Hybrid radar emitter recognition based on rough k-means classifier and SVM
- Zhilu Wu^{1},
- Zhutian Yang^{1}Email author,
- Hongjian Sun^{2},
- Zhendong Yin^{1}Email author and
- Arumugam Nallanathan^{2}
DOI: 10.1186/1687-6180-2012-198
© Wu et al.; licensee Springer. 2012
Received: 25 November 2011
Accepted: 2 September 2012
Published: 18 September 2012
Abstract
Due to the increasing complexity of electromagnetic signals, there exists a significant challenge for recognizing radar emitter signals. In this article, a hybrid recognition approach is presented that classifies radar emitter signals by exploiting the different separability of samples. The proposed approach comprises two steps, i.e., the primary signal recognition and the advanced signal recognition. In the former step, the rough k-means classifier is proposed to cluster the samples of radar emitter signals by using the rough set theory. In the latter step, the samples within the rough boundary are used to train the support vector machine (SVM). Then SVM is used to recognize the samples in the uncertain area; therefore, the classification accuracy is improved. Simulation results show that, for recognizing radar emitter signals, the proposed hybrid recognition approach is more accurate, and has a lower time complexity than the traditional approaches.
Keywords
Emitter recognition Rough boundary Uncertain boundary Training sample Time complexityIntroduction
Radar emitter recognition is a critical function in radar electronic support system, for determining the type of radar emitter[1]. Emitter classification based on a collection of received radar signals is a subject of wide interest in both civil and military applications. For example, in battlefield surveillance applications, radar emitter classification provides an important means to detect targets employing radars, especially those from hostile forces. In civilian applications, the technology can be used to detect and identify navigation radars deployed on ships and cars used for criminal activities[2].
The recent proliferation and complexity of electromagnetic signals encountered in modern environments is greatly complicating the recognition of radar emitter signals[1]. Traditional recognition methods are becoming inefficient against this emerging issue[3]. Many new radar emitter recognition methods were proposed, e.g., intra-pulse feature analysis[4], stochastic context-free grammars analysis[1], and artificial intelligence analysis[5–8]. In particular, the artificial intelligence analysis approach attracted much attention. Among the artificial intelligence approaches, neural network and support vector machine (SVM) are widely used for the radar emitter recognition. In[6], Zhang et al. proposed a method based on rough sets theory and radial basis function (RBF) neural networks. Yin et al.[7] proposed a radar emitter recognition method using the single parameter dynamic search neural network. However, the predication accuracy of the neural network approaches is not high and the application of neural networks requires large training sets, which may be infeasible in practice. Compared to the neural network, the SVM yields higher prediction accuracy while requiring less training samples. Ren et al.[2] proposed a recognition method using fuzzy C-means clustering SVM. Lin et al. proposed to recognize radar emitter signals using the probabilistic SVM[8] and multiple SVM classifiers[9]. These proposed SVM approaches can improve the accuracy of recognition. Unfortunately, the time complexity of SVM increases rapidly with the increasing number of training samples. The classification method with high accuracy and low time complexity is becoming the focus of research.
Classifiers can be categorized into linear classifiers and nonlinear classifiers. A linear classifier can classify linear separable samples, but cannot classify linearly inseparable samples efficiently. A nonlinear classifier can classify linearly inseparable samples, nevertheless the time complexity of the nonlinear classifier will be increased when processing linearly separable samples. In practice, the radar emitter signals consist of both linearly separable samples and linearly inseparable samples, which makes classification challenging. In the traditional recognition approach, only one classifier is used; thus, it is difficult to classify all radar emitter signal samples. In this article, a hybrid recognition method based on the rough k-means theory and the SVM is proposed. To deal with the drawback of the traditional recognition approaches, we apply two classifiers to recognize linearly separable samples and linearly inseparable samples respectively. Samples are firstly recognized by the rough k-means classifier, while linearly inseparable samples are picked up and further recognized by using RBF-SVM in the advanced recognition. The simulation results show that the proposed approach can recognize radar emitter signals more accurate and has a lower time complexity when compared with the existing approaches.
The rest of the article is organized as follows. In Section ‘Basic concepts’, some basic concepts are reviewed. In Section ‘Radar emitter recognition system’, a novel radar emitter recognition model is proposed. The performance of the proposed approach is analyzed in Section ‘Simulation results’, and conclusions are given in Section ‘Conclusions’.
Basic concepts
Rough sets
An information system can be expressed by a four-parameters group[10]: S = {U R V f}. U is a finite and non-empty set of objects called the universe, and R = C ∪ D is a finite set of attributes, where C denotes the condition attributes and D denotes the decision attributes. V =∪ v_{ r },(r∈R) is the domain of the attributes, where v_{ r } denotes a set of values that the attribute r may take. f:U × R→V is an information function. The equivalence relation R partitions the universe U into subsets. Such a partition of the universe is denoted by U/R = E_{1},E_{2},…,E_{ n }, where E_{ i } is an equivalence class of R. If two elements u v ∈ U belong to the same equivalence class E ⊆ U/R, u and v are indistinguishable, denoted by ind(R). If ind(R) = ind(R−r), r is unnecessary in R. Otherwise, r is necessary in R.
where$\underset{\_}{R}\left(X\right)$ represents the set that can be merged into X positively, and$\overline{R}\left(X\right)$ represents the set that is merged into X possibly.
where$\text{PO}{S}_{Q}\left(P\right)=\cup \underset{\_}{Q}\left(x\right)$ and 0 ≤ γ_{ Q }≤ 1. The value of γ_{ Q } reflects the dependent degree of knowledge P to knowledge Q. γ_{ Q }= 1 shows knowledge P is dependent on knowledge Q completely; γ_{ Q } close to 1 shows knowledge P is dependent on knowledge Q highly. γ_{ Q }= 0 shows knowledge P is independent of knowledge Q.
Rough k-means algorithm
where x denotes the sample to cluster, X_{ i }denotes the cluster i, card(X_{ i }) denotes the number of the elements in X_{ i }, and I denotes the number of clusters.
SVM
The aim of SVM is to find the hyperplane which makes the samples with the same label at the same side of the hyperplane. The quantity$\frac{\left|\right|\mathbf{w}\left|\right|}{2}$ is named the margin, and optimal separating hyperplane (OSH) is the separating hyperplane which maximizes the margin. The larger the margin, the better the generalization is expected to be[16].
where α = (α_{1},…,α_{ N }) denotes the non-negative Lagrange multipliers, x_{ i } denotes the input of the training data and y_{ i }denotes the output of the training data[17].
subject to (12) and ξ_{ i }> 0. The parameter ∑ξ_{ i }is the upper bound on the number of training errors and C is the penalty parameter to control errors.
The result of the minimization is determined by the selection of parameters C and γ. Usually, C and γ are determined by using cross validation.
Radar emitter recognition system
In this section, a hybrid radar emitter recognition approach that consists of a rough k-means classifier in the primary recognition and a SVM classifier in the advanced recognition is proposed. This approach is based on the fact that in the k-means clustering, the linearly inseparable samples are mostly at the margins of clusters, which makes it difficult to determine which cluster they belong to. To solve this problem, a linear classifier based on the rough k-means and a nonlinear classifier SVM are adopted. This approach can classify linearly separable samples and pick up those linearly inseparable samples to be classified in the advanced recognition using SVM.
where A_{total} is the accuracy of the hybrid recognition, A_{primary} is the accuracy of the primary recognition, A_{advanced} is the accuracy of the advanced recognition, N_{WIU} is the number of samples which are falsely classified in uncertain area, and N_{ W } is the number of wrong classified samples.
Primary recognition based on improved rough k-means
where max(d_{ x }) is the distance from the farthest sample to the center.
In a cluster, The area beyond uncertain boundary (d_{ x }> R_{un}) is the uncertain area. When unknown samples are recognized, they will be distributed into the nearest cluster. If d_{ x }> R_{un}, these samples will be further recognized by the advanced recognition. For other unknown samples, the result of the primary recognition will be final.
- 1.
Classification rules are obtained based on the rough sets theory.
- 2.
The mean value of every class is obtained.
- 3.Define the mean values as the initial clustering centers. The clustering number equals to the number of rules:${t}_{p}=\frac{\sum _{x\in {X}_{p}}x}{\text{card}\left({X}_{p}\right)}$(20)
where X_{ p }denotes the set of samples in the classification rule p of the rough sets theory.
- 1.
Compute the Euler distance of every object to K class clustering centers and distance matrix D(i,j).
- 2.
Compute the minimum value d _{min}(i) in every row of matrix D(i,j).
- 3.
Compute distance between every object and other class center d(i) and d _{ t }(i,j) = d(i)−d _{min}(i).
- 4.
Obtain the minimum value d _{ s }(i) (except zero) in every row.
- 5.
λ is chosen from the minimum value d _{ s }(i).
After that, known samples are clustered by using (5). The cluster centers C, the rough boundary R_{ro} and the uncertain boundary R_{ un }are determined.
The time complexity of the hybrid recognition approach
The time complexity of the approach proposed in this article consists of two parts, namely the time complexity of the primary recognition and the time complexity of the advanced recognition.
In the training of the primary recognition, samples are clustered by using rough k-means. The time complexity of the rough k-means is$\mathcal{O}\left(\text{dmt}\right)$, where d, m, and t denote the dimensionality of samples, the number of training samples and the iterations, respectively. In this article, the optimal initial centers are determined by analyzing the knowledge rule of the training sample set based on rough set theory, instead of iteration. Thus, the time complexity of the primary recognition is$\mathcal{O}\left(\text{dm}\right)$.
The SVM is used as the advanced recognition in our approach. The time complexity of SVM has nothing with the dimension of samples, but is related with the number of samples. The time complexity of SVM training is discussed with respect to the complexity of the quadratic programming. Standard SVM training has$\mathcal{O}\left({m}^{3}\right)$ time complexity[21].
In conclusion, the time complexity of our hybrid recognition is$\mathcal{O}\left(\text{dm}\right)+\mathcal{O}\left({m}^{\prime 3}\right)$, where m^{ ′ } denotes the number of training samples for SVM in the advanced recognition (After the primary recognition, the training samples for SVM is reduced). In general,$\mathcal{O}\left(\text{dm}\right)$ is far less than$\mathcal{O}\left({m}^{\prime 3}\right)$. Therefore, the time complexity of the hybrid recognition training is regard as$\mathcal{O}\left({m}^{\prime 3}\right)$.
Simulation results
Data set description and experiment design
The validity and efficiency of the proposed approach is proved by simulations. In the first simulation, radar emitter signals are recognized. The type of radar emitter is the recognition result. The pulse describing words of the radar emitter signal include a radio frequency (RF), a pulse repeating frequency (PRF), antenna rotate rate (ARR) and a pulse width (PW). 240 groups of data are generated on above original radar information for training, while 200 groups are generated for testing. This simulation is repeated 100 times, and the average recognition is obtained. Another simulation is adopted to test the efficiency of the hybrid recognition with the Iris data set. Iris data set contains 150 patterns belonging to three classes. There are 50 exemplars for each class and each input is a four-dimensional real vector[22]. The recognition accuracy and time complexity are compared between SVM and our approach. There are two parts in this simulation. In the first part, all 150 samples are used in training. And these 150 samples are used to test the training accuracy. In the second part, 60 samples from the Iris data set are used to train classifiers and other 90 samples are used for test. The generalization of the proposed approach is proved.
Results of experiment 1: classification of the radar emitter signals
Information of known radar emitter signals
No. | RF (MHz) | PRF (Hz) | ARR (round/s) | PW (us) | Type |
---|---|---|---|---|---|
1 | 6558 | 1319 | 2 | 1.61 | 1 |
2 | 5436 | 2530 | 1 | 0.62 | 1 |
3 | 1984 | 1276 | 2 | 0.99 | 2 |
4 | 3787 | 145 | 3 | 0.38 | 2 |
5 | 4406 | 601 | 2 | 0.34 | 2 |
6 | 7745 | 1698 | 3 | 3.81 | 3 |
7 | 3214 | 2083 | 2 | 0.71 | 3 |
8 | 2460 | 1793 | 2 | 1.33 | 3 |
Discrete information of known radar emitter signals
No. | A | B | C | D | Type |
---|---|---|---|---|---|
1 | 3 | 2 | 2 | 2 | 1 |
2 | 3 | 3 | 1 | 1 | 1 |
3 | 1 | 2 | 2 | 1 | 2 |
4 | 2 | 1 | 3 | 1 | 2 |
5 | 2 | 1 | 2 | 1 | 2 |
6 | 3 | 2 | 3 | 3 | 3 |
7 | 2 | 3 | 2 | 1 | 3 |
8 | 1 | 2 | 2 | 2 | 3 |
Knowledge rules
No. | A | B | D | Type |
---|---|---|---|---|
1 | 3 | 2 | 2 | 1 |
2 | 3 | 3 | - | 1 |
3 | - | 2 | 1 | 2 |
4 | - | 1 | - | 2 |
5 | - | - | 3 | 3 |
6 | 2 | 3 | - | 3 |
7 | 1 | - | 2 | 3 |
Parameters in primary recognition
Cluster | Center | R _{ro} | R _{un} |
---|---|---|---|
1 | (6567,1324,1.650) | 225 | 662 |
2 | (5643,2569,0.520) | 231 | 578 |
3 | (2196,1534,1.142) | 149 | 356 |
4 | (3987,132,0.430) | 130 | 407 |
5 | (7845,1654,3.940) | 465 | 913 |
6 | (3213,2093,0.695) | 200 | 466 |
7 | (2459,1783,1.331) | 128 | 401 |
Confusion matrices of radar emitter recognition
Subc. 1 | Subc. 2 | Subc. 3 | Subc. 4 | Subc. 5 | Subc. 6 | Subc. 7 | |
---|---|---|---|---|---|---|---|
Subclass 1 | 32 | 0 | 0 | 0 | 2 | 0 | 0 |
Subclass 2 | 0 | 36 | 0 | 0 | 0 | 0 | 0 |
Subclass 3 | 0 | 0 | 34 | 0 | 0 | 0 | 3 |
Subclass 4 | 0 | 0 | 0 | 33 | 0 | 0 | 0 |
Subclass 5 | 0 | 0 | 0 | 0 | 20 | 0 | 0 |
Subclass 6 | 1 | 0 | 0 | 0 | 0 | 18 | 0 |
Subclass 7 | 0 | 0 | 5 | 0 | 0 | 0 | 16 |
Results of radar emitter recognition methods
Recognition method | Average recognition accuracy |
---|---|
RBF neural network | 92.0% |
RBF-SVM | 92.5% |
PSVM | 94.0% |
Method in this article | 94.5% |
Results of experiment 2: classification of the data set Iris
Recognition results of Iris
Method | Recognition accuracy | The number of training samples for SVM | The time complexity |
---|---|---|---|
SVM in the first part | 98.67% | 150 | $\mathcal{O}\left(15{0}^{3}\right)$ |
Our method in the first part | 99.33% | 70 | $\mathcal{O}\left(7{0}^{3}\right)$ |
SVM in the second part | 93.33% | 60 | $\mathcal{O}\left(6{0}^{3}\right)$ |
Our method in the second part | 97.78% | 36 | $\mathcal{O}\left(3{6}^{3}\right)$ |
In addition, let’s compare the time complexities of SVM and the proposed approach. The time complexity of SVM is$\mathcal{O}\left({m}^{3}\right)$, and that of the proposed approach is$\mathcal{O}\left({m}^{\prime 3}\right)$, where m and m^{ ′ }are the number of training samples for the SVM and the number of training samples for the SVM in the advanced recognition of the hybrid recognition, respectively.
When 150 samples are used as training samples, all of them are used to train the classical SVM. m = 150 and the time complexity of the classical SVM is$\mathcal{O}\left(15{0}^{3}\right)$. In our approach, training samples are clustered in the primary recognition, and only the rough samples are used to train the SVM in the advanced recognition. More specifically, there are 70 training samples for the SVM in the advanced recognition, i.e.,${m}^{\prime}=70$, so the time complexity is$\mathcal{O}\left(7{0}^{3}\right)$. Similarly, when 60 samples are used as training samples, all of these samples are used to train the classical SVM, while there are 36 training samples for the SVM in the advanced recognition of the hybrid recognition, i.e., m = 60 and m^{ ′ }= 36. So in the second part, the time complexity of the classical SVM is$\mathcal{O}\left(6{0}^{3}\right)$, while the time complexity of the proposed approach is$\mathcal{O}\left(3{6}^{3}\right)$.
From the comparison above, we can know that the time complexity of the hybrid recognition is obviously lower than the classical SVM.
Conclusions
In this article, a hybrid recognition method has been proposed to recognize radar emitter signals. The hybrid classifier consists of a rough k-means classifier (linear classifier) and a SVM (nonlinear classifier). Based on the linear separability of the classifying sample, the sample is classified by the suitable classifier. Thus for the radar emitter sample set containing both linearly separable samples and linearly inseparable samples, the approach can achieve a higher accuracy.
A linear classifier based on the rough set and the rough k-means has been proposed, i.e., the rough k-means classifier. The rough k-means clustering can reduce the radius of the clusters and increase the accuracy of the primary recognition. The initial centers for the rough k-means are computed based on the rough set, which can reduce the time complexity of the rough k-means clustering. The rough k-means classifier can classify linear separable samples efficiently and pick up linearly inseparable samples. These linear inseparable samples are processed by the SVM in the advanced recognition. Therefore, the training samples for the SVM in the advanced recognition are reduced. Simulation results have shown that the proposed approach can achieve a higher accuracy and a lower time complexity, when compared with existing approaches.
The hybrid recognition approach in this article is suitable for the classification of the radar emitter signal sample set containing both linearly separable and linearly inseparable samples. We admit that our hybrid recognition approach is based on the fact that these linearly inseparable samples which reduce the accuracy of clustering are mostly at the edges of clusters. From (18), we know that if the linearly inseparable sample appears frequently in the center region instead of the edge, the accuracy of recognition will be reduced. How to solve this problem is the focus of our future study.
Declarations
Acknowledgements
The authors would like to thank the editors and reviewers for helpful comments and suggestions. This study was supported by a grant from National Natural Science Foundation of China (grant number: 61102084).
Authors’ Affiliations
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