0143]

[0144] In the formula, e is the first eccentricity of the meridian ellipse;

[0145] a is the long semi-axis of the earth ellipsoid;

[0146] (2) The rectangular coordinate system error of the target in the north-east coordinate system of the supported station

[0147]

[0148]

[0149]

[0150] In the formula, are the prior system error components of the position coordinates of the target on the x, y and z axes of the north-east coordinate system of the supported station respectively;

[0151] are the prior system error components of the position coordinates of the target on the x, y and z axes of the north-east coordinate system of the supporting station respectively;

[0152] are the prior systematic errors of the radar longitude, latitude and height of the supporting station site positioning, respectively;

[0153] are the prior systematic errors of the radar longitude, latitude and height of the aided station site positioning, respectively; the maximum value of the prior systematic error components of the position coordinates of the target on the x, y, z axes of the north-east coordinate system of the aided station is

[0154]

[0155]

[0156]

[0157] wherein, are the maximum values of the prior systematic error components of the position coordinates of the target on the x, y, z axes of the north-east coordinate system of the aided station, respectively;

[0158] the maximum value of the distance error of the target is δ max

[0159]

[0160] Step 7: calculate and output the polar coordinate error of the target in the north-east coordinate system of the aided station;

[0161] the random error mean square of the slant range R2 of the target relative to the aided station is

[0162]

[0163] If the covariance is set as then

[0164]

[0165] the systematic error of the slant range R2 of the target relative to the aided station is

[0166]

[0167] the maximum value of the systematic error of the slant range R2 of the target relative to the aided station is

[0168]

[0169] the random error mean square of the elevation angle ε2 of the target relative to the aided station is

[0170]

[0171] If the covariance is set as​​​​ but

[0172]

[0173] Systematic error of the elevation angle ε2 of the target relative to the aid station for

[0174]

[0175] The maximum value of the systematic error of the elevation angle ε2 of the target relative to the aid station for

[0176]

[0177] The root mean square of the random error of the azimuth angle β2 of the target relative to the recipient station for

[0178]

[0179] If we define the covariance but

[0180]

[0181] Systematic error of the azimuth angle β2 of the target relative to the recipient station for

[0182]

[0183] The maximum systematic error of the target's azimuth angle β2 relative to the recipient station is

[0184]

[0185] As mentioned above, (R2, ε2, β2) represent the slant distance, elevation angle, and azimuth angle of the target relative to the receiving station, respectively, and are calculated using the following formula.

[0186]

[0187]

[0188]

[0189] In one specific embodiment of the present invention, ε = 0.1s.

[0190] In another specific embodiment of the present invention, k = 0.5.

[0191] This invention utilizes target trajectory information provided by support station radar to predict the instantaneous encounter point of interceptor missiles at the recipient station. It predicts the target trajectory information from the support station radar to the predicted encounter point, calculates the error of the target trajectory in the support station radar's north-sky-east coordinate system, and then transfers the error of the target in the support station radar's north-sky-east coordinate system to the recipient station's north-sky-east coordinate system. It evaluates the random error, root mean square error, and systematic error of the target's predicted trajectory relative to the recipient station in terms of slant range, elevation angle, and azimuth angle. This provides decision support for the recipient station to conduct external information-guided interception operations using target coordinates provided by the support station radar. Attached Figure Description

[0192] Figure 1 A schematic diagram of the process for assessing the quality of predicted tracks using coordinate support;

[0193] Figure 2 Define the radar measurement coordinate system;

[0194] Figure 3 This is a schematic diagram illustrating the prediction of the instantaneous encounter point between the interceptor missile and the target. Specific implementation methods

[0195] like Figure 1 As shown, the specific steps of the coordinate support prediction track quality assessment method proposed in this invention are as follows:

[0196] Step 1: Convert the target's 3D trajectory tracked in the support station's North-East coordinate system to the recipient station's North-East coordinate system.

[0197] (1) Definition of radar measurement coordinate system

[0198] like Figure 2 As shown, the radar measurement coordinate system is a ground rectangular coordinate system centered on the radar station deployment point.

[0199] o s — Coordinate origin, radar vehicle deployment point (usually the radar antenna rotation center);

[0200] o s x s Axis — for o s The earth meridian plane and the inclusion of o s The line of intersection of the plane perpendicular to the normal points north of the Earth (towards the minor axis of the Earth's ellipsoid).

[0201] o s y s Axis — with o s The points coincide with the normals to the Earth's ellipsoid and point outwards (upwards) from the Earth's ellipsoid.

[0202] o s z s Axis and o s xs 、o s y s The axis constitutes a right-handed rectangular coordinate system, i.e. pointing to the east of the earth.

[0203] The ground rectangular coordinate system is also called the north-up-east (NUE) coordinate system, which is a surface relative coordinate system, is fixed with the earth surface and moves with the earth, is a calculation coordinate system, and is generally used for calculating the motion parameters of a relative station of a detected air target (i.e. describing a target track) by a radar.

[0204] The direct observation value of a target obtained by a radar adopts a ground spherical coordinate:

[0205] R - slant range, is the distance from the coordinate origin o s to the observation point;

[0206] ε - elevation angle, is the included angle between the line of sight (a ray pointing from the coordinate origin o s to the observation point) and the horizontal plane, the angle is positive when the horizontal plane is turned upward, and the variation range is -90°-90°;

[0207] β - azimuth angle, is the included angle between the projection of the line of sight on the horizontal plane and the north direction, the angle is positive when the north direction is turned clockwise, and the variation range is 0°-360°.

[0208] (2) Conversion of target position and velocity

[0209] The target position and velocity tracked by a radar of a supporting station in a north-up-east coordinate system are converted to those in a north-up-east coordinate system of a supported station, and the formula is as follows:

[0210]

[0211]

[0212]

[0213]

[0214]

[0215] In the formula, M1 and M2 are coordinate conversion matrices;

[0216] m ij (i, j = 1, 2, 3) are elements in the coordinate conversion matrix M1;

[0217] (L1, B1, H1) are respectively the longitude, latitude and geodetic height (CGCS2000 national geodetic coordinate system) of the site of the radar of the supporting station;

[0218] (X1, Y1, Z1) is the geocentric rectangular coordinate of the radar station site in CGCS2000 national geodetic coordinate system;

[0219] (L2, B2, H2) are respectively the longitude, latitude and geodetic height of the aided station site (CGCS2000 national geodetic coordinate system);

[0220] (X2, Y2, Z2) is the geocentric rectangular coordinate of the aided station site in CGCS2000 national geodetic coordinate system;

[0221] (x1, y1, z1) are respectively the coordinates of the target in the north-sky-east coordinate system of the aided station x (north), y (sky), z (east) axis;

[0222] are respectively the velocities of the target in the north-sky-east coordinate system of the aided station x (north), y (sky), z (east) axis;

[0223] (x2, y2, z2) are respectively the coordinates of the target in the north-sky-east coordinate system of the aided station x (north), y (sky), z (east) axis;

[0224] are respectively the velocities of the target in the north-sky-east coordinate system of the aided station x (north), y (sky), z (east) axis.

[0225] Step 2: predict the instantaneous encounter point of the aided station to the target at the current moment, calculate the time T z .

[0226] As shown in Figure 2 , the target keeps its heading unchanged from the current position and flies at a constant speed in a straight line, if the aided station launches a missile at this moment, the encounter conditions of the missile and the target are that the target flies to the T' point after T tz , the oblique distance of the T' point from the aided station is R z , the height is h z , and the time for the missile to fly to the T' point is T mz , if |T mz -T tz |≤ε (ε is a threshold parameter of the subscription, for example, take 0.1s), the missile encounters the target.

[0227] The iterative algorithm steps of the instantaneous encounter point prediction are as follows:

[0228] (1) extrapolate the target from the current position to the nearest point of the radar station, the extrapolation time is T tz0

[0229]

[0230] In the formula, S tis the course distance of the target relative to the assisted station;

[0231] V t is the magnitude of the target speed.

[0232] (2) Calculate the extrapolated slant range R tz0 and altitude h z after the target is extrapolated by time T z

[0233]

[0234] (3) Calculate the average flight speed of the missile

[0235] The average flight speed V of the missile[[ID=Q23]] ave is the fitting function of the slant range R of the T' point from the assisted station z and the altitude h of the T' point from the assisted station at the encounter altitude, that is z V ave

[0236] z = f(R z ave h)

[0237] Note: The fitting function formula of the average flight speed V of the missile mz is obtained by fitting a large amount of ballistic simulation data and live-fire interception data. Different missile models have different forms of the average flight speed fitting function formula.

[0238] (4) Calculate the time T for the missile to fly to the extrapolated point of the target mz

[0239]

[0240] (5) If T tz > T mz or T m_max > T m_max (T mz is the maximum flight time of the interceptor and is the initial binding parameter), then it cannot be intercepted, there is no encounter point, and return; otherwise, go to step (6).

[0241] (6) If |T tz - T z | ≤ ε, then stop the calculation, let the time T for the target to fly to the instantaneous encounter point tz0 = T tz , and go to step (15) for the final judgment of whether there is an encounter point; otherwise, go to step (7).

[0242] (7) The time T for the target to extrapolate forward from the current point tz0 = T tz×k (k is the calculation coefficient of extrapolation time, k=0.5)

[0243] (8) Calculate the target extrapolation T tz after the slope distance R z and height h z .

[0244] (9) Calculate the average flight speed V ave of the missile according to the method in step (3).

[0245] (10) Calculate the time T mz for the missile to fly to the target extrapolation point according to the method in step (4).

[0246] (11) If |T mz -T tz |≤ε, stop calculation, let the time T z for the target to fly to the instantaneous encounter point be T tz , and go to step (15) to make the final judgment of whether there is an encounter point; otherwise, go to step (12).

[0247] (12) If T mz >T tz , let the time T tz for the target to be extrapolated forward from the current point be T tz +(T tz0 -T tz )×k, repeat steps (8)-(11); otherwise, go to step (13).

[0248] (13) If T mz >T m_max , it is impossible to intercept, there is no encounter point, and return; otherwise, go to step (14).

[0249] (14) Let the time T tz for the target to be extrapolated forward from the current point be T tz -T tz ×k, repeat steps (8)-(11). (15) If T z <T m_min (T m_min is the minimum flight time of the interceptor missile, and is the initial subscription parameter), it is impossible to intercept, there is no encounter point, and return; otherwise, there is an encounter point, and continue to step 3.

[0250]

[0251] Step 4: Convert the extrapolated rectangular coordinates of the target in the north-east-up coordinate system of the support station into polar coordinates, with the formula

[0252]

[0253]

[0254] where (x1, y1, z1) are the rectangular coordinates of the target in the north-east-up coordinate system of the support station after extrapolation in Step 3;

[0255] (R1, ε1, β1) are the slant range, elevation angle, and azimuth angle of the target relative to the support station after extrapolation in Step 3.

[0256] Step 5: Calculate the rectangular coordinate error of the target in the north-east-up coordinate system of the support station.

[0257] (1) Random error

[0258] The rectangular coordinate covariance matrix D1 of the target in the north-east-up coordinate system of the support station is

[0259]

[0260]

[0261]

[0262]

[0263] where are the prior random error variances of the slant range, elevation angle, and azimuth angle of the target measured by the radar of the support station, and are the initial setting parameters;

[0264] are the variances of the x, y, and z coordinates of the target in the north-east-up coordinate system of the support station;

[0265] are the covariances of the x and y coordinates of the target in the north-east-up coordinate system of the support station;

[0266] are the covariances of the x and z coordinates of the target in the north-east-up coordinate system of the support station;

[0267] are the covariances of the y and z coordinates of the target in the north-east-up coordinate system of the support station.

[0268] (2) System error

[0269] The rectangular coordinate system error of the target in the north-east-up coordinate system of the support station is

[0270]

[0271] where, are the prior system error components of the target's position coordinates on the x, y, z axes of the north-east-up coordinate system of the support station, respectively; are the prior system errors of the slant range, elevation angle and azimuth angle of the support station, respectively.

[0272] The maximum value of the system error is

[0273]

[0274] Step 6: Transfer the rectangular coordinate error of the target in the north-east-up coordinate system of the support station to the north-east-up coordinate system of the supported station.

[0275] (1) Rectangular coordinate random error covariance of the target in the north-east-up coordinate system of the supported station

[0276] The rectangular coordinate random error covariance matrix D2 of the target in the north-east-up coordinate system of the supported station is

[0277]

[0278]

[0279]

[0280]

[0281]

[0282]

[0283]

[0284]

[0285]

[0286] where, are the prior fluctuation error variances of the radar longitude, latitude and geodetic height site positioning of the support station, respectively;

[0287] are the prior fluctuation error variances of the radar longitude, latitude and geodetic height site positioning of the supported station, respectively;

[0288]

[0289]

[0290]

[0291]

[0292]

[0293]

[0294]

[0295]

[0296]

[0297]

[0298]

[0299]

[0300]

[0301]

[0302]

[0303]

[0304]

[0305]

[0306]

[0307]

[0308]

[0309]

[0310]

[0311]

[0312]

[0313]

[0314] In the formula, x tr y tr z tr These represent the coordinate translations along the x, y, and z axes of the support station's north-east coordinate system to the recipient station's north-east rectangular coordinate system.

[0315]

[0316]

[0317] z tr = -(N1+H1)cosB1sin(L2-L1) ;

[0318]

[0319]

[0320]

[0321]

[0322]

[0323]

[0324]

[0325]

[0326]

[0327]

[0328]

[0329] In the formula, N1 and N2 are the radii of curvature of the prime vertical at the sites of the supporting station and the supported station, respectively;

[0330]

[0331]

[0332] In the formula, e is the first eccentricity of the meridian ellipse, e = 0.0818191910428;

[0333] a is the long semi-axis of the earth ellipsoid, a = 6378137 m.

[0334] (2) The rectangular coordinate system error of the target in the north-east coordinate system of the supported station

[0335]

[0336]

[0337]

[0338] wherein, are the prior system error components of the position coordinates of the target in the x, y, z axes of the north-east coordinate system of the aided station, respectively;

[0339] are the prior system error components of the position coordinates of the target in the x, y, z axes of the north-east coordinate system of the aided station, respectively; are the prior system errors of the longitude, latitude and geodetic height of the radar station of the aided station, respectively.

[0340] are the prior system errors of the longitude, latitude and geodetic height of the radar station of the aided station, respectively. The maximum value of the prior system error components of the position coordinates of the target in the x, y, z axes of the north-east coordinate system of the aided station is

[0341]

[0342]

[0343]

[0344] wherein, are the maximum values of the prior system error components of the position coordinates of the target in the x, y, z axes of the north-east coordinate system of the aided station, respectively.

[0345] The maximum value of the distance error of the target is max

[0346]

[0347] Step 7: Calculate and output the polar coordinate error of the target in the north-east coordinate system of the aided station.

[0348] The random error mean square of the slant range R2 of the target relative to the aided station is

[0349]

[0350] If the covariance is then

[0351]

[0352] The system error of the slant range R2 of the target relative to the aided station is

[0353]

[0354] The maximum value of the system error of the slant range R2 of the target relative to the aided station is

[0355] ​​​

[0356] Random error mean square variance of the target's elevation angle relative to the station of aid, ε2 is

[0357]

[0358] Let the covariance be then

[0359]

[0360] System error of the target's elevation angle relative to the station of aid, ε2 is

[0361]

[0362] Maximum value of the system error of the target's elevation angle relative to the station of aid, ε2 is

[0363]

[0364] Random error mean square variance of the target's azimuth angle relative to the station of aid, β2 is

[0365]

[0366] Let the covariance be then

[0367]

[0368] System error of the target's azimuth angle relative to the station of aid, β2 is

[0369]

[0370] Maximum value of the system error of the target's azimuth angle relative to the station of aid, β2 is

[0371]

[0372] As mentioned above, (x2, y2, z2) are the coordinates of the target in the station's north-east-up coordinate system x (north), y (up), z (east) axis, which are converted from the coordinates of the target in the station's north-east-up coordinate system (x1, y1, z1) according to the method of step 1.

[0373] As mentioned above, (R2, ε2, β2) are the slant range, elevation angle and azimuth angle of the target relative to the station of aid, which are calculated according to the following formulas

[0374]

[0375]

Claims

1. A method for evaluating the quality of coordinate-supported prediction tracks, characterized in that, The specific steps are as follows: Step 1: Convert the target's 3D trajectory tracked in the support station's North-East coordinate system to the recipient station's North-East coordinate system; (1) Definition of radar measurement coordinate system The radar measurement coordinate system is a ground rectangular coordinate system centered on the radar station deployment point; o s —Original coordinate point, radar vehicle deployment point; o s x s Axis — for o s The earth meridian plane and the inclusion of o s The line of intersection of the plane and the plane perpendicular to the normal points in the direction of north on the earth. o s y s Axis — with o s The points coincide with the normals to the Earth's ellipsoid and point outward from the Earth's ellipsoid. o s z s Axis and o s x s o s y s The axes form a right-handed rectangular coordinate system, pointing eastwards. Radar acquires direct observations of targets using ground spherical coordinates: R—slope distance, which is the coordinate origin o. s Distance to the observation point; ε—Elevation angle, is the angle between the target's line of sight and the horizontal plane. With the horizontal plane as the reference, the upward angle is positive, and the range of variation is -90° to 90°. β—azimuth, the angle between the projection of the target's line of sight onto the horizontal plane and the due north direction. With due north as the reference, looking down from above, the angle rotated clockwise is positive, and the range of variation is 0° to 360°. (2) Target position and velocity conversion The formula for converting the target position and velocity tracked by the support station radar in the North-Eastern Sky coordinate system to the North-Eastern Sky coordinate system of the recipient station is as follows: In the formula, M1 and M2 are coordinate transformation matrices; m ij Let i be an element in the coordinate transformation matrix M1, where i, j = 1, 2, 3; (L1, B1, H1) represent the longitude, latitude, and elevation of the support station radar site, respectively. (X1, Y1, Z1) are the geocentric rectangular coordinates of the support station radar site in the CGCS2000 national geodetic coordinate system; (L2, B2, H2) represent the longitude, latitude, and elevation of the site of the aid station, respectively. (X2, Y2, Z2) are the geocentric rectangular coordinates of the site of the aid station in the CGCS2000 national geodetic coordinate system; (x1, y1, z1) are the coordinates of the target on the x, y, and z axes of the North-Sky-East coordinate system of the support station, respectively, where x, y, and z are North, Sky, and East, respectively. These represent the target's velocity along the x, y, and z axes in the support station's north-east coordinate system; (x2, y2, z2) are the coordinates of the target on the x, y, and z axes of the North-East coordinate system of the aid station, respectively. These represent the velocity of the target along the x, y, and z axes in the North-East coordinate system of the aid station; Step 2: Predict the instantaneous encounter point when the recipient station launches a missile at the target, and calculate the time T it takes for the target to reach the encounter point. z ; The target maintains its course and flies in a straight line at a constant speed from its current position. If the support station launches a missile during this process, the conditions for the missile's encounter with the target are: the target's flight time T. tz It then flies to point T′, and the slant distance between point T′ and the rescue station is R. z The height is h z The time it takes for the missile to reach point T′ is T. mz If |T mz -T tz If |≤ε′, where ε′ is the threshold parameter for the loading, then the missile encounters the target; The iterative algorithm steps for instantaneous encounter point prediction are given below: (1) Extrapolate the target from its current position to the point closest to the radar station, with an extrapolation time of T. tz0 In the formula, S t The heading distance of the target relative to the aid station; V t The magnitude of the target speed; (2) Calculate the target extrapolation T tz0 The slant distance R afterward z and height h z (3) Calculate the average flight speed of the missile missile average flight speed V ave R is the slant distance R from point T′ to the aid station. z And the altitude h of the encounter height T′ point from the rescue station z The fitting function, i.e. V ave =f(R z ,h z ) (4) Calculate the time T for the missile to reach the target extrapolation point. mz (5) If T mz >T tz or T mz >T m_max T m_max If the maximum flight time of the interceptor missile is given, and the initial parameters are given, then it cannot be intercepted, there is no encounter point, and it returns; otherwise, proceed to step (6). (6) If |T mz -T tz If |≤ε′, then stop the calculation and let T be the time it takes for the target to reach the instantaneous encounter point. z =T tz0 Proceed to step (15) to make a final judgment on whether an encounter point exists; otherwise, proceed to step (7). (7) The time T for the target to be shifted backward from the current point tz =T tz0 ×k, where k is the calculation coefficient for extrapolation time; (8) Calculate the target extrapolation T according to steps (1) and (2). tz The slant distance R afterward z and height h z ; (9) Calculate the missile's average flight speed V according to the method in step (3). ave ; (10) Calculate the time T for the missile to reach the target extrapolation point according to the method in step (4). mz ; (11) If |T mz -T tz If |≤ε′, then stop the calculation and let T be the time it takes for the target to reach the instantaneous encounter point. z =T tz Proceed to step (15) to make a final judgment on whether an encounter point exists; otherwise, proceed to step (12). (12) If T mz >T tz Let the time T be the time to push the target forward from the current point. tz =T tz +(T tz0 -T tz )×k, repeat steps (8) to (11); otherwise, go to step (13); (13) If T mz >T m_max If the interception fails, there is no encounter point, and the process returns; otherwise, proceed to step (14). (14) Let the time T be the time it takes for the target to move forward from the current point. tz =T tz -T tz ×k, repeat steps (8) to (11); (15) If T z <T m_min T m_min If the minimum flight time of the interceptor missile is given, and the initial parameters are given, then interception is not possible, there is no encounter point, and the process returns; otherwise, an encounter point exists, and the calculation continues in step 3. Step 3: In the support station's North-East coordinate system, extend the target outward in a straight line from its current position at a constant velocity using a step size of ΔT, where ΔT represents the missile guidance period. The formula is as follows: Step 4: Convert the extrapolated rectangular coordinates of the target in the support station's North-East coordinate system to polar coordinates, using the formula: In the formula, (x1, y1, z1) are the rectangular coordinates of the target in the North-East coordinate system of the support station after extrapolation in step 3; (R1, ε1, β1) are the slant distance, elevation angle, and azimuth angle of the target relative to the support station after extrapolation in step 3, respectively. Step 5: Calculate the rectangular coordinate error of the target in the support station's North-East coordinate system; (1) Random error The target's Cartesian coordinate covariance matrix D1 in the support station's North-East coordinate system is: In the formula, These are the root mean square errors of the prior random errors in the target slant range, elevation angle, and azimuth angle measured by the support station radar, respectively, and are the initial setup parameters; These are the variances of the x, y, and z coordinates of the target in the North-East coordinate system of the support station; Let x and y coordinates of the target be defined in the North-East coordinate system of the support station. Let x and z coordinates of the target be defined in the North-East coordinate system of the support station. Let the covariance of the y and z coordinates of the target in the North-East coordinate system of the support station be the covariance of the target. (2) Systematic error The error of the rectangular coordinate system of the target in the support station's north-east coordinate system is: In the formula, These are the prior system error components of the target's position coordinates on the x, y, and z axes of the support station's north-east coordinate system; These are the prior systematic errors of the support station's slant distance, elevation angle, and azimuth angle, respectively. The maximum value of the system error is Step 6: Transfer the rectangular coordinate error of the target in the support station's North-East coordinate system to the recipient station's North-East coordinate system; (1) Random error covariance of the rectangular coordinates of the target in the North-East coordinate system of the aid station The random error covariance matrix D2 of the target's rectangular coordinates in the North-East coordinate system of the aid station is: In the formula, These are the prior fluctuation error variances for the radar longitude, latitude, and geodetic height location of the support station, respectively; These are the prior fluctuation error variances for radar longitude, latitude, and geodetic elevation location of the aid station, respectively; In the formula, x tr y tr z tr These represent the coordinate translations along the x, y, and z axes of the support station's north-east coordinate system to the recipient station's north-east rectangular coordinate system. z tr =-(N1+H1)cosB1sin(L2-L1); In the formula, N1 and N2 are the radii of curvature of the zonal loops at the locations of the support station and the recipient station, respectively. In the formula, e is the first eccentricity of the meridional ellipse; a is the semi-major axis of the Earth's ellipsoid; (2) Error of the rectangular coordinate system of the target in the North-East coordinate system of the aid station In the formula, These are the prior system error components of the target's position coordinates on the x, y, and z axes of the North-East coordinate system of the aid station; These are the prior system error components of the target's position coordinates on the x, y, and z axes of the support station's north-east coordinate system; These are the prior system errors for the radar longitude, latitude, and geodetic height location of the support station, respectively; These represent the prior systematic errors for radar longitude, latitude, and geodetic elevation location of the aid station; the maximum value of the prior systematic error components for the target's position coordinates on the x, y, and z axes of the North-East coordinate system of the aid station is... In the formula, These represent the maximum values ​​of the prior system error components of the target's position coordinates on the x, y, and z axes of the North-East coordinate system of the aid station; Maximum target distance error δ max for Step 7: Calculate and output the polar coordinate error of the target in the North-East coordinate system of the aid station; The root mean square of the random error of the slant distance R² between the target and the recipient station for If we define the covariance but Systematic error of the slant distance R2 between the target and the recipient station for The maximum systematic error of the slant distance R2 between the target and the recipient station is The root mean square error of the elevation angle ε2 of the target relative to the aid station for If we define the covariance but Systematic error of the elevation angle ε2 of the target relative to the aid station for The maximum value of the systematic error of the elevation angle ε2 of the target relative to the aid station for The root mean square of the random error of the azimuth angle β2 of the target relative to the recipient station for If we define the covariance but Systematic error of the azimuth angle β2 of the target relative to the recipient station for The maximum systematic error of the target's azimuth angle β2 relative to the recipient station is As mentioned above, (R2, ε2, β2) represent the slant distance, elevation angle, and azimuth angle of the target relative to the receiving station, respectively, and are calculated using the following formula.

2. The coordinate support prediction track quality assessment method as described in claim 1, characterized in that, The binding threshold parameter ε′ = 0.1s.

3. The coordinate support prediction track quality assessment method as described in claim 1, characterized in that, k＝0.5。

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