CN113867342A - Anti-ship missile formation recognition target selection system based on Hough transformation and optimized K-means clustering - Google Patents

Abstract

The invention discloses an anti-ship missile formation recognition target selection system based on Hough transformation and optimized K-means clustering, which comprises a motion situation monitoring module, a formation contour recognition module, a target situation establishing module, a hit target acquisition module and a target hit module, wherein the motion situation monitoring module is used for monitoring the motion situation of a target; the invention provides a method for selecting and modeling the anti-ship missile formation recognition target based on Hough transformation and an optimized K-means clustering algorithm, improves the efficiency, enhances the engineering operability and has important significance for anti-ship combat simulation.

Description

Anti-ship missile formation recognition target selection system based on Hough transformation and optimized K-means clustering

Technical Field

The invention relates to the field of formation identification, in particular to an anti-ship missile formation identification target selection system based on Hough transformation and optimized K-means clustering.

Background

The target selection of the anti-ship missile generally comprises two technologies of characteristic identification and formation identification. The characteristic identification depends on single characteristics or multi-characteristic weighted comprehensive characteristics of a designated target different from other vessels in formation, but with the increase of self-control time caused by the increase of the range of the anti-ship missile, the change of the situation of the tail end formation does not accord with the characteristics determined before launching, thereby exceeding the capability of the anti-ship missile characteristic identification. The formation identification is a process of comparing the formation situation obtained by searching and catching the guided missile terminal guided radar with the formation situation existing on the missile (real-time detection at a target indication stage or pre-storage in an information database), matching the formation characteristic similarity degrees of the two situations, and identifying the formation preset target in sequence to accurately strike.

The first type of formation identification method is to combine formation templates to directly calculate and judge in a measurement space according to the relevant parameters of formation. For example, 1) the array form of the observation and template is described by taking the maximum potential matching subset center of the array member position observation set and the prior array form template as a reference point, and the target array form of the observation array group is identified through array form description matching, so that the method has weak engineering operability; 2) and establishing a space scene direction similarity discrimination function according to the direction distance between the formation template and the azimuth angle of each ship of the formation to be identified to discriminate the formation. The requirement for the known formation ordering is too high, the applicability of the method is reduced, the judgment discrimination of different formation forms is not high, and the influence of the alignment angle on the judgment is too large; 3) and establishing a formation linear formation template by using the number of the formation lines and the formation angles, and providing a mathematical model of the relative formation directions and the similarity measurement of the reference target and other targets so as to judge whether the targets are positioned in the same formation line, clustering to obtain the number of the formation lines, so as to identify the formation, wherein the similarity measurement requires that the deviation of the azimuth angle is smaller than the detection error, and the judgment that the targets are positioned in the same formation line is not strict.

The other type of formation identification is to convert a target from a measurement space to a parameter space parameter, perform matching judgment by combining a formation template, for example, establish a characteristic model and a characteristic template aiming at the formation shape and the distribution rule of group members in the formation shape, and identify the type of the formation based on template sliding matching, wherein the method can identify the type of the linear formation, but the clustering process is complex and the real-time performance is weak; meanwhile, a method of optimizing a K-means clustering algorithm of a clustering number by a D/L cost function exists, the D/L cost function has a degressive characteristic, clustering number optimization and clustering iteration processes are mutually independent, and the problems that a plurality of local optimal values exist, the distinguishing degree of key clustering number segments is not obvious, and the optimization number of a typical clustering problem is slightly higher than a theoretical value exist. The common problem is that the influence of the detection interval on the clustering effect is not considered.

Disclosure of Invention

The invention aims to provide an anti-ship missile formation recognition target selection system based on Hough transformation and optimized K-means clustering.

And the motion situation monitoring module monitors the coordinates of all members in the target formation to obtain the motion situation of the target formation. And the formation contour identification module performs Hough transformation on the motion situation of the target formation and identifies the formation contour of the target formation. And the target situation establishing module establishes a target situation model according to the formation contour of the target formation and carries out sequencing numbering on all members in the target formation. The striking target acquisition module selects a striking target P in the target formation and determines the relative number B-P of the striking target. And B is the number of the reference ship in the target formation. The target striking module launches a missile to a striking target. The missile is provided with an end guidance radar. And after the self-control flight of the missile is finished, starting the missile terminal guidance radar. And the last-guided radar acquires the current motion situation of the target formation and performs Hough transformation, so that the current formation profile of the target formation is identified. And the last-guided radar carries out sequencing numbering on each echo signal of the target formation, compares the target formation number and the current sequencing number in the target situation establishing module and determines a hit target P. The missile captures and tracks the hitting target P and completes the hitting.

Further, the step of identifying the formation profile of the target formation comprises:

1) establishing a measurement space by using a Hough transformation function based on duality of point and line

Interior points and parameter space

The corresponding relationship of the curves of (1). (X, Z) are coordinates;

for any point in the measurement space

The Hough transform function is as follows:

ρ＝X cosθ+Z sinθ

in the formula, θ is an included angle formed by a perpendicular line from the measurement space origin to any straight line passing through the point and the positive direction of the X axis. | ρ | is the vertical length.

2) Recording target formation member coordinates of measurement space

In the parameter space there is a corresponding sinusoid of l_i. i-1, 2, …, N, a set of enqueue targets in a measurement space

In the parameter space, there are corresponding sinusoidal clusters

Selecting a broken line of a measurement space

And calculating to obtain the sine curve intersection point corresponding to the parameter space

Thereby forming a set of data samples

i＝1,2,…,(N-1)。

3) And clustering the intersection points of the Hough curves by using an optimized K-means clustering method to obtain the formation profile of the target formation. Further, an objective function E for optimizing the K-means clustering method is as follows:

in the formula, k is the number of clusters.

Is of the type W_jCluster center of the medium sample. n is_jIs of the type W_jNumber of data samples.

Optimal clustering number K for optimizing K-means clustering method^*As follows:

wherein F (D, L) is a disparity cost function,

is of the type W_jAny sample object contained. k is a radical of_maxIn the upper limit of the range,

indicating a rounding down.

Further, the step of clustering the intersection points of the Hough curves by using the optimized K-means clustering method comprises the following steps:

1) randomly selecting k samples from a data sample set X as initial clustering centers, and calculating an objective function matrix D from each sample in the data sample set X to each initial clustering center, namely:

in the formula (d)_ijRepresents the i + (j-1). times.n elements of the objective function matrix D.

Is W_jAnd (4) clustering centers. j is 1, …, c. k is 1,2, …, n.

Representing the ith sample of the set of data samples X.

2) Calculating a column vector

And corresponding cluster number column vector

Namely:

in the formula, the column vector

The element in (1) includes the sum of the squares of the minimum distances of the samples to the cluster centers. min D (i,: indicates the sum of the squares of the minimum distances from the ith sample to the centers of the clusters.

3) Based on column vectors

And cluster number column vector

And initially classifying the data sample set X, and calculating the number of various samples.

4) Multi-sample update clustering, comprising the steps of: 4.1) column vector according to cluster number

Cluster number with varying number of cluster samples

Updating clusters of changesCenter and number of samples varied. The varying objective function matrix D is then calculated from the varying cluster centers. 4.2) processing the clusters that become empty sets. 4.3) calculating an objective function value E, judging whether the objective function E is reduced or not, if not, entering the step 5), and if so, temporarily storing the cluster number column vector

And an objective function value. 4.4) calculating the column vector consisting of the least sum of squares of the distances from each sample to each cluster center by the formula (5)

And corresponding cluster number column vector

4.5) column vector according to new cluster number

And old cluster number column vector

Determines the sample with the changed cluster number, and writes the sample number corresponding to the sample into the column vector

In (1).

Column vector

As follows:

judging the sum of squares of distances from the samples with changed cluster numbers to the center of a new cluster_iIf it is less than the sum of squared distances d' from the sample to the old cluster center, if not, then from the column vector

The sample number corresponding to the sample is deleted.

Column vector

The update is as follows:

where [ ] indicates no element, reducing the number of column vector rows.

4.6) column vectors

The new cluster number in (1) replaces the original cluster number of the sample, and a cluster number vector with the changed number of samples in the cluster is obtained

Returning to the step 4) until

Become [ 2 ]]And the multi-sample updating iteration converges, and the single-sample updating clustering stage is switched.

Cluster number vector

As follows:

where c represents the total number of clusters and i e [. cndot. ] represents the element to which i belongs to the array [. cndot. ].

5) Updating clustering of single samples, comprising the following steps:

5.1) calculating an objective function matrix Del of a sample set with single sample clustering, namely:

in the formula (I), the compound is shown in the specification,

is W_jCenter of cluster, m_jThe number of samples for cluster number j. sgn_ijIs a symbolic function.

5.2) calculating the minimum distance square sum of each sample in the objective function matrix Del to each cluster center by using the formula (5), and writing the minimum distance square sum into a column vector

Writing the least distance square sum corresponding to the cluster number into the column vector of the cluster number

5.3) judging the column vector of the cluster number

And cluster number column vector

And (4) judging whether a difference exists, if not, judging the updating iteration convergence of the single sample, and if so, entering the step 5.4).

5.4) updating the column vector

Namely:

in the formula (I), the compound is shown in the specification,

a sample number column vector representing the change in cluster number of the last iteration. min (·) represents the smallest element in the vector, mod (n) represents the modulo operation. In updating the column vector using equation (10)

Time of flight

Are all single element vectors.

Calculating the number of movements and applying new column vectors

Assigning to the column vector of the last iteration

Thereby obtaining the moving cluster number single element column vector of the current iteration and the last iteration

Namely:

5.5) updating the objective function value E and the clustering number column vector

Number of clustered samples m_jCluster center

Cluster number vector

And returns to step 5.1).

Objective function value E, cluster number column vector

Respectively as follows:

number of clustered samples m_jAnd a cluster center

Respectively as follows:

cluster number vector with varying number of samples in a cluster

As follows:

6) judging whether each sample is an empty set or not, and calculating an objective function matrix D (D) from each sample to each clustering center_ij)_n×kThereby obtaining the column vector in the objective function matrix

Namely:

in the formula, id_iIndicating the cluster number to which the sample belongs. D (i + (id)_i-1) · n) denotes the i + (id) th in the objective function matrix D_i-1) n elements.

Calculating to obtain accumulated column vector according to the column vector

And an objective function

Accumulating column vectors

As follows:

finishing one clustering iteration, and repeating the steps 1) to 6) until all the clustering iterations are traversed

And comparing the objective function values of rep clustering iterations to obtain the optimal clustering of the clustering number k.

7) And (4) calculating a diversity cost function of the cluster number k according to the formula (3), and repeating the steps 1) to 6) until all cluster numbers k are traversed to be 1,2, …, n. And (5) comparing the clustering number k with 1,2, …, and n iteration difference cost functions to obtain the optimal clustering number, the clustering center and the corresponding classification.

8) And (3) clustering the sample under the optimal clustering number by using a formula (18) to obtain the corresponding straight line in the original measurement space by reflection.

The slope a and the intercept b of the line obtained by inverse mapping are respectively as follows:

in the formula, ρ₀、ρ_π/2And ρ_πAnd represents an angle ρ corresponding to θ ═ 0, π/2, and π/2.

Further, the target situation model establishes a plane rectangular coordinate system by taking the queue course of the target indication stage as the positive direction of the Z axis and the right-hand direction perpendicular to the Z axis as the positive direction of the X axis, and marks out the formation queue in the plane rectangular coordinate system. The formation queue comprises a reference warship J, a queue line, a queue heading gamma, a formation interval D, a flush angle alpha and a queue angle beta. The queue line refers to a connecting line of points where the ships in the queue start from the reference ship. The queue course gamma refers to an included angle between a ship bow stern line of the reference ship and the due north direction. The flush angle alpha refers to the included angle between the ship bow and stern lines and the queue line of other ships. The queue angle beta is 180-alpha, which means the included angle between the ship bow and stern line and the queue line of the reference ship.

Further, according to different formation profiles of the target formation, the coordinates of each naval vessel in the measurement space and the coordinates of the reference vessel comprise the following three conditions:

situation one) when the formation contour of the target formation is a V-shaped formation, the reference ship is taken as a naval ship at the joint of two wings of the V-shaped formation, and the included angle of the two wings is the sum of the alignment angles of the wings. The queue angles of the left wing and the right wing are both beta, the queue course is gamma-0 DEG, and the coordinate of the reference ship is (J)_X,J_Z) The total number of the ships in the formation is T, and the coordinates (X) of each ship in the V-shaped formation in the measurement space_n,Z_n) As follows:

left wing:

right wing:

wherein n is 1,2,3, …, T.

Reference ship coordinate (J)_X,J_Z) As follows:

wherein (X, Z) is the intersection point coordinate of the two wing queue lines.

Case two) when the formation contour of the target formation is parallel formation, each naval vessel is in the measuring spaceCoordinate of (X)_n,Z_n) As follows:

reference ship coordinate (J)_X,J_Z) As follows:

(J_X,J_Z)＝(X₁,Z₁) (23)

situation three) when the formation contour of the target formation is the annular formation, the coordinates (X) of each naval vessel in the measurement space of the horizontal queue_n,Z_n) As follows:

coordinates (X) of each naval vessel in the measurement space in the vertical queue_n,Z_n) As follows:

2) formation recognition target ordering

Reference ship coordinate (J)_X,J_Z) As follows:

further, before the missile is launched to start the missile end-guided radar, if the formation turns around a certain rotation point, the ship coordinates (X) of the target formation ship after the missile end-guided radar is started_n′,Z_n') as follows:

in the formula (X)₀,Z₀) Is the rotation center point coordinate. q is the angle of rotation。

Further, before the missile is launched to start the missile end-directed radar, if the target formation distance changes, the target formation naval vessel coordinate (X) after the missile end-directed radar is started_n′,Z_n') or target formation interval (D)_h′,Z_z') as follows:

in the formula, when k₁、k₂When the element belongs to (0,1), the formation pitch is reduced. k is a radical of₁、k₂E (1, ∞) is the queue pitch amplification. When k is₁＝k₂The target formation is scaled equally.

Further, before the missile is launched to start the missile end-guided radar, if a plurality of false targets exist in the target formation, the false target coordinates (C) after the missile end-guided radar is started_X1,C_Z1) False target coordinates (C)_X2,C_Z2) False target coordinates (C)_X3,C_Z3) False target coordinates (C)_X4,C_Z4) As follows:

in the formula, R is the distance between the false target and the naval vessel. Gamma ray_D([-180°,0°]∪[0°,180°]) Is the direction of the incoming missile. And epsilon and delta are angles between a connecting line of the false target and the naval vessel and the incoming direction of the missile. Reference ship coordinate (J)_X,J_Z) Is a true target.

The technical effects of the invention are undoubted, and compared with the prior art, the invention has the advantages that: 1) compared with the conventional method, the provided clustering number optimization cost function has more obvious optimization effect, is not limited to a local optimal value, and is more real for a typical sample clustering optimization result; 2) clustering iteration combining multi-sample updating clustering and single-sample updating clustering is carried out, and the iteration optimization searching efficiency is improved; 3) the iteration of the optimized clustering number and the iteration of clustering are fused and iterated, so that the defect that the conventional K-means clustering method is blind and low in efficiency is overcome; 4) the sample points are detected by adopting the mobile detection interval, so that the problem of wrong clustering caused by the lack of corresponding mechanisms of sample points at two side edges of a normal detection interval is solved, and the clustering effect is better; 5) the formation can be integrally detected and identified at one time by using an image identification method, one-to-one matching is not required according to a formation template library, the calculation is simple, and the calculation amount is relatively small; 6) all description parameters are calculated according to the local measurement, certain fault tolerance and robustness are achieved for the condition that the boundary of the region is interfered by noise or covered by other targets to cause certain discontinuity, and a good identification effect is kept. 7) The invention provides a method for selecting and modeling the anti-ship missile formation recognition target based on Hough transformation and an optimized K-means clustering algorithm, improves the efficiency, enhances the engineering operability and has important significance for anti-ship combat simulation.

Drawings

FIG. 1 is a flow chart of formation identification target selection for anti-ship missiles; FIG. 2 is a schematic diagram of queue elements; FIG. 3 is a schematic view of a V-formation; FIG. 4 is a schematic diagram of a double row formation; FIG. 5 is a schematic diagram of a double vertical formation; FIG. 6 is a schematic diagram of a circular air defense formation; FIG. 7 is a schematic diagram of a queue heading change; FIG. 8 is a schematic diagram of scaling; FIG. 9 is a schematic diagram of a pseudo-target "square" arrangement pattern; FIG. 10 is a schematic diagram of a "rectangular" arrangement pattern of decoys;

FIG. 11 is a schematic diagram of a pseudo-target "diamond" arrangement pattern; FIG. 12 is a V-shaped team item orientation map; FIG. 13 is a Hough parameter space diagram of the V-shaped formation view indication situation; FIG. 14 is a comparison of various clustering number optimization methods; FIG. 15 is a Hough parameter space diagram after V-shaped formation catalog trend clustering; FIG. 16 is a situation diagram after V-shaped convoy directory indicates situation clustering; FIG. 17 is a diagram of the situation of V-shaped formation end-guided radar; FIG. 18 is a diagram of a V-shaped formation end-guidance radar situation formation identification process; FIG. 19 is a diagram of missile versus V-formation target hit; FIG. 20 is a view of a double-row program trend chart;

FIG. 21 is a Hough parameter space diagram of the double-row formation directory pointing situation; FIG. 22 is a Hough parameter space diagram after double-row formation category trend clustering; FIG. 23 is a situation diagram after double-row formation category indicates situation clustering; FIG. 24 is a diagram of the situation of an end-guided radar of a double-row formation; FIG. 25 is a diagram of a process of identifying the formation of the situation of the double-row formation end-guided radar; FIG. 26 is a diagram of a missile versus a target hit for a double-row formation; FIG. 27 is a view of the annular air defense formation view; FIG. 28 is a Hough parameter space diagram of the ring air defense formation view indication situation of a mobile detection interval; FIG. 29 is a Hough parameter space diagram after the ring air defense formation catalog orientation situation clustering of the mobile detection interval; FIG. 30 is a view showing the situation of the annular air defense formation category in the mobile detection area;

FIG. 31 is a diagram of the situation of an annular formation last-guidance radar; FIG. 32 is a diagram of a process of identifying the situation formation of the last-guided radar of the annular air defense formation; FIG. 33 is a diagram of missile-to-annular air defense formation target hitting. FIG. 34 is a Hough parameter space diagram after the ring air defense formation catalog orientation situation clustering of the original detection interval; fig. 35 is an original detection interval annular air defense formation catalog orientation recognition diagram.

Detailed Description

The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.

Example 1:

referring to fig. 1 to 35, an anti-ship missile formation recognition target selection system based on Hough transformation and optimized K-means clustering comprises a motion situation monitoring module, a formation contour recognition module, a target situation establishment module, a hit target acquisition module and a target hit module.

And the motion situation monitoring module monitors the coordinates of all members in the target formation so as to obtain the motion situation of the target formation. And the formation contour identification module performs Hough transformation on the motion situation of the target formation and identifies the formation contour of the target formation. And the target situation establishing module establishes a target situation model according to the formation contour of the target formation and carries out sequencing numbering on all members in the target formation. The striking target acquisition module selects a striking target P in the target formation and determines the relative number B-P of the striking target. And B is the number of the reference ship in the target formation. The target striking module launches a missile to a striking target. The missile is provided with an end guidance radar. And after the self-control flight of the missile is finished, starting the missile terminal guidance radar. And the last-guided radar acquires the current motion situation of the target formation and performs Hough transformation, so that the current formation profile of the target formation is identified. And the last-guided radar carries out sequencing numbering on each echo signal of the target formation, compares the target formation number and the current sequencing number in the target situation establishing module and determines a hit target P. The missile captures and tracks the hitting target P and completes the hitting.

The step of identifying the formation contour of the target formation comprises the following steps:

1) establishing a measurement space by using a Hough transformation function based on duality of point and line

Interior points and parameter space

The corresponding relationship of the curves of (1). (X, Z) are coordinates;

for any point in the measurement space

The Hough transform function is as follows:

ρ＝X cosθ+Z sinθ

in the formula, θ is an included angle formed by a perpendicular line from the measurement space origin to any straight line passing through the point and the positive direction of the X axis. | ρ | is the vertical length.

2) Recording target formation member coordinates of measurement space

In the parameter space there is a corresponding sinusoid of l_i. i-1, 2, …, N, a set of enqueue targets in a measurement space

In the parameter space, there are corresponding sinusoidal clusters

Selecting a broken line of a measurement space

And calculating to obtain the sine curve intersection point corresponding to the parameter space

Thereby forming a set of data samples

i＝1,2,…,(N-1)。

3) And clustering the intersection points of the Hough curves by using an optimized K-means clustering method to obtain the formation profile of the target formation. The objective function E for optimizing the K-means clustering method is as follows:

in the formula, k is the number of clusters.

Is of the type W_jCluster center of the medium sample. n is_jIs of the type W_jNumber of data samples.

Optimal clustering number K for optimizing K-means clustering method^*As follows:

wherein F (D, L) is a disparity cost function,

is of the type W_jAny sample object contained. k is a radical of_maxIn the upper limit of the range,

indicating a rounding down.

The step of clustering the intersection points of the Hough curves by using the optimized K-means clustering method comprises the following steps:

1) randomly selecting k samples from a data sample set X as initial clustering centers, and calculating an objective function matrix D from each sample in the data sample set X to each initial clustering center, namely:

in the formula (d)_ijRepresents the i + (j-1). times.n elements of the objective function matrix D.

Is W_jAnd (4) clustering centers. j is 1, …, c. k is 1,2, …, n.

Representing the ith sample of the set of data samples X.

2) Calculating a column vector

And corresponding cluster number column vector

Namely:

in the formula, the column vector

The element in (1) includes the sum of the squares of the minimum distances of the samples to the cluster centers. minD (i,: indicates the sum of the squares of the minimum distances from the ith sample to the centers of the clusters.

3) Based on column vectors

And cluster number column vector

And initially classifying the data sample set X, and calculating the number of various samples.

4) Multi-sample update clustering, comprising the steps of:

4.1) column vector according to cluster number

Cluster number with varying number of cluster samples

The changed cluster centers and the changed sample numbers are updated. The varying objective function matrix D is then calculated from the varying cluster centers. 4.2) removing the clusters that become empty sets. 4.3) calculating an objective function value E, judging whether the objective function E is reduced or not, if not, entering the step 5), and if so, temporarily storing the cluster number column vector

And an objective function value. 4.4) calculating the current column vector

And corresponding cluster number column vector

4.5) column vector according to new cluster number

With old polymerClass number column vector

Determines the sample with the changed cluster number, and writes the sample number corresponding to the sample into the column vector

In (1).

Column vector

As follows:

judging the sum of squares of distances from the samples with changed cluster numbers to the center of a new cluster_iIf it is less than the sum of squared distances d' from the sample to the old cluster center, if not, then from the column vector

The sample number corresponding to the sample is deleted.

Column vector

The update is as follows:

where [ ] indicates no element, reducing the number of column vector rows.

4.6) column vectors

The new cluster number in (1) replaces the original cluster number of the sample, and a cluster number vector with the changed number of samples in the cluster is obtained

Returning to the step4) Up to

Become [ 2 ]]And the multi-sample updating iteration converges, and the single-sample updating clustering stage is switched.

Cluster number vector

As follows:

where c represents the total number of clusters and i e [. cndot. ] represents the element to which i belongs to the array [. cndot. ].

5) Updating clustering of single samples, comprising the following steps:

5.1) calculating an objective function matrix Del of a sample set with single sample clustering, namely:

in the formula (I), the compound is shown in the specification,

is W_jCenter of cluster, m_jThe number of samples for cluster number j. sgn_ijIs a symbolic function.

5.2) calculating the minimum distance square sum of each sample in the objective function matrix Del to each cluster center by using the formula (5), and writing the minimum distance square sum into a column vector

Writing the least distance square sum corresponding to the cluster number into the column vector of the cluster number

5.3) judging the column vector of the cluster number

And cluster number column vector

And (4) judging whether a difference exists, if not, judging the updating iteration convergence of the single sample, and if so, entering the step 5.4).

5.4) updating the column vector

Namely:

in the formula (I), the compound is shown in the specification,

a sample number column vector representing the change in cluster number of the last iteration. min (·) represents the smallest element in the vector, mod (n) represents the modulo operation. In updating the column vector using equation (10)

Time of flight

Are all single element vectors.

Calculating the number of movements and applying new column vectors

Assigning to the column vector of the last iteration

Thereby obtaining the moving cluster number single element column vector of the current iteration and the last iteration

Namely:

5.5) updating the objective function value E and the clustering number column vector

Number of clustered samples m_jCluster center

Cluster number vector

And returns to step 5.1).

Objective function value E, cluster number column vector

Respectively as follows:

number of clustered samples m_jAnd a cluster center

Respectively as follows:

cluster number vector with varying number of samples in a cluster

As follows:

6) judging whether each sample is an empty set or not, and calculating an objective function matrix D (D) from each sample to each clustering center_ij)_n×kThereby obtaining the column vector in the objective function matrix

Namely:

in the formula, id_iIndicating the cluster number to which the sample belongs. D (i + (id)_i-1) · n) denotes the i + (id) th in the objective function matrix D_i-1) n elements.

Calculating to obtain accumulated column vector according to the column vector

And an objective function

Accumulating column vectors

As follows:

finishing one clustering iteration, and repeating the steps 1) to 6) until all the clustering iterations are traversed

And comparing the objective function values of rep clustering iterations to obtain the optimal clustering of the clustering number k.

7) And (4) calculating a diversity cost function of the cluster number k according to the formula (3), and repeating the steps 1) to 6) until all cluster numbers k are traversed to be 1,2, …, n. And (5) comparing the clustering number k with 1,2, …, and n iteration difference cost functions to obtain the optimal clustering number, the clustering center and the corresponding classification.

8) And (3) clustering the sample under the optimal clustering number by using a formula (18) to obtain the corresponding straight line in the original measurement space by reflection.

The slope a and the intercept b of the line obtained by inverse mapping are respectively as follows:

in the formula, ρ₀、ρ_π/2And ρ_πAnd represents an angle ρ corresponding to θ ═ 0, π/2, and π/2.

And the target situation model establishes a plane rectangular coordinate system by taking the queue course of the target indication stage as the positive direction of a Z axis and the right-hand direction perpendicular to the Z axis as the positive direction of an X axis, and marks out the formation queue in the plane rectangular coordinate system. The formation queue comprises a reference warship J, a queue line, a queue heading gamma, a formation interval D, a flush angle alpha and a queue angle beta.

The queue line refers to a connecting line of points where the ships in the queue start from the reference ship. The queue course gamma refers to an included angle between a ship bow stern line of the reference ship and the due north direction. The flush angle alpha refers to the included angle between the ship bow and stern lines and the queue line of other ships. The queue angle beta is 180-alpha, which means the included angle between the ship bow and stern line and the queue line of the reference ship.

According to different formation profiles of the target formation, the coordinates of each naval vessel in the measurement space and the coordinates of the reference vessel comprise the following three conditions:

situation one) when the formation contour of the target formation is the V-shaped formation, the reference ship is taken as a naval ship at the joint of two wings of the V-shaped formation, the included angle of the two wings is the sum of the alignment angles of the wings, the formation angles of the left wing and the right wing are both beta, the formation course is gamma-0 degrees, and the coordinate of the reference ship is (J)_X,J_Z) The total number of the ships in the formation is T, and the coordinates (X) of each ship in the V-shaped formation in the measurement space_n,Z_n) See equation (19) for the left wing, equation (20) for the right wing, and reference vessel coordinates (J) as follows_X,J_Z) See equation (21):

wherein (X, Z) is the intersection point coordinate of the two wing queue lines.

Case two) when the formation contour of the target formation is parallel formation, the coordinates (X) of each naval vessel in the measuring space_n,Z_n) Reference ship coordinate (J)_X,J_Z) As follows:

(J_X,J_Z)＝(X₁,Z₁) (23)

situation three) when the formation contour of the target formation is the annular formation, the coordinates (X) of each naval vessel in the measurement space of the horizontal queue_n,Z_n) As follows:

coordinates (X) of each naval vessel in the measurement space in the vertical queue_n,Z_n) As follows:

reference ship coordinate (J)_X,J_Z) As follows:

before the missile is launched to start the missile end-guided radar, if the formation turns around a certain rotation point, the coordinates (X) of the target formation naval vessel after the missile end-guided radar is started_n′,Z_n') as follows:

in the formula (X)₀,Z₀) Is the rotation center point coordinate. q is a rotation angle.

Before the missile is launched to start the missile end-directed radar, if the target formation distance changes, the coordinates (X) of the target formation naval vessel after the missile end-directed radar is started_n′,Z_n') or target formation interval (D)_h′,Z_z') as follows:

in the formula, when k₁、k₂When the element belongs to (0,1), the formation pitch is reduced. k is a radical of₁、k₂E (1, ∞) is the queue pitch amplification. When k is₁＝k₂The target formation is scaled equally.

Before the missile is launched to the missile end-guided radar to be started, if a plurality of false targets exist in the target formation, the false target coordinate (C) after the missile end-guided radar is started_X1,C_Z1) False target coordinates (C)_X2,C_Z2) False target coordinates (C)_X3,C_Z3) False target coordinates (C)_X4,C_Z4) As follows:

and R is the distance between the false target and the naval vessel. Gamma ray_D([-180°,0°]∪[0°,180°]) Is the direction of the incoming missile. And epsilon and delta are angles between a connecting line of the false target and the naval vessel and the incoming direction of the missile. Reference ship coordinate (J)_X,J_Z) Is a true target.

Example 2:

the anti-ship missile formation identification target selection method based on Hough transformation and optimized K-means clustering mainly comprises the following steps:

1) formation identification target selection process of anti-ship missile

Establishing a formation matching identification model of the anti-ship missile, and firstly selecting the characteristics of a naval vessel formation. Although the number of ship formation is variable under different conditions, the common formation linear formation forms include V-shaped formation, parallel formation, annular air defense formation and the like according to tactical purposes. The common formation is the most basic combination of straight lines or circles and has more typical geometrical characteristics. As long as the basic linear or annular shape can be identified, the formation of the ships can be judged, and the formation matching identification is completed according to the relative position relationship among the ships. In order to make Hough change and optimized K-means clustering jointly play a role in formation identification, the algorithm should include the following main steps:

1.1) obtaining the coordinates of the target formation members (namely obtaining the target situation), carrying out Hough transformation, and mapping the measurement space coordinates to a parameter space.

Hough transformation is an effective method for detecting shapes of straight lines, circles and the like in the field of pattern recognition and image processing, and is essentially used for establishing a measurement space by utilizing duality of points and lines

Interior points and parameter space

The corresponding relation of the curves converts the problem of approximate line detection in the original measurement space into the problem of clustering for searching curve intersection points in the parameter space, namely converts the overall detection characteristic into the local detection characteristic. For any point in the measurement space

The Hough transform function form of the movable detection interval is as follows:

ρ＝X cosθ+Z sinθ

wherein theta is an included angle formed by a perpendicular line from the original point of the measurement space to any straight line passing through the point and the positive direction of the X axis, the value range of theta is called a detection interval and is generally taken as [0, pi ]; when a sample point formed by the intersection point of the Hough curves is distributed in [0, 5. delta. theta ]. sup. [ pi-5. delta. theta, pi ], a mobile detection interval is adopted; | ρ | is the length of the perpendicular, ρ may be positive or negative.

The Hough transformation has the advantages of certain robustness on random noise, suitability for parallel processing, strong pertinence, no influence of space and curve shapes and the like, but has the obvious defect of easy prejudgment in the process of searching local peak values in an accumulation matrix. Because the standard Hough transform usually adopts a threshold method to extract the peak value, some higher secondary peak values usually appear near the maximum peak value, and if the peak value is extracted by simply adopting the threshold method, some peak values exceeding the threshold value around the maximum peak value are extracted, so that the peak clustering phenomenon is caused. For a single target situation, the clustering phenomenon is very serious under a low threshold, and the missing detection occurs under a multi-target situation when the threshold is increased.

1.2) solving the intersection point of the Hough curve and optimizing the K-means clustering.

Formation target for measurement space

i 1,2, …, N, there being a corresponding sinusoid l in the parameter space_i，i＝1,2, …, N; formation target set of measurement space

In the parameter space, there are corresponding sinusoidal clusters

Selecting a broken line of the measurement space

i is 1,2, …, (N-1), and the intersection point of the sine curve corresponding to the parameter space is obtained

i-1, 2, …, (N-1) constituting a set of data samples

The K-means clustering principle is that a certain distance from a data point to a class center is used as similarity measurement, the sum of squares of the certain distance is established as an optimized objective function, and the objective function value is minimized through a series of iterative operations, so that the optimal classification method corresponding to the cluster center is obtained. Suppose that

Is a data set having n samples,

is a data sample with m-dimensional variables, the goal is to divide the data set into k classes: w₁,W₂,…,W_kThe optimized K-means clustering algorithm adopts a certain distance | · | (Euclidean distance, Manhattan distance, Minkowss distance and the like) error square sum as a target function, and performs iterative clustering and class center updating by using a certain distance error square sum minimum criterion defined by the formula (2):

and calculating the optimal clustering number k by adopting the formula (3)^*The values are such that the intra-class variability D within the same class (cluster) is minimal and the inter-class variability L between different classes (clusters) is maximal:

wherein: f (D, L) is a disparity cost function,

is of the type W_jAny of the sample objects contained therein may be,

is of the type W_jCluster center of middle sample, n_jIs of the type W_jThe number of medium data samples; k is the number of clusters, k_maxIn the upper limit of the range,

indicating a rounding down.

In the problem of formation identification, when intersection points of curves in a Hough parameter space are taken as data points, the characteristics that system noise and measurement noise are interfered, data positions fluctuate in a certain distribution range, formation geometry characteristic rules are obvious, data center positions are relatively concentrated and the like exist. Therefore, in the invention, based on the basic idea of K-means clustering and the characteristics of the problem of formation recognition, the basic steps for obtaining the optimized K-means clustering algorithm are as follows:

a) and starting an optimized clustering number k iteration, wherein k is 1,2, … and n.

b) Starting clustering iteration aiming at a certain clustering number k,

randomly selecting k samples from a sample set X according to a uniform distribution rule as initial clustering centers, and calculating a target function matrix from each sample to each initial clustering center according to a formula (4):

wherein d is_ijThe i + (j-1). times.n-th element of D,

is W_jThe cluster center, j is 1, …, c, and the column vector formed by the sum of squares of the minimum distances from each sample to each cluster center is determined by the formula (5)

And corresponding cluster number column vector

Initial classification is performed and the number of samples of each class is calculated.

Then, clustering iteration is carried out, and the sequence is divided into two stages: a multi-sample update clustering stage and a single-sample update clustering stage.

c) Multi-sample update clustering stage

I) Column vector according to cluster number

Cluster number increased or decreased with sample

(see step V) equation (8)) updating the changed cluster centers and the number of changed samples in batches; the varying objective function matrix D is then calculated in batches from the varying cluster centers.

II) processing the clusters that become empty sets.

And III) calculating the objective function value according to the formula (2) and judging whether the objective function value is reduced. If not, withdrawing the iteration step number of one step, returning to the clustering center of the iteration step, calculating the number of various samples, and switching to single sample to update the clustering orderA segment; if so, temporarily storing the row vector of the cluster number

And an objective function value.

IV) column vector composed of the least sum of squares of distances from each sample to each cluster center determined by equation (5) simultaneously

And corresponding cluster number column vector

V) comparing new and old cluster number column vectors by equation (6)

Whether or not to change, determining which samples change clustering, and shifting (sample number of cluster number change) column vectors

Where [ ] indicates no elements, reducing the number of column vector rows.

If there is a change, the sum of squares of the distances from the centers of the new and old clusters to the sample is compared by equation (7) to determine whether to decrease, and the moving column vector is changed

Then, the new cluster number is used for replacing the current cluster number of the sample, and the cluster number vector of the increased or decreased sample is obtained

Where c represents the total number of clusters and i e [. cndot. ] represents the element to which i belongs to the array [. cndot. ].

d) Single sample update clustering stage

I) For cluster number column vectors

The objective function matrix Del with a single-sample cluster (at least one cluster exists, the number of samples is 1) sample set is calculated by equation (8) for the case of the changed samples, both single-sample and multi-sample:

wherein the content of the first and second substances,

is W_jCenter of cluster, m_jThe number of samples for the cluster No. j,

a cluster number vector in which the samples obtained by equation (15) are increased or decreased.

II) temporarily storing the cluster number column vector

And objective function value, and determining column vector composed of minimum distance square sum of Del samples to cluster centers by formula (5)

And corresponding cluster number column vector

III) comparing the new and old cluster number column vectors by equation (6)

If the distance between the two clusters is not reduced, determining which samples change the clusters, if so, comparing the distance between the centers of the samples to the new cluster and the old cluster by the formula (7) to determine whether the distance is reduced; and if the single sample updating iteration is not changed, judging that the single sample updating iteration is converged.

IV) further movement according to formula (10)

(single element). If the column vector is shifted

Movement less than last iteration

(single element), the iteration continues.

Where min (·) represents the smallest element in the vector, and mod (n) represents the modulo operation.

Calculating the number of movements and adding new ones

Assigning to the singleton of the last iteration

Temporary storage of new and old mobile cluster number single element column vectors by equation (11)

V) updating the objective function value, cluster number column vector by equation (12)

The number of samples of the cluster is updated by equation (13), and the cluster center is updated by equation (14):

obtaining a 2-element cluster number vector with increased and decreased samples by equation (15)

Repeating step d) only until convergence of the single sample update is completed.

e) Judging whether each sample is an empty set after each clustering iteration, and calculating a target function matrix D (D) from each sample to each clustering center_ij)_n×kFrom the known cluster number column vector according to equation (16)

The column vector formed by the least square sum of the distances from each sample to each cluster center in the target function matrix can be obtained

Wherein id_iPresentation sampleThe cluster number 1,2, …, k, D (i + (id) to which this belongs_i-1) · n) denotes the i + (id) th in the objective function matrix D_i-1) n elements.

Aligned column vector

Accumulating according to each cluster, obtaining an accumulated column vector according to the formula (16)

Then add up to obtain

Finishing one clustering iteration, and repeating the steps 1) to 6) until all the clustering iterations are traversed

And comparing the objective function values of rep clustering iterations to obtain the optimal cluster with a certain cluster number k.

f) And (4) calculating a diversity cost function of the clustering number k according to the formula (3), and repeating the steps a) to f) until all clustering numbers k are traversed to be 1,2, …, n. And (5) comparing the clustering number k with 1,2, …, and n iteration difference cost functions to obtain the optimal clustering number, the clustering center and the corresponding classification.

And 1.3) reflecting the clustered intersection points back to the corresponding straight lines in the original measurement space by the formula (18).

If judging whether each point is on a straight line or a circle in the radar situation map, the method is equivalent to finding the intersection point of a sine curve in the corresponding parameter space. If the intersection point between the sine curves is (theta, rho), the expression of the slope a and the intercept b of the straight line reflected to the original measurement space can be obtained according to the definition of the parameter space coordinates as follows:

where ρ is₀、ρ_π/2And ρ_πDenotes ρ corresponding to θ ═ 0, π/2, and π/2.

1.4) identifying the formation form contour according to the reverse mapping straight line, judging the specific formation form and composition condition by combining the motion information of each warship in the formation, and carrying out target sequencing on formation targets.

1.5) selecting the target needing striking.

1.6) the formation target rotates, scales or is interfered during the time from the launching of the missile to the ending of the missile, when the self-control flight section enters the starting search and tracking stage of the terminal guidance radar. After the guided missile terminal-guided radar is started, the member coordinates of the target formation (namely the situation of the terminal-guided radar) are obtained, Hough transformation is carried out, and the coordinates are mapped to a parameter space.

1.7) repeating the steps 1.2) to 1.4), judging the formation of the enemy formation and the target sorting condition when the terminal guided radar is started, and comparing the situation with the target situation so as to confirm the target issued.

According to the algorithm flow, the formation matching identification flow of the anti-ship missiles can be summarized by combining the actual use of the anti-ship missile battle, as shown in fig. 1.

2) Formation target presetting and selection model

The formation matching, identifying and modeling processes of the anti-ship missile are all carried out in the same plane, and when the target situation is modeled, a plane rectangular coordinate system is established by uniformly taking the queue course of a target indication stage as the positive direction of a Z axis and the right-hand direction perpendicular to the Z axis as the positive direction of an X axis. The used formation queue elements comprise a reference ship J, a queue line, a queue course gamma, a formation interval D, a neat angle alpha and a queue angle beta. As shown in fig. 2.

A reference vessel refers to a vessel used to provide a relative positional reference for the entire fleet. Typically at a more specific geometric location in the queue.

The queue line refers to a connecting line of points where the ships in the queue start from the reference ship.

The queue course gamma refers to an included angle between a ship bow stern line of the reference ship and the due north direction.

The formation distance D refers to the straight line distance between vessels. For convenience of description, the transverse spacing D along the bow-stern line of the vertical reference vessel can be decomposed into_hAnd the longitudinal distance D along the bow and stern line direction of the reference vessel_z。

The flush angle alpha refers to the included angle between the ship bow and stern lines and the queue line of other ships. Calculated from the reference vessel to the left (starboard) from 0 ° to 180 °.

The queue angle beta refers to an included angle between a ship bow and stern line and a queue line of the reference ship. Calculated from the reference vessel to the left (starboard) from 0 ° to 180 °.

β＝180°-α (19)

Before the formation model is built, the following assumptions exist: 1) the distance directions of different ships in the formation can be distinguished by the sensor; 2) the position positioning error of the naval vessels and the detection error of the sensor in the formation accord with white noise distribution; 3) target change in the terminal guidance radar starting search tracking phase does not change the formation type of the target indication phase, and target position exchange in the formation does not occur.

2.1) V-shaped formation model

a) And (3) formation target simulation: the V-shaped formation is a common formation in the formation fighting process, so that the air-defense fire of the naval vessels in the formation can be fully exerted, and the shooting dead zone of the formation can be reduced to the greatest extent. As shown in fig. 3.

The V-shaped formation is characterized in that a naval vessel at the joint of two wings of the V-shaped formation is taken as a reference vessel, the included angle of the two wings is the sum of the viewing angles of the wings, and the heading of the reference vessel determines the heading of the formation. In the rectangular coordinate system shown in fig. 2, it is assumed that the queue angles of the left wing and the right wing are both β, the queue heading is γ equal to 0 °, and the reference ship coordinate is (J)_X,J_Z) The coordinate of each naval vessel in the V-shaped formation in the measuring space can be obtained as (X)_n,Z_n)(n＝1,2,3,…,T)：

The left wing is shown in equation (20), and the right wing is shown in equation (21):

b) formation recognition target ordering

Left wing parameters for V-shaped formation parameter space characteristics

And right wing parameters

Is represented by theta₁And theta₂Is the parameter space clustering center c₁And c₂Theta parameters of (1), the object-pointing phase and the last guidance phase substantially maintaining relative parameters

And is not changed. Parameter spatial clustering center c₁And c₂Corresponding to the two-wing queue lines of the measuring space, and obtaining the V-shaped formation queue line identification criterion as the intersection of the two-wing queue lines identified by the important geometrical characteristics of the V-shaped formation, wherein the intersection point is near the reference ship. The echo signal closest to the intersection point is used as a reference ship, ships represented by other echoes can be confirmed according to the relative position of the reference ship in the formation and sequenced, and the reference ship can be used as a basis for establishing a V-shaped formation target capture model. With a sine curve passing through c simultaneously₁And c₂A clustering region (a circle with a clustering center as a circle center and a radius as a farthest sample) which is used as a center corresponds to a reference ship, the bow-stern line of the reference ship points to the forward direction, and parameter spaces are respectively provided with

Root sinusoid through c₁And c₂The cluster region as the center corresponds to the left wing and the right wing of the measurement space respectively

A vessel. The coordinates of each naval vessel passing through the left wing and the right wing from left to right are (X)_n,Z_n) (target number n is 1,2,3, …, T), and if the intersection of two identified straight lines is (X, Z), the reference ship coordinate (J) is set as_X,J_Z) Can be expressed as

In the target indicating stage, the reference ship number is known as B, and if the preset target number is P, the relative number of the preset target is P-B. And in the terminal guidance radar starting search and tracking stage, if the number of the reference ship is known to be B and the relative number of the preset target is known to be P-B, the number of the preset target is B + (P-B) ═ P.

2.2) parallel formation model

a) Formation target simulation

The parallel formation is one of the simplest and easiest formation, is a common formation in the formation maneuvering process, and has great tactical significance. Parallel formation can be subdivided into double horizontal formation and double vertical formation. The geometric characteristics of the double-row formation are that the ship alignment angles alpha of the same row are always 90 degrees, and the geometric characteristics of the double-row formation are that the ship alignment angles alpha of the same longitudinal formation are always 0 degrees, as shown in fig. 4 and 5. Functionally, the double-row fleet is convenient for increasing the detection range and effect of the bow active sonar of each naval vessel in the formation to the maximum extent, so that the double-row fleet is often used for forming the anti-submarine formation of the formation; the double longitudinal lines are more convenient to transmit foil strips to the front and the back of the navigation direction for centroid type interference, and the electromagnetic interference reverse conducting effect is good.

For parallel fleets, the ship or the designated direction at the head of each queue is usually taken as a reference ship (both port and starboard directions). Taking a double-platoon as an example, if the heading of the queue is gamma-0 DEG, the coordinate of the reference ship in the platoon is (J)_X,J_Z) And the total number of the ships in the formation is T, so that the coordinates of the ships of each horizontal formation in the single/double horizontal formation in the measurement space can be obtained as (X)_n,Z_n)(n＝1,2,3,…,T)：

When the queue heading γ is 90 ° and the justification angle α is always 0 °, the double-row becomes double-column. Since the double column itself can be obtained by rotating the double row by 90 °.

b) Formation recognition target ordering

Parallel formation (double horizontal/longitudinal) parameter space features use of heel/left wing parameters

And prostate/right wing parameters

Is represented by theta₁And theta₂Is the parameter space clustering center c₁And c₂The target phase and the final guidance phase substantially maintain the relative parameter | Delta theta₁₂|＝|θ₁-θ₂I ≈ 0. Parameter spatial clustering center c₁And c₂Corresponding to the two wing queue lines of the measuring space, and obtaining a parallel formation shape recognition criterion as two approximately parallel straight lines according to the important geometrical characteristics of parallel formation; the parameter spaces respectively have

Root sinusoid through c₁And c₂Clustering as center, corresponding to the rear row/left wing and the front row/rear wing of the measurement space respectively

A vessel. Selecting 1 ship along the heading direction of the ship in the queue and the starboard ship

The warship of the warship is the reference warship, warships represented by other echoes can be confirmed according to the relative position of the reference warship in the formation and sequenced, and the warship can be used as a basis for establishing a parallel formation target capture model. If the total number of the ships in the formation is T, the coordinates of each ship are (X)_n,Z_n) (n-1, 2,3, …, T) the reference ship coordinate (J) can be obtained_X,J_Z) Can be expressed as

(J_X,J_Z)＝(X₁,Z₁) (24)

Because the parallel fleet has axial symmetry and central symmetry, in order to avoid the confusion of directions, the reference warship identified every time is used as the No. 1 warship to number other warships in the formation, rather than setting a numbering rule in advance.

2.3) annular formation model

a) Formation target simulation

The annular air defense formation is a common formation in the formation operation process, is convenient for fully exerting the air detection capability of the peripheral guard vessels to realize the optimal early warning effect, is also beneficial to the fire cooperation of the guard vessels to the air target attacking in each direction, and is used for protecting important vessels in the formation. As shown in fig. 6. The annular air defense formation usually takes the most middle ships and the most important ships needing protection as reference ships. The geometric characteristics are that the vessel alignment angles alpha of the horizontal queue are always 90 degrees and the vessel alignment angles alpha of the vertical queue are always 0 degrees based on the fore-aft line of the reference vessel. Setting the course of the queue as gamma-0 deg. and the coordinate of the reference ship in the transverse queue as (J)_X,J_Z) And the total number of the ships in the formation is T, so that the coordinates of each ship in the annular air defense formation in the measurement space can be obtained as (X)_n,Z_n)(n＝1,2,3,…,T)：

The horizontal queue is shown in formula (25), and the vertical queue is divided into two sections, as shown in formula (26):

b) formation recognition target ordering

Horizontal formation parameter for annular formation parameter space characteristic

And the longitudinal parameters

Is represented by theta₁And theta₂Is the parameter space clustering center c₁And c₂The target phase and the final guidance phase substantially maintain a relative parameter | theta₁₂|＝|θ₁-θ₂And | ≈ pi/2 does not change. Parameter spatial clustering center c₁And c₂Two queue lines correspond to the measuring space, and the identification criterion of the queue shape of the annular formation can be obtained by the important geometrical characteristics of the annular formation, namely two straight lines (approximately vertical) with intersection points are identified, and the intersection points are near the reference ship. The echo signal closest to the intersection point is used as a reference ship, ships represented by other echoes can be confirmed according to the relative position of the reference ship in the formation and sequenced, and the reference ship can be used as a basis for establishing an annular formation target capture model. With a sine curve passing through c simultaneously₁And c₂A clustering region (a circle with a clustering center as a circle center and a radius as a farthest sample) which is used as a center corresponds to a reference ship, the bow-stern line of the reference ship points to the forward direction, and parameter spaces are respectively provided with

Root sinusoid through c₁And c₂The cluster region as the center corresponds to the horizontal line and the vertical line of the measurement space respectively

A vessel. The coordinates of each ship passing through the transverse team from left to right are (X)_n,Z_n) (object number)

) The coordinates of each ship sequentially passing through the longitudinal team from top to bottom are (X)_n,Z_n) (object number)

). If the intersection point of the two identified straight lines is (X, Z), the coordinate (J) of the reference ship_X,J_Z) Can be expressed as

3) Formation target change model

In the formation fighter plane, even if the same formation is kept, the formation can change the elements of each formation according to tactical requirements and actual conditions of a battlefield environment, so that the purpose of adjusting the formation is achieved, including changing the course of the formation (formation rotation), increasing/decreasing the formation interval (formation scaling), performing dilution type interference (target quantity increase) and the like. Particularly, when the anti-ship missile is resisted, the formation can adopt all feasible means to resist under the unified command of a commander, so that the possibility that the formation situation obtained by searching and catching of a last guidance radar is different from the formation situation when a target instruction is issued must be considered when the formation matching identification is carried out, namely, the formation of an enemy formation is adjusted in the missile automatic control flight stage. In addition, due to the complex battlefield situation, when the guided missile terminal radar starts to search and catch, part of targets may be missed, so that the number of targets is inconsistent with the number of targets issued by the target, and the situation also needs to be considered. The changes of the target formation form and the degree of each change are considered to be random in the invention and are unrelated to the self-control flight time of the missile.

3.1) rotating the model: when the queue course changes, the whole formation is turned around a certain rotation point under the unified command of a formation commander, so that the purpose of adjusting the queue course is achieved. As shown in fig. 7.

If the coordinate of the center point of rotation is (X)₀,Z₀) The rotation angle is q (anticlockwise), and the coordinate of the ship before rotation is (X)_n,Z_n) And the coordinate of the naval vessel after the rotation is finished is (X)_n′,Z_n') can be expressed as:

3.2) scaling the model: scaling, i.e., increasing/decreasing the formation spacing, is a process commonly used in formation navigation and combat, in which the formation spacing is adjusted to contract or expand the formation to cope with changes in the battlefield environment without destroying the overall formation. As shown in fig. 8.

Let k₁、k₂The scaling coefficients are respectively an abscissa and an ordinate, and the coordinate of the n warship in the formation before scaling change is (X)_n,Z_n) (ii) a The coordinate of the n warship after scaling change is (X)_n′,Z_n') then the following expression holds:

or scaling the pre-change queuing interval (D)_h,Z_z) Scaling the changed queuing interval (D)_h′,Z_z') the relationship is as follows:

wherein when k is₁、k₂When the element belongs to (0,1), k is reduced for the formation interval₁、k₂E (1, ∞) is the queue pitch amplification. In particular, when k is₁＝k₂Time, scaling is equal.

3.3) dilution type interference model

At present, radar passive interference devices such as foil strips and inflatable corner reflectors are widely equipped with warships in various countries. When an incoming missile is detected, the formation of the enemy naval vessels uses a passive interference device to arrange a false target, namely dilute interference, before the guided radar at the end of the missile is started, so that the probability of the formation naval vessels being captured by the missile is reduced. Therefore, the possibility that an enemy formation uses a passive jamming device to resist an incoming missile is a problem that formation matching identification cannot be avoided.

In order to ensure the interference effect, the decoy is usually arranged in the search range of the missile terminal-guided radar of the surface naval vessel. Common spatial arrangement modes include square arrangement, rectangular arrangement, rhombic arrangement and the like. As shown in fig. 9, 10 and 11.

Whether the mode is a square arrangement mode, a rectangular arrangement mode or a diamond arrangement mode, the common characteristic of the modes is that a connecting line of a false target and a naval vessel forms a fixed angle with the incoming direction of a missile, and the angle is marked as epsilon and delta. If the coordinate of the central naval vessel is (J)_X,J_Z) The distance between the false target and the naval vessel is R, and the incoming direction of the missile is gamma_D([-180°,0°]∪[0°,180°]) Four false targets (C)_X1,C_Z1)、(C_X2,C_Z2)、(C_X3,C_Z3)、(C_X4,C_Z4) The coordinates of (a) are:

specifically, for a square array, e ═ δ ═ 45 °; for rectangular array, epsilon is delta; for the diamond-shaped array, epsilon is not equal to delta.

It can be easily found that several space arrangement modes commonly used at present have more regular geometric shapes. When a formation recognition problem model facing to dilution type interference of an enemy is established, geometric characteristics of a dilution type interference space arrangement mode are grasped, and a false target is set according to the arrangement mode near a target which is considered to be required to be protected by the enemy, so that the modeling problem is converted into a problem of adding the false target on the basis of a typical formation recognition model.

Example 3:

situation scenario is as follows: in the battle sea area, I plan to use anti-ship missiles to intensively attack No. 3 ships in the enemy V-shaped naval vessel formation. Influence of sea conditions, weather and grid power space environment conditions on the missile is ignored; the enemy boat formation is assumed to have no any resisting and avoiding action.

The radar situation when the target indicates to be issued is shown in fig. 12. The formation factors of the formation of the enemy V-shaped naval vessel are set as follows: the reference ship J is a No. 5 ship, the queue course gamma is 0 DEG, and the formation transverse distance D_h0.5nmile, longitudinal spacing D_zThe left and right wing alignment angles α are 26.6 ° for 1 nmile. Before the missile is launched, the formation elements and the preset target are bound to a missile comprehensive control computer.

In order to discuss and verify the model accuracy in a noise state, the system noise and the noise interference are simulated by normal distribution random numbers with the transverse interval mean value of 0, the mean square error of 0.1, the longitudinal interval mean value of 0 and the mean square error of 0.3. In order to discuss the identification performance of the model on the formation shape generating rotation, the heading of the formation queue of the enemy boat is changed to 330 degrees in the period from the missile launching to the missile ending self-control flight section entering the terminal guided radar starting search and tracking stage.

And mapping each target coordinate point to a sinusoidal curve corresponding to the Hough parameter space, solving the intersection point between the sinusoidal curves, and marking on the graph 13. As shown in fig. 14, the D/L method, the existing L + D method, and the L + D method of the present invention are used to perform optimized K-means clustering on each intersection point, so as to obtain an optimal clustering number of 2 classes, and the clustering result is shown in fig. 15. Left wing parameter P₁(2.6920,5) and right wing parameter P₂(0.5059,5)，|θ₁₂|＝π-|θ₁-θ₂|＝0.9539。

And (3) substituting the obtained two types of points into a formula (2), calculating to obtain a final clustering center coordinate, and drawing a corresponding straight line in the target situation. And then sorting according to the formation recognition result, wherein the selected target No. 3 ship is marked by a square, as shown in FIG. 16. According to the selected number 3 target, the ship launches an anti-ship missile. When the terminal guidance radar is started, the formation situation of the enemy boat is shown in fig. 17, and the heading of the formation of the enemy boat is found to be 330 degrees.

Mapping each target coordinate point to corresponding positive of Hough parameter spaceOn the chord curve, the intersection point between the sine curves is found and marked on the graph. And performing clustering analysis according to the same method, and finally drawing a corresponding straight line on the situation map. As shown in fig. 18. Left wing parameter P₁(0.0740,5) and right wing parameter P₂(1.0295,5)，|θ₁₂|＝|θ₁-θ₂|＝0.9555。

It can be found that even if the enemy ship formation is steered, two straight lines with intersection points can be still identified in the formation, and the formation can be judged to be V-shaped. If the target closest to the intersection point of the straight lines where the two sub-queues are located is the reference ship 5 of the V-shaped formation, the relative position of the ship 3 in the queue can be judged, and therefore the corresponding hit target is identified. As shown in fig. 19, target sorting is performed according to the V-team target capture model, and the carrier marked with a square is the identified carrier 3 set as the target.

Example 4:

the parallel formation can be subdivided into a double-horizontal formation and a double-vertical formation, and the double-horizontal formation is taken as an example in the simulation experiment.

Situation scenario is as follows: in the battle sea area, I plan to use anti-ship missiles to intensively attack No. 4 ships in the enemy double-horizontal naval vessel formation. Influence of sea conditions, weather and grid power space environment conditions on the missile is ignored; the enemy boat formation is assumed to have no any resisting and avoiding action.

The radar situation when the target indicates to be issued is shown in fig. 20. The formation elements of the enemy cross formation are set as follows: the reference ship J is No. 1 ship, the queue course gamma is 0 DEG, and the formation transverse distance D_h1nmile, longitudinal separation D _z1 nmile. In order to discuss and verify the model accuracy in a noise state, the system noise and the noise interference measurement are simulated by normal distribution random numbers with the transverse spacing, the longitudinal spacing mean value of 0 and the mean square error of 0.1. In order to discuss the identification performance of the model on the formation shape generating rotation, the heading of the formation queue of the enemy boat is changed to 330 degrees in the period from missile launching to missile ending self-control flight section entering a terminal guidance radar searching and tracking stage. Each target coordinate point is mapped to a sinusoidal curve corresponding to the Hough parameter space, and the intersection point between sinusoidal curves is found and marked on fig. 21. To pairAnd performing optimized K-means clustering on each intersection point to obtain 2 types of optimal clustering numbers, wherein the clustering result is shown in figure 22. Parameter P in the latter column₁(1.5777,5) and the prostate parameter P₂(1.5746,5)，|Δθ₁₂|＝|θ₁-θ₂|≈0。

And (3) substituting the obtained two types of points into a formula (2), calculating to obtain a final clustering center coordinate, and drawing a corresponding straight line in the target situation. And then sorted according to the formation recognition result, as shown in fig. 23. Wherein the selected target number 4 vessel is marked with a square. And according to the selected number 4 target, the ship launches an anti-ship missile. When the terminal guidance radar is started, the formation situation of the enemy boat is shown in figure 24, and the fact that the heading of the formation of the enemy boat is changed to 330 degrees can be found, and the formation distance is enlarged to 1.5nmile after the formation amplification. As shown in fig. 25, each target coordinate point is mapped to a sinusoid corresponding to the Hough parameter space, and an intersection point between the sinusoids is obtained and marked on the graph. And performing clustering analysis according to the same method, and finally drawing a corresponding straight line on the situation map. Parameter P in the latter column₁(2.0758,5) and the prostate parameter P₂(2.1207,5)，|Δθ₁₂|＝|θ₁-θ₂|≈0。

It can be found that even if the enemy ship formation turns and scales, two straight lines without intersection points can be identified in the formation, and the enemy ship formation can be judged as a double-row formation. If the left 1 st ship in the back row is judged to be the reference ship 1, the relative position of the 4 th ship in the row can be judged. As shown in fig. 26, the one marked with squares is the identified target ship No. 4.

Example 5:

situation scenario is as follows: in the battle sea area, I plan to use anti-ship missiles to intensively attack No. 3 ships in the enemy annular anti-aircraft naval vessel formation. Neglecting the influence of sea conditions, weather and network electromagnetic space environment conditions on the missile; the enemy boat formation is assumed to have no any resisting and avoiding action.

The radar situation when the target indication is given is shown in fig. 27. The formation elements of the enemy annular air defense formation are set as follows: the reference ship J is a No. 3 ship, the queue course gamma is 0 DEG, and the formation transverse distance D_h＝1nmile，Longitudinal distance D_z＝1nmile。

In order to discuss and verify the model accuracy in a noise state, the system noise and the interference of the measured noise are simulated by normal distribution random numbers with the transverse spacing, the longitudinal spacing mean value of 0 and the mean square error of 0.1; in order to discuss the identification performance of the model on the formation which generates rotation, the heading of the formation of the enemy ship is changed into 330 degrees in the period from the missile launching to the missile ending self-control flight section entering the terminal guidance radar searching and tracking stage; in order to discuss whether the model can deal with dilution type interference, after the formation receives early warning of incoming missile, the false target is released in a rectangular matrix mode near an important No. 3 ship immediately. Using the movement detection interval [5 · Δ θ, pi +5 · Δ θ), each target coordinate point is mapped onto a sinusoid corresponding to the Hough parameter space, and the intersection point between the sinusoids is found and marked on fig. 28.

And performing optimized K-means clustering on each intersection point to obtain the optimal clustering number of 2 classes, wherein the clustering result is shown in figure 29. Parameter P of the platoon₁(1.5414,5) and a column parameter P₂(3.0918,5), relative parameter | θ₁₂|＝|θ₁-θ₂|＝1.5504≈π/2。

And (3) substituting the obtained two types of points into a formula (2), calculating to obtain a final clustering center coordinate, and drawing a straight line in the target situation. And then sorting according to the formation recognition result, wherein the selected target No. 3 ship is marked by a square, as shown in FIG. 30. And according to the selected target ship No. 3, launching an anti-ship missile. When the terminal guidance radar is started, the formation situation of the enemy boat is shown in figure 31, and the direction of the incoming missile is gamma_DWhen the formation course of the enemy boat is changed to 330 degrees, 4 false targets are placed, and the original formation is severely disturbed. As shown in fig. 32, each target coordinate point is mapped to a sinusoid corresponding to the Hough parameter space, and an intersection point between the sinusoids is obtained and marked on the graph. And performing clustering analysis according to the same method, and finally drawing a corresponding straight line on the situation map. Parameter P of the platoon₁(2.0650,5) and a column parameter P₂(0.4738,5), relative parameter | θ₁₂|＝|θ₁-θ₂|＝1.5912≈π/2。

It can be found that even if the enemy ship formation turns and releases a false target, two straight lines with intersection points in a given range can be identified in the formation, and the intersection points are near the reference ship, so that the annular air defense formation can be judged. If the target closest to the intersection point of the straight lines where the two sub-queues are located is considered as the reference ship 3, the relative position of the ship 3 in the queue can be judged, and therefore the corresponding hit target is identified. As shown in fig. 33, the one marked with squares is the identified target ship No. 3.

When the original detection interval is adopted in the target stage, as shown in fig. 34, the clustering effect of the sample points is poor; as shown in fig. 35, although the target stage can identify the 3-warship, the nearest target of the intersection point of the straight lines where the two sub-queues are located is the 8-warship of the reference warship, so that the 3-warship cannot be identified in the last guidance stage.

Claims (9)

1. An anti-ship missile formation recognition target selection system based on Hough transformation and optimized K-means clustering is characterized in that: the system comprises a motion situation monitoring module, a formation contour recognition module, a target situation establishing module, a hit target obtaining module and a target hitting module.

The motion situation monitoring module monitors the coordinates of all members in the target formation so as to obtain the motion situation of the target formation;

the formation contour identification module carries out Hough transformation on the motion situation of the target formation and identifies the formation contour of the target formation;

the target situation establishing module establishes a target situation model according to the formation contour of the target formation, and sequences and numbers all members in the target formation;

the striking target acquisition module selects a striking target P in the target formation and determines the relative number B-P of the striking target; b is the number of the reference ship in the target formation;

the target striking module launches a missile to a striking target; the missile is provided with a terminal guidance radar;

after the self-control flight of the missile is finished, starting a missile terminal guidance radar; the terminal guidance radar acquires the current motion situation of the target formation and performs Hough transformation, so that the current formation profile of the target formation is identified;

the last-guided radar carries out sequencing numbering on each echo signal of the target formation, compares the target formation number and the current sequencing number in the target situation establishing module, and determines a hit target P;

the missile captures and tracks the hitting target P and completes the hitting.

2. The system for selecting the identification target of the anti-ship missile formation based on the Hough transform and the optimized K-means clustering, according to claim 1, is characterized in that the step of identifying the formation contour of the target formation comprises the following steps:

1) establishing a measurement space by using a Hough transformation function based on duality of point and line

Interior points and parameter space

The corresponding relationship of the curves of (a); (X, Z) are coordinates;

for any point in the measurement space

The Hough transform function is as follows:

ρ＝X cosθ+Z sinθ

in the formula, theta is an included angle formed by a perpendicular line from the original point of the measurement space to any straight line passing through the point and the positive direction of the X axis; | ρ | is the vertical length;

2) recording target formation member coordinates of measurement space

In the parameter space there is a corresponding sinusoid of l_i(ii) a i-1, 2, …, N, a set of enqueue targets in a measurement space

In the parameter space, there are corresponding sinusoidal clusters

Selecting a broken line of a measurement space

And calculating to obtain the sine curve intersection point corresponding to the parameter space

Thereby forming a set of data samples

3) And clustering the intersection points of the Hough curves by using an optimized K-means clustering method to obtain the formation profile of the target formation.

3. The system for selecting the anti-ship missile formation recognition target based on the Hough transform and the optimized K-means clustering according to claim 2, wherein an objective function E of the optimized K-means clustering method is as follows:

in the formula, k is the number of clustering clusters;

is of the type W_jThe cluster center of the middle sample; n is_jIs of the type W_jThe number of medium data samples;

optimizing K is equalOptimal clustering number k of value clustering method^*As follows:

wherein F (D, L) is a disparity cost function,

is of the type W_jAny sample object contained; k is a radical of_maxIn the upper limit of the range,

indicating a rounding down.

4. The system for selecting the anti-ship missile formation recognition target based on the Hough transform and the optimized K-means clustering, according to claim 3, is characterized in that the step of clustering the intersection points of the Hough curve by using the optimized K-means clustering method comprises the following steps:

1) randomly selecting k samples from a data sample set X as initial clustering centers, and calculating an objective function matrix D from each sample in the data sample set X to each initial clustering center, namely:

in the formula (d)_ijThe i + (j-1) x n elements of the objective function matrix D are represented;

is W_jClustering centers; j is 1, …, c; k is 1,2, …, n;

an ith sample representing a set of data samples X;

2) calculating a column vector

And corresponding cluster number column vector

Namely:

in the formula, the column vector

The element(s) in (1) comprises the sum of the squares of the minimum distances from each sample to each cluster center; minD (i,: indicates the sum of the squares of the minimum distances from the ith sample to the centers of the clusters;

3) based on column vectors

And cluster number column vector

Carrying out initial classification on the data sample set X, and calculating the number of various samples;

4) multi-sample update clustering, comprising the steps of:

4.1) column vector according to cluster number

Cluster number with varying number of cluster samples

Updating the changed cluster center and the number of changed samples; then calculating a changed objective function matrix D by the changed clustering center;

4.2) processing the clusters which become empty sets;

4.3) calculating an objective function value E, judging whether the objective function E is reduced or not, and if not, entering the stepStep 5), if decreasing, temporarily storing the cluster number column vector

And an objective function value;

4.4) calculating the column vector consisting of the least sum of squares of the distances from each sample to each cluster center by the formula (5)

And corresponding cluster number column vector

4.5) column vector according to new cluster number

And old cluster number column vector

Determines the sample with the changed cluster number, and writes the sample number corresponding to the sample into the column vector

Performing the following steps;

column vector

As follows:

judging the sum of squares of distances from the samples with changed cluster numbers to the center of a new cluster_iIf it is less than the sum of squared distances d' from the sample to the old cluster center, if not, then from the column vector

Deletion inThe sample number corresponding to the sample;

column vector

The update is as follows:

wherein [ ] indicates no element, reducing the number of rows of column vectors;

4.6) column vectors

The new cluster number in (1) replaces the original cluster number of the sample, and a cluster number vector with the changed number of samples in the cluster is obtained

Returning to the step 4) until

Become [ 2 ]]Updating iteration convergence of multiple samples, and switching to a single sample updating clustering stage;

cluster number vector

As follows:

where c represents the total number of clusters and i e [. cndot. ] represents the element to which i belongs to the array [. cndot. ].

5) Updating clustering of single samples, comprising the following steps:

5.1) calculating an objective function matrix Del of a sample set with single sample clustering, namely:

in the formula (I), the compound is shown in the specification,

is W_jCenter of cluster, m_jThe number of samples for cluster number j; sgn_ijIs a sign function;

5.2) calculating the minimum distance square sum of each sample in the objective function matrix Del to each cluster center by using the formula (5), and writing the minimum distance square sum into a column vector

Writing the least distance square sum corresponding to the cluster number into the column vector of the cluster number

5.3) judging the column vector of the cluster number

And cluster number column vector

Whether a difference exists or not is judged, if not, the single sample updating iteration convergence is judged, and if yes, the step 5.4) is carried out;

5.4) updating the column vector

Namely:

in the formula (I), the compound is shown in the specification,

representing the aggregation of the last iterationA sample number column vector in which the class number changes; min (·) represents the smallest element in the vector, mod (n) represents the modulo operation; in updating the column vector using equation (10)

Time of flight

Are all single element vectors;

calculating the number of movements and applying new column vectors

Assigning to the column vector of the last iteration

Thereby obtaining the moving cluster number single element column vector of the current iteration and the last iteration

Namely:

5.5) updating the objective function value E and the clustering number column vector

Number of clustered samples m_jCluster center

Cluster number vector

And returning to the step 5.1);

objective function value E, cluster number column vector

Respectively as follows:

number of clustered samples m_jAnd a cluster center

Respectively as follows:

cluster number vector with varying number of samples in a cluster

As follows:

6) judging whether various samples are empty sets or not, and calculating a target function matrix from each sample to each clustering center

Thereby obtaining the column vector in the objective function matrix

Namely:

in the formula, id_iRepresents the cluster number to which the sample belongs; d (i + (id)_i-1) · n) denotes the i + (id) th in the objective function matrix D_i-1) n elements;

calculating to obtain accumulated column vector according to the column vector

And an objective function

Accumulating column vectors

As follows:

finishing one clustering iteration, and repeating the steps 1) to 6) until all the clustering iterations are traversed

Comparing the objective function values of rep clustering iterations to obtain the optimal clustering of the clustering number k;

7) calculating a difference cost function of the clustering number k according to the formula (3), and repeating the steps 1) to 6) until all clustering numbers k are traversed to be 1,2, …, n; comparing the clustering number k with 1,2, …, n iteration difference degree cost function to obtain the optimal clustering number, clustering center and corresponding classification;

8) using a formula (18) to perform clustering on the samples under the optimal clustering number to obtain the corresponding straight line in the original measurement space;

the slope a and the intercept b of the line obtained by inverse mapping are respectively as follows:

in the formula, ρ₀、ρ_π/2And ρ_πAnd represents an angle ρ corresponding to θ ═ 0, π/2, and π/2.

5. The system for selecting the target for identifying anti-ship missile formation based on Hough transform and optimized K-means clustering according to claim 1, wherein the target situation model establishes a planar rectangular coordinate system by taking the queue heading of a target indication stage as the positive direction of a Z axis and the right-hand direction perpendicular to the Z axis as the positive direction of an X axis, and marks out the formation queue in the planar rectangular coordinate system; the formation queue comprises a reference warship J, a queue line, a queue course gamma, a formation interval D, a neat angle alpha and a queue angle beta;

the queue line refers to a connecting line of points where all ships are located in the queue from the reference ship;

the queue course gamma refers to an included angle between a ship bow stern line of the reference ship and the due north direction;

the flush angle alpha refers to an included angle between the ship bow and stern lines and the queue line of other ships;

the queue angle beta is 180-alpha, which means the included angle between the ship bow and stern line and the queue line of the reference ship.

6. The system for selecting the identification target of the anti-ship missile formation based on the Hough transform and the optimized K-means clustering as claimed in claim 5, wherein the coordinates of each ship in the measurement space and the coordinates of the reference ship comprise the following three situations according to different formation profiles of the target formation:

situation one), when the formation contour of the target formation is V-shaped formation, recording that the reference ship is a naval ship at the joint of two wings of the V-shaped formation, and the included angle of the two wings is the sum of the alignment angles of the wings; the queue angles of the left wing and the right wing are both beta, the queue course is gamma-0 DEG, and the coordinate of the reference ship is (J)_X,J_Z) The total number of the ships in the formation is T, and the coordinates (X) of each ship in the V-shaped formation in the measurement space_n,Z_n) As follows:

left wing:

right wing:

wherein n is 1,2,3, …, T;

reference ship coordinate (J)_X,J_Z) As follows:

wherein, (X, Z) is the intersection point coordinate of the two wing queue lines;

case two) when the formation contour of the target formation is parallel formation, the coordinates (X) of each naval vessel in the measuring space_n,Z_n) As follows:

reference ship coordinate (J)_X,J_Z) As follows:

(J_X,J_Z)＝(X₁,Z₁) (23)

situation three) when the formation contour of the target formation is the annular formation, the coordinates (X) of each naval vessel in the measurement space of the horizontal queue_n,Z_n) As follows:

coordinates (X) of each naval vessel in the measurement space in the vertical queue_n,Z_n) As follows:

reference ship coordinate (J)_X,J_Z) As follows:

7. the system for selecting the target for identifying the anti-ship guided missile formation based on the Hough transform and the optimized K-means clustering, according to claim 1, is characterized in that before the guided missiles are launched to the guided missile end-guided radar to be started, if the formation turns around a certain rotation point, the ship coordinates (X) of the target formation ship after the guided missile end-guided radar is started_n′,Z_n') as follows:

X_n′＝(X_n-X₀)·cos q-(Z_n-Z₀)·sin q+X₀ (27)

Z_n′＝(X_n-X₀)·sin q+(Z_n-Z₀)·cos q+Z₀

in the formula (X)₀,Z₀) Is the coordinate of the rotation center point; q is a rotation angle.

8. The system for selecting the anti-ship guided missile formation recognition target based on the Hough transform and the optimized K-means clustering, according to claim 1, is characterized in that before the guided missile is launched to start the guided missile end-guided radar, if the target formation distance changes, the ship coordinates (X) of the target formation ship after the guided missile end-guided radar is started_n′,Z_n') as follows:

or, target formation interval (D)_h′,Z_z') as follows:

in the formula, when k₁、k₂When the element belongs to (0,1), the formation space is reduced; k is a radical of₁、k₂E (1, ∞) is the queue pitch amplification. When k is₁＝k₂The target formation is scaled equally.

9. The system for selecting the anti-ship guided missile formation recognition target based on the Hough transform and the optimized K-means clustering, according to claim 1, is characterized in that before guided missiles are launched to start a guided missile end-guided radar, if a plurality of false targets exist in the target formation, the coordinates (C) of the false targets after the guided missile end-guided radar is started are determined_X1,C_Z1) False target coordinates (C)_X2,C_Z2) False target coordinates (C)_X3,C_Z3) False target coordinates (C)_X4,C_Z4) As follows:

in the formula, R is the distance between the false target and the naval vessel; gamma ray_D([-180°,0°]∪[0°,180°]) The direction of the incoming missile; epsilon and delta are angles between a connecting line of the false target and the naval vessel and the incoming direction of the missile; reference ship coordinate (J)_X,J_Z) Is a true target.

Images