CN108334893B - Underwater slender body feature identification method based on multi-bright-spot cluster analysis - Google Patents

Underwater slender body feature identification method based on multi-bright-spot cluster analysis Download PDF

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CN108334893B
CN108334893B CN201711487435.3A CN201711487435A CN108334893B CN 108334893 B CN108334893 B CN 108334893B CN 201711487435 A CN201711487435 A CN 201711487435A CN 108334893 B CN108334893 B CN 108334893B
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刘宇
朱晓萌
马晓川
鄢社锋
侯朝焕
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Abstract

The invention relates to a method for identifying characteristics of an underwater slender body by multi-bright-point cluster analysis, which comprises the following steps: calculating the length and the movement direction of the underwater slender body target by using the spatial distribution of the bright spots of the underwater slender body target; and (4) combining a cluster analysis method, obtaining a cluster center of the target point by adopting an expected maximum EM algorithm under a constraint condition, and estimating the course and the length of the target according to the cluster center. The invention adopts an EM algorithm with constraint conditions, and estimates the advancing direction (course) and the scale of the underwater target with the shape of the slender body by utilizing the information of a plurality of bright spots; and the method has the characteristics of simplicity, feasibility and reliable work.

Description

Underwater slender body feature identification method based on multi-bright-spot cluster analysis
Technical Field
The invention relates to the field of underwater vehicles, in particular to an underwater slender body feature identification method based on multi-bright-point cluster analysis
Background
The underwater target feature recognition is one of the important research points in the sonar signal processing field, and the main purpose of the underwater target feature recognition is to acquire underwater target characteristics including position information, speed, advancing direction, size and the like. For the detection of underwater objects, sonar is generally used. The tracking algorithm of the underwater maneuvering target calculates the relative distance, direction and relative speed of the target according to the echo characteristics of the target, and then estimates the motion characteristics of the target according to a target motion equation and a filtering algorithm. However, due to the particularity of the underwater environment, the estimation error of the distance, the direction and the radial speed of the underwater target through the sonar echo is large; meanwhile, the propagation speed of sound in water is only about 1500m/s, so that echo data available in the whole tracking process are less, and the target feature estimation accuracy is not high. At the present stage, underwater maneuvering target tracking is still a problem to be further studied.
The development of the modern Autonomous Underwater Vehicle (AUV) technology provides another idea for tracking underwater targets. The AUV can continuously track the underwater target through self motion, and the problem of less echo data is solved to a certain extent; on the other hand, by carrying out the approaching reconnaissance on the target, the near field information of the target can be obtained, and the accuracy of target feature identification is favorably improved. However, tracking underwater targets by using kalman filtering (or extended kalman filtering, particle filtering, etc.) on the AUV platform requires accurate navigation (position, speed, etc.) information of the AUV itself, which is generally difficult for the AUV platform. That is, the lack of high-precision navigation information limits the accuracy of target tracking by the AUV platform. Particularly when underwater targets are maneuvered, it is more difficult to track them with high accuracy, and usually a certain data accumulation is required, which causes a large degree of estimation lag. How to provide a high-precision and effective target feature identification method aiming at the characteristics of underwater targets becomes an urgent need in the field of underwater target tracking.
In recent years, clustering analysis methods have been widely used in medical image processing and radar signal processing. An improved algorithm based on fuzzy mean clustering is provided for medical images, and the three-dimensional structure of the skeleton can be reconstructed clearly. Fuzzy clustering analysis-based methods have also been applied to passive radar target identification and extraction of radar target three-dimensional scattering centers.
Typically, the large underwater targets are shaped substantially as similarly ellipsoidal elongated bodies of revolution. Although the topography of the target has some effect on the bright spot distribution, this effect can be neglected as long as the aspect ratio of the target is rather large. At this time, the width of the target has no effect on analyzing the bright point distribution. Thus, for a large scale target having the characteristics of an elongated body, ignoring the target width, the target is considered to be a line segment whose bright spots all have their reflection centers collinear — all lying on the target longitudinal axis.
The K-means clustering algorithm (K-means) is a widely used clustering algorithm, which aims at assigning observations to K different classes. The algorithm is computationally efficient and can quickly converge to a local optimum. One of the disadvantages of the K-means clustering algorithm is the poor robustness to outliers. The underwater environment is complex, and the measurement noise is non-Gaussian and unknown, so that outliers can often appear, and the data acquired in the underwater environment is not suitable for a K-means algorithm.
The expectation-maximum (EM) clustering algorithm is an algorithm that finds the maximum likelihood estimate or maximum a posteriori probability of a parameter in a probabilistic model, and its main idea is to establish the expectation bound of the log-likelihood estimate of the complete data by iteration and then maximize the log-likelihood function of the incomplete data.
The expectation-maximum (EM) clustering algorithm differs from the K-means clustering algorithm in that the EM algorithm is a soft-distribution clustering based on a posterior probability, whereas the K-means algorithm is a hard-distribution clustering of data points. To some extent, the K-means clustering algorithm can be considered as an EM algorithm in the extreme case. However, the EM algorithm is good in robustness, and can conveniently process the clustering analysis problem with constraints.
Disclosure of Invention
The invention aims to provide an estimation algorithm for the underwater slender body target reflection center by the clustering problem with the constraint characteristic aiming at the characteristics.
In order to achieve the above object, the present invention provides a method for identifying characteristics of an underwater elongated body by multi-bright-point cluster analysis, the method comprising the steps of: calculating the length and the movement direction of the underwater slender body target by using the spatial distribution of the bright spots of the underwater slender body target; and (4) combining a cluster analysis method, obtaining a cluster center of the target point by adopting an expected maximum EM algorithm under a constraint condition, and estimating the course and the length of the target according to the cluster center.
Preferably, the method is combined with a cluster analysis method, an expected maximum EM algorithm under a constraint condition is adopted to obtain a cluster center of a target point, and the heading and the length of the target can be estimated according to the cluster center, and the method comprises the following steps: obtaining an initial value by solving an unconstrained EM clustering problem; estimating a posterior probability by calculation; when the clustering center keeps a fixed value, updating the collinear coefficient; estimating a clustering center according to the collinear coefficient; and calculating the course and the length of the target according to the initial value, the posterior probability, the collinear coefficient and the clustering center parameter.
Preferably, the initial value is calculated by the following formula:
Figure GDA0002839581680000031
wherein, muk0Is an initial value, NkIs the effective spot number in spot center k.
Preferably, the posterior probability is calculated by the following formula:
Figure GDA0002839581680000032
wherein, gamma (Z)nk) To a posterior probability, pikIs the posterior probability of the kth cluster center.
Preferably, said collinear coefficients present a constant t and a vector C; wherein, the vector C is obtained by the formula:
Figure GDA0002839581680000033
wherein, M ═ mu1,…μk],
Figure GDA0002839581680000034
Then, normalize C ← C/| C | Y survival to C2Ensure | | C | non-conducting phosphor 21 is ═ 1; the constant t is obtained by the following formula.
Figure GDA0002839581680000041
Preferably, the step of estimating the cluster center from the collinearity coefficients comprises: constructing a Lagrangian function of the log-likelihood function:
Figure GDA0002839581680000042
l to mukCalculating the partial derivatives, and making them equal to 0, then having,
Figure GDA0002839581680000043
the two sides of the above formula are simultaneously multiplied by sigmakThen, left-riding CTAnd use of CTμkWhen + t is 0, it is available,
Figure GDA0002839581680000044
thus, the cluster center is:
Figure GDA0002839581680000045
wherein N iskIs the effective spot number in spot center k.
Preferably, the heading and length of the target are obtained by the following formula:
φ＝±atan2(C1,C2),
Figure GDA0002839581680000046
wherein C ═ C1 C2]TVector C represents the slope of the line and t represents the position of the line in the plane.
The invention has the following advantages in three aspects:
1. the self position information of the underwater vehicle is not needed, the high-precision course estimation is carried out on the target, and the estimation result is prevented from being influenced by the lower positioning precision of the underwater vehicle.
2. The target maneuvering model is not required to be introduced, and estimation delay is not generated when the target maneuvers, because the course estimation of the method is based on the instantaneous result of the current bright point distribution and does not involve any previous information.
3. The method provided by the invention can estimate the length of the target.
The method has the advantages that the EM algorithm with the constraint condition is adopted, and the advancing direction (course) and the scale of the underwater target with the shape of the slender body are estimated by utilizing the information of the multiple bright spots; and the method has the characteristics of simplicity, feasibility and reliable work.
Drawings
Fig. 1 is a schematic flow chart of a method for identifying characteristics of an underwater elongated body by multi-bright-spot cluster analysis according to an embodiment of the present invention;
FIG. 2 is a schematic view of a bright spot and a reflection center of an underwater elongated body scale target;
FIG. 3 is a diagram of cluster center estimates and their covariance;
FIG. 4 is a schematic view of the underwater target and sonar position;
FIG. 5 shows the scale and heading estimation error (σ) for different distances and viewing anglesR＝10m，σα＝0.1°)。
Detailed Description
Other features, characteristics and advantages of the present invention will become more apparent from the following detailed description of embodiments of the present invention, which is to be read in connection with the accompanying drawings.
For a large scale target with the characteristics of an elongated body, the target is regarded as a line segment under the condition of neglecting the width of the target, and all reflection centers of bright spots of the target are collinear, namely, the bright spots are positioned on the longitudinal axis of the target. The method focuses on the estimation of the reflection center of the large target by the clustering problem with the constraint characteristic.
At least 2 bright spots are needed in order to determine the target motion characteristics of the underwater elongated body, so that a longitudinal axis baseline of the underwater target can be determined. The number of the bright spots is increased, so that on one hand, constraint conditions can be increased, and the estimation has more robustness; on the other hand, as the number of the bright spots increases, if the distance between the bright spots is too small (even smaller than the width of the target), the target width is not negligible, and the constraint condition of the co-linearity of the bright spots is no longer satisfied. Therefore, the number of the bright spots needs to be comprehensively considered. From the practical physical significance, the bright spots are set to be three, namely the head part, the enclosing shell and the tail part, and the method is a better processing method.
For large scale underwater moving objects with elongated shapes, incident sound waves can be reflected by the hull and the internal cabin, but most of the reflected energy comes from the head, hull, tail of the object where the incident angle varies greatly. Many researches show that the echo of a large underwater target mainly consists of a moving bright spot formed by surface mirror reflection and a fixed bright spot formed by corner angle reflection. Whether moving or fixed, they correspond to a certain location on the target. The bright spot model of the target can be equivalent to three rigid balls, namely three bright spots which respectively represent the head, the surrounding shell and the tail of the underwater moving target. Different radii of the rigid sphere represent different target strengths.
In combination with both practical needs and theoretical considerations, the present application assumes that a large target includes three scattering centers, a head, a mantle and a tail, respectively, as shown in fig. 2.
The underwater environment is complex, wild points are likely to appear in a plurality of bright points of a target, and a clustering algorithm with high robustness needs to be selected. According to the above mentioned concept, all bright spot centers mu of the underwater targetkThe direction of advance of the object is strictly defined. From the two aspects of algorithm robustness and convenience in processing constraint conditions, the EM algorithm is more suitable for processing and analyzing underwater target bright spots than the K-mean algorithm.
For underwater targets having an elongated body, if the effect of water flow is neglected, the longitudinal axis direction can be considered as the target heading direction, and the target length can be estimated by the longest distance between the reflection centers.
The distribution of the bright spots in space is represented by a mixed Gaussian model composed of K Gaussian components, each Gaussian distribution represents the distribution of bright spots at the periphery of a reflection center,
Figure GDA0002839581680000061
(1) wherein x ∈ R2，N(x|μk,Σk) Gaussian distribution in 2-dimensional space:
Figure GDA0002839581680000062
wherein, mukIs a 2-dimensional clustering center, sigmakIs a 2 x 2 dimensional covariance matrix; pikThe posterior probability of the k-th clustering center is expressed to satisfy
Figure GDA0002839581680000063
Furthermore, for large scale underwater targets with elongated bodies, as mentioned before, their cluster centers are collinear, i.e. there is a constant t and a vector C ∈ R2Satisfies the conditions
||C||21 and CTμk＝t k＝1…K (4)
The target tracking problem translates into: when the collinearity constraint condition C is satisfiedTμkWhen t, K is 1 … K, the parameters are estimated
Figure GDA0002839581680000071
And further estimating the target course and scale.
Fig. 1 is a schematic flow chart of a method for identifying characteristics of an underwater elongated body by multi-bright-spot cluster analysis according to an embodiment of the present invention. As shown in fig. 1
Mu can be obtained by solving the unconstrained EM clustering problemk(K ═ 1 … K) initial values, the derivation process is described briefly as follows:
the log-likelihood function of the bright spot is as follows:
Figure GDA0002839581680000072
the above formula is to mukThe partial derivatives, can be written as:
Figure GDA0002839581680000073
wherein the content of the first and second substances,
Figure GDA0002839581680000074
if the above formula is made to be equal to 0, then,
Figure GDA0002839581680000075
thus, μ can be obtainedkInitial value of (a):
Figure GDA0002839581680000076
at this time, NkIs the effective spot number in spot center k.
Figure GDA0002839581680000081
πkThe posterior probability of the kth clustering center;
log-likelihood function value pair pikThe partial derivatives can be written as:
Figure GDA0002839581680000082
by using constraints
Figure GDA0002839581680000083
A lagrangian function of the log-likelihood function is constructed,
Figure GDA0002839581680000084
then, suppose
Figure GDA0002839581680000085
We obtained the following formula,
Figure GDA0002839581680000086
therefore, the temperature of the molten metal is controlled,
Figure GDA0002839581680000087
πkthe posterior probability of the kth clustering center;
log-likelihood function value pair
Figure GDA0002839581680000088
Making a partial derivative, and assuming
Figure GDA0002839581680000089
It is possible to obtain,
Figure GDA00028395816800000810
the collinear constraint on the cluster center is not actually equal to the linear constraint, so that the cluster analysis problem with the collinear constraint is difficult to solve an analytic solution. And then, solving the clustering analysis problem with the collinearity constraint by adopting an iterative algorithm similar to an EM (effective magnetic field) algorithm. The estimation process can be divided into the following two steps:
step I:
the collinear coefficients C and t are updated while the cluster center remains at a fixed value.
Assuming that all K cluster centers are collinear, there is a constant t and a vector C, such that the following equation holds:
CTμk+t＝0,||C2＝1，k＝1…K. (16)
condition CTμk+ t ═ 0 is equivalent to:
CTμk+t～N(0,σ2), (17)
where σ is an arbitrarily small position constant. Thus, the vector C can be obtained by a least squares method, as follows:
Figure GDA0002839581680000091
wherein, M ═ mu1,…μk],
Figure GDA0002839581680000092
Then, normalize C ← C/| C | Y survival to C2Ensure | | C | non-conducting phosphor 21. Finally, t can be obtained using the following equation:
Figure GDA0002839581680000093
step II:
assuming C and t are known, the cluster center μ can be estimatedk. Constructing a Lagrangian function of the log-likelihood function:
Figure GDA0002839581680000094
l to mukCalculating the partial derivatives, and making them equal to 0, then having,
Figure GDA0002839581680000095
the two sides of the above formula are simultaneously multiplied by sigmakThen, left-riding CTAnd use of CTμkWhen + t is 0, it is available,
Figure GDA0002839581680000096
thus, the cluster center is:
Figure GDA0002839581680000101
wherein N iskIs defined by formula (10).
Summary of the Algorithm
Summary the algorithm herein is as follows:
using conventional EM algorithms, initial values are obtained, including μ, Σ, π.
The posterior probability is estimated by equation (6).
The parameters C, t, μ are estimated using equations (18), (19), (9), (15), (14), respectivelyk,Σk,πk。
And repeating the steps of 2-3 until the algorithm converges.
After the parameters are obtained, the target advancing direction phi and the target length l can be obtained by the following equation calculation,
φ＝±atan2(C1,C2), (24)
Figure GDA0002839581680000102
wherein C ═ C1 C2]T
In the above algorithm, the vector C represents the slope of the straight line, t represents the position of the straight line on the plane, and the formula (24) is a formula for obtaining the heading according to the slope of the straight line.
The target course obtained by the embodiment of the application may have 180-degree ambiguity, that is: by simply using the spatial distribution information of the bright spots, whether the target sails towards the sonar or away from the sonar cannot be distinguished. In this case, the true heading of the target may be determined from the distance or radial velocity information. It should be noted, however, that this is different from the algorithm that uses information of the distance and radial velocity measured multiple times for kalman filtering.
The method adopts an EM algorithm with constraint conditions, utilizes multi-bright-spot information, and estimates the advancing direction (course) and the scale of the underwater target with the shape of the slender body; and the method has the characteristics of simplicity, feasibility and reliable work.
Only the embodiments of the invention have been described in the specification. Although the embodiments of the present invention have been described with reference to the accompanying drawings, those skilled in the art will be able to make various changes and modifications within the scope of the appended claims.
Algorithm validation
The implementation example is as follows: the target length is 120m, assuming there are three bright spot centers, target head, target tail and hull.
All bright spots, estimated cluster centers, heading (heading) and length, and covariance (4 standard deviations) for each cluster center are shown in fig. 3. The bright spots and cluster centers in the figure are indicated by dots and "+" respectively. As shown, the algorithm proposed by the present invention ensures that the cluster centers are in a collinear position. The estimated target length is 118m compared to the actual target length 120 m. In addition, as can be easily found from the figure, the discrete value has almost no influence on the estimation result, and the algorithm has better robustness.
To further validate the algorithm presented herein, a Monte Carlo simulation was performed. Assuming a target length of 100m and a heading of 0 degrees, the positions of the centers of the three bright spots are the head, the hull at the length from the head 1/3, and the tail, respectively. The sonar is at a distance R from the tail and at an angle alpha to the line of sight, as shown in fig. 4. The noise of distance measurement (distance measurement) and direction measurement (direction finding) of sonar system follows zero mean value Gaussian distribution, and the standard deviation is sigmaRAnd σαFor targets at different positions, the course and the length of the targets are calculated according to the algorithm provided by the text, the error of the algorithm is analyzed, and the error result is the average value of 1000 Monte Carlo simulation results.
Fig. 5 is a simulation of target feature estimation in the case where the sonar system has high direction-finding accuracy. The simulation conditions were as follows:
measuring the standard deviation of 10 m;
standard deviation of direction measurement is 0.1 degree;
the distance is 200 m-800 m;
the visual angle is 10-90 degrees.
As can be seen from the figure, the closer the underwater target is, the more accurate the estimation of the heading is; when the line-of-sight angle is less than 70 degrees, the relation between the estimation accuracy of the target scale and the distance is not large, and only when the line-of-sight angle is greater than 70 degrees, the accuracy of scale estimation is seriously influenced by the target distance. This shows that when the sonar direction-finding accuracy is high and the target is not in the normal direction of the observation point, the algorithm has little relation between the accuracy of scale estimation and the distance and distance measurement accuracy.
It will be obvious that many variations of the invention described herein are possible without departing from the true spirit and scope of the invention. Accordingly, all changes which would be obvious to one skilled in the art are intended to be included within the scope of this invention as defined by the appended claims. The scope of the invention is only limited by the claims.

Claims (4)

1. A method for identifying the characteristics of an underwater slender body by multi-bright-spot cluster analysis is characterized in that,
calculating the length and the movement direction of the underwater slender body target by using the spatial distribution of the bright spots of the underwater slender body target;
combining a cluster analysis method, obtaining a cluster center of a target point by adopting an expected maximum EM algorithm under a constraint condition, and estimating the course and the length of the target according to the cluster center;
the method for obtaining the clustering center of the target point by adopting the expected maximum EM algorithm under the constraint condition and estimating the course and the length of the target according to the clustering center comprises the following steps: obtaining an initial value by solving an unconstrained EM clustering problem; estimating a posterior probability by calculation; when the clustering center keeps a fixed value, updating the collinear coefficient; estimating a clustering center according to the collinear coefficient; calculating the course and the length of the target according to the initial value, the posterior probability, the collinear coefficient and the clustering center parameter; wherein updating the co-linearity coefficients when the cluster center maintains a fixed value comprises:
the collinear coefficient has a constant t and a vector C; wherein, the vector C is obtained by the following formula:
Figure FDA0002839581670000011
wherein the content of the first and second substances,
Figure FDA0002839581670000012
then, normalize C ← C/| C | Y survival to C2Ensure | | C | non-conducting phosphor21 is ═ 1; then the constant t is obtained by the following formula,
Figure FDA0002839581670000013
wherein, mukThe vector C represents the slope of a straight line, and t represents the position of the straight line on a plane;
the estimating the cluster center from the collinearity coefficients comprises:
constructing a Lagrangian function of the log-likelihood function:
Figure FDA0002839581670000014
wherein, the collinearity constraint condition is satisfied
Figure FDA0002839581670000019
In the case of (2), the parameter is estimated
Figure FDA0002839581670000015
L to mukCalculating the partial derivatives, and making them equal to 0, then having,
Figure FDA0002839581670000016
the two sides of the above formula are simultaneously multiplied by sigmakThen, left-riding CTAnd use of
Figure FDA00028395816700000110
It is possible to obtain,
Figure FDA0002839581670000017
γ(Znk) To a posterior probability, sigmakRepresenting a 2 x 2 dimensional covariance matrix;
thus, the cluster center is:
Figure FDA0002839581670000018
wherein N iskIs the effective spot number in spot center k.
2. The method of claim 1, wherein the initial value is obtained by calculating according to the following formula:
Figure FDA0002839581670000021
wherein, muk0Is an initial value, NkIs the effective spot number in spot center k.
3. The method of claim 1, wherein the posterior probability is calculated by the following formula:
Figure FDA0002839581670000022
wherein, gamma (Z)nk) To a posterior probability, pikIs the posterior probability of the kth cluster center.
4. The method of claim 1, wherein the heading and length of the target are obtained by the following formula:
φ＝±atan2(C1,C2),
Figure FDA0002839581670000023
wherein C ═ C1 C2]TVector C represents the slope of the line and t represents the position of the line in the plane.
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