CN114594463A - Sea surface small target feature detection method based on combined convex hull - Google Patents

Abstract

The invention discloses a sea surface small target characteristic detection method based on a combined convex hull, which comprises the following steps: acquiring an observation vector; calculating a Doppler magnitude spectrum for the observation vector, and performing whitening pretreatment; extracting three characteristics in a time domain and a frequency domain; constructing three-dimensional test statistics; designing a non-convex judgment region; and judging the detection result. The invention provides three new characteristics, and makes full use of the differences of clutter and targets in time domain and frequency domain. Meanwhile, a large amount of calculation cost of the time-frequency domain is avoided, and the performance matched with the characteristics of the time-frequency domain can be obtained; a combined convex hull algorithm is provided, and a 3D non-convex decision area is realized. Compared with the original convex hull judgment area, the volume of the non-convex judgment area is smaller, so that higher detection performance can be obtained; the invention improves the detection probability of the small sea-surface target under the condition of low signal-to-clutter ratio and provides a new idea for designing a non-convex decision device.

Description

Sea surface small target feature detection method based on combined convex hull

Technical Field

The invention relates to the technical field of radar signal processing, in particular to a sea surface small target characteristic detection method based on a combined convex hull.

Background

For high resolution ocean radars, it is a long and difficult task to achieve detection of small sea-surface targets such as ice floes, boats, frogs, and airplane debris at small ground angles. The main reason for this is that small targets tend to have a slow moving speed and a small signal-to-noise ratio (SCR), and in this case, the detection of the sea radar often has the problems of low detection probability and many false alarm points. Therefore, the detection of small targets under the background of high-resolution sea clutter is always a hotspot and difficulty for researchers inside and outside the sea.

Feature-based detection has been considered to be an effective method to compress the difference between the sea clutter and the target-containing echoes into features, which are then detected in a feature space. As the number of features in combination increases, there is some performance improvement in the detector performance. However, more feature combinations bring difficulties to the design of the decision region, and also take more time to be spent. The combination of the three characteristics is a compromise choice considering the performance improvement and the calculation cost. The difficulty of the detector is therefore mainly the extraction of valid features and the acquisition of three-dimensional (3D) false alarm controllable decision areas. With respect to the first difficulty, under long-term observation, many methods have been developed to extract features of different domains. From the time domain perspective, a Relative Average Amplitude (RAA) is proposed by scholars to describe the difference between clutter and target in power. The learners propose a fractal Hurst index to describe the fractal characteristics of the sea clutter time sequence. From a frequency domain perspective, researchers use Relative Doppler Peak Height (RDPH) and Relative Vector Entropy (RVE) to reflect geometric features. These two features plus the RAA form a typical three feature based detector, opening up the feature detection framework. From the perspective of the time-frequency domain, a learner extracts three time-frequency features from the intensity and geometric attributes of the time-frequency image. In general, a two-dimensional time-frequency domain can obtain more information than a one-dimensional time-frequency domain, but the two-dimensional time-frequency domain is obviously complex in computation. For the second difficulty, the fast convex hull algorithm is the most typical 3D single classifier algorithm, and can obtain a decision region with controllable false alarm. Subsequently, some researchers have proposed an algorithm of one-class support vector machine (OSVM), which can obtain a non-convex decision region, thereby improving performance. However, in order to control the false alarm rate, the classifier needs to search a large number of parameters and the false alarm control has a limited accuracy. Therefore, how to design a non-convex algorithm with a precisely controllable false alarm is the focus of research.

Disclosure of Invention

The purpose of the invention is as follows: in order to overcome the defects in the background art, the invention discloses a sea surface small target feature detection method based on a combined convex hull, which can fully utilize the characteristics of time domain and frequency domain through three newly extracted features, integrates the characteristic of accurately controlling false alarm by an original convex hull through a combined convex hull algorithm, and simultaneously obtains a non-convex judgment region to realize the stable detection of the sea surface small target under different detection environments.

The technical scheme is as follows: the invention discloses a sea surface small target characteristic detection method based on a combined convex hull, which comprises the following steps:

s1, assuming that the radar receives N consecutive pulses in a range unit, the N pulses form an observation vector z ═ z (1), z (2),.., z (N)]^TCalled the cell to be detected CUT; meanwhile, obtaining observation vectors z of P reference units around CUT_pP-1, 2.., P, constructing a target detection problem;

s2, comparing the CUT observation vector z in S1 with the observation vector z of the reference unit_pConverting the frequency domain to obtain a Doppler amplitude spectrum by calculation; whitening processing is carried out on the frequency spectrum vector of the CUT by utilizing the frequency spectrum vector of the reference unit to obtain a whitened frequency spectrum;

s3, in the time domain, carrying out segmentation processing on the observation vector in the S1, setting the average amplitude value of each segment of pulse echo as a weighting factor, and calculating the relative weighted average amplitude;

in a frequency domain, for the frequency spectrum and the whitening frequency spectrum in S2, respectively extracting two characteristics of a relative variation coefficient and a measured whitening peak height ratio, and measuring the geometric difference of the frequency spectrum;

s4, constructing a three-dimensional feature space by using the three features extracted in S3 to form a feature vector xi which is used as a test statistic;

s5, under the condition of a given false alarm rate, firstly, dividing a sea clutter training sample into K clusters by adopting a clustering algorithm, then, carrying out a convex hull algorithm on each cluster, and finally, combining the K convex hulls to form a final non-convex judgment region omega;

s6, calculating the position of the test statistic xi and the position of the judgment region omega, and judging whether a target exists in the observation vector z:

if xi is equal to omega, the observation vector z is shown to contain the target echo;

if it is not

It indicates that the observation vector z does not contain the target echo.

In S1, the target detection problem is classified as the following binary hypothesis testing problem:

wherein c represents a sea clutter vector, s represents a target vector, c_pIndicating that the p-th element is a sea clutter vector, H₀Suppose that the observation vector contains only sea clutter, H₁Assuming that the observation vector contains a target;

the essence of detection is to judge which class the CUT observation vector belongs to, and consider the detection problem as a two-class problem, H₀Assume first class, H₁Assume the second class.

Further, for the CUT observation vector z in S1, the calculated doppler magnitude spectrum is:

wherein f represents a frequency variable, f_rIs the pulse repetition frequency, exp (.) represents an exponential function;

and whitening the frequency spectrum of the CUT, wherein the whitening spectrum WS is calculated according to the following formula:

wherein Z is_p(f) Representing the doppler magnitude spectrum of the p-th reference cell.

Further, the method comprises the following steps of extracting time domain features:

based on the assumption that the sea clutter and the target short time sequence are unchanged, the observation vector in S1 is firstly divided into Q segments

Where L denotes the number of pulses per segment, and L × Q ═ N is satisfied, and the weighted average amplitude WAA is defined as:

wherein, ω is_qA weighting factor representing the q-th segment, the relative weighted average amplitude RWAA being defined as:

extracting frequency domain features:

in order to measure the geometric difference between the sea clutter and the target echo-containing frequency spectrum, a relative variation coefficient RCV is defined as:

wherein, CV is a variation coefficient CV for describing a difference of the spectral fluctuation, and is calculated according to the following formula:

for the whitened spectrum in S2, the whitening peak height ratio WPHR is defined as:

where # Θ represents the operator for the number of elements in the set Θ, given by:

Θ＝[-f_r/2,f_max-Δ]∪[f_max+Δ,f_r/2]

wherein f is_maxIs the frequency value with the maximum whitened spectrum, Δ is f_maxThe surrounding protected area.

Further, the three features extracted in S3, RWAA, RCV, WPHR, are respectively marked as ξ₁,ξ₂,ξ₃(ii) a With each feature as a dimension, a three-dimensional feature space is constructed, and then the CUT observation vector in S1 is converted into a 3D feature vector:

the feature amount is used as a test statistic to be discriminated.

Further, S5 specifically includes the following steps:

s5.1, obtaining a large number of sea clutter samples by a radar, constructing a 3D training sample set according to S2-S4, and supposing that a false alarm controllable convex decision area is obtained according to an original convex hull algorithm, wherein the area comprises A samples;

s5.2 in the sample set A, randomly selecting K samples as clustering centroids, and recording the clustering centroids as

The remaining samples are classified into K classes according to the criterion of Euclidean distance closest to the cluster centroid

S5.3 in each cluster, calculating a new clustering centroid

Wherein, N_kIs the number of samples in the kth cluster, all samples are redistributed by the above equation;

s5.4 repeats step S5.3 until all samples in a have no cluster transform, the set a is fully divided by K clusters, i.e. a ═ a₁∪A₂∪...∪A_K；

S5.5 in the kth class, the convex hull passes through G_kThe polyhedron formed by the triangular surfaces surrounds N_kWrapping K clusters by a convex hull algorithm for each sample, so that K convex hulls obtain a combined convex hull, namely a final non-convex decision region omega

Ω＝{CH(A₁)，CH(A₂)，...,CH(A_K)}

Where ch (a) denotes that a convex hull is formed for the sample set of a.

Has the advantages that: compared with the prior art, the invention has the advantages that: three new characteristics are provided, and differences of clutter and targets in a time domain and a frequency domain are fully utilized. Meanwhile, a large amount of calculation cost of the time-frequency domain is avoided, and the performance matched with the characteristics of the time-frequency domain can be obtained; a combined convex hull algorithm is provided, and a 3D non-convex decision area is realized. Compared with the original convex hull judgment area, the volume of the non-convex judgment area is smaller, so that higher detection performance can be obtained; by the method, the detection probability of the small sea-surface target under the condition of low signal-to-clutter ratio is improved, and a new idea of designing a non-convex decision device is provided.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

FIG. 2 is a histogram plot of three features in simulation 2;

FIG. 3 is a comparison graph of two decision regions in a 3D feature space in simulation 3;

FIG. 4 is a graph of the results of testing measured IPIX data in simulation 4 based on a Hurst index detector, an original three feature detector and the proposed detector of the basic inventive method.

Detailed Description

The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.

The sea surface small target feature detection method based on the combined convex hull shown in fig. 1 comprises the following steps:

step 1, obtaining observation vectors

Suppose that the radar receives N consecutive pulses in a range unit, the N pulses forming an observation vector, which is denoted z ═ z (1), z (2),.., z (N)]^T. The distance cell is called a Cell Under Test (CUT). There are P reference cells around the CUT, and their observation vectors are denoted as z_pP is 1, 2. Then, the target detection problem can be classified as the following binary hypothesis testing problem:

wherein c represents a sea clutter vector, s represents a target vector, c_pIndicating that the p-th element is a sea clutter vector. H₀Assuming that the observation vector contains only sea clutter; h₁Assume that the observation vector contains a target. The essence of the detection is to determine which class of assumptions the CUT observation vector belongs to.

Step 2, frequency domain preprocessing

2.1) calculating the Doppler magnitude spectrum of the CUT observation vector z in the step (1) as follows:

wherein f represents a frequency variable, f_rIs the pulse repetition frequency, exp (.) represents an exponential function.

2.2) carrying out whitening pretreatment on the frequency spectrum of the CUT to realize the suppression of the sea clutter. The Whitening Spectrum (WS) is calculated as follows:

wherein Z is_p(f) Representing the doppler amplitude frequency of the p-th reference cell.

Step 3, extracting three characteristics

3.1) time-Domain features

Based on the assumption that the sea clutter and the target short time sequence are unchanged, firstly, the observation vector in the step 1) is divided into Q sections

Wherein, L represents the pulse number per segment, and satisfies L multiplied by Q ═ N. Then, a Weighted Average Amplitude (WAA) is defined as:

wherein, ω is_qRepresenting the weighting factor of the q-th segment. Finally, a Relative Weighted Average Amplitude (RWAA) is defined as:

3.2) frequency domain characterization

3.2a) in order to measure the geometrical difference between the sea clutter and the spectrum containing the target echo, a Relative Coefficient of Variation (RCV) is defined as:

wherein, CV is a Coefficient of Variation (CV) for describing a difference of the spectral fluctuation, and is calculated according to the following formula:

3.2b) for the whitened spectrum in step (2.2), defining a Whitened Peak Height Ratio (WPHR) as:

where # Θ represents the operator for the number of elements in the set Θ, given by:

Θ＝[-f_r/2,f_max-Δ]∪[f_max+Δ,f_r/2]

wherein f is_maxIs the frequency value with the maximum whitened spectrum, Δ is f_maxThe surrounding protected area.

Step 4, constructing three-dimensional test statistic

Marking the three characteristics of RWAA, RCV and WPHR in the step (3) as xi respectively₁,ξ₂,ξ₃. And constructing a three-dimensional feature space by taking each feature as a dimension. Then, the CUT observation vector of step 1) is converted into a 3D feature vector:

the feature amount is used as a test statistic to be discriminated.

Step 5, designing a non-convex judgment region

In order to further minimize the convex decision region, a combined convex hull algorithm is realized through a K-means clustering algorithm, and then a non-convex decision region is constructed.

And 5.1) obtaining a large number of sea clutter samples after the radar is started, and constructing a 3D training sample set according to the steps from step 2 to step 4. Assume that a false alarm controlled convex decision region containing a number of samples a has been obtained according to the original convex hull algorithm.

5.2) in the sample set A, randomly selecting K samples as clustering centroids, and recording the clustering centroids as

The remaining samples are classified into K classes according to the criterion of euclidean distance closest to the cluster centroid:

5.3) in each cluster, a new cluster centroid is calculated:

wherein N is_kIs the number of samples in the kth cluster. All samples are then redistributed by the above equation.

5.4) repeat step (5.3) until all samples in A have no cluster transform. Finally, the set a is completely divided by K clusters, i.e. a ═ a₁∪A₂∪...∪A_K。

5.5) in the kth class, the convex hull passes through the filter_kThe polyhedron formed by the triangular surfaces surrounds N_kAnd (4) sampling. Wrapping the K clusters by a convex hull algorithm, so that the K convex hulls obtain a combined convex hull, namely a final non-convex decision region omega

Ω＝{CH(A₁)，CH(A₂)，...,CH(A_K)}

Where ch (a) denotes that a convex hull is formed for the sample set of a.

Step 6, judging the detection result

And calculating the positions of the test statistic xi and the judgment region omega, and judging whether the target exists in the CUT.

If xi e omega, it indicates that there is no target echo in the CUT,

if it is not

It indicates that the CUT contains the target echo.

The effect of the present invention will be further described with reference to the experimental results of the measured data.

This example uses a database collected in 1993 from an IPIX radar published on the web. The database is the current internationally recognized small target measured data, and the data name adopted in the experiment is 19931118_023604_ stareC0000280. The pulse repetition frequency of the X-band radar is 1000Hz, the distance resolution is 30m, the radar works in a dwell mode, and HH polarization is realized. The test target is a steel wire ball with the diameter of 1m, the signal-to-noise ratio is 4dB, and the low signal-to-noise ratio condition is achieved.

Simulation 1, a flow chart of a three feature detector based on a combined convex hull according to the method is given, as shown in fig. 1.

Simulation 2, analyzing the separation capability of three new features on sea clutter and target-containing echoes, and the result is shown in fig. 2, wherein:

FIG. 2(a) is a histogram of the RWAA features, which measure the power difference between sea clutter and target-containing echoes. This difference is more pronounced as the signal-to-noise ratio increases.

Fig. 2(b) is a histogram of the RCV feature, which measures the dissimilarity of the two echo spectrum fluctuations. Because the frequency spectrum containing the target echo contains the sea clutter, the frequency spectrum difference of the two cases is smaller under the condition of low signal-to-clutter ratio.

Fig. 2(c) is a histogram of the WPHR features, and it can be seen that the two hypotheses under WPHR are farthest apart from the center, and thus have the best feature separation capability.

The three effective characteristics are jointly used, so that the robust detection performance can be obtained under the conditions of different signal-to-noise ratios.

Simulation 3 demonstrates the acquisition of a false alarm controlled decision region, the result of which is shown in fig. 3. And (3) constructing a decision region by utilizing 10210 sea clutter samples, wherein 10 samples are false alarm points. Firstly, a sample set is divided into 3 cluster clusters through a K-means clustering algorithm, and then the cluster clusters are converted into a combined convex hull through a convex hull algorithm. It can be known from the figure that the combined convex hull algorithm can further reduce the area of the convex hull, and realize the non-convex decision area with the accurate and controllable false alarm point.

Simulation 4, verifying the detection algorithm provided by the invention, accumulating 256 pulse numbers, and setting the false alarm rate to 10^-3The results are shown in FIG. 4. The results of the detection based on the Hurst index detector, the original three feature detector and the proposed detector are included in fig. 4.

In fig. 4(a), the performance of detection based on the Hurst index is the worst, the detection probability is 0.131, and the detector cannot operate. The main reasons for the poor performance of this detector are the poor detection capability of the individual features and the severe performance loss of this detector below the second level.

In fig. 4(b), the original three-feature based detector performance is suboptimal with a detection probability of 0.469. Compared with a Hurst index detector, the performance improvement method has the key point of joint use of three features, and characteristics of a time domain and a frequency domain are mined. However, the performance of this detector is highly dependent on the signal-to-noise ratio, with a large performance penalty at low signal-to-noise ratios.

In fig. 4(c), the proposed combined convex hull based three feature detector performs optimally with a detection probability of 0.941. Compared with the Hurst index detector and the original three-feature-based detector, the performance of the proposed detector is remarkably improved under the condition of low signal-to-clutter ratio. In fact, this advantage mainly stems from three well-designed features and non-convex decision regions. Thus, the proposed detector may be employed instead of the original three-feature based detector in consideration of the actual detection environment.

Claims (6)

1. A sea surface small target feature detection method based on a combined convex hull is characterized by comprising the following steps:

s1, assuming that the radar receives N consecutive pulses in a range unit, the N pulses form an observation vector z ═ z (1), z (2),.., z (N)]^TCalled the cell to be detected CUT; meanwhile, obtaining observation vectors of P reference units around CUTz_pP ═ 1,2,. and P, construct the target detection problem;

s2, comparing the CUT observation vector z in S1 with the observation vector z of the reference unit_pConverting to a frequency domain, and calculating to obtain a Doppler amplitude spectrum; whitening processing is carried out on the frequency spectrum vector of the CUT by utilizing the frequency spectrum vector of the reference unit to obtain a whitened frequency spectrum;

s3, in the time domain, carrying out segmentation processing on the observation vector in the S1, setting the average amplitude value of each segment of pulse echo as a weighting factor, and calculating the relative weighted average amplitude;

in a frequency domain, for the frequency spectrum and the whitening frequency spectrum in S2, respectively extracting two characteristics of a relative variation coefficient and a measured whitening peak height ratio, and measuring the geometric difference of the frequency spectrum;

s4, constructing a three-dimensional feature space by using the three features extracted in S3 to form a feature vector xi which is used as a test statistic;

s5, under the condition of a given false alarm rate, firstly, dividing a sea clutter training sample into K clusters by adopting a clustering algorithm, then, carrying out a convex hull algorithm on each cluster, and finally, combining the K convex hulls to form a final non-convex judgment region omega;

s6, calculating the position of the test statistic xi and the position of the judgment region omega, and judging whether a target exists in the observation vector z:

if xi is equal to omega, the observation vector z is shown to contain the target echo;

if it is not

It indicates that the observation vector z does not contain the target echo.

2. The sea surface small target feature detection method based on the combined convex hull as claimed in claim 1, wherein: the target detection problem is classified in S1 as the following binary hypothesis testing problem:

wherein c represents a sea clutter vector, s represents a target vector, c_pIndicating that the p-th element is a sea clutter vector, H₀Suppose that the observation vector contains only sea clutter, H₁Assuming that the observation vector contains a target;

the essence of detection is to determine which class the CUT observation vector belongs to, and consider the detection problem as a two-classification problem, H₀Assume first class, H₁Assume the second class.

3. The sea surface small target feature detection method based on the combined convex hull as claimed in claim 2, characterized in that: for the CUT observation vector z in S1, the calculated doppler magnitude spectrum is:

wherein f represents a frequency variable, f_rIs the pulse repetition frequency, exp (.) represents an exponential function;

and whitening the frequency spectrum of the CUT, wherein the whitening spectrum WS is calculated according to the following formula:

wherein Z is_p(f) Representing the doppler magnitude spectrum of the p-th reference cell.

4. The sea surface small target feature detection method based on the combined convex hull as claimed in claim 3, characterized in that: the method comprises the following steps of extracting time domain features:

based on the assumption that the sea clutter and the target short time sequence are unchanged, the observation vector in S1 is firstly divided into Q segments

Where L denotes the number of pulses per segment, and L × Q ═ N is satisfied, and the weighted average amplitude WAA is defined as:

wherein, ω is_qA weighting factor representing the q-th segment, the relative weighted average amplitude RWAA being defined as:

extracting frequency domain features:

in order to measure the geometric difference between the sea clutter and the target-containing echo spectrum, a relative variation coefficient RCV is defined as:

wherein, CV is a variation coefficient CV for describing a difference of the spectral fluctuation, and is calculated according to the following formula:

for the whitened spectrum in S2, the whitening peak height ratio WPHR is defined as:

where # Θ represents the operator for the number of elements in the set Θ, given by:

Θ＝[-f_r/2,f_max-Δ]∪[f_max+Δ,f_r/2]

wherein f is_maxIs the frequency value with the maximum whitened spectrum, Δ is f_maxThe surrounding protected area.

5. The sea surface small target feature detection method based on the combined convex hull as claimed in claim 4, characterized in that: marking the three characteristics extracted in the S3, namely RWAA, RCV and WPHR as xi respectively₁,ξ₂,ξ₃(ii) a With each feature as a dimension, a three-dimensional feature space is constructed, and then the CUT observation vector in S1 is converted into a 3D feature vector:

the feature amount is used as a test statistic to be discriminated.

6. The sea surface small target feature detection method based on the combined convex hull as claimed in claim 5, wherein S5 specifically comprises the following steps:

s5.1, obtaining a large number of sea clutter samples by a radar, constructing a 3D training sample set according to S2-S4, and supposing that a false alarm controllable convex decision area is obtained according to an original convex hull algorithm, wherein the area comprises A samples;

s5.2 in the sample set A, randomly selecting K samples as clustering centroids, and recording the clustering centroids as

The remaining samples are classified into K classes according to the criterion of Euclidean distance closest to the cluster centroid

S5.3 in each cluster, calculating a new clustering centroid

Wherein N is_kIs the number of samples in the kth cluster, all samples are redistributed by the above equation;

s5.4 repeats step S5.3 until all samples in a have no cluster transform, the set a is fully divided by K clusters, i.e. a ═ a₁∪A₂∪...∪A_K；

S5.5 in the kth class, the convex hull passes through G_kThe polyhedron formed by the triangular surfaces surrounds N_kWrapping K clusters by a convex hull algorithm for each sample, so that K convex hulls obtain a combined convex hull, namely a final non-convex decision region omega

Ω＝{CH(A₁)，CH(A₂)，...,CH(A_K)}

Where ch (a) denotes convex hull formation for the sample set of a.

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