CN111856412B - Anti-deception false target interference method based on ship-shake compensation data fusion - Google Patents

Anti-deception false target interference method based on ship-shake compensation data fusion Download PDF

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CN111856412B
CN111856412B CN202010729316.XA CN202010729316A CN111856412B CN 111856412 B CN111856412 B CN 111856412B CN 202010729316 A CN202010729316 A CN 202010729316A CN 111856412 B CN111856412 B CN 111856412B
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ship
target
radar
coordinate system
value
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CN111856412A (en
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周宇
马忠晗
张诗羽
张林让
李亚超
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Xidian University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/36—Means for anti-jamming, e.g. ECCM, i.e. electronic counter-counter measures
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/414—Discriminating targets with respect to background clutter
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/415—Identification of targets based on measurements of movement associated with the target

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  • Computer Networks & Wireless Communication (AREA)
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Abstract

The invention provides a deception false target interference prevention method based on ship shake compensation data fusion, which comprises the following implementation steps: 1. acquiring a measurement value of the ship-borne radar; 2. constructing a coordinate conversion matrix according to the ship swing angle; 3. performing ship-borne radar measurement values through a coordinate conversion matrix to perform ship-borne compensation, and converting the ship-borne radar measurement values into a normalized coordinate system; 4. solving a target positioning error covariance matrix; 5. associating the trace information in each carrier-borne radar; 6. and carrying out hypothesis testing on the true and false targets. The invention can be used for target detection and deception false target interference resistance under the condition of actual ship swinging. The influence of the actual ship swinging condition on the interference resistance of the ship formation radar networking is solved, and the detection probability of a real target is improved.

Description

Anti-deception false target interference method based on ship-shake compensation data fusion
Technical Field
The invention belongs to the technical field of radars, and further relates to a deception false target interference prevention method based on ship shake compensation data fusion in the technical field of interference prevention. The invention can be used for target detection and deception false target interference resistance under the condition of actual ship swinging.
Background
The active deception decoy interference is that a forwarding type jammer copies and modulates a radar signal and forwards a decoy echo with different time delay from a real target. Under the interference of the active deception false targets, the anti-interference capability of the single-station radar is greatly limited, so that the true and false targets cannot be identified. The networking radar system can detect the target from multiple view angles, share and fuse the characteristic information of the target, and therefore the true and false targets can be identified.
Zhao Yanli in its published paper "distributed networking radar anti-multi-false target spoofing interference processing method" (electro-optical and control, 2011.3, 3 rd phase) a networking radar track information fusion anti-interference data processing method is provided. The implementation steps of the method are as follows: firstly, each radar station independently performs multi-target tracking to obtain each track corresponding to a true target and a false target in each station; secondly, carrying out association test on tracks from different radar stations, so that the tracks corresponding to true targets are reserved, and the tracks of false targets are eliminated; thirdly, fusing the tracks passing the association test in a fusion center, thereby improving the tracking precision of the target. However, the method still has the defect that the method does not consider the influence of the actual ship swaying factor on the ship-borne radar, and cannot be used for target detection and anti-deception jamming under the ship swaying condition.
Zhao Shanshan in its published paper, "method for combining point trace information of networking radar to prevent false target interference" (university of electronic technology, 2014.3, stage 2) a method for combining point trace information of networking radar to prevent false target interference is proposed. The implementation steps of the method are as follows: firstly, carrying out target detection by a radar and converting detection values of a plurality of radars into a unified coordinate system; secondly, calculating a positioning error covariance matrix of the target; thirdly, matching measurement values of the same target in different radars by utilizing nearest neighbor correlation; and fourthly, calculating test statistics and carrying out hypothesis testing to identify true and false targets. The method has the defects that the current algorithm does not consider the influence of actual ship swaying factors and cannot be used for target detection and anti-deception interference under the ship swaying condition.
Disclosure of Invention
The invention aims to overcome the defects of the prior networking radar information fusion anti-deception false target method, and provides a deception false target interference method based on ship sway compensation data fusion, so as to solve the influence of actual ship sway conditions on the networking anti-interference performance of a ship formation radar, and improve the detection probability of a real target.
The method for achieving the aim of the invention is characterized in that the existing networking radar data fusion method for identifying true and false targets is improved, ship-borne radar target measured values are subjected to ship-borne compensation to offset the influence of ship-borne swinging on target measurement, then the target measured values obtained by all ship-borne radars are subjected to data fusion, the positioning error covariance matrix of the targets is solved through ship-borne radar measurement errors and increased ship attitude measurement errors, and finally the true and false targets are identified through solving the mahalanobis distance.
The specific steps for realizing the aim of the invention comprise the following steps:
(1) Acquiring a measurement value of the ship-borne radar:
at [ -10,10]Obtaining the measurement value of each target in the air within the range of the ship swing angle
Figure BDA0002602402790000021
Wherein (1)>
Figure BDA0002602402790000022
Representing the distance measurement value in the polar coordinate system of the kth target relative to the ith carrier-borne radar,/>
Figure BDA0002602402790000023
Represents the azimuth angle measurement value in the polar coordinate system of the kth target relative to the ith carrier-borne radar,/>
Figure BDA0002602402790000024
Representing pitch angle measurement values in a polar coordinate system of the kth target relative to the ith carrier-borne radar;
(2) Constructing a coordinate transformation matrix:
acquiring a roll angle, a pitch angle and a bow angle of a ship where the carrier-based radar is positioned corresponding to the measurement value of each target in the air by using platform compass equipment of each ship, and constructing a coordinate transformation matrix of each ship;
(3) Converting a coordinate system:
(3a) Converting each measurement value acquired by each carrier-based radar from the polar coordinate system to the rectangular coordinate system of the carrier-based radar by using a conversion formula from the polar coordinate system to the rectangular coordinate system of the radar;
(3b) Calculating a target positioning value in each ship-based radar ship geographic coordinate system according to the following steps:
Figure BDA0002602402790000025
wherein,,
Figure BDA0002602402790000026
and->
Figure BDA0002602402790000027
Respectively representing a target positioning value of a kth target in an x-axis direction, a target positioning value in a y-axis direction and a target positioning value in a z-axis direction in a geographic coordinate system of the ith carrier-borne radar ship;
(3c) Converting each target positioning value into a return right angle coordinate system with the first ship-based radar as an origin;
(4) Solving an error covariance matrix:
(4a) The differential coefficient matrix C is calculated according to 1 And C 2 ：
Figure BDA0002602402790000031
Wherein d represents a differentiating operation,
Figure BDA0002602402790000032
and->
Figure BDA0002602402790000033
Respectively representing a target positioning value of a kth target of the ith radar in an x-axis direction, a target positioning value of a y-axis direction and a target positioning value of a z-axis direction in a return right angle coordinate system;
(4b) Calculating a positioning error covariance matrix according to the following formula:
Figure BDA0002602402790000034
wherein E []Representing the expected value solving operation, diag represents the diagonal matrix, T represents the transpose operation,
Figure BDA0002602402790000035
Figure BDA0002602402790000036
and->
Figure BDA0002602402790000037
Respectively representing the ranging error, azimuth angle measurement error and pitch angle measurement error of the ship-borne radar equipment; />
Figure BDA0002602402790000038
And->
Figure BDA0002602402790000039
Respectively representing a ship roll angle measurement error, a pitch angle measurement error and a bow roll angle measurement error of the platform compass device;
(5) Associating trace information:
(5a) In a return right angle coordinate system, selecting the carrier-based radar with the least measurement value as a reference radar, respectively calculating Euclidean distances between each measurement value of the reference radar and each measurement value of the other carrier-based radars, and selecting measurement values in the two carrier-based radars corresponding to the least Euclidean distances from all the Euclidean distances to form a matched measurement value;
(5b) Obtaining a matching measurement value of the reference radar and each other carrier-based radar by adopting the same operation as the step (5 a);
(5c) Forming an associated measurement sequence by all the matched measurement values;
(6) Hypothesis testing is carried out on true and false targets:
calculating the mahalanobis distance between two different ship-based radar measurement values in the associated measurement sequence; if all the mahalanobis distances are smaller than the threshold value, the target corresponding to the association measurement sequence is judged to be a true target, and if at least one group of the mahalanobis distances are larger than the threshold value, the target corresponding to the association measurement sequence is judged to be a false target.
Compared with the prior art, the invention has the following advantages:
firstly, the invention realizes the ship-sway compensation of the target measured value in the ship swaying state by calculating the target positioning value in each ship-borne radar ship geographic coordinate system, and solves the problems that the prior art cannot detect the target and resist deceptive interference under the ship swaying condition, so that the invention can resist deceptive false target interference in the actual ship swaying state.
Secondly, the invention comprehensively considers the measurement error and the attitude measurement error factor of the ship-borne radar when calculating the positioning error covariance matrix, and solves the problem that the true target identification probability is too low due to too small error covariance matrix because the ship swaying condition is not considered in the prior art, so that the invention improves the true target identification probability on the basis that the false target false identification probability is basically unchanged.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph showing the error distribution of the target ranging and angle measurement in the simulation experiment of the present invention;
FIG. 3 is a graph of discrimination probability versus the method of the present invention and the prior art.
Detailed Description
The following describes the embodiments of the present invention in further detail with reference to the accompanying drawings.
The specific implementation of the present invention will be described in further detail with reference to fig. 1.
And step 1, acquiring a measurement value of the ship-borne radar.
At [ -10,10]Obtaining the measurement value of each target in the air within the range of the ship swing angle
Figure BDA0002602402790000041
Wherein (1)>
Figure BDA0002602402790000042
Representing the distance measurement value in the polar coordinate system of the kth target relative to the ith carrier-borne radar,/>
Figure BDA0002602402790000043
Representing the kth target relative to the ith partAzimuth measurement value in carrier-borne radar polar coordinate system, < >>
Figure BDA0002602402790000044
Representing pitch angle measurement values in a polar coordinate system of the kth target relative to the ith carrier-borne radar;
and 2, constructing a coordinate transformation matrix.
The platform compass device of each ship is utilized to collect the roll angle, the pitch angle and the bow angle of the ship where the carrier-based radar is located, which correspond to the measurement value of each target in the air, and the coordinate transformation matrix of each ship is constructed according to the following steps:
Figure BDA0002602402790000051
wherein T is i Coordinate transformation matrix representing ith ship, m i Representing the roll angle of the ith carrier-borne radar, n i Representing the pitch angle, q, of the ith carrier-borne radar i Representing the yaw angle and cosn of the ith carrier-borne radar i Representing cosine operations, sinn i Representing a sinusoidal operation.
And 3, converting a coordinate system.
Converting each measurement value acquired by each carrier-borne radar from a polar coordinate system into a rectangular coordinate system of the carrier-borne radar according to the following steps:
Figure BDA0002602402790000052
Figure BDA0002602402790000053
Figure BDA0002602402790000054
wherein,,
Figure BDA0002602402790000055
measurement values respectively representing the targets +.>
Figure BDA0002602402790000056
Converting from a polar coordinate system to an x-axis target positioning value, a y-axis target positioning value and a z-axis target positioning value in a radar rectangular coordinate system, < >>
Figure BDA0002602402790000057
Representing cosine operations +.>
Figure BDA0002602402790000058
Representing a sinusoidal operation.
Calculating a target positioning value in each ship-based radar ship geographic coordinate system according to the following steps:
Figure BDA0002602402790000059
wherein,,
Figure BDA00026024027900000510
and->
Figure BDA00026024027900000511
Respectively representing the target positioning value of the kth target in the x-axis direction, the target positioning value in the y-axis direction and the target positioning value in the z-axis direction in the geographic coordinate system of the ith carrier-borne radar ship.
Each target positioning value is converted into a return right angle coordinate system with the first ship-based radar as an origin according to the following steps:
Figure BDA00026024027900000512
wherein xr is i 、yr i And zr i Respectively an x-axis positioning value, a y-axis positioning value and a z-axis positioning value of the ith carrier-borne radar in a return right angle coordinate system,
Figure BDA0002602402790000061
and->
Figure BDA0002602402790000062
The x-axis positioning value, the y-axis positioning value and the z-axis positioning value of the kth target in the return right angle coordinate system are respectively.
And 4, solving an error covariance matrix.
Deriving the coordinates of the target in a unified rectangular coordinate system to obtain a relational expression between the target positioning error and the radar measurement error and between the target positioning error and the attitude measurement error and a differential coefficient matrix C 1 And C 2 ：
Figure BDA0002602402790000063
Wherein d represents a differentiating operation,
Figure BDA0002602402790000064
and->
Figure BDA0002602402790000065
The target positioning value of the kth target of the ith radar in the x-axis direction, the target positioning value of the y-axis direction and the target positioning value of the z-axis direction in the return right angle coordinate system are respectively represented.
Obtaining a differential coefficient matrix C 1 And C 2 Expressed as:
Figure BDA0002602402790000066
wherein C is 11 -C 36 The specific expression of (2) is shown as follows
Figure BDA0002602402790000067
Figure BDA0002602402790000068
Figure BDA0002602402790000069
Figure BDA00026024027900000610
C 15 ＝0
Figure BDA00026024027900000611
Figure BDA00026024027900000612
Figure BDA0002602402790000071
Figure BDA0002602402790000072
Figure BDA0002602402790000073
Figure BDA0002602402790000074
Figure BDA0002602402790000075
Figure BDA0002602402790000076
Figure BDA0002602402790000077
Figure BDA0002602402790000078
Figure BDA0002602402790000079
Figure BDA00026024027900000710
Figure BDA00026024027900000711
Positioning error of target
Figure BDA00026024027900000712
Radar measurement error->
Figure BDA00026024027900000713
And attitude measurement error dr= [ dm ] i ,dn i ,dq i ] T The following relationship can be simplified to be expressed:
dX＝C 1 dV+C 2 dR
from the above relation, after the target is converted into the normalized coordinate system, the positioning error of the target is in a linear relation with the radar measurement error and the ship attitude measurement error, and the radar measurement error and the ship attitude measurement error are considered to be subjected to Gaussian distribution, so that the positioning error of the target is also subjected to Gaussian distribution with the average value of 0.
Calculating a positioning error covariance matrix of the target:
P＝E[dXdX T ]
＝C 1 E[dVdV T ]C 1 T +C 2 E[dRdR T ]C 2 T
wherein,,
Figure BDA0002602402790000081
Figure BDA0002602402790000082
wherein,,
Figure BDA0002602402790000083
and->
Figure BDA0002602402790000084
Respectively representing a ranging error, a measured azimuth angle error and a measured pitch angle error of the ship-borne radar; />
Figure BDA0002602402790000085
And->
Figure BDA0002602402790000086
Respectively representing the ship roll angle measurement error, the pitch angle measurement error and the bow roll angle measurement error.
And 5, associating the trace information.
In a return right angle coordinate system, the carrier-based radar with the least measurement value is selected as a reference radar, euclidean distances between each measurement value of the reference radar and each measurement value of the other carrier-based radars are calculated respectively, and measurement values in the two carrier-based radars corresponding to the least Euclidean distances are selected from all Euclidean distances to form a matched measurement value.
And obtaining matching measurement values of the reference radar and other carrier-based radars by adopting the same operation, and then forming an associated measurement sequence by all the matching measurement values.
And 6, carrying out hypothesis testing on the true and false targets.
Calculating the difference delta Z=dZ of measurement errors of any two carrier-borne radars j -dZ k ～N(0,Σ jk )：
Σ jk ＝E[(dZ j -dZ k )(dZ j -dZ k ) T ]＝P j +P k
Wherein dZ j Indicating the measurement error, dZ, of the measurement value j k Representing the measurement error of the measurement value k, Δz follows a gaussian distribution of zero mean when both measurement values are true targets.
The mahalanobis distance between two different ship-borne radar measurement values in a correlation sequence is calculated according to the following formula:
Figure BDA0002602402790000087
wherein Z is j Represents the j-th measurement value, Z k Represents the kth measurement.
The hypothesis test of the true and false targets is carried out below to propose two opposite hypotheses H 0 And H 1 ：
Suppose H 0 The two measurement values are generated in different ship-borne radars for the same real target.
Suppose H 1 For two measurement values, two true-false targets or two false targets.
Distance d of Marshall jk As test statistics, at H 0 Under the condition of establishment, the mahalanobis distance d jk Obeying the chi-square distribution, the discrimination threshold eta can be determined after the significance level is given, and the hypothesis test is carried out on the true and false targets:
if d jk If eta is not more than eta, then consider H 0 Is true, i.e. judge Z j And Z k Measuring values of real targets in different ship-borne radars;
if d jk If > η is true, then consider H 1 Is true, i.e. judge Z j And Z k Is the measurement value of the false target in different ship-borne radars.
The effect of the invention can be further demonstrated by the following simulation experiment.
1. Simulation conditions:
the simulation experiment is realized through Matlab simulation software, the networking model comprises 3 carrier-based radars as node radars, 1 true target is set, and a false target with the deception distance delta d is set for each carrier-based radar. The ship makes roll, pitch and yaw movements with the range of the sway angle of-10 degrees to 10 degrees, and the information of each ship-borne radar is shown in table 1:
TABLE 1 parameter information Table for each Ship-borne radar
Ship-borne radar [x i ,y i ,z i ]/km Distance measurement accuracy/m Angular accuracy/rad Attitude angle measurement error/rad
R 1 [0,0,0] 50 0.001 0.001
R 2 [50,0,0] 50 0.001 0.001
R 3 [100,0,0] 50 0.001 0.001
According to the actual situation, the true target is arranged at the position with better anti-interference performance [50km,1km ]. The Monte Carlo simulation experiment is carried out on the position point for 1 ten thousand times, and the significance level alpha=0.01 of the test model is assumed, and the detection threshold eta=11.34.
2. Simulation content and result analysis
The simulation experiment of the invention has two.
The simulation experiment 1 is to simulate the target positioning errors under different swinging modes and swinging angles by adopting the anti-deception false target method based on the ship swinging compensation data fusion, so as to identify the effectiveness of ship swinging compensation and obtain the target ranging angle measurement error distribution diagram of fig. 2.
FIG. 2 is a graph of target positioning errors after roll compensation at different roll patterns and different roll angles. FIG. 2 (a) shows a target ranging goniometer error map for a ship in roll mode, with the abscissa representing the roll angle, the roll angle range being [ -10,10] degrees, in degrees; the ordinate represents the range error, azimuth error and pitch error of the target, respectively, in meters, radians and radians, and the trace marked with stars in fig. 2 (a) represents the range error, azimuth error and pitch error at the current angle, respectively. FIG. 2 (b) shows a target ranging goniometer error map of a ship in pitching mode, the abscissa representing the sway angle, the sway angle range being [ -10,10] degrees, in degrees; the ordinate represents the range error, azimuth error and pitch error of the target, respectively, in meters, radians and radians, and the trace marked with a star in fig. 2 (b) represents the range error, azimuth error and pitch error at the current angle, respectively. FIG. 2 (c) shows a target ranging goniometer error map of a ship in a bow-tie mode, with the abscissa representing the roll angle, the roll angle range being [ -10,10] degrees in degrees; the ordinate represents the range error, azimuth error and pitch error of the target, respectively, in meters, radians and radians, and the trace marked with a star in fig. 2 (c) represents the range error, azimuth error and pitch error at the current angle, respectively.
As can be seen from fig. 2 (a) -2 (c), the azimuth angle error and the pitch angle error of the target after the ship swaying compensation are both within 0.005rad based on the consideration of the attitude measurement error and the radar measurement error, the distance error is within 100 meters, the measurement error of the target accords with gaussian distribution, is consistent with the previous deduction, and cannot change along with the change of the ship swaying angle, so that the influence of the ship swaying motion on the target measurement is well counteracted by the ship swaying compensation.
The simulation experiment 2 is to perform anti-deception decoy interference by adopting the anti-deception decoy interference method of the invention and the anti-deception decoy interference method based on data fusion in the prior art. Setting a roll angle of 5 degrees, a pitch angle of 2 degrees and a bow roll angle of 3 degrees, and simulating true target identification probability and false target misjudgment probability under two methods through multiple Monte Carlo experiments under different deception distances to obtain an identification probability comparison graph of fig. 3.
The abscissa in fig. 3 (a) represents the spoofing distance of the spoofing type decoy, the ordinate represents the authentication probability of the true target, the curve marked with a circle represents the authentication probability curve of the true target for resisting spoofing by the method of the present invention, and the curve marked with a five-pointed star represents the authentication probability curve of the true target by the method of resisting spoofing type decoy based on data fusion in the prior art. The abscissa in fig. 3 (b) represents the spoofing distance of the spoofing decoy, the ordinate represents the false positive probability of the decoy, the curve marked by a circle represents the false positive probability curve of the decoy resisting spoofing interference by the method of the present invention, and the curve marked by a five-pointed star represents the false positive probability curve of the decoy based on the data fusion anti-spoofing decoy interference method of the prior art.
As can be seen from fig. 3 (a), the probability of identifying a true target is improved in the present invention compared with the prior art method for resisting spoofing false target based on data fusion under the condition that the measured value of the target includes an attitude measurement error. As can be seen from fig. 3 (b), compared with the prior art, the false target based on the data fusion anti-spoofing false target interference method of the present invention has substantially the same false target judgment probability. When the spoofing distance is 500m, the difference value of the true target discrimination probability of the invention and the prior art reaches 1%, and the false target false discrimination probability of the active is basically the same.

Claims (4)

1. The anti-deception false target interference method based on ship-borne radar data fusion is characterized in that the ship-borne radar data fusion is performed before true and false targets are identified, the influence of ship-borne radar target detection and anti-deception interference caused by ship-borne swinging factors is counteracted, and the method comprises the following specific steps:
(1) Acquiring a measurement value of the ship-borne radar:
at [ -10,10]Obtaining the measurement value of each target in the air within the range of the ship swing angle
Figure FDA0002602402780000011
Wherein (1)>
Figure FDA0002602402780000012
Representing the distance measurement value in the polar coordinate system of the kth target relative to the ith carrier-borne radar,/>
Figure FDA0002602402780000013
Represents the azimuth angle measurement value in the polar coordinate system of the kth target relative to the ith carrier-borne radar,/>
Figure FDA0002602402780000014
Representing pitch angle measurement values in a polar coordinate system of the kth target relative to the ith carrier-borne radar;
(2) Constructing a coordinate transformation matrix:
acquiring a roll angle, a pitch angle and a bow angle of a ship where the carrier-based radar is positioned corresponding to the measurement value of each target in the air by using platform compass equipment of each ship, and constructing a coordinate transformation matrix of each ship;
(3) Converting a coordinate system:
(3a) Converting each measurement value acquired by each carrier-based radar from the polar coordinate system to the rectangular coordinate system of the carrier-based radar by using a conversion formula from the polar coordinate system to the rectangular coordinate system of the radar;
(3b) Calculating a target positioning value in each ship-based radar ship geographic coordinate system according to the following steps:
Figure FDA0002602402780000015
wherein,,
Figure FDA0002602402780000016
and->
Figure FDA0002602402780000017
Respectively representing a target positioning value of a kth target in an x-axis direction, a target positioning value in a y-axis direction and a target positioning value in a z-axis direction in a geographic coordinate system of the ith carrier-borne radar ship;
(3c) Converting each target positioning value into a return right angle coordinate system with the first ship-based radar as an origin;
(4) Solving an error covariance matrix:
(4a) The differential coefficient matrix C is calculated according to 1 And C 2 ：
Figure FDA0002602402780000021
Wherein d represents a differentiating operation,
Figure FDA0002602402780000022
and->
Figure FDA0002602402780000023
Target positioning values respectively representing x-axis directions of kth targets of ith radar in return-to-right angle coordinate systemA target positioning value in the y-axis direction and a target positioning value in the z-axis direction;
(4b) Calculating a positioning error covariance matrix according to the following formula:
Figure FDA0002602402780000024
wherein E []Representing the expected value solving operation, diag represents the diagonal matrix, T represents the transpose operation,
Figure FDA0002602402780000025
Figure FDA0002602402780000026
and->
Figure FDA0002602402780000027
Respectively representing the ranging error, azimuth angle measurement error and pitch angle measurement error of the ship-borne radar equipment; />
Figure FDA0002602402780000028
And->
Figure FDA0002602402780000029
Respectively representing a ship roll angle measurement error, a pitch angle measurement error and a bow roll angle measurement error of the platform compass device;
(5) Associating trace information:
(5a) In a return right angle coordinate system, selecting the carrier-based radar with the least measurement value as a reference radar, respectively calculating Euclidean distances between each measurement value of the reference radar and each measurement value of the other carrier-based radars, and selecting measurement values in the two carrier-based radars corresponding to the least Euclidean distances from all the Euclidean distances to form a matched measurement value;
(5b) Obtaining a matching measurement value of the reference radar and each other carrier-based radar by adopting the same operation as the step (5 a);
(5c) Forming an associated measurement sequence by all the matched measurement values;
(6) Hypothesis testing is carried out on true and false targets:
calculating the mahalanobis distance between two different ship-based radar measurement values in the associated measurement sequence; if all the mahalanobis distances are smaller than the threshold value, the target corresponding to the association measurement sequence is judged to be a true target, and if at least one group of the mahalanobis distances are larger than the threshold value, the target corresponding to the association measurement sequence is judged to be a false target.
2. The anti-deception decoy disturbance method based on ship-roll compensation data fusion according to claim 1, wherein the coordinate transformation matrix of each ship in the step (2) is as follows:
Figure FDA0002602402780000031
wherein T is i Coordinate transformation matrix representing ith ship, m i Representing the roll angle of the ith carrier-borne radar, n i Representing the pitch angle, q, of the ith carrier-borne radar i The bow and roll angle of the ith ship-borne radar is represented, cos represents cosine operation, and sin represents sine operation.
3. The anti-spoofing decoy disturbance method based on vessel sway compensation data fusion of claim 2, wherein the polar coordinate system to radar rectangular coordinate system conversion formula in step (3 a) is as follows:
Figure FDA0002602402780000032
Figure FDA0002602402780000033
Figure FDA0002602402780000034
wherein,,
Figure FDA0002602402780000035
measurement values respectively representing the targets +.>
Figure FDA0002602402780000036
And converting the polar coordinate system into an x-axis target positioning value, a y-axis target positioning value and a z-axis target positioning value in a radar rectangular coordinate system.
4. The anti-fraud decoy disturbance method based on ship-borne compensation data fusion according to claim 1, wherein the converting each target location value into a return right angle coordinate system with the first ship-borne radar as an origin in step (3 c) is accomplished by the following formula:
Figure FDA0002602402780000037
wherein xr is i 、yr i And zr i Respectively an x-axis positioning value, a y-axis positioning value and a z-axis positioning value of the ith carrier-borne radar in a return right angle coordinate system,
Figure FDA0002602402780000038
and->
Figure FDA0002602402780000039
The x-axis positioning value, the y-axis positioning value and the z-axis positioning value of the kth target in the return right angle coordinate system are respectively.
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