Radar target classification method with high accuracy and decision speed performance using MUSIC spectrum vectors and PCA projection

Authors


Abstract

[1] This paper introduces the performance of an electromagnetic target recognition method in resonance scattering region, which includes pseudo spectrum Multiple Signal Classification (MUSIC) algorithm and principal component analysis (PCA) technique. The aim of this method is to classify an “unknown” target as one of the “known” targets in an aspect-independent manner. The suggested method initially collects the late-time portion of noise-free time-scattered signals obtained from different reference aspect angles of known targets. Afterward, these signals are used to obtain MUSIC spectrums in real frequency domain having super-resolution ability and noise resistant feature. In the final step, PCA technique is applied to these spectrums in order to reduce dimensionality and obtain only one feature vector per known target. In the decision stage, noise-free or noisy scattered signal of an unknown (test) target from an unknown aspect angle is initially obtained. Subsequently, MUSIC algorithm is processed for this test signal and resulting test vector is compared with feature vectors of known targets one by one. Finally, the highest correlation gives the type of test target. The method is applied to wire models of airplane targets, and it is shown that it can tolerate considerable noise levels although it has a few different reference aspect angles. Besides, the runtime of the method for a test target is sufficiently low, which makes the method suitable for real-time applications.

1. Introduction

[2] The radar target classification is an important and challenging problem in radar applications. In radar target classification methods, the main goal is to distinguish targets by using similarities between the features of test target and known (candidate) targets. These features are generally obtained by processing scattered signals from targets in noncooperative target recognition [Skolnik, 2001; Tait, 2009]. However, the scattered signal from a target is highly dependent on operating frequency, polarization and aspect angle; therefore, a designed classification method should be independent of these parameters as possible. Besides, additional random noise makes the classification problem more complicated and reduces the accuracy rate of the methods. In order to minimize adverse effect of the noise an intelligent classifier containing sufficiently noise-resistant target features is needed. Decision speed is also an important criterion for a classification method that the method should be fast in order to be convenient for real-time applications.

[3] An electromagnetic target has three different scattering regions (Rayleigh, resonance and optical) when operating wavelength (λ) is compared to target's size. If the target's size (d) is much larger than operating wavelength (dλ), the scattering region is optical region, where radar systems generally operate at this region. If the target's size is comparable with operating wavelength (0.1λ < d < 10λ), the target is in resonance region, where creeping waves are very effective [Barton, 2005]. There are many military and civil applications for this resonance region in the literature such as landmine and unexploded ordnance detection using ground penetrating radar (GPR) [Peters et al., 1994; Chen and Peters, 1997], security system applications [Harmer et al., 2009] and even biomedical applications [Huo et al., 2004]. In this paper, it is mainly aimed to develop a target classification method suitable for this resonance scattering region as in the mentioned applications, where targets' dimensions are close to the wavelength of the incident electromagnetic signal of the application. Moreover, it is targeted to make this classification with satisfactory accuracy rate and decision speed performances.

[4] In resonance scattering region, according to singularity expansion method (SEM), the late-time portion of scattered signal of a target is expressed as the sum of damped sinusoidal signals [Chuang et al., 1985; Baum et al., 1991; Mooney et al., 1996].

equation image

where Ω represents aspect angle and polarization dependency; bn(Ω) and δn(Ω) are aspect and polarization dependent amplitude and phase constant of nth damped sinusoids, respectively; αn and fn are aspect and polarization independent parameters of nth damped sinusoids. The resonance frequencies fn are unique to a target that radar cross section (RCS) or scattered field of a target in frequency domain gives peak values at about fn values [Van Bladel, 2007]. These unique resonance frequencies are only dependent on the physical (shape, length, etc.) and material (conductivity, permittivity or permeability) properties of the target; however, theoretically, they do not vary even if aspect angle or polarization of the incident or scattered field changes.

[5] In this study, a highly aspect-independent target classification method is proposed, which utilizes from the effects of aspect-independent resonance frequencies fn in the resonance region scattering problem. The feature extraction stage of the developed method starts with noise-free scattered signals obtained from K different reference aspect angles for a fixed polarization for each known target. Late-time portion of each signal, which begins after the interaction between incident wave and target vanishes [Van Bladel, 2007], is then processed with pseudo spectrum Multiple Signal Classification (MUSIC) algorithm. The MUSIC algorithm is a parametric frequency estimation method [Bienvenu and Kopp, 1983; Schmidt, 1986; Stoica and Moses, 2005] and it is commonly used in radar imaging and target recognition problems due to its high resolution property as compared to conventional fast Fourier transform (FFT) [Odendaal et al., 1994; Zhang, 1995; Kim et al., 2002; Tait, 2009]. Statistically, when this algorithm is applied to a signal as in (1), it constitutes a spectrum, which has peak values at about fn frequencies in (1). However, in target classification methods, using only one reference scattered signal for each target is insufficient in order to collect necessary feature information for the target [Secmen and Turhan-Sayan, 2009]. Therefore, multiple reference scattered signals obtained from multiple different aspect angles for each target should be used. For this purpose, when MUSIC is applied to K reference signals for a target, K different MUSIC spectrum vectors are obtained. Because the resonance frequencies are independent from the aspect angle for the target, it is expected statistically that all resulting MUSIC spectrum vectors of the target should have same peak frequencies at fn values of the target. However, this increases the complexity and dimensionality in the problem when a test target's feature is compared with these K different vectors. For this purpose, principal component analysis (PCA) is used after the process of MUSIC algorithm has finished. PCA technique is mainly used in data compression and dimensionality reduction problems [Duda et al., 2001; Jackson, 2003] and is again an important tool in electromagnetic target recognition applications [Kim et al., 2002; Turhan-Sayan, 2005; Lee et al., 2008; Huang and Lee, 2010]. By applying PCA projection technique, only one MUSIC spectrum vector is obtained for the target from K different vectors. According to PCA theory, the gathered vector for the target is expected to be highly correlated with K different MUSIC spectrum vectors. Therefore, the vector should have same peak frequencies with the preceding K spectrums but its peak heights at the resonance frequencies may be different than these spectrums. This PCA vector is assigned as main feature of the target. This procedure is repeated for other “known” targets and one feature vector to be stored in classification database is obtained for each target. Consequently, when an analogy between electromagnetic and signal processing is established for the targets, the information about physical and material properties of a target is converted to resonance frequencies information of the target by using MUSIC algorithm and PCA and they are reserved in the spectrum of the target.

[6] The classification (test) stage of the proposed method is initiated with time-scattered signal of a test target, which may be noise-free or noisy as in real radar target applications. Then, same late-time portion (used in the feature extraction stage) of this signal is subjected to MUSIC algorithm and MUSIC spectrum vector of test target is obtained. Finally, the test vector is correlated with feature vectors of known targets one by one and the classification (decision) is made according to the highest correlation coefficient. Because the physical or material properties of the targets are different, their feature MUSIC spectrum vectors after PCA process should be different with respect to peak (resonance) frequencies. Therefore, the correlation between test vector belonging to any aspect angle condition and “matched” MUSIC spectrum vector should be high since they contain same peak frequencies. On the other hand, the correlation values between test vector and MUSIC spectrum vectors of other targets should be low since their peak frequencies in the vectors are different. Correspondingly, the suggested method including MUSIC algorithm and PCA technique is expected to classify the test targets reliably and it can give high accuracy rates for the applications.

[7] In sections 26, the theory and details of feature extraction and classification stages of the proposed method are explained. Then, the performance of the method is given for a target set of wire models of airplane targets modeled by thin, straight and conducting wires. In this part, the accuracy rate performance of the proposed method is initially compared with the method using conventional FFT for noise-free test signals. It is shown that the proposed method is highly superior to FFT method with respect to accuracy rate performance for noise-free test signals. The noise performance of the method is then investigated showing that the method gives sufficient accuracy rates within a low computational time even for very noisy signals and small number of reference aspect angles.

2. Feature Extraction Stage

[8] The proposed method starts by assuming M different known targets to be classified and the aim in the feature extraction stage is to provide one feature vector for each target. Each target has K different reference scattered signals obtained from K different predetermined aspect angles. Therefore, a total of K × M different scattered signals is available in the feature extraction signal database. By considering one of these reference signals, the late-time portion of this signal given in (1) is generally expressed as in (2) in discrete-time domain by including noise:

equation image

where w(n) is the noisy part of the signal, L is the number of effective damped exponentials and Δt is sampling period. Because the noise-free reference signals are used in the feature extraction stage, only x(n) is taken into account for the following steps of feature extraction stage. Next, MUSIC algorithm is used for the signal in (2), where MUSIC algorithm is well-known to have super-resolution property as compared to Fourier transform [Yamada et al., 1991]. Besides, it has a statistical advantage over FFT algorithm especially in low noise levels that the standard deviation of estimated frequencies with MUSIC algorithm caused by the random changes of amplitude and phase terms of sinusoidal signals due to different aspect angle conditions are generally lower than FFT algorithm [Reinhold, 2009]. As noise level increases, MUSIC algorithm is known to be more subject to estimation errors due to noise than FFT algorithm. However, super-resolution ability is more important and dominant to this noise sensitivity effect in the view of accuracy rate performance of the suggested method that this statement will be supported with the results given in the application of this paper.

[9] Although the signal in (2) is composed of the superposition of complex frequencies (damped exponentials), the designed classification method obtains the spectrum of the signal in real frequency domain rather than complex frequency domain [Li et al., 1998; Secmen and Turhan-Sayan, 2009]. Consequently, MUSIC algorithm is deliberately used to increase the speed of the method significantly. In MUSIC algorithm, the covariance matrix of the signal is estimated by using the vector X(n) given as [Shan et al., 1985; Stoica and Moses, 2005].

equation image

where T is transpose operator, m is the user-defined MUSIC parameter and Rxx is the estimated covariance matrix with dimensions m by m. The selection of the value of m parameter is critical that large m values increase the dimensions of Rxx covariance matrix, equivalently, the computational complexity and small m values decrease the resolution ability of the method. In order to balance the trade-off between complexity and resolution, the parameter m is selected as N/2 in the method [Li et al., 1998; Kim et al., 2002; Secmen and Turhan-Sayan, 2009]. Using this covariance matrix, the pseudo spectrum MUSIC vector of the signal with respect to real frequency is given as

equation image
equation image

where s is the number of frequency sample and vk is the kth right-singular vector (eigenvector) in singular value decomposition (SVD) of Rxx matrix. When the SEM theory is considered, this vector should give again peak values at fn values in (1).

[10] The procedure described above is repeated for all reference signals and K different normalized MUSIC spectrum vectors are obtained for the target. All resulting vectors have maximums at the same frequency values but with different peak amplitudes due to aspect angle dependency. However, if these K different vectors for the target are stored as feature vectors and classification is done by comparing a test vector with feature vectors one by one, it can cause an important increase in both memory storage and computational complexity. Therefore, a single feature for each vector, which has highest correlation with these K vectors, should be extracted in order to decrease redundancy and dimensionality. In the proposed method, this part is achieved with PCA-based reduction technique, in which a matrix, whose rows are mean-extracted PMUSIC vectors, is constructed as follows:

equation image

where PMUSIC,i (i = 1,2, …, K) is the vector regarding to ith aspect angle. The covariance matrix of G matrix is defined in (7) as

equation image

where cij defines the covariance between vectors Gi and Gj. By using the matrix C, the principal component row vectors (z1, z2, …, zK) are evaluated as

equation image

where the vectors, u1, u2, …, uK are normalized column eigenvectors of matrix C corresponding to the eigenvalues of matrix C arranged in nonincreasing order as λ1λ2 ≥ … ≥ λK. Finally, the single feature vector F for this target is obtained as

equation image

However, if the percentage of λ1 in the summation of eigenvalues (λi values) is sufficiently large (for instance, higher than 90%), the other principal components can be neglected and the feature vector F becomes equal to first principal component z1 only. However, the contributions of other components should be considered if the percentage of first component is inadequate. The mentioned steps so far for the extraction of feature vector of a single target are repeated for each known target and a total of M feature vectors for M targets is stored to feature database.

3. Classification Stage

[11] In the classification stage, a test scattered signal obtained from an unknown target and unknown aspect angle is initially considered. Since this test signal may be noise-free or noisy, x(n) is replaced by z(n) in (3) and the covariance matrix Rzz is constructed. The remaining steps for the evaluation of MUSIC spectrum vector of test signal (Ptest) are same as those described in the feature extraction stage. Since test target is actually one of the known targets, test MUSIC spectrum vector has theoretically same resonance frequencies with the feature vector of this known target. On the other hand, the peak amplitude levels of the test vector can be different from the feature vector of this known target due to aspect angle dependency, autocorrelation matrix estimation errors or computation precision. However, in the suggested method the locations of peaks in the frequency axis corresponding to resonance frequencies are important rather than peak amplitude information. In other words, as long as the resonance frequencies in the vector of the test target match with the frequencies of one of the known targets, their (test and the matched targets) correlation in terms of vectors will be adequately high even if peak amplitudes are different (provided that these differences are not extreme). Therefore, test MUSIC spectrum vector should have highly correlated with the matched target and low correlations with others. For this purpose, test vector (Ptest) is compared with the stored feature vectors Fi (i = 1,2, …, M) by using a simple correlation coefficient evaluation given as

equation image

where verticals indicate the norm operator, Fi is the feature vector belonging to ith known target and r(i) is the correlation coefficient between Ptest and Fi vectors. Finally, test target is classified as one of the known targets that this known (matched) target has the highest correlation (highest r value) with test target among all possible known targets.

[12] This template matching approach given in the classification stage of the proposed method is considered for the cases where the number of targets in the applications is low or moderate, i.e., it is equal to four for the following wire models of airplane targets application. If the number of targets increases so much, the decision speed of the method may become significantly slow. For these cases, the classification stage based on comparison of correlation coefficients in this paper can be replaced by the methods depending on neural networks or support vector machines, which are expected to be faster than correlation method for the applications with high number of target. This will be considered as a future work for possible subsequent studies.

4. Application of the Method to Wire Models of Airplane Targets

[13] The developed target classification method is applied to a target set, which consists of four wire models of airplane targets (Airbus, Boeing 747, Caravelle and Tu 154). These airplane targets are modeled by perfectly conducting, straight and thin wires. All airplane targets, whose dimensions are given in Table 1, are scaled down by a factor of 100 [Kim et al., 2000]. The geometrical orientation for airplane targets and incident wave is given in Figure 1, where k vector shows the direction of incidence and E vector is the electric field of the incident wave.

Figure 1.

The geometry for wire models of airplane targets where k is the direction of incident wave and E is electric field oriented in ϕ direction.

Table 1. The Dimensions of Airplane Targets Used in the Application
 Target 1 (Airbus)Target 2 (Boeing 747)Target 3 (Caravelle)Target 4 (Tu 154)
Body length (m)0.54080.70660.32000.4790
Wing length (m)0.44840.59640.34400.3755
Tail length (m)0.16260.22170.10920.1340

4.1. Collection of Scattered Signals

[14] The backscattered (monostatic) frequency responses of all targets are generated by using CST Microwave Studio for a fixed elevation angle θ = 60° and linear polarization in ϕ direction for both incident and scattered fields as shown in Figure 1. Scattered fields are obtained for several azimuth angles at ϕ = 0°, 2.5°, 5°, …, 87.5°, 90° (a total of 37 azimuth angles). The frequency bandwidth of the responses is 4–1024 MHz. When the dimensions of the targets are considered, all targets are said to be safely in resonance scattering region that the largest dimension, body length of Boeing 747 (0.7066 m), is at most 2.4λ for the given frequency bandwidth. The frequency resolution is chosen as Δf = 4 MHz in order to be consistent with the studies in [Kim et al., 2000; Secmen and Turhan-Sayan, 2009] following that the synthesized responses have 256 frequency points. The frequency responses are converted into time domain scattered signals by using inverse FFT and 1% low-pass Gaussian window in MATLAB environment. Consequently, time domain responses of the targets for an incident Gaussian pulse having approximately 1 ns pulse width are synthesized, where incident Gaussian pulse is commonly used as an approximation to the impulse response [Rao, 1999]. Two sample scattered signals among all resulting signals, which belong to Caravelle at ϕ = 5° and Tu-154 at ϕ = 5°, are given in Figure 2.

Figure 2.

The scattered signals for Caravelle at ϕ = 5° and Tu-154 at ϕ = 5°.

4.2. Construction of Feature Vectors

[15] The reference signals for the construction of feature vectors are selected as time responses coming from only 5 aspect angles (ϕ = 5°, 22.5°, 45°, 67.5° and 85°) out of 37 aspect angles for each target. Next, the late-time portions of these signals are considered for the following steps. As explained before, the late-time portion of the signals starts after the incident wave has no influence on the target. By using this definition, the start time instant can be approximated as Tstart = Tp + 2Td, where Tp is the pulse duration (about 1 ns in this application) and Td is the duration for the incident wave to fully pass the target [Rothwell et al., 1994]. In this application, for the sake of guarantee, Td is selected as its highest value for all signals, which is equal to Td = Dmax/c, where Dmax is the longest linear dimension for all airplane targets and c is the speed of light. Dmax corresponds to the diagonal dimension of Boeing 747, which has the longest body and wing dimensions among all targets. Therefore, Td is approximately evaluated as 3 ns and Tstart is calculated to be 7 ns.

[16] The selection of late-time duration is crucial that it should not be too long or short. As time passes, the amplitude of the late-time signal decreases due to damped behavior in SEM. Hence, with the additional noise, the effective signal-to-noise ratios (SNR) of long-duration late-time signals significantly decrease as compared to late-time signals having shorter duration. The decrease in SNR generally causes an important degradation in noise performance of the classification methods. Besides, short-duration late-time signals have lower number of time samples for a fixed time resolution, which decreases the resolution performance of MUSIC algorithm. Therefore, an optimum late-time duration, which balances MUSIC and noise performances, should be chosen. In this application, the duration of late-time portion of the signals are selected as about 31 ns (from 7 ns to 38 ns) giving N = 64 time samples, where the number of time samples is deliberately chosen as the power of two in order to increase the speed of algorithm in MATLAB. After the determination of late-time portion of reference signals, the MUSIC vectors, PMUSIC, are constructed as described in feature extraction stage. The relevant MUSIC parameter in MUSIC algorithm part is selected as m = N/2= 32. In order to find the number of natural resonance frequencies (L), a model order estimation method is used [Kitamura et al., 1999], which is mainly based on minimum description length (MDL) principle. When this method is applied to all reference scattered signals, the value of parameter L is found to be 4 at most. Thus, in order not to underestimate the model order of the signals, L is selected as 4 for all reference and test signals of the application. By using these parameter values, normalized MUSIC spectrum vectors for reference scattered signals are constructed. A sample normalized MUSIC spectrum vector belonging to Tu-154 at ϕ = 67.5° is given in Figure 3 that two dominant frequencies (peak values) are about 236 and 348 MHz. In order to compare MUSIC algorithm with FFT algorithm, FFT vectors corresponding to both same late-time portion of the scattered signal (from 7 ns to 38 ns) and whole late-time scattered signal (full signal after 7 ns) are also given in Figure 3. It can be shown from Figure 3 that the resonance frequency 236 MHz, which is clearly shown in MUSIC vector, is not visible (or may be hardly visible) in both FFT vectors; and even if it is assumed to be resolved by FFT algorithm for this noise free case, this resonance frequency can be easily disappeared with the addition of low noise levels. Therefore, FFT vectors have low resolution property as compared to MUSIC vector even for this noise-free signal.

Figure 3.

FFT vectors belonging to two different late-time durations and MUSIC spectrum vector for Tu-154 at ϕ = 67.5°.

[17] After the evaluation of MUSIC spectrum vectors for each reference signals, PCA technique is applied to each target. For this purpose, five different MUSIC spectrum vectors obtained for five reference signals are used and PCA steps are processed for each target. In PCA stage, for the given application, the percentages of the highest eigenvalue (λ1) in the summation of all eigenvalues are 82.64, 74.62, 80.56 and 85.97 for Airbus, Boeing 747, Caravelle and Tu 154, respectively. Therefore, instead of using the first principal component, the first and second principal components having total eigenvalue percentages of 95.57, 91.58, 97.45 and 98.79 for Airbus, Boeing 747, Caravelle and Tu 154, respectively, are used in the construction of feature vectors. In order to demonstrate the correlation between feature vectors and MUSIC vectors belonging to different aspect angles, the correlation coefficient values are given in Table 2. In Table 2, for instance, the value 0.9183 is the correlation between the feature vector of the target given at leftmost of the row (Airbus) and MUSIC vector of the same target at the aspect angle given at the top of the column (5°). According Table 2 results, the minimum of these correlation values is found to be 0.6008. Finally, the resulting feature vectors for each target are shown in Figure 4 that all vectors have length of 256. From Figure 4, the resonance frequencies are obtained from peaks as 204 and 296 MHz for Airbus, 156 and 224 MHz for Boeing 747, 332 and 444 MHz for Caravelle and 236 and 340 MHz for Tu-154. When the dimensions of the airplane targets are linked with these frequencies, one wavelength (λ) belonging to relatively higher resonance frequency for each target roughly equals to the sum of body length and wing length of each target, whereas half wavelength corresponding to lower resonance frequency roughly equals to the sum of body length and tail length for each target.

Figure 4.

The feature vectors for each airplane target.

Table 2. The Correlation Coefficient Values Between MUSIC Spectrum Vectors of Reference Signals and Feature Vectors of Airplane Targets
Airplaneϕ = 5°ϕ = 22.5°ϕ = 45°ϕ = 67.5°ϕ = 85°
Airbus0.91830.96740.97540.76780.6008
Boeing 7470.83100.93680.94540.76830.6284
Caravelle0.95220.95140.95830.73460.6088
Tu 1540.94090.97310.98900.78220.6890

5. Results for the Application

[18] In the classification part, all scattered signals including the reference ones are used for testing purpose, which corresponds to 37 × 4 = 148 signals for each SNR level and trial and classification decisions are done according to steps mentioned in classification stage.

5.1. Results for Noise-Free Test Signals

[19] The proposed method is initially applied to noise-free signals of test targets. For this purpose, the selected late-time portions (from 7 ns to 38 ns) of these signals are taken and corresponding MUSIC spectrum vectors are generated by using the same parameters in feature vector construction part. Then, these vectors are compared with the feature vectors given in Figure 4 one by one and test targets are classified as one of the airplane targets according to highest correlation coefficient. For example, a test signal, Airbus at ϕ = 30°, has normalized MUSIC spectrum vector as shown in Figure 5. The correlation coefficient values between this vector and feature vectors are 0.9816, 0.0531, 0.0259 and 0.0370 for Airbus, Boeing 747, Caravelle and Tu 154, respectively. Therefore, this test target is correctly classified as Airbus. When all test signals are considered, the proposed method can correctly identify all test targets that the noise-free accuracy rate is 100% for this application. In order to show the performance of MUSIC algorithm being superior to FFT algorithm, the same application is tested with the methods where MUSIC spectrum vectors are replaced by ones obtained by FFT and other steps remain same. Here, as plotted in Figure 3 for a reference signal, two different FFT vectors for each signal are extracted using same late-time portions of the signals (7 ns-38 ns) and full late-time signals (full signal after 7 ns). The corresponding accuracy rates for both FFT methods cannot exceed 85% accuracy rates even for these noise-free test signals; correspondingly, the accuracy rates of FFT methods are not adequate even for noise-free test signals. This significant difference between accuracy rates of MUSIC and FFT algorithms results from high resolution ability of MUSIC algorithm for this noise-free test signals.

Figure 5.

MUSIC spectrum vector for a noise-free test signal of Airbus at ϕ = 30°.

5.2. Results for Noisy Test Signals

[20] After the testing of noise-free signals, the proposed classification method is investigated for the given application with noisy scattered signals. For this purpose, first of all, the noise-free test signals (full scattered signals) are contaminated by additive zero-mean Gaussian noises with SNR levels of 20, 15, 10, 5, 0, −2.5 and −5 dB. Afterward, the mention steps of the classification method are again applied to these noisy signals. In order to reduce the noise dependency, 50 independent trials for each SNR level are generated; therefore, a total of 148 × 50 = 7400 noisy signals for each SNR level is used in classification stage. The average accuracy percentage (Pc) for a SNR level is evaluated as

equation image

where nc is the number of correct classifications. The average accuracy rates with respect to different SNR levels are given in Table 3 that the proposed method provides highly satisfactory accuracy rates even for very noisy signals (88.61% accuracy for −5 dB SNR level) and small number of reference signals. When these accuracy rates are examined and compared with FFT algorithm, the accuracy rate of the suggested method even at the SNR level of −5 dB (88.61%) is greater than the accuracy rate of FFT algorithm at the noise-free case (about 85%). However, when the decrease in percentage of accuracy rate of FFT algorithm with the increase in noise level is examined, it is obtained only 3% drop for FFT algorithm from noise-free case (about 85%) to SNR= −5 dB (about 82%) case; whereas it is about 11% (from 100% to 88.61%) for MUSIC case. This result is consistent with the lower noise sensitivity of FFT algorithm for high noise levels as explained before. However, because the effect of super-resolution ability of MUSIC algorithm highly surpasses this noise sensitivity drawback, MUSIC algorithm's accuracy rate performance even at SNR= −5 dB level almost drops to the noise-free performance of FFT algorithm.

Table 3. The Average Accuracy Rates of the Proposed Method for Different SNR Levels
 SNR Level (dB)
20151050−2.5−5
Accuracy Rate (%)10098.7398.1497.5997.2496.0093.0988.61

[21] When the decision speed (computation time) of the proposed method is considered, the proposed method is sufficiently fast that it has approximately 24 ms runtime on the average for a sample noiseless or noisy test signal with an Intel Core2 Duo 2.4 GHz microprocessor computer on MATLAB environment. Therefore, this high speed property makes the proposed method suitable for real-time electromagnetic classification applications.

[22] As the performance comparison of the suggested method with other similar published works, a target classification method, which uses the wire model of airplane target set as the application, is handled [Kim et al., 2000]. This method mainly utilizes from adaptive Gaussian representation (AGR), principal component analysis (PCA) and neural network techniques. However, even for three-target classification experiment (Airbus, Boeing 747 and Caravelle), the method can not exceed 95% accuracy rate for almost noise-free test signals and drops to 75% for SNR=0 dB, where the accuracy rates are comparably higher for the suggested method in this paper. Another study demonstrating same target set is described by Secmen and Turhan-Sayan [2009]. In that study, a similar accuracy rate performance is achieved by using fewer of number of test signals (aspect angles) as compared to this paper. However, because matrices are used in the study as the features of the targets, it causes a significant retardation in the decision speed of the method that a typical decision time for a test target is about 1.7 s for the study, whereas it is only 24 ms for the suggested method in this paper. Therefore, the suggested method in this paper makes a progressive contribution to the field by improving either the accuracy rate or decision speed performance of the classification as compared to other similar works.

[23] In order to demonstrate the variation of the accuracy rates with respect to variable m, the accuracy rates of the proposed method for different m values by taking other parameters constant are given in Table 4. According to the results in Table 4, the selected value m = N/2 = 32 has higher accuracy percentages than those of m = 16 and 24 cases. The rates belonging to m = 40 and 48 cases are very similar to the results of m = 32 case; however, the runtime values for m = 40 and 48 cases are approximately 30 ms and 36 ms on the average, respectively, which are slower than the proposed method with m = 32 case. Therefore, the selection of m = 32 is optimum when both accuracy percentages and computational time are considered.

Table 4. The Accuracy Percentage Results of the Proposed Method for Different m Values
 SNR Level (dB)
20151050−2.5−5
m = 1698.6597.2396.3095.0392.9389.6287.2381.35
m = 2498.6597.0396.3195.1594.0991.8089.3584.51
m = 3210098.7398.1497.5997.2496.0093.0988.61
m = 4010098.7098.1297.5397.2495.9293.3488.31
m = 4810098.5998.1897.6997.5095.8593.6988.58

[24] As mentioned before, the duration of late-time interval is important. For this purpose, the accuracy rates of the proposed method are evaluated for different late-time durations, equivalently, different number of time samples. The yielding results for N = 32 corresponding to late-time interval (7 ns-22.5 ns) and N = 128 corresponding to late-time interval (7 ns-69 ns) are given in Table 5 along with the results of N = 64. The accuracy rates for N = 32 are lower than those of N = 64 and the difference in accuracy percentages increases as SNR decreases. This is due to low number of time samples degrading the resolution of MUSIC algorithm. The accuracy rates for N = 128 case are close to the rates of N = 64 case for high SNR levels. However, as SNR level decreases, the effective SNR of the selected portion of late-time signal significantly reduces more than the signal with N = 64. Therefore, the accuracy rates of N = 128 reasonably lessens below N = 64 case especially for low SNR levels. As a result, the value of N = 64 is a good choice for satisfying high accuracy performance within a wide SNR range.

Table 5. The Average Accuracy Rates (%) of the Proposed Method for Different Late-Time Durations
 SNR Level (dB)
20151050−2.5−5
Late-Time Duration: 7 ns – 38 ns (N = 64)10098.7398.1497.5997.2496.0093.0988.61
Late-Time Duration: 7 ns – 22.5 ns (N = 32)94.5994.5394.1193.8593.1589.2084.4378.42
Late-Time Duration: 7 ns – 69 ns (N = 128)10097.8897.3696.5995.1992.5088.9182.54

5.3. Performance of the Method for Different Elevation Angles and Polarization

[25] For the application given above, the performance of the method is tested only for azimuth angle (ϕ) variations of test signals in Figure 1 that the elevation angles (θ = 60°) and polarizations (ϕ polarized in Figure 1) of the signals are kept same with reference signals. Therefore, in order to measure elevation angle and polarization performances of the method, different cases consisting of different elevation angle and polarization conditions are constituted. This diversity is also important to comprehend the validity domain of the method on aspect angles θ and ϕ for this application. In these cases, the reference signals, therefore, the feature vectors for the targets are kept constant and different test signals are considered. For the initial cases, test signals are selected as having different elevation angles (θ = 150° or θ = 30° due to the symmetry in Figure 1) but same polarization states (ϕ polarized). For azimuth angles, two different test groups are realized, which are −45° ≤ ϕ ≤ 45° and −20° ≤ ϕ ≤ 20° with 2.5° increment for both groups as in the test case of section 5.2. These conditions can be separately regarded as tests for classical airplane and usual fighter aircraft cases, respectively. The corresponding accuracy rates for these two cases are given in Table 6 as cases 1 and 2 that the method can exceed 85% accuracy even for SNR= −5 dB level for both cases. The following test cases are realized to demonstrate the polarization performance of the method for this application that in these cases all parameters except polarization kept constant with cases 1 and 2, and polarization state of the incident wave is changed to θ polarization referring to Figure 1. The accuracy rate results belonging to these cases (cases 3 and 4) are also included in Table 6 that the method has minimum about 82% accuracy rate even for SNR= −5 dB. Therefore, in the view of accuracy rates, it can be concluded that the performance of the method does not change dramatically even the elevation angles and polarization states of test signals are moderately different than reference signals. However, in order to show the aspect angle domain of the method, in which a satisfactory accuracy rate performance is achieved (for example, higher than 80% accuracy even for SNR= −5 dB), some extreme test cases are also investigated. For these extreme cases, aspect angles are selected as θ = 90° and 80° ≤ ϕ ≤ 100° and both polarization states (ϕ polarization and θ polarization) are considered. Especially for θ polarized case, the incident wave probably can not excite or very weakly excite resonance modes within the given frequency bandwidth; consequently, an important degradation in accuracy rate performance can be observed. According to the results of these cases given in Table 7, ϕ polarized case shows a moderate drop in accuracy rates that correct decision decreases below 80% for SNR= −5 dB. Consequently, these azimuth and elevation angle ranges may be excluded from the validity domain of the method for ϕ polarized test signals according to predetermined accuracy criterion of the method for the application (for example, the criterion of having minimum 80% accuracy for SNR= −5 dB). On other hand, as expected, θ polarized case has dramatic reduction in accuracy rates that the rate is below 80% even for the noise-free test signals. Therefore, when θ polarized test cases are regarded; the angles belonging to this extreme case must be removed from validity aspect angle domain of the method for this application.

Table 6. The Average Accuracy Rates (%) of the Proposed Method for Moderate Test Cases With Different Elevation Angles and Polarization States
 SNR Level (dB)
20151050−2.5−5
Case 1: −45° ≤ ϕ ≤ 45° θ = 150°, ϕ polarized10099.8199.7199.4798.8997.0893.5988.46
Case 2: −20° ≤ ϕ ≤ 20° θ = 150°, ϕ polarized10099.5399.0198.6597.4296.3391.8185.26
Case 3: −45° ≤ ϕ ≤ 45° θ = 150°, θ polarized10099.0098.9798.0896.5893.9791.0585.18
Case 4: −20° ≤ ϕ ≤ 20° θ = 150°, θ polarized10099.8399.5398.3997.3992.8387.5681.94
Table 7. The Average Accuracy Rates (%) of the Proposed Method for Extreme Test Cases With Different Elevation Angles and Polarization States
 SNR Level (dB)
20151050−2.5−5
Case 1: 80° ≤ ϕ ≤ 100° θ = 90°, ϕ polarized10094.3391.6788.6487.3684.5881.2577.64
Case 2: 80° ≤ ϕ ≤ 100° θ = 90°, θ polarized77.7768.0666.1165.1964.1762.9661.3054.54

6. Conclusion

[26] In this paper, an electromagnetic target classification method for single targets is proposed in resonance region by utilizing from the resolution performance of MUSIC algorithm and dimension reduction property of PCA technique. The method initially extracts MUSIC spectrum vectors belonging to optimum late-time portion of selected reference scattered signals. Afterward, the dimension of MUSIC spectrum vectors is reduced to a single vector with PCA technique for each target and this single vector is assigned as feature vector of the target. In test phase, MUSIC spectrum vector of a test signal is obtained and it is compared with feature vectors one by one. Finally, the highest correlation gives the type of test target. The suggested method is demonstrated for a target set of wire models of airplane targets modeled by perfectly conducting, straight and thin rods. The method gives 100% accuracy rate for noise-free test signals although only 5 reference signals for each target are used. Besides, the method is compared to FFT-based methods and it is shown to be highly superior to these methods even for noise-free signals. A noise performance for this application is also analyzed that the method is found to be robust to noise effects by providing approximately 88.5% accuracy rate for noisy test signals with SNR = −5 dB. Besides, the method has very low overall computational time, only 24 ms for a test target, which makes it suitable for real-time applications. The effects of selections of different parameter values and late-time durations on accuracy rates of the method are performed. Finally, the elevation angle and polarization variation of the method for the given application is investigated that the method provides higher than 80% accuracy for moderate elevation angle and polarization changes. Besides, it gives moderate accuracy rates for ϕ polarization even extreme cases are taken into consideration. As a conclusion, the suggested classification method is very simple, computationally efficient by providing low memory storage (a single vector for each target) and high accuracy rates within a wide SNR range.

Acknowledgments

[27] This work is supported by TUBITAK with grant 111E064.

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