CN109633624B - RGPO interference identification method based on filtering data processing - Google Patents
RGPO interference identification method based on filtering data processing Download PDFInfo
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- CN109633624B CN109633624B CN201910012514.1A CN201910012514A CN109633624B CN 109633624 B CN109633624 B CN 109633624B CN 201910012514 A CN201910012514 A CN 201910012514A CN 109633624 B CN109633624 B CN 109633624B
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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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/66—Radar-tracking systems; Analogous systems
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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
- G01S7/38—Jamming means, e.g. producing false echoes
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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
- G01S7/41—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
Abstract
The invention discloses an RGPO interference identification method based on filtering data processing, which mainly solves the problem that false tracks appearing at certain moments are difficult to distinguish under the condition of short duration of RGPO interference in the prior art. The scheme is as follows: a single target in the simulation plane does uniform linear motion to obtain a real track of the target; measuring values before and after the radar is interfered by the RGPO are obtained according to the real track of the target; filtering according to the measured value observed by the radar, and calculating the innovation normalized distance d at each moment in the filtering process k Determining d k The distribution of (a); calculating interference discrimination factor lambda k (ii) a Constructing hypothesis test; from d k Is derived from the distribution of k Is determined as k A discrimination threshold eta; comparison of lambda k And the magnitude of η: if λ k When the distance is less than or equal to eta, the radar is in a normal tracking state; otherwise, the radar is subjected to RGPO interference. The method can effectively identify RGPO interference, identify false tracks at certain moments, reduce the deception probability of the radar, and can be applied to single radar tracking.
Description
Technical Field
The invention relates to the technical field of radars, in particular to a backward-towed RGPO interference identification method for a range gate, which can be used for a single radar system to effectively identify false tracks appearing at certain moments and realize the identification of track deception interference by the radar system.
Background
In recent decades, the electronically perturbed ECM has played an increasingly important role in military operations, and its associated research has also advanced unprecedentedly. Radar electronic interference measures include active interference and passive interference, and the active interference can be classified into press type interference and deception type interference. The deception jamming is that a jammer duplicates and forwards a radar transmitting signal to generate a plurality of false target jamming so as to deceive and confuse an enemy radar and make the enemy radar difficult to distinguish true from false. Compared with the suppression type interference, the deception interference is stronger in deception, and the pulse pressure gain in radar signal processing can be utilized, so that the transmitting power of an interference machine can be effectively reduced. Particularly, due to the rapid development of a Digital Radio Frequency Memory (DRFM), the forwarding jammer can rapidly store and forward radar transmission signals, accurately copy the intercepted enemy radar transmission waveforms and generate a large number of high-fidelity deception fake targets with different distance distributions near the real target.
The range-gate-towed interference is one of the effective electronic interference modes, is common active deception interference and is divided into two forms, namely a front-towed RGPI and a rear-towed RGPO. The RGPI interference is difficult to implement, and in practice, RGPO interference is often adopted, which tracks a false target through a deception radar, and drags a range gate to a direction far away from the radar, so that the target is lost finally. The range gate dragging interference is one of the most effective means for interfering the monopulse system tracking radar which is widely used at present. The basic principle is as follows: after receiving the radar transmission pulse, the interference machine immediately forwards back a pulse which has the same Doppler frequency, pulse width, bandwidth and carrier frequency as the target echo, and the interference power is greater than the echo power scattered at the interference machine. The function of the radar is to induce the radar to wrongly track the interference signal in a distance deception mode, and finally the radar loses a target, thereby achieving the purpose of interfering the normal work of the radar.
Most of the current methods for identifying RGPO interference are based on signal level processing. Such as signal-to-noise ratio detection, χ 2 The method comprises methods such as detection and N/M logic detection, and the methods have poor instantaneity on interference discrimination, are greatly influenced by echo signal-to-noise ratio and clutter density, and are easy to have errors of 'abandoning truth' and 'extracting false'. Here, "false" error refers to an error probability that interference is not detected when RGPO interference exists, and "false" refers to an error probability that interference is determined to exist when there is no interference. Signal-to-noise ratio detectionThe probability of false judgment of 'abandon true' is increased by comparing a certain measured signal-to-noise ratio in the echo wave gate of the people falling with a threshold corresponding to the signal-to-noise ratio. Chi shape 2 The "false-drop" error probability of a test is controlled primarily by the level of significance, and is generally small, at high signal-to-noise ratios. And at lower signal-to-noise ratios, the "false" probability is very high. Some researchers propose to combine the detection methods, so that the probability of false judgment of 'leave-true' and 'get-false' is simultaneously as small as possible, but under the condition that the duration of RGPO interference is short, because the measured value obtained after the radar passes through the detection method is reduced, whether the radar is interfered by the RGPO is difficult to identify.
Disclosure of Invention
The invention aims to provide an RGPO interference identification method based on filtering data processing aiming at the defects of the prior art, so as to accurately judge false tracks appearing at certain moments under the condition of short duration of RGPO interference and reduce the deception probability of radar.
The technical scheme of the invention is realized as follows:
technical principle
The single radar detects, tracks and filters the target, the position information of the real target is irrelevant to the radar station arrangement position, the position information of the false target measured observed after the radar is interfered by RGPO is jointly determined by the real target position and the radar position and is distributed on the sight of the real target and the radar station, when the radar position is not in the moving direction of the target, the radar can generate obvious break points in the towing period through the track formed by the false target measurement through filtering, and the radar can easily judge the false track. When the radar is positioned in the moving direction of the target, the track formed by the radar after filtering measured by the false target and the track of the real target are approximately on the same straight line, the radar cannot obtain the position information of the real target, and actually, the filtered track of the radar at each moment after being interfered has a deviation in the moving direction of the target compared with the real track. The deviation can be effectively measured by using a certain statistical distance of the radar in tracking filtering, namely an interference discrimination factor.
Second, the technical scheme
According to the above principle, the implementation scheme of the invention comprises the following steps:
(1) Simulating a single target to do uniform linear motion in a two-dimensional plane to obtain a real track of the target;
(2) Obtaining a real measurement value before the radar is interfered and a false measurement value after the radar is interfered by the real track of the target;
(3) Filtering according to the measured value observed by the radar, and calculating the innovation normalized distance d at each moment in the filtering process k ：
Where k =2, \8230, 100 denotes the sampling time, v k Represents an innovation, S k Represents an innovation covariance matrix, [ ·] T Representing by transposing matrices [ ·] -1 Representation matrix inversion, then d k Chi-squared distribution obeying m degrees of freedom, denoted d k ～χ 2 (m), m is the dimension of the measurement vector;
(4) Calculating an interference discrimination factor lambda according to the innovation normalization distance at each moment k ：
When k is more than or equal to 10, the time window T is taken according to the thought of the sliding window method win =10, then
Wherein j is E [ k-T win +1,k]；
When k < 10, the arithmetic mean is calculated for the normalized distance of the innovation before the k time, i.e.
Wherein j ∈ [1,k ]]；
(5) By d k Is derived with respect to the interference discrimination factor lambda k Distribution of (a):
when k is greater than or equal to 10, T win λ k Obey T win χ of m degrees of freedom 2 Distribution, i.e. T win λ k ～χ 2 (T win m), i.e. dividing by T on the basis of the chi-square distribution win To obtain lambda k Approximately obey the chi-square distribution of the formula
When k < 10, k λ k χ obeying km degrees of freedom 2 Distribution, i.e. k λ k ～χ 2 (km), i.e. dividing by k on the basis of the chi-square distribution, to give lambda k The expression approximately obeys a chi-square distribution of
(6) And (3) construction hypothesis testing: let H be the event that the radar is not interfered by RGPO in the tracking process 0 The event that the radar is interfered by RGPO at a certain time is H 1 ；
(7) Determining a discrimination threshold eta according to the results of (5) and (6):
Pr{λ k ＞η|H 0 }＝α，
wherein, alpha is the misjudgment probability, the value is 0.05 or 0.01 or 0.1, pr {. Cndot } represents the probability of solving a certain distribution;
(8) Comparing interference discrimination factors lambda k With respect to the magnitude of the discrimination threshold eta, if lambda k When the distance is less than or equal to eta, the radar is in a normal tracking state; otherwise, the radar is interfered by RGPO.
Compared with the prior art, the invention has the advantages of
1. Because the data level is processed, the calculation speed is high, the real-time performance is strong, the interference discrimination factor can be used for judging the real-time change of the flight path, and compared with the signal-to-noise ratio detection and N/M logic detection methods of the existing signal level, the identification probability of the deceptive interference is improved;
2. the invention can amplify the difference between the false measurement and the predicted value in the filtering by using the measurement information observed by the radar at each moment, and compared with the prior art, the false track can be effectively identified even if the towing speed is kept very low and the towing time is very short in the towing interference process, thereby further reducing the deception probability of the radar.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a graph of the results of tracking filtering for an emulated radar in scene one;
FIG. 3 is a graph of simulated interference discrimination factor variation with sampling time in scenario one;
FIG. 4 is a graph of the results of tracking filtering for an emulated radar in scene two;
FIG. 5 is a graph of simulated interference discrimination factor variation with sampling time in scene two;
FIG. 6 is a graph of the results of tracking filtering for a simulated radar in scenario three;
fig. 7 is a graph of simulated interference discrimination factor versus sampling time in scenario three.
Detailed Description
Referring to fig. 1, the specific implementation steps of the present invention are as follows:
step 1, simulating a single target to do uniform linear motion in a two-dimensional plane to obtain a real track of the target.
Considering the position information [ x ] of the target k y k ] T As the measurement value, i.e., the measurement equation is linear, the tracking filter algorithm used by the radar in this example is a typical kalman filter, i.e., a KF algorithm, which is implemented as follows:
establishing a rectangular coordinate system unified with the system, and setting the initial state vector of the target as
Setting a motion model of the target as a uniform motion model:
X k ＝F k X k-1 +V k ， <1>
wherein, F k State transition matrix:
where T is the sampling time interval, V k To have covariance Q k Zero mean, white gaussian process noise of (1), i.e.
k. j each represents a sampling time [ ·] T The expression is given as a matrix transpose, δ kj As function of Kronecker Delta:
obtaining the real track of the target, namely the real state information, from the motion model of the target, namely the state transfer equation
Wherein x is k 、
Position information and velocity information, y, respectively, of the target true state in the x-direction k 、
Respectively, position information and speed information of the target true state y direction.
And 2, obtaining a real measurement value before the radar is interfered and a false measurement value after the radar is interfered according to the real track of the target.
After the radar stably tracks the target, the jammer of the target forwards RGPO interference, after the target enters a dragging period, because the power of an interference signal is greater than the power of a real target echo, the radar automatic gain circuit tracks the interference signal, namely a false target, so that a tracking gate of the radar is gradually far away from the real target, namely a measured value observed by the radar before and after the radar is interfered by the RGPO has a great error, and the method specifically comprises the following steps:
2a) The position of the radar under the rectangular coordinate system is set as (x) r y r ) Obtaining the real state information of the target according to the step 1
Calculating polar coordinate information of the target relative to the radar:
where ρ (k) is radial distance information and θ (k) is angle information [ ·] T Represents the transposition of the matrix, arctan [ ·]Representing an inverse tangent function;
2b) Suppose at k 1 Forwarding RGPO interference by an interference machine of the target at the moment, implementing constant-speed dragging, setting v as the speed during the constant-speed dragging, and calculating the distance rho between the radar and a false target detected after the radar is interfered by the RGPO f (k)：
ρ f (k)＝ρ(k)+v·(k-k 1 )，k≥k 1 ； <4>
2c) Converting the polar coordinate measurement information of the radar relative to the target into a uniform rectangular coordinate system, and considering the measurement noise
The measured value Z of the radar k ＝[x' k y' k ] T Obtained according to the following formula:
wherein, x' k Represents the measurement Z k X position information of (1), y' k Indicating measurement Z k Y position information of (a).
Step 3, filtering is carried out according to the measured value observed by the radar, and the innovation normalization distance of each moment is calculated in the filtering processDistance d k 。
3a) Calculating innovation in the filtering process:
3a1) Computing one-step predictions of target states
Wherein the content of the first and second substances,
as a filtered estimate of the radar, F k Is a state transition matrix;
3a2) Computing a prediction error covariance matrix P kk-1 ：
Wherein, [ ·] T Representing by transposing a matrix, Q k Is a covariance matrix of state noise, P k-1|k-1 Is composed of
The covariance matrix of (a);
3a3) The innovation v is calculated using the following formula k ：
Wherein Z is k As a measured value of radar, H k For measuring the matrix, since the filter starts to work from the 2 nd moment, i.e. the innovation can be obtained at the 2 nd moment and later, the value of k is k =2, \ 8230;, 100;
3b) The innovation covariance matrix S is calculated using the following formula k ：
Wherein R is k A covariance matrix for the measured noise;
3c) The innovation covariance matrix is used for carrying out normalization processing on the innovation, and the innovation normalization distance d of the radar at each moment in the filtering process is calculated k ：
Where k =2, \8230;, 100 denotes the sampling time, v k Denotes innovation, S k Represents an innovation covariance matrix, [ ·] T Representing by transposing matrices [ ·]- 1 The reason why k does not take 1 is to indicate that the matrix inversion is performed is that the innovation is obtained at the 2 nd and later times, where d is given 1 ＝d 2 Then d is k Chi-square distribution obeying m degrees of freedom, denoted d k ～χ 2 (m), m being the dimension of the measurement vector.
When k is more than or equal to 10, the time window T is taken according to the thought of the sliding window method win =10, then
Wherein j is E [ k-T win +1,k]；
When k < 10, the arithmetic mean is calculated for the normalized distance of the innovation before the k time, i.e.
Wherein j ∈ [1,k ]]。
When k is 10 or more, since d k Chi-squared distribution obeying m degrees of freedom, according to the nature of the chi-squared distribution, then
Compliance with T win A chi-square distribution of m degrees of freedom, and
then T win λ k Obey T win Chi-square distribution of m degrees of freedom, expressed as: t is win λ k ～χ 2 (T win m), i.e. dividing by T on the basis of the chi-square distribution win To obtain lambda k Approximately obey the chi-square distribution of the formula
When k < 10, since d k Chi-square distribution obeying m degrees of freedom, according to the nature of chi-square distribution
Obey a chi-square distribution of km degrees of freedom, and
then k λ k Chi-squared distribution obeying km degrees of freedom, expressed as: k lambda k ～χ 2 (km), i.e. dividing by k on the basis of the chi-square distribution, to give lambda k Approximately obey the chi-square distribution of the formula
And 6, determining a discrimination threshold eta.
6a) And (3) construction hypothesis testing: let H be the event that the radar is not interfered by RGPO in the tracking process 0 The event that the radar is interfered by RGPO at a certain time is H 1 ；
6b) According to the interference discrimination factor lambda in the step 5 k And 6 a), calculating a discrimination threshold eta by using the following formula:
Pr{λ k ＞η|H 0 }＝α， <12>
wherein, alpha is the misjudgment probability, the value is 0.05 or 0.01 or 0.1, and the value is 0.01 in the embodiment; pr {. Cndot } represents the probability of finding a certain distribution.
And 7, judging the radar tracking state.
Discriminating factor lambda from interference k And comparing with a discrimination threshold eta: if λ k When the eta is less than or equal to eta, the radar is in a normal tracking state; otherwise, the radar is interfered by the RGPO, and the identification result of the RGPO interference is obtained.
The advantages of the present invention can be further verified by the following simulations.
1. An experimental scene is as follows:
scene one:
setting a target in a scene, wherein the initial position of the target is (-500,500) m, and the target makes uniform linear motion on a two-dimensional plane at a speed of (10,0) m/s, namely the initial state vector of the target is X 1 ＝[-500 10 500 0] T The motion model of the object following<1>Equation, set the process noise covariance matrix Q k Is 0.
The position coordinate of the radar is (-1000, 0) m, and the measurement precision of the radar is as follows: the x-direction was 5m and the y-direction was 3m.
The total simulation time is set to be 100s, the radar is assumed to be interfered by RGPO in 71-100 s, the situation is set to be a constant-speed dragging interference scene, and the dragging speed is 1m/s.
Scene two: the position coordinate of the radar is (-1000,500) m, namely the radar is in the moving direction of the target, and other parameters are unchanged.
Scene three: the position coordinate of the radar is (-1000,500) m, the towing speed when the uniform-speed towing interference is applied is changed to 8m/s, and other parameters are unchanged.
2. Experimental contents and analysis:
simulation 1, in the case of scene one, the radar performs tracking filtering on the target to obtain a tracking filtering result of the radar, as shown in fig. 2, where a solid line is a real position of the target, a dotted line is a measurement value of the radar, and a dot-dash line is a filtering value of the radar. The filtered flight path in fig. 2 can determine that the radar is interfered at a certain time, but cannot accurately obtain the sampling time when the radar starts to be interfered.
Using the interference discrimination factor lambda of the invention k And a discrimination threshold eta, the radar tracking state shown in fig. 2 is judged, whether the radar is interfered by the RGPO at a certain moment is judged, and the result is shown in fig. 3, wherein the solid line is the discrimination threshold, the dotted line is the variation curve of the interference discrimination factor before and after the interference by the RGPO, and as can be seen from fig. 3, when the radar performs normal tracking filtering, lambda is k Are all less than the threshold, at the 74 th sampling instant, λ k Initially greater than the threshold, thereby determining that the radar is experiencing RGPO interference at this time.
As can be seen from FIG. 3, the error at the beginning of the track is relatively large, plus λ when k < 10 k The values are calculated in a short time window and therefore have a large error with the interference discrimination factor at k ≧ 10, as indicated by the dashed line in FIG. 3. From λ k Approximately obeying a chi-square distribution
And obtaining a threshold eta when k is less than 10, wherein the threshold is larger than the threshold value at each later moment and is more consistent with the setting of the threshold.
And 2, in the case of the second scene, the radar performs tracking filtering on the target to obtain a tracking filtering result of the radar, as shown in fig. 4. Where the solid line is the true position of the target, the dashed line is the measured value of the radar, and the dash-dot line is the filtered value of the radar. Since the filtered track in fig. 4 is similar to the real track of the target, it cannot be determined whether the radar is interfered by RGPO, and actually, the filtered track of each sampling time after the radar is interfered has a deviation from the real track, only the towing speed is relatively low, and the deviation cannot be clearly distinguished according to fig. 4.
Using the interference discrimination factor lambda of the invention k And a discrimination threshold η, wherein the radar tracking state in fig. 4 is determined to determine whether the radar is interfered by RGPO at a certain time, and the result is shown in fig. 5, where a solid line is the discrimination threshold, and a dotted line is a change curve of interference discrimination factors before and after the radar is interfered by RGPO, and as can be seen from fig. 5, when the radar performs normal tracking filtering, λ is k Are all less than the threshold, at 7 th4 sampling instants, λ k Initially greater than the threshold, and thus determines that the radar is experiencing RGPO interference at this time.
And 3, in the case of the third scene, the radar performs tracking filtering on the target to obtain a tracking filtering result of the radar, as shown in fig. 6. It can be determined from the filtered path in fig. 6 that the radar is interfered by RGPO, and the interference signal drags the tracking gate of the radar to a distance in the direction of the movement of the target, and gradually moves away from the real path of the target.
Using the interference discrimination factor lambda of the invention k And a discrimination threshold η, wherein the radar tracking state shown in fig. 6 is determined to determine whether the radar is interfered by RGPO at a certain time, and the result is shown in fig. 7, where a solid line is the discrimination threshold, and a dotted line is a change curve of interference discrimination factors before and after the radar is interfered by RGPO, and as can be seen from fig. 7, when the radar performs normal tracking filtering, λ is k Are all less than the threshold, at the 72 th sampling time, lambda k Initially greater than the threshold, and thus determines that the radar is experiencing RGPO interference at this time. And it can be seen from fig. 7 that after the radar is interfered by RGPO, the magnitude of the interference discrimination factor gradually reaches 10 3 。
Through the simulation result analysis of the 3 scenes, whether the radar is interfered by the RGPO can be identified more effectively through the change curve of the interference discrimination factor, and the larger the dragging speed is, the larger the value of the interference discrimination factor is, the more violent the change is, the more obvious the influence of the radar by the RGPO interference is, and the more accurate the time point of the radar subjected to the interference is deduced.
The experimental result verifies the effectiveness and reliability of the method, and the RGPO interference can be successfully identified, so that the deception probability of the radar is reduced.
Claims (3)
1. An RGPO interference identification method based on filtering data processing is characterized by comprising the following steps:
(1) Simulating a single target to do uniform linear motion in a two-dimensional plane to obtain a real track of the target;
(2) Obtaining a real measurement value before the radar is interfered and a false measurement value after the radar is interfered by the real track of the target;
(3) Filtering according to the measured value observed by the radar, and calculating the innovation normalized distance d at each moment in the filtering process k ：
Where k =2, \8230;, 100 denotes the sampling time, v k Denotes innovation, S k Represents an innovation covariance matrix, [ ·] T Representation matrix transposition, [ ·] -1 Representation matrix inversion, then d k Chi-square distribution obeying m degrees of freedom, denoted d k ～χ 2 (m), m being the dimension of the measurement vector;
(4) Calculating an interference discrimination factor lambda according to the innovation normalization distance at each moment k ：
When k is more than or equal to 10, taking the time window T according to the thought of the sliding window method win =10, then
Wherein j is E [ k-T win +1,k]；
When k < 10, the arithmetic mean is taken over the normalized distance of the innovation before the time k, i.e.
Wherein j ∈ [1,k ]]；
(5) Through d k Is derived with respect to the interference discrimination factor lambda k Distribution of (a):
when k is greater than or equal to 10, T win λ k Obey T win χ of m degrees of freedom 2 Distribution, i.e. T win λ k ～χ 2 (T win m), i.e. dividing by T on the basis of chi-square distribution win To obtain λ k Approximately obey the chi-square distribution of the formula
When k < 10, k λ k χ obeying km degrees of freedom 2 Distribution, i.e. k λ k ～χ 2 (km), i.e. k divided on the basis of the chi-square distribution, to give λ k Approximately obey the chi-square distribution of the formula
(6) And (3) construction hypothesis testing: let H be the event that the radar is not interfered by RGPO in the tracking process 0 The event that the radar is interfered by RGPO at a certain time is H 1 ；
(7) Determining a discrimination threshold eta according to the results of (5) and (6):
Pr{λ k ＞η|H 0 }＝α，
wherein, alpha is the misjudgment probability, the value is 0.05 or 0.01 or 0.1, and Pr {. Cndot } represents the probability of solving a certain distribution;
(8) Comparing interference discrimination factors lambda k With respect to the magnitude of a decision threshold eta, if lambda k When the distance is less than or equal to eta, the radar is in a normal tracking state; otherwise, the radar is interfered by RGPO.
2. The method according to claim 1, wherein (2) obtaining the real measurement value before the radar is interfered and the false measurement value after the radar is interfered from the real track of the target comprises the following steps:
2a) Targeting true state information
The position of the radar under the rectangular coordinate system is (x) r y r ) Then, the polar coordinate information of the target relative to the radar is:
wherein x is k 、
Position information and velocity information, y, respectively, of the target true state in the x-direction k 、
Position information and velocity information of the target in the y direction, respectively, ρ (k) is radial distance information of the target with respect to the radar, θ (k) is angle information of the target with respect to the radar, [ ·] T Representing transpose of the solved matrix, arctan [. Cndot]Representing an inverse tangent function;
2b) Suppose at k 1 Forwarding RGPO interference by an interference machine of the target at the moment, implementing constant-speed dragging, setting v as the speed during the constant-speed dragging, and calculating the distance rho between the radar and a false target detected after the radar is interfered by the RGPO f (k)：
ρ f (k)＝ρ(k)+v·(k-k 1 )，k≥k 1 ；
2c) Converting the polar coordinate measurement information of the radar relative to the target into a uniform rectangular coordinate system, and considering the measurement noise
The measured value Z of the radar k ＝[x' k y' k ] T Obtained according to the following formula:
wherein, x' k Represents the measurement Z k X position information of (1), y' k Indicating measurement Z k Y-position information of (a).
3. The method of claim 1, wherein in (3)Calculating the normalized distance d of innovation at each time k It is implemented as follows:
3a) Calculating innovation in the filtering process:
3a1) Computing one-step predictions of target states
Wherein the content of the first and second substances,
as a filtered estimate of the radar, F k Is a state transition matrix;
3a2) Computing a prediction error covariance matrix P k|k-1 ：
Wherein [ ·] T Representation matrix transposition, Q k Is a covariance matrix of state noise, P k-1|k-1 Is composed of
The covariance matrix of (a);
3a3) The innovation v is calculated using the following formula k ：
Wherein Z is k As a measured value of radar, H k For measuring the matrix, since the filter starts to work from the 2 nd moment, i.e. the innovation can be obtained at the 2 nd moment and later, the value of k is k =2, \ 8230;, 100;
3b) The innovation is calculated by the following formulaCovariance matrix S k ：
Wherein R is k A covariance matrix for the measured noise;
3c) The innovation covariance matrix is used for carrying out normalization processing on the innovation, and the innovation normalization distance d of the radar at each moment in the filtering process is calculated k ：
Where k =2, \8230, 100 denotes the sampling time, v k Denotes innovation, S k Represents an innovation covariance matrix, [ ·] -1 The reason why k does not take 1 is that an innovation is obtained at the 2 nd and later time, where d is given 1 ＝d 2 。
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