- Email: [email protected]
Automatic classification of radar targets with micro-motions using entropy segmentation and time-frequency features
Int. J. Electron. Commun. (AEÜ) 65 (2011) 806–813
Contents lists available at ScienceDirect
International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.de/aeue
Automatic classification of radar targets with micro-motions using entropy segmentation and time-frequency features Peng Lei ∗ , Jun Wang ∗ , Peng Guo, Duoduo Cai School of Electronic and Information Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 18 June 2010 Accepted 19 January 2011 Keywords: Micro-Doppler Radar target classification Spectrogram Entropy Feature extraction
a b s t r a c t Micro-Doppler (mD) signatures have great potential in the radar micro-dynamic target classification. An automatic classification method for radar targets with micro-motions is proposed based on the idea of entropy and feature extraction from the spectrogram. In this method, the measurement of entropy is firstly conducted over the time-frequency distribution associated with the minimum filtering operation, the threshold discrimination and the region focusing to obtain the region of interest corresponding to mD signatures in the original spectrogram. It helps acquire the valid region in the time-frequency domain and reduce the computational burden in the following processing. Next, invariant moments and geometric characteristics of time-frequency distribution of mD signatures are extracted from the segmented spectrogram to construct mD feature vectors. A support vector machine (SVM) with decision-tree architecture is then used for multiclass micro-dynamic target classification from radar echoes. Finally, some experimental tests with simulated mD data are carried out to confirm the effectiveness of the proposed method and evaluate the performance under different conditions of signal-to-noise ratio (SNR), training set and feature vector. In addition, issues related to the improvement of classification performance are also discussed. © 2011 Elsevier GmbH. All rights reserved.
1. Introduction Automatic target classification has been an essential goal in the development of modern radar systems. This technique could be implemented in space exploration, geophysical discovery, medical diagnosis, and especially has the promising application in national security and defense research. However, as technology progress in electronic countermeasures and target protection, some classification approaches using classical characteristics of radar objects, such as the radar cross section and the high-range resolution profile, are confronted with enormous challenges. It is well known that an object or any of its structures generally have some micro-motions in addition to the bulk translation. For radar return signals, these micro-motions would cause corresponding frequency modulations, which are often inversely used to analyze behavioral states of objects. This phenomenon is called the micro-Doppler (mD) effect [1]. Considering the uniqueness of electromagnetic properties in radar echoes from micro-dynamic targets, mD signatures could be considered as a viable candidate for the radar target classification [2]. Some efforts have been made to apply the mD based target classification in theoretical research and practical systems. From the viewpoint of frequency domain, prin-
∗ Corresponding authors. E-mail addresses: [email protected] (P. Lei), [email protected] (J. Wang). 1434-8411/$ – see front matter © 2011 Elsevier GmbH. All rights reserved. doi:10.1016/j.aeue.2011.01.013
cipal component analysis was used to extract mD features from the normalized power spectrums, and three targets were classified by the naïve Bayesian classifier [3]. Furthermore, since the time-varying characteristics of mD frequency indicate the microdynamic state, shape and other information of the target, which is mostly absent in the power spectrum, more attention is given to the research in the time-frequency domain for mD analysis and classification. In [2], local orientations were extracted as mD features from the time-frequency distributions of mD signatures by Gabor filtering, and several classifiers were then demonstrated to be applicable in the micro-dynamic target classification. To discriminate different human activities and vehicles from radar echoes, time-frequency transforms were utilized and features of time-frequency representations, such as the mD frequency offset, number of mD signal components and others, were selected to construct the feature vector for classifiers [4,5]. In the radar signal processing, the effective area of timefrequency representation depends on the measurement duration and sampling frequency. It is noted that mD signatures are generally distributed in a limited part of the time-frequency domain, while the remaining region is only filled with noise, clutter or other unwanted signals. However, previous algorithms mentioned above directly use the raw time-frequency responses for feature extraction or only take the empirical threshold for de-noising in a given scene. It inevitably results in a waste of computing resources and the difficulty of flexibility to other different applications. In this
P. Lei et al. / Int. J. Electron. Commun. (AEÜ) 65 (2011) 806–813
work, we firstly achieve a new method using the entropy measurement for automatic segmentation of mD region from the original time-frequency representation. It could help narrow the mD region of interest with the purpose of computational savings and disturbance suppression, and then improve the follow-up feature extraction from the time-frequency domain. In addition, distinct mD features based on invariant moments are extracted from the segmented time-frequency representation. They would constitute the full feature space together with geometric characteristics. After feature extraction, a support vector machine (SVM) with decisiontree architecture, which is an extended form of the basic SVM for multiclass classification, is used in the training and testing phases. Here, three typical micro-motion classes, including cone-shaped targets with spinning and coning motions and cylinder targets with rotation, are modeled to generate training and test data for classification, respectively. The proposed method performs the micro-dynamic target classification without the requirement of human operation. It means that this automatic classification could avoid the subjective uncertainty and have higher efficiency for large-sized data sets. Furthermore, the general applicability of the method allows for better performance in radar mD classification with proper feature selection. In this paper, Section 2 briefly presents the mD effect in radar systems and the time-frequency representation used in the work. In Section 3, the classification method is described in three parts: segmentation of the mD region, feature extraction and SVM classifier. In Section 4, some experiments are carried out and results are discussed subsequently. Concluding remarks are given in Section 5. 2. MD effect in radar and time-frequency representation
dlmDi (t) i (t) , ·n dt
frequency and time implies the particular micro-motion state of an target. For example, the rate of change in the mD frequency may correspond to the period of an individual or synthetic micromotion, while the number of mD signal components could reflect the amount of principal scattering centers of a micro-dynamic target. However, the classical Fourier transform can only provide the global information of analyzed signals in the frequency domain, which does not describe the local frequency spectrum over short periods of time. The time-frequency analysis could map the signal energy in the two-dimensional domain for the time-frequency localization. Hence, it is applicable for mD signatures to represent the time-varying mD frequency. In this work, the Short Time Fourier Transform (STFT) is used to generate the spectrogram for the time-frequency representation of mD signatures. According to the definition in [8], the spectrogram of radar mD signature could be expressed as the magnitude of its STFT result as follows
SG(, fmD ) =
+∞
xmD (t)w(t − )e
−j2fmD t
−∞
dt
(2)
where xmD (t) denotes the radar mD signature and w(t) denotes the short time window function in STFT. Fig. 1 illustrates the simulated mD signatures in the time-frequency domain (spectrogram) using the STFT and in the frequency domain (power spectrum) using the fast Fourier transform, respectively, which correspond to radar echoes from targets with some typical micro-motions under noise environment.
3. Classification method based on mD
It is common that many objects or their structures have micromotions besides translational motion of bulk, such as dynamics of space objects in attitude control, rotation of rotor blades in helicopters and arm swinging of walking persons. Similarly to the Doppler phenomenon induced by the bulk translation, micromotions could also cause frequency modulation in the radar echoes, i.e., the mD frequency. Since micro-motions are always of the periodicity or quasi-periodicity coexisting with the bulk translation, the instantaneous mD frequency would distribute around the corresponding Doppler frequency. Moreover, in the power spectrum, the mD appears as sidebands about the target’s Doppler shift. In this work, considering the radar operating in the high-frequency regime, the scattering response of an object to radar signals could approximately be modeled by the sum of independent scattering centers, namely, the point scatterer model [6]. What is more, this model could simplify the analysis with the preservation of mD features of radar targets [1,2,7]. Additionally, as the Doppler frequency shift may have an impact on the performance of feature extraction and classification, here we assume that the motion compensation is carried out to remove its influence, which could result in the Doppler frequency fd → 0 Hz. Therefore, the mD frequency of the radar target can be represented as 2f0 2f v (t) = 0 fmDi (t) = c mDi c
807
i = 1, 2, . . . , N (1)
where f0 is the carrier frequency of the transmitted radar signal, c is the speed of light, N is the number of scattering centers, and vmDi (t), l i (t) are the instantaneous micro-motion velocity commDi (t) and n ponent in the direction of the radar line of sight (LOS), position vector and LOS unit vector of the ith scatterer, respectively. It can be seen from Eq. (1) that the mD frequency has the time-varying characteristics, and the relationship between the mD
The automatic classification of micro-dynamic targets refers to the assignment of the micro-motion state discrimination of unknown targets, in this work, based on time-frequency features extracted from radar mD signatures. As mentioned in Section 2, the distribution of mD signatures in the time-frequency domain characterizes corresponding micro-motions, thus the spectrogram could be used for mD feature extraction effectively. The typical radar classification system for micro-dynamic targets comprises the preprocessing, feature extraction and selection, training and class discrimination, where the training and class discrimination are also combined as the classifier design. The preprocessing phase is firstly used to remove noise, clutter, jamming and other interference from spectrograms. In the feature extraction and selection phase, a parsimonious set of reliable and stable features are created from the spectrograms of mD signatures. The feature selection process reflects the concern that computational requirements and the difficulty to train the classifier are highly correlated with the number of features used in the classification process. After the feature extraction process is completed, the resulting feature sets are used to train a predictive model and decision rules for classification of mD signatures. Finally, the trained predictive model is used to produce estimated target class assignments for test data. In this work, a preprocessing approach based on entropy is exploited to narrow the mD region of interest from the original spectrogram. After this segmentation, invariant moments and geometric characteristics of mD distribution are extracted as time-frequency features. Lastly, a decision-tree SVM classifier is applied for multiclass micro-dynamic target classification. Here three typical micro-motion classes, including cone-shaped targets with spinning and coning and cylinder targets with rotation, are modeled to be classified objects. An overview of the proposed classification method for radar micro-dynamic targets is shown in Fig. 2.
808
P. Lei et al. / Int. J. Electron. Commun. (AEÜ) 65 (2011) 806–813
Fig. 2. Block diagram of radar target classification using mD signatures.
(1) the value of H(x) reaches its minimum, 0, under the unique condition that the probability of only a state of the event x is equal to one while the others are all zero; (2) the value of H(x) reaches its maximum, log m, under the unique condition that probabilities of event states obey the uniform distribution. Fig. 1. Spectrograms and power spectrums of mD signatures from radar targets with typical micro-motions.
3.1. Segmentation of the mD region Assume that the event x has m possible states. Let pl denote the corresponding probability of the state l with 0 ≤ pl ≤ 1 and pl = 1, where l = 1,2, . . ., m. Then, the (Shannon) entropy could be defined as [9] m
H(x) = −
pl log pl
(3)
l=1
According to the statistical knowledge, the boundary of entropy in two extreme cases could be derived as
More generally, the value of H(x) is becoming larger as the probability distribution of event states becomes more random, and vice versa. Hence, as shown in case (1), when the states of event x are absolutely certain, the value of entropy is the minimum. On the contrary, in case (2), the event states are the most unpredictable, which accordingly leads to the peak entropy. Thus, the entropy can be used to describe the randomness of event states. In mD spectrograms, ranges of time and frequency depend on the measurement duration and sampling frequency. Nevertheless, the mD region of interest always holds a limited frequency band in the observation, while only noise is left in the other time-frequency areas, such as those shown in Fig. 1. From the uncertainty point of view, the pure noise region corresponds to more randomness than that in the mD region, which consists of the mD signatures and noise. Therefore, the entropy is adopted to segment the mD
P. Lei et al. / Int. J. Electron. Commun. (AEÜ) 65 (2011) 806–813
809
Fig. 3. Process of entropy-based region segmentation for mD distribution.
region of interest from the original spectrogram with the purpose of simplifying the following processing. In this entropy segmentation, amplitudes of the spectrogram for each frequency are firstly normalized in time using Eq. (4) as follows SG(i , fj )
SG (i , fj ) =
i
SG(i , fj )
(4)
where i = 1,2, . . ., M denotes the time samples and j = 1,2, . . ., N denotes the frequency samples. It can be seen that the normalized amplitude could be considered as the probability of a sample in the spectrogram for corresponding frequency. Substituting Eq. (4) into Eq. (3), the entropy of the spectrogram could be given by M
HmD (fj ) = −
SG (i , fj ) log SG (i , fj )
(5)
i=1
In addition, on account of the possible impact by noise and constant Doppler line (CDL) in the spectrogram, the minimum filter is utilized to smooth the fluctuation caused by them in HmD (fj ). Then the median value acts as the threshold to indicate the rough mD region and the focusing processing is followed to refine the result. Here, the region focusing is to concentrate the broad area after the median threshold discrimination by means of the boundary shift. This expansion problem is the by-product of minimum filtering, where the filter encompasses a neighborhood for the minimum value and the number of boundary shift units is also related to the filter kernel size. In order to make the segmentation mentioned above clear, we depict its process flow with corresponding simulation results, as shown in Fig. 3, where the spectrogram in Fig. 1(a) is used because noise, CDL and mD signal components with time-varying frequency are all contained. Fig. 3(b) presents the entropy of the original spectrogram. The values in the noise region are above the median threshold, whereas the false alarm peaks induced by noise and the salient by CDL in the mD region could confuse the segmentation. As seen in Fig. 3(c), the minimum filtering is effective to get rid of those distortions but yet introduces the expansion problem into the mD region. In Fig. 3(d), the area, where the entropy values are
below the threshold, is discriminated as the mD region, and the focusing processing is then utilized to obtain the refined result. Fig. 3(e) illustrates the final mD region based on the entropy segmentation. Comparing with Fig. 3(a), the segmented spectrogram has smaller time-frequency area only covering the frequency band of mD signatures. Hence, substituting the segmented spectrogram for the original one in the following feature extraction, it is beneficial to reduce the computational burden without loss of the mD information. 3.2. MD feature extraction For various micro-motions, the time-frequency representations generally display different geometric distribution in the twodimensional domain, such as spectrograms shown in Fig. 1. This indicates that some quantities describing the geometric relationship among mD signal components could be used as mD features for classification. In this work, the CDL and symmetry of components in the spectrogram are chosen as geometric characteristics, which are well representative of typical micro-motions according to Table 1 and experiments in [10]. The morphological algorithm and spatial filtering with unsharp filters [11] are firstly applied to the segmented spectrogram. After the peak detection, both geometric characteristics are then obtained. If there exists the CDL, the flag is set to one, otherwise it is to zero. The symmetry of mD signal components is measured by a ratio in range [0,1], where the larger ratio denotes a higher degree of symmetry of the mD signature in the time-frequency distribution. In addition, considering the spectrogram as a two-dimensional image, curves of the time-varying frequency corresponding to mD Table 1 Geometric characteristics of the general time-frequency distribution for three micro-motion classes. Geometric characteristics
CDL Symmetry
Classes Spinning
Coning
Rotation
Yes Yes
No No
No Yes
810
P. Lei et al. / Int. J. Electron. Commun. (AEÜ) 65 (2011) 806–813
signatures could be dealt with as objects of interest in the image. Although geometric characteristics are invariant for a given micromotion, the offset and rate of change in the mD frequency could be distinct under different conditions of LOS direction, target size and micro-motion velocity according to Eq. (1). From the viewpoint of imaging, it means that features independent of scale, position and orientation may be applicable in micro-dynamic target classification on the basis of the spectrogram. Hu derived seven nonlinear functions of invariant moments for the visual pattern recognition [12]. They are formed by the second and third order central moments with normalization, and invariant to translation, scaling and rotation in the case of continuity. In order to be applied in mD spectrograms, the modified Hu’s invariant moments [13] for discrete events are adopted in this work to characterize the invariance of mD features in the time-frequency domain. Let SG (i, j) be the segmented spectrogram, where i = 1,2, . . ., M and j = 1,2, . . ., L(L ≤ N). The normalized central moment of order (p + q) of SG (i,j) is defined as
M L
pq =
i=1
M i=1
(i − x) (j − y) SG (i, j) p
j=1
q
(p+q+2)/2
L
(6)
SG (i, j) j=1
¯ is its center of gravity and p + q ≥ 2. Then in terms where (¯x, y) of Hu’s invariant moments, the moment based characteristics of mD signatures in the time-frequency distribution are given by 1
= 20 + 02
2
=
(7)
(20 − 02 )2 + 411 2 1
3
=
(30 − 312 )2 + (321 − 03 )2 1
4
= =
(9)
3
(10)
3
= =
Spinning
Coning
Rotation
1
2
1
2
1
2
3
Height (m) Bottom radius (m) Spin frequency (Hz) Coning frequency (Hz) Coning angle (◦ )
2.0 0.5 2.5 N N
2.2 1.0 1.5 N N
2.0 0.5 N 0.5 20
2.0 1.0 N 0.3 10
1.2 0.4 N N N
2.0 1.0 N N N
0.8 0.3 N N N
Rotation angular velocity (rad/s)
N N N
N N N
N N N
N N N
3.1 3.1 3.1
2.1 2.4 3.1
−3.1 1.6 3.1
in the multiclass classification. In order to extend the application of SVM, some multiclass SVM approaches have been developed to act in the multiclass situation. The typical ones include the one-against-all SVM, one-against-one SVM and decision-tree SVM [17,18]. In this work, the decision-tree SVM is used in the training and class discrimination of time-frequency features from three types of radar micro-dynamic targets. It introduces the binary tree architecture in decision theory into the basic SVM. The decisiontree SVM approach assigns SVMs to each node of the tree, where the binary decision is made to separate the input data into two proper classes saved at the respective subnodes. Repeat this classifying process sequentially until every leaf node, i.e., the furthest extremity of a branch in the tree architecture, contains only one class of data. Comparing with the other two multiclass SVM approaches mentioned above, the decision-tree SVM has the advantage of simple architecture and low computational complexity. The related theoretical analysis and experiments are presented with more details in [19].
In this section, the performance of the proposed classification method for radar micro-dynamic targets is discussed and
6
(20 − 02 )[(30 + 12 )2 − (21 + 03 )2 ] + 411 (30 + 12 )(21 + 03 ) 1
7
Classes
(30 − 312 )(30 + 12 )[(30 + 12 )2 − 3(21 + 03 )2 ] + (321 − 03 )(21 + 03 )[3(30 + 12 )2 − (21 + 03 )2 ] 1
6
Parameters
4. Experimental results and discussion
(30 + 12 )2 + (21 + 03 )2 1
5
(8)
2
Table 2 Parameters of micro-dynamic targets in experiments.
4
(321 − 03 )(30 + 12 )[(30 + 12 )2 − 3(21 + 03 )2 ] − (30 − 312 )(21 + 03 )[3(30 + 12 )2 − (21 + 03 )2 ] 1
6
3.3. SVM classifier The SVM is a machine learning algorithm based on the structural risk minimization. Because of its generalization ability and good performance in the case of small-sized training data, it has been widely used in the research field of radar target classification [14–16]. The basic principle of SVM is to determine the optimal hyperplane when the two sets of input data are linearly separable. Here, the optimal hyperplane refers to the surface which not only separates the two sets of data but also produces the largest margin between them. It can be observed that this optimal hyperplane, which helps the classifier minimize the generalization error, is actually supported by the data located on it. Accordingly, these data are support vectors. For nonlinearly separable data, the SVM would map them into a higher-dimensional space using some kernel functions, which convert the nonlinear problem into a linear one. Thus, the optimal hyperplane of nonlinear data could be found by SVM in a high-dimensional space. The SVM is originally proposed for the binary classification problem. However, more tasks in actual practice would yet be involved
(11)
(12)
(13)
evaluated according to experimental results. The simulated database applied in this work includes three micro-dynamic object classes: cone-shaped targets with spinning and coning motions and cylinder targets with rotation. For the spinning and coning classes, each data were obtained from two different cones, while the data of rotation class were acquired from three cylinders. The parameters of micro-dynamic targets in experiments are listed in Table 2. On the whole, a three-class classification problem comprising seven micro-dynamic targets is studied here. To be close to real scenarios, the additive white Gaussian noise with zero-mean is used to contaminate radar echoes according to a certain signal-to-noise ratio (SNR). In the training phase, mD signatures from each target are generated under various conditions of initial Euler angles at SNR of 20 dB. These angles in the three-dimensional space obey the uniform distribution. It also indicates that the training data are sampled at equal intervals of aspect angles in statistics, and the number of samples is dependent on the specified size of training data. For this three-class classification problem, the corresponding class labels of training data are denoted as 1, 2 and 3, respec-
P. Lei et al. / Int. J. Electron. Commun. (AEÜ) 65 (2011) 806–813
811
Fig. 4. Sample spectrograms of the testing set in classification.
efficiency of training and the above results, the training set with the size of 600 frames per target is adopted and the number of Monte-Carlo simulations is still set to 200. Fig. 6 illustrates the corresponding classification accuracy using different feature vectors. It can be observed that the accuracy using two-dimensional feature vector slightly increases from about 78.1% to about 83.5% in the SNR range between 5 and 20 dB. The loss of classification performance here is mainly attributed to the extraction error of symmetry characteristic. Nevertheless, when using the seven- or nine-dimensional feature vector instead in the high SNR range, the classification accuracy would be much improved. Especially at the SNR levels above 12 dB, the average classification rate based on the nine features approximately reaches 92.4%, which is higher than that of about 90.3% based on the seven features. However, in the SNR range between 5 and 12 dB, the accuracy of the former declines more rapidly and is lower than that of the latter. Therefore, the classification of targets with micro-motions based on nine timefrequency features could achieve good performance at high SNR
100 95
Classification Accuracy / %
tively. All these labeled mD signatures would constitute the training set. In the testing phase, 50 frames of mD signatures for each micro-dynamic target with respect to different aspect angles are randomly produced at given SNR in every experiment. Hence, a testing set, including unlabeled mD signatures from seven targets, comprises a total of 350 frames. Assume that the radar operates at f0 = 5 GHz, the pulse repetition frequency is 1.5 kHz, and the duration of each observation is 2 s. The Hamming window is used in STFT for the time-frequency analysis. As the classes of training data are known, the suitable window size could be selected according to the corresponding class label, while the testing set is processed automatically over a fixed 0.07 s time window. Some sample spectrograms of the testing set using the STFT are shown in Fig. 4. Firstly, we study the performance of the classification method for micro-dynamic targets under the condition of different training data sizes. After generating a training set of 1000 frames for each target, another two sets with the size of 600 and 300 frames for each target are obtained by the uniform sampling, respectively. In order to simplify the expressions, the three training sets are denoted as Sets A, B and C through their different sizes (size of A > B > C). The nine-dimensional feature vector in this investigation is composed of two geometric characteristics and seven invariant moments. Fig. 5 shows the results of 200 Monte-Carlo simulations. It can be seen that the classification accuracy in all three cases of training sets tends to remain stable and almost identical to reach an average rate of about 92.7% at the SNR levels above 14 dB. In the SNR range between 5 and 14 dB, the accuracy declines rapidly as the SNR decreases, and the classification rate based on Set A is at most only about 2.3% and 6.6% higher than those based on Sets B and C, respectively. The results suggest that the proposed method could still be effective in the case of limited-sized training set. This performance is mainly ascribed to the good generalization of SVM and high distinguishability of mD features for the three classes of targets. Secondly, the effect of time-frequency features used in this work on classification results is investigated. Besides the ninedimensional feature vector, the two-dimensional feature vector of only geometric characteristics and the seven-dimensional feature vector of only invariant moments are utilized for both training and testing to evaluate this method, respectively. Considering the
90 85 80 75 70 65
1000 training data 600 training data 300 training data
60 55 50
5
8
11
14
17
20
SNR / dB Fig. 5. Classification accuracy in different training set sizes with the increasing SNR.
812
P. Lei et al. / Int. J. Electron. Commun. (AEÜ) 65 (2011) 806–813
100
Classification Accuracy / %
95 90 85 80 75 70 65
9 features 7 features 2 features
60 55 50
5
8
11
14
17
20
SNR / dB Fig. 6. Classification accuracy in different dimensions of feature vectors with the increasing SNR.
Spinning Coning Rotation
Acknowledgements The authors would like to acknowledge helpful comments from the anonymous reviewers and valuable support from K. Li at Harvard University to improve the paper.
Table 3 Confusion matrix of classification results at SNR = 20 dB. Test data
order to take into account some possible occasions in practice, we have further conducted experiments under different conditions of SNR, training set and feature vector with the decision-tree SVM, and then discussed the performance to assess the validity of the proposed method. It is found that this method is applicable in the radar microdynamic target classification both with a limited-sized training set and over a wide SNR range. The classification accuracy is over 90% at high SNR levels (≥12 dB), and even in low SNR range between 5 and 7 dB, the accuracy of around 80% may be achieved by proper feature selection. It should be mentioned that in order to focus on the highlight of this work, we only adopt the classical STFT in the timefrequency analysis of mD signatures. According to the investigation in Section 4, we can expect that the classification performance of this method could be further improved if new adaptive algorithms of time-frequency analysis are exploited to optimize the feature information in the spectrogram, especially at some unfavorable aspect angles.
Predicted classes Spinning
Coning
Rotation
99.9% 0.0% 1.2%
0.0% 85.7% 6.7%
0.1% 14.3% 92.1%
levels (≥12 dB). Although its accuracy falls to about 65.8% because of the influence of noise on invariant moments at low SNR levels (5–7 dB), some improvement, such as the selection of proper features according to Fig. 6 and the above analysis, could be carried out in this method to obtain better performance. Table 3 presents the detailed classification results of 200 MonteCarlo simulations between the three classes at SNR of 20 dB with the training set of 600 frames per target and nine-dimensional feature vector. It indicates that the spinning targets could successfully be discriminated from the other two classes in the testing set with the remarkable accuracy of about 99.9%, while the classification performance between the coning class and the rotation class degrades. This may be attributed to their small ranges of mD frequency. Additionally, it should be noted that the time-frequency distribution at some unfavorable aspect angles is very difficult for the correct feature extraction, as shown in Fig. 4(g)–(i), thus, possible errors in the training or testing set would lead to wrong decisions in the classification. 5. Conclusions In this paper, we have presented a new automatic classification method for radar micro-dynamic targets. The first contribution emphasized here is the entropy-based region segmentation of spectrograms. It takes advantage of the difference between mD signatures and noise in the time-frequency domain and is capable of being applied to various cases. The segmented results would be beneficial to the reduction of computational burden without loss of mD information and the improvement of the follow-up feature extraction. The second contribution is the extraction of modified invariant moments as mD features. We have analyzed their properties and given the mathematical expressions in the mD spectrogram. They indicate the ability to serve as a novel set of mDbased classification features with high distinguishability. Finally, in
References [1] Chen VC, Li F, Ho SS, Wechsler H. Micro-doppler effect in radar: phenomenon, model and simulation study. IEEE Trans Aerosp Electron Syst 2006;42:2–21. [2] Lei J, Lu C. Target classification based on micro-doppler signatures. In: Proceedings of IEEE international radar conference, Arlington, USA. 2005. p. 179–83. [3] Smith GE, Woodbridge K, Baker CJ. Naïve Bayesian radar micro-doppler recognition. In: Proceedings of international conference on radar, Adelaide, Australia. 2008. p. 111–6. [4] Nanzer JA, Rogers RL. Bayesian classification of humans and vehicles using micro-doppler signals from a scanning-beam radar. IEEE Microw Wireless Compon Lett 2009;19:338–40. [5] Kim Y, Ling H. Human activity classification based on micro-doppler signatures using a support vector machine. IEEE Trans Geosci Remote Sens 2009;47:1328–37. [6] Keller JB. Geometrical theory of diffraction. J Opt Soc Am 1962;52:116–30. [7] Thayaparan T, Abrol S, Riseborough E, Stankovic L, Lamothe D, Duff G. Analysis of radar micro-doppler signatures from experimental helicopter and human data. IET Radar Sonar Navig 2007;1:289–99. [8] Chen VC, Ling H. Time-frequency transforms for radar imaging and signal analysis. Boston: Artech House; 2002. [9] Shannon CE. A mathematical theory of communication. Bell Syst Tech J 1948;27, 379–423, 623–56. [10] Lei J. Pattern recognition based on time-frequency distributions of radar micro-doppler dynamics. In: Proceedings of the sixth international conference on software engineering, artificial intelligence, networking and parallel/distributed computing and first ACIS international workshop on selfassembling wireless networks, Towson, USA. 2005. p. 14–8. [11] Gonzales RC, Woods RE. Digital image processing. 3rd edition NJ: Pearson Prentice Hall; 2007. [12] Hu MK. Visual pattern recognition by moment invariants. IRE Trans Inf Theory 1962;8:179–87. [13] Fu Y, Lv J. Recognition of SAR image based on SVM and new invariant moment feature extraction. In: Proceedings of the second international symposium on knowledge acquisition and modeling, Wuhan, China. 2009. p. 15–8. [14] Lardeux C, Frison PL, Tison C, Souyris JC, Stoll B, Fruneau B, et al. Support vector machine for multifrequency sar polarimetric data classification. IEEE Trans Geosci Remote Sens 2009;47:4143–52. [15] Anagnostopoulos GC. SVM-based target recognition from synthetic aperture radar images using target region outline descriptors. Nonlinear Anal 2009;71:e2934–9. [16] Yeary MB, Nemati S, Yu TY, Wang Y, Zhai Y. A support-vector-machine-based approach to RF sensor spectral signature classifications. IEEE Trans Instrum Meas 2009;58:221–8. [17] Foody GM, Mathur A. A relative evaluation of multiclass image classification by support vector machines. IEEE Trans Geosci Remote Sens 2004;42:1335–43. [18] Horng MH. Multi-class support vector machine for classification of the ultrasonic images of supraspinatus. Expert Syst Appl 2009;36:8124–33. [19] Fei B, Liu J. Binary tree of SVM: a new fast multiclass training and classification algorithm. IEEE Trans Neural Netw 2006;17:696–704.
P. Lei et al. / Int. J. Electron. Commun. (AEÜ) 65 (2011) 806–813 Peng Lei was born in Shaanxi, China, in 1985. He received the B.S. degree in electronic and information engineering from the Beijing University of Aeronautics and Astronautics (BUAA), Beijing, China, in 2006. He is currently working towards the Ph.D. degree in signal and information processing from BUAA. His current research interests include signal processing, radar feature extraction, image processing, target recognition, and DSP applications.
Jun Wang was born in Shaanxi, China, in 1972. He graduated from School of Electronic Engineering, Northwestern Polytechnical University, in 1995, and received the master and Ph.D. degrees in signal and information processing from Beijing University of Aeronautics and Astronautics (BUAA) in 1995 and 2001. He is now an associate professor in School of Electronic and Information Engineering, BUAA. He is interested in real-time DSP system design and implementation, wireless communications, SAR image processing and so on.
813
Peng Guo was born in Beijing, China, in 1986. She received the B.S. degree in electronics and information engineering from the Beijing University of Aeronautics and Astronautics (BUAA), Beijing, China, in 2008. She is now working towards the master degree in information and communication engineering at BUAA. Her principal interest is in the simulation of radar signal processing.
Duoduo Cai was born in HuBei, China, in 1987. He received the B.S. degree in communication engineering from the HuaZhong University of Scinence and Technology, WuHan, China, in 2009. Now he is studying for master degree in signal and information processing at the Beijing University of Aeronautics and Astronautics (BUAA), mainly on radar signal processing and stepped-frequency radar system simulation.
Contents lists available at ScienceDirect
International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.de/aeue
Automatic classification of radar targets with micro-motions using entropy segmentation and time-frequency features Peng Lei ∗ , Jun Wang ∗ , Peng Guo, Duoduo Cai School of Electronic and Information Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 18 June 2010 Accepted 19 January 2011 Keywords: Micro-Doppler Radar target classification Spectrogram Entropy Feature extraction
a b s t r a c t Micro-Doppler (mD) signatures have great potential in the radar micro-dynamic target classification. An automatic classification method for radar targets with micro-motions is proposed based on the idea of entropy and feature extraction from the spectrogram. In this method, the measurement of entropy is firstly conducted over the time-frequency distribution associated with the minimum filtering operation, the threshold discrimination and the region focusing to obtain the region of interest corresponding to mD signatures in the original spectrogram. It helps acquire the valid region in the time-frequency domain and reduce the computational burden in the following processing. Next, invariant moments and geometric characteristics of time-frequency distribution of mD signatures are extracted from the segmented spectrogram to construct mD feature vectors. A support vector machine (SVM) with decision-tree architecture is then used for multiclass micro-dynamic target classification from radar echoes. Finally, some experimental tests with simulated mD data are carried out to confirm the effectiveness of the proposed method and evaluate the performance under different conditions of signal-to-noise ratio (SNR), training set and feature vector. In addition, issues related to the improvement of classification performance are also discussed. © 2011 Elsevier GmbH. All rights reserved.
1. Introduction Automatic target classification has been an essential goal in the development of modern radar systems. This technique could be implemented in space exploration, geophysical discovery, medical diagnosis, and especially has the promising application in national security and defense research. However, as technology progress in electronic countermeasures and target protection, some classification approaches using classical characteristics of radar objects, such as the radar cross section and the high-range resolution profile, are confronted with enormous challenges. It is well known that an object or any of its structures generally have some micro-motions in addition to the bulk translation. For radar return signals, these micro-motions would cause corresponding frequency modulations, which are often inversely used to analyze behavioral states of objects. This phenomenon is called the micro-Doppler (mD) effect [1]. Considering the uniqueness of electromagnetic properties in radar echoes from micro-dynamic targets, mD signatures could be considered as a viable candidate for the radar target classification [2]. Some efforts have been made to apply the mD based target classification in theoretical research and practical systems. From the viewpoint of frequency domain, prin-
∗ Corresponding authors. E-mail addresses: [email protected] (P. Lei), [email protected] (J. Wang). 1434-8411/$ – see front matter © 2011 Elsevier GmbH. All rights reserved. doi:10.1016/j.aeue.2011.01.013
cipal component analysis was used to extract mD features from the normalized power spectrums, and three targets were classified by the naïve Bayesian classifier [3]. Furthermore, since the time-varying characteristics of mD frequency indicate the microdynamic state, shape and other information of the target, which is mostly absent in the power spectrum, more attention is given to the research in the time-frequency domain for mD analysis and classification. In [2], local orientations were extracted as mD features from the time-frequency distributions of mD signatures by Gabor filtering, and several classifiers were then demonstrated to be applicable in the micro-dynamic target classification. To discriminate different human activities and vehicles from radar echoes, time-frequency transforms were utilized and features of time-frequency representations, such as the mD frequency offset, number of mD signal components and others, were selected to construct the feature vector for classifiers [4,5]. In the radar signal processing, the effective area of timefrequency representation depends on the measurement duration and sampling frequency. It is noted that mD signatures are generally distributed in a limited part of the time-frequency domain, while the remaining region is only filled with noise, clutter or other unwanted signals. However, previous algorithms mentioned above directly use the raw time-frequency responses for feature extraction or only take the empirical threshold for de-noising in a given scene. It inevitably results in a waste of computing resources and the difficulty of flexibility to other different applications. In this
P. Lei et al. / Int. J. Electron. Commun. (AEÜ) 65 (2011) 806–813
work, we firstly achieve a new method using the entropy measurement for automatic segmentation of mD region from the original time-frequency representation. It could help narrow the mD region of interest with the purpose of computational savings and disturbance suppression, and then improve the follow-up feature extraction from the time-frequency domain. In addition, distinct mD features based on invariant moments are extracted from the segmented time-frequency representation. They would constitute the full feature space together with geometric characteristics. After feature extraction, a support vector machine (SVM) with decisiontree architecture, which is an extended form of the basic SVM for multiclass classification, is used in the training and testing phases. Here, three typical micro-motion classes, including cone-shaped targets with spinning and coning motions and cylinder targets with rotation, are modeled to generate training and test data for classification, respectively. The proposed method performs the micro-dynamic target classification without the requirement of human operation. It means that this automatic classification could avoid the subjective uncertainty and have higher efficiency for large-sized data sets. Furthermore, the general applicability of the method allows for better performance in radar mD classification with proper feature selection. In this paper, Section 2 briefly presents the mD effect in radar systems and the time-frequency representation used in the work. In Section 3, the classification method is described in three parts: segmentation of the mD region, feature extraction and SVM classifier. In Section 4, some experiments are carried out and results are discussed subsequently. Concluding remarks are given in Section 5. 2. MD effect in radar and time-frequency representation
dlmDi (t) i (t) , ·n dt
frequency and time implies the particular micro-motion state of an target. For example, the rate of change in the mD frequency may correspond to the period of an individual or synthetic micromotion, while the number of mD signal components could reflect the amount of principal scattering centers of a micro-dynamic target. However, the classical Fourier transform can only provide the global information of analyzed signals in the frequency domain, which does not describe the local frequency spectrum over short periods of time. The time-frequency analysis could map the signal energy in the two-dimensional domain for the time-frequency localization. Hence, it is applicable for mD signatures to represent the time-varying mD frequency. In this work, the Short Time Fourier Transform (STFT) is used to generate the spectrogram for the time-frequency representation of mD signatures. According to the definition in [8], the spectrogram of radar mD signature could be expressed as the magnitude of its STFT result as follows
SG(, fmD ) =
+∞
xmD (t)w(t − )e
−j2fmD t
−∞
dt
(2)
where xmD (t) denotes the radar mD signature and w(t) denotes the short time window function in STFT. Fig. 1 illustrates the simulated mD signatures in the time-frequency domain (spectrogram) using the STFT and in the frequency domain (power spectrum) using the fast Fourier transform, respectively, which correspond to radar echoes from targets with some typical micro-motions under noise environment.
3. Classification method based on mD
It is common that many objects or their structures have micromotions besides translational motion of bulk, such as dynamics of space objects in attitude control, rotation of rotor blades in helicopters and arm swinging of walking persons. Similarly to the Doppler phenomenon induced by the bulk translation, micromotions could also cause frequency modulation in the radar echoes, i.e., the mD frequency. Since micro-motions are always of the periodicity or quasi-periodicity coexisting with the bulk translation, the instantaneous mD frequency would distribute around the corresponding Doppler frequency. Moreover, in the power spectrum, the mD appears as sidebands about the target’s Doppler shift. In this work, considering the radar operating in the high-frequency regime, the scattering response of an object to radar signals could approximately be modeled by the sum of independent scattering centers, namely, the point scatterer model [6]. What is more, this model could simplify the analysis with the preservation of mD features of radar targets [1,2,7]. Additionally, as the Doppler frequency shift may have an impact on the performance of feature extraction and classification, here we assume that the motion compensation is carried out to remove its influence, which could result in the Doppler frequency fd → 0 Hz. Therefore, the mD frequency of the radar target can be represented as 2f0 2f v (t) = 0 fmDi (t) = c mDi c
807
i = 1, 2, . . . , N (1)
where f0 is the carrier frequency of the transmitted radar signal, c is the speed of light, N is the number of scattering centers, and vmDi (t), l i (t) are the instantaneous micro-motion velocity commDi (t) and n ponent in the direction of the radar line of sight (LOS), position vector and LOS unit vector of the ith scatterer, respectively. It can be seen from Eq. (1) that the mD frequency has the time-varying characteristics, and the relationship between the mD
The automatic classification of micro-dynamic targets refers to the assignment of the micro-motion state discrimination of unknown targets, in this work, based on time-frequency features extracted from radar mD signatures. As mentioned in Section 2, the distribution of mD signatures in the time-frequency domain characterizes corresponding micro-motions, thus the spectrogram could be used for mD feature extraction effectively. The typical radar classification system for micro-dynamic targets comprises the preprocessing, feature extraction and selection, training and class discrimination, where the training and class discrimination are also combined as the classifier design. The preprocessing phase is firstly used to remove noise, clutter, jamming and other interference from spectrograms. In the feature extraction and selection phase, a parsimonious set of reliable and stable features are created from the spectrograms of mD signatures. The feature selection process reflects the concern that computational requirements and the difficulty to train the classifier are highly correlated with the number of features used in the classification process. After the feature extraction process is completed, the resulting feature sets are used to train a predictive model and decision rules for classification of mD signatures. Finally, the trained predictive model is used to produce estimated target class assignments for test data. In this work, a preprocessing approach based on entropy is exploited to narrow the mD region of interest from the original spectrogram. After this segmentation, invariant moments and geometric characteristics of mD distribution are extracted as time-frequency features. Lastly, a decision-tree SVM classifier is applied for multiclass micro-dynamic target classification. Here three typical micro-motion classes, including cone-shaped targets with spinning and coning and cylinder targets with rotation, are modeled to be classified objects. An overview of the proposed classification method for radar micro-dynamic targets is shown in Fig. 2.
808
P. Lei et al. / Int. J. Electron. Commun. (AEÜ) 65 (2011) 806–813
Fig. 2. Block diagram of radar target classification using mD signatures.
(1) the value of H(x) reaches its minimum, 0, under the unique condition that the probability of only a state of the event x is equal to one while the others are all zero; (2) the value of H(x) reaches its maximum, log m, under the unique condition that probabilities of event states obey the uniform distribution. Fig. 1. Spectrograms and power spectrums of mD signatures from radar targets with typical micro-motions.
3.1. Segmentation of the mD region Assume that the event x has m possible states. Let pl denote the corresponding probability of the state l with 0 ≤ pl ≤ 1 and pl = 1, where l = 1,2, . . ., m. Then, the (Shannon) entropy could be defined as [9] m
H(x) = −
pl log pl
(3)
l=1
According to the statistical knowledge, the boundary of entropy in two extreme cases could be derived as
More generally, the value of H(x) is becoming larger as the probability distribution of event states becomes more random, and vice versa. Hence, as shown in case (1), when the states of event x are absolutely certain, the value of entropy is the minimum. On the contrary, in case (2), the event states are the most unpredictable, which accordingly leads to the peak entropy. Thus, the entropy can be used to describe the randomness of event states. In mD spectrograms, ranges of time and frequency depend on the measurement duration and sampling frequency. Nevertheless, the mD region of interest always holds a limited frequency band in the observation, while only noise is left in the other time-frequency areas, such as those shown in Fig. 1. From the uncertainty point of view, the pure noise region corresponds to more randomness than that in the mD region, which consists of the mD signatures and noise. Therefore, the entropy is adopted to segment the mD
P. Lei et al. / Int. J. Electron. Commun. (AEÜ) 65 (2011) 806–813
809
Fig. 3. Process of entropy-based region segmentation for mD distribution.
region of interest from the original spectrogram with the purpose of simplifying the following processing. In this entropy segmentation, amplitudes of the spectrogram for each frequency are firstly normalized in time using Eq. (4) as follows SG(i , fj )
SG (i , fj ) =
i
SG(i , fj )
(4)
where i = 1,2, . . ., M denotes the time samples and j = 1,2, . . ., N denotes the frequency samples. It can be seen that the normalized amplitude could be considered as the probability of a sample in the spectrogram for corresponding frequency. Substituting Eq. (4) into Eq. (3), the entropy of the spectrogram could be given by M
HmD (fj ) = −
SG (i , fj ) log SG (i , fj )
(5)
i=1
In addition, on account of the possible impact by noise and constant Doppler line (CDL) in the spectrogram, the minimum filter is utilized to smooth the fluctuation caused by them in HmD (fj ). Then the median value acts as the threshold to indicate the rough mD region and the focusing processing is followed to refine the result. Here, the region focusing is to concentrate the broad area after the median threshold discrimination by means of the boundary shift. This expansion problem is the by-product of minimum filtering, where the filter encompasses a neighborhood for the minimum value and the number of boundary shift units is also related to the filter kernel size. In order to make the segmentation mentioned above clear, we depict its process flow with corresponding simulation results, as shown in Fig. 3, where the spectrogram in Fig. 1(a) is used because noise, CDL and mD signal components with time-varying frequency are all contained. Fig. 3(b) presents the entropy of the original spectrogram. The values in the noise region are above the median threshold, whereas the false alarm peaks induced by noise and the salient by CDL in the mD region could confuse the segmentation. As seen in Fig. 3(c), the minimum filtering is effective to get rid of those distortions but yet introduces the expansion problem into the mD region. In Fig. 3(d), the area, where the entropy values are
below the threshold, is discriminated as the mD region, and the focusing processing is then utilized to obtain the refined result. Fig. 3(e) illustrates the final mD region based on the entropy segmentation. Comparing with Fig. 3(a), the segmented spectrogram has smaller time-frequency area only covering the frequency band of mD signatures. Hence, substituting the segmented spectrogram for the original one in the following feature extraction, it is beneficial to reduce the computational burden without loss of the mD information. 3.2. MD feature extraction For various micro-motions, the time-frequency representations generally display different geometric distribution in the twodimensional domain, such as spectrograms shown in Fig. 1. This indicates that some quantities describing the geometric relationship among mD signal components could be used as mD features for classification. In this work, the CDL and symmetry of components in the spectrogram are chosen as geometric characteristics, which are well representative of typical micro-motions according to Table 1 and experiments in [10]. The morphological algorithm and spatial filtering with unsharp filters [11] are firstly applied to the segmented spectrogram. After the peak detection, both geometric characteristics are then obtained. If there exists the CDL, the flag is set to one, otherwise it is to zero. The symmetry of mD signal components is measured by a ratio in range [0,1], where the larger ratio denotes a higher degree of symmetry of the mD signature in the time-frequency distribution. In addition, considering the spectrogram as a two-dimensional image, curves of the time-varying frequency corresponding to mD Table 1 Geometric characteristics of the general time-frequency distribution for three micro-motion classes. Geometric characteristics
CDL Symmetry
Classes Spinning
Coning
Rotation
Yes Yes
No No
No Yes
810
P. Lei et al. / Int. J. Electron. Commun. (AEÜ) 65 (2011) 806–813
signatures could be dealt with as objects of interest in the image. Although geometric characteristics are invariant for a given micromotion, the offset and rate of change in the mD frequency could be distinct under different conditions of LOS direction, target size and micro-motion velocity according to Eq. (1). From the viewpoint of imaging, it means that features independent of scale, position and orientation may be applicable in micro-dynamic target classification on the basis of the spectrogram. Hu derived seven nonlinear functions of invariant moments for the visual pattern recognition [12]. They are formed by the second and third order central moments with normalization, and invariant to translation, scaling and rotation in the case of continuity. In order to be applied in mD spectrograms, the modified Hu’s invariant moments [13] for discrete events are adopted in this work to characterize the invariance of mD features in the time-frequency domain. Let SG (i, j) be the segmented spectrogram, where i = 1,2, . . ., M and j = 1,2, . . ., L(L ≤ N). The normalized central moment of order (p + q) of SG (i,j) is defined as
M L
pq =
i=1
M i=1
(i − x) (j − y) SG (i, j) p
j=1
q
(p+q+2)/2
L
(6)
SG (i, j) j=1
¯ is its center of gravity and p + q ≥ 2. Then in terms where (¯x, y) of Hu’s invariant moments, the moment based characteristics of mD signatures in the time-frequency distribution are given by 1
= 20 + 02
2
=
(7)
(20 − 02 )2 + 411 2 1
3
=
(30 − 312 )2 + (321 − 03 )2 1
4
= =
(9)
3
(10)
3
= =
Spinning
Coning
Rotation
1
2
1
2
1
2
3
Height (m) Bottom radius (m) Spin frequency (Hz) Coning frequency (Hz) Coning angle (◦ )
2.0 0.5 2.5 N N
2.2 1.0 1.5 N N
2.0 0.5 N 0.5 20
2.0 1.0 N 0.3 10
1.2 0.4 N N N
2.0 1.0 N N N
0.8 0.3 N N N
Rotation angular velocity (rad/s)
N N N
N N N
N N N
N N N
3.1 3.1 3.1
2.1 2.4 3.1
−3.1 1.6 3.1
in the multiclass classification. In order to extend the application of SVM, some multiclass SVM approaches have been developed to act in the multiclass situation. The typical ones include the one-against-all SVM, one-against-one SVM and decision-tree SVM [17,18]. In this work, the decision-tree SVM is used in the training and class discrimination of time-frequency features from three types of radar micro-dynamic targets. It introduces the binary tree architecture in decision theory into the basic SVM. The decisiontree SVM approach assigns SVMs to each node of the tree, where the binary decision is made to separate the input data into two proper classes saved at the respective subnodes. Repeat this classifying process sequentially until every leaf node, i.e., the furthest extremity of a branch in the tree architecture, contains only one class of data. Comparing with the other two multiclass SVM approaches mentioned above, the decision-tree SVM has the advantage of simple architecture and low computational complexity. The related theoretical analysis and experiments are presented with more details in [19].
In this section, the performance of the proposed classification method for radar micro-dynamic targets is discussed and
6
(20 − 02 )[(30 + 12 )2 − (21 + 03 )2 ] + 411 (30 + 12 )(21 + 03 ) 1
7
Classes
(30 − 312 )(30 + 12 )[(30 + 12 )2 − 3(21 + 03 )2 ] + (321 − 03 )(21 + 03 )[3(30 + 12 )2 − (21 + 03 )2 ] 1
6
Parameters
4. Experimental results and discussion
(30 + 12 )2 + (21 + 03 )2 1
5
(8)
2
Table 2 Parameters of micro-dynamic targets in experiments.
4
(321 − 03 )(30 + 12 )[(30 + 12 )2 − 3(21 + 03 )2 ] − (30 − 312 )(21 + 03 )[3(30 + 12 )2 − (21 + 03 )2 ] 1
6
3.3. SVM classifier The SVM is a machine learning algorithm based on the structural risk minimization. Because of its generalization ability and good performance in the case of small-sized training data, it has been widely used in the research field of radar target classification [14–16]. The basic principle of SVM is to determine the optimal hyperplane when the two sets of input data are linearly separable. Here, the optimal hyperplane refers to the surface which not only separates the two sets of data but also produces the largest margin between them. It can be observed that this optimal hyperplane, which helps the classifier minimize the generalization error, is actually supported by the data located on it. Accordingly, these data are support vectors. For nonlinearly separable data, the SVM would map them into a higher-dimensional space using some kernel functions, which convert the nonlinear problem into a linear one. Thus, the optimal hyperplane of nonlinear data could be found by SVM in a high-dimensional space. The SVM is originally proposed for the binary classification problem. However, more tasks in actual practice would yet be involved
(11)
(12)
(13)
evaluated according to experimental results. The simulated database applied in this work includes three micro-dynamic object classes: cone-shaped targets with spinning and coning motions and cylinder targets with rotation. For the spinning and coning classes, each data were obtained from two different cones, while the data of rotation class were acquired from three cylinders. The parameters of micro-dynamic targets in experiments are listed in Table 2. On the whole, a three-class classification problem comprising seven micro-dynamic targets is studied here. To be close to real scenarios, the additive white Gaussian noise with zero-mean is used to contaminate radar echoes according to a certain signal-to-noise ratio (SNR). In the training phase, mD signatures from each target are generated under various conditions of initial Euler angles at SNR of 20 dB. These angles in the three-dimensional space obey the uniform distribution. It also indicates that the training data are sampled at equal intervals of aspect angles in statistics, and the number of samples is dependent on the specified size of training data. For this three-class classification problem, the corresponding class labels of training data are denoted as 1, 2 and 3, respec-
P. Lei et al. / Int. J. Electron. Commun. (AEÜ) 65 (2011) 806–813
811
Fig. 4. Sample spectrograms of the testing set in classification.
efficiency of training and the above results, the training set with the size of 600 frames per target is adopted and the number of Monte-Carlo simulations is still set to 200. Fig. 6 illustrates the corresponding classification accuracy using different feature vectors. It can be observed that the accuracy using two-dimensional feature vector slightly increases from about 78.1% to about 83.5% in the SNR range between 5 and 20 dB. The loss of classification performance here is mainly attributed to the extraction error of symmetry characteristic. Nevertheless, when using the seven- or nine-dimensional feature vector instead in the high SNR range, the classification accuracy would be much improved. Especially at the SNR levels above 12 dB, the average classification rate based on the nine features approximately reaches 92.4%, which is higher than that of about 90.3% based on the seven features. However, in the SNR range between 5 and 12 dB, the accuracy of the former declines more rapidly and is lower than that of the latter. Therefore, the classification of targets with micro-motions based on nine timefrequency features could achieve good performance at high SNR
100 95
Classification Accuracy / %
tively. All these labeled mD signatures would constitute the training set. In the testing phase, 50 frames of mD signatures for each micro-dynamic target with respect to different aspect angles are randomly produced at given SNR in every experiment. Hence, a testing set, including unlabeled mD signatures from seven targets, comprises a total of 350 frames. Assume that the radar operates at f0 = 5 GHz, the pulse repetition frequency is 1.5 kHz, and the duration of each observation is 2 s. The Hamming window is used in STFT for the time-frequency analysis. As the classes of training data are known, the suitable window size could be selected according to the corresponding class label, while the testing set is processed automatically over a fixed 0.07 s time window. Some sample spectrograms of the testing set using the STFT are shown in Fig. 4. Firstly, we study the performance of the classification method for micro-dynamic targets under the condition of different training data sizes. After generating a training set of 1000 frames for each target, another two sets with the size of 600 and 300 frames for each target are obtained by the uniform sampling, respectively. In order to simplify the expressions, the three training sets are denoted as Sets A, B and C through their different sizes (size of A > B > C). The nine-dimensional feature vector in this investigation is composed of two geometric characteristics and seven invariant moments. Fig. 5 shows the results of 200 Monte-Carlo simulations. It can be seen that the classification accuracy in all three cases of training sets tends to remain stable and almost identical to reach an average rate of about 92.7% at the SNR levels above 14 dB. In the SNR range between 5 and 14 dB, the accuracy declines rapidly as the SNR decreases, and the classification rate based on Set A is at most only about 2.3% and 6.6% higher than those based on Sets B and C, respectively. The results suggest that the proposed method could still be effective in the case of limited-sized training set. This performance is mainly ascribed to the good generalization of SVM and high distinguishability of mD features for the three classes of targets. Secondly, the effect of time-frequency features used in this work on classification results is investigated. Besides the ninedimensional feature vector, the two-dimensional feature vector of only geometric characteristics and the seven-dimensional feature vector of only invariant moments are utilized for both training and testing to evaluate this method, respectively. Considering the
90 85 80 75 70 65
1000 training data 600 training data 300 training data
60 55 50
5
8
11
14
17
20
SNR / dB Fig. 5. Classification accuracy in different training set sizes with the increasing SNR.
812
P. Lei et al. / Int. J. Electron. Commun. (AEÜ) 65 (2011) 806–813
100
Classification Accuracy / %
95 90 85 80 75 70 65
9 features 7 features 2 features
60 55 50
5
8
11
14
17
20
SNR / dB Fig. 6. Classification accuracy in different dimensions of feature vectors with the increasing SNR.
Spinning Coning Rotation
Acknowledgements The authors would like to acknowledge helpful comments from the anonymous reviewers and valuable support from K. Li at Harvard University to improve the paper.
Table 3 Confusion matrix of classification results at SNR = 20 dB. Test data
order to take into account some possible occasions in practice, we have further conducted experiments under different conditions of SNR, training set and feature vector with the decision-tree SVM, and then discussed the performance to assess the validity of the proposed method. It is found that this method is applicable in the radar microdynamic target classification both with a limited-sized training set and over a wide SNR range. The classification accuracy is over 90% at high SNR levels (≥12 dB), and even in low SNR range between 5 and 7 dB, the accuracy of around 80% may be achieved by proper feature selection. It should be mentioned that in order to focus on the highlight of this work, we only adopt the classical STFT in the timefrequency analysis of mD signatures. According to the investigation in Section 4, we can expect that the classification performance of this method could be further improved if new adaptive algorithms of time-frequency analysis are exploited to optimize the feature information in the spectrogram, especially at some unfavorable aspect angles.
Predicted classes Spinning
Coning
Rotation
99.9% 0.0% 1.2%
0.0% 85.7% 6.7%
0.1% 14.3% 92.1%
levels (≥12 dB). Although its accuracy falls to about 65.8% because of the influence of noise on invariant moments at low SNR levels (5–7 dB), some improvement, such as the selection of proper features according to Fig. 6 and the above analysis, could be carried out in this method to obtain better performance. Table 3 presents the detailed classification results of 200 MonteCarlo simulations between the three classes at SNR of 20 dB with the training set of 600 frames per target and nine-dimensional feature vector. It indicates that the spinning targets could successfully be discriminated from the other two classes in the testing set with the remarkable accuracy of about 99.9%, while the classification performance between the coning class and the rotation class degrades. This may be attributed to their small ranges of mD frequency. Additionally, it should be noted that the time-frequency distribution at some unfavorable aspect angles is very difficult for the correct feature extraction, as shown in Fig. 4(g)–(i), thus, possible errors in the training or testing set would lead to wrong decisions in the classification. 5. Conclusions In this paper, we have presented a new automatic classification method for radar micro-dynamic targets. The first contribution emphasized here is the entropy-based region segmentation of spectrograms. It takes advantage of the difference between mD signatures and noise in the time-frequency domain and is capable of being applied to various cases. The segmented results would be beneficial to the reduction of computational burden without loss of mD information and the improvement of the follow-up feature extraction. The second contribution is the extraction of modified invariant moments as mD features. We have analyzed their properties and given the mathematical expressions in the mD spectrogram. They indicate the ability to serve as a novel set of mDbased classification features with high distinguishability. Finally, in
References [1] Chen VC, Li F, Ho SS, Wechsler H. Micro-doppler effect in radar: phenomenon, model and simulation study. IEEE Trans Aerosp Electron Syst 2006;42:2–21. [2] Lei J, Lu C. Target classification based on micro-doppler signatures. In: Proceedings of IEEE international radar conference, Arlington, USA. 2005. p. 179–83. [3] Smith GE, Woodbridge K, Baker CJ. Naïve Bayesian radar micro-doppler recognition. In: Proceedings of international conference on radar, Adelaide, Australia. 2008. p. 111–6. [4] Nanzer JA, Rogers RL. Bayesian classification of humans and vehicles using micro-doppler signals from a scanning-beam radar. IEEE Microw Wireless Compon Lett 2009;19:338–40. [5] Kim Y, Ling H. Human activity classification based on micro-doppler signatures using a support vector machine. IEEE Trans Geosci Remote Sens 2009;47:1328–37. [6] Keller JB. Geometrical theory of diffraction. J Opt Soc Am 1962;52:116–30. [7] Thayaparan T, Abrol S, Riseborough E, Stankovic L, Lamothe D, Duff G. Analysis of radar micro-doppler signatures from experimental helicopter and human data. IET Radar Sonar Navig 2007;1:289–99. [8] Chen VC, Ling H. Time-frequency transforms for radar imaging and signal analysis. Boston: Artech House; 2002. [9] Shannon CE. A mathematical theory of communication. Bell Syst Tech J 1948;27, 379–423, 623–56. [10] Lei J. Pattern recognition based on time-frequency distributions of radar micro-doppler dynamics. In: Proceedings of the sixth international conference on software engineering, artificial intelligence, networking and parallel/distributed computing and first ACIS international workshop on selfassembling wireless networks, Towson, USA. 2005. p. 14–8. [11] Gonzales RC, Woods RE. Digital image processing. 3rd edition NJ: Pearson Prentice Hall; 2007. [12] Hu MK. Visual pattern recognition by moment invariants. IRE Trans Inf Theory 1962;8:179–87. [13] Fu Y, Lv J. Recognition of SAR image based on SVM and new invariant moment feature extraction. In: Proceedings of the second international symposium on knowledge acquisition and modeling, Wuhan, China. 2009. p. 15–8. [14] Lardeux C, Frison PL, Tison C, Souyris JC, Stoll B, Fruneau B, et al. Support vector machine for multifrequency sar polarimetric data classification. IEEE Trans Geosci Remote Sens 2009;47:4143–52. [15] Anagnostopoulos GC. SVM-based target recognition from synthetic aperture radar images using target region outline descriptors. Nonlinear Anal 2009;71:e2934–9. [16] Yeary MB, Nemati S, Yu TY, Wang Y, Zhai Y. A support-vector-machine-based approach to RF sensor spectral signature classifications. IEEE Trans Instrum Meas 2009;58:221–8. [17] Foody GM, Mathur A. A relative evaluation of multiclass image classification by support vector machines. IEEE Trans Geosci Remote Sens 2004;42:1335–43. [18] Horng MH. Multi-class support vector machine for classification of the ultrasonic images of supraspinatus. Expert Syst Appl 2009;36:8124–33. [19] Fei B, Liu J. Binary tree of SVM: a new fast multiclass training and classification algorithm. IEEE Trans Neural Netw 2006;17:696–704.
P. Lei et al. / Int. J. Electron. Commun. (AEÜ) 65 (2011) 806–813 Peng Lei was born in Shaanxi, China, in 1985. He received the B.S. degree in electronic and information engineering from the Beijing University of Aeronautics and Astronautics (BUAA), Beijing, China, in 2006. He is currently working towards the Ph.D. degree in signal and information processing from BUAA. His current research interests include signal processing, radar feature extraction, image processing, target recognition, and DSP applications.
Jun Wang was born in Shaanxi, China, in 1972. He graduated from School of Electronic Engineering, Northwestern Polytechnical University, in 1995, and received the master and Ph.D. degrees in signal and information processing from Beijing University of Aeronautics and Astronautics (BUAA) in 1995 and 2001. He is now an associate professor in School of Electronic and Information Engineering, BUAA. He is interested in real-time DSP system design and implementation, wireless communications, SAR image processing and so on.
813
Peng Guo was born in Beijing, China, in 1986. She received the B.S. degree in electronics and information engineering from the Beijing University of Aeronautics and Astronautics (BUAA), Beijing, China, in 2008. She is now working towards the master degree in information and communication engineering at BUAA. Her principal interest is in the simulation of radar signal processing.
Duoduo Cai was born in HuBei, China, in 1987. He received the B.S. degree in communication engineering from the HuaZhong University of Scinence and Technology, WuHan, China, in 2009. Now he is studying for master degree in signal and information processing at the Beijing University of Aeronautics and Astronautics (BUAA), mainly on radar signal processing and stepped-frequency radar system simulation.