Meteor radar data are continuously collected by different radar systems that operate throughout the year. Analyzing this fast growing, large data set requires efficient and reliable detection routines. Currently most meteor echo routines search for underdense meteor trails, often discarding overdense and nonspecular meteor trails. This is because their main purpose is the study of mesospheric winds. But the study of meteor flux requires the unique identification of each type of meteor reflections. In this paper, a multilayer radar detection and classification algorithm is proposed to correctly identify multiple types of meteor trail reflections. The process consists of two steps. The first step is based on the time-frequency waveform detector. In this step, we start by selecting low signal-to-noise ratio (SNR) values in order to detect all types of radar echoes; however, a high probability offalse alarm is often produced. In the second step, several features from the detected echoes in step one are extracted and a support vector machine (SVM) classifier is constructed to further classify these echoes. The algorithm was tested using data collected from a 50-MHz radar stationed near Salinas, Puerto Rico, on April 5, 1998. A total of 270 detected echoes were labeled as underdense, overdense, nonspecular, other ionospheric echoes, and noise. We used 50% of the labeled echoes as training samples and divided the rest 50% testing samples as 10 subsets for testing. This technique successfully classified about 85% of the testing samples. Details concerning implementation, feature extraction, and data visualization are presented and discussed.
 Every day millions of meteoroids enter the Earth's atmosphere and create long plasma trails, which can be monitored using different types of radar systems. The understanding of the meteor flux is important for several fields ranging from solar system evolution to the composition of the MLT region. It is still unknown how changes in the meteor flux influence these phenomena. Current estimates for the global meteor flux vary from 2,000–200,000 tons per year, and values of the average meteor velocity range between 10 km/s and 70 km/s [Dyrud et al., 2004].
 Since a radar system can detect in time thousands of meteor trails, it is crucial to accurately identify each type of meteor reflection in order to understand the observation biases introduced by different radar systems when studying the meteor flux in the upper atmosphere. In this paper, we present a multilayer meteor detection and classification algorithm that automatically identifies different types of meteor trails and other ionosphere backscatter reflections from the midlatitude atmosphere.
 There are three primary types of meteor radar reflections: (1) traditional specular meteor trails, which are detected when the trajectory of the meteor is perpendicular to the radar k vector [Ceplecha et al., 1998]; (2) nonspecular trails, which result from plasma instability and turbulence generated field-aligned irregularities (FAI) and can be exclusively detected when the radark vector is oriented perpendicular to the Earth's magnetic field B [Dyrud et al., 2002]; and (3) meteor head echoes, which are reflected from radar targets moving at the speed of the meteoroid [Janches et al., 2000; Close et al., 2002]. Additionally, specular meteor echoes can be further classified into two subtypes: underdense and overdense, which is determined by the trail's plasma density. Overdense trails have a plasma frequency that exceeds the probing radar frequency which occurs when the trail electron line density (the number of electrons per meter along the trail) is greater than 2 × 1014 electrons per meter [Ceplecha et al., 1998].
 Traditional meteor radar systems generally use wide beam antennas and interferometric techniques, which are capable of observing meteors throughout the whole sky [Hocking et al., 2001]. There are three types of meteor radars, two commercial: (1) SKiYMET build by Genesis Software in Australia and Mardoc in Canada (http://www.gsoft.com.au/; http://mardoc-inc.com/) and (2) ATRAD systems build by ATRAD in Australia (http://www.atrad.com.au/). The third type are hybrids of these systems or systems that are supposedly built by a particular group with no commercial applications. Examples of these are the MEDAC system [Avery et al., 1990], the COBRA system [Lau et al., 2006], the new Penn State Meteor Radar [Seal, 2011], and others.
 Specular trails detected by traditional meteor radars are used primarily to determine winds in the MLT region and typically operate with small transmitting power system (less than 10 kWs). By contrast, head echoes and nonspecular trails are typically studied by high power radars (order of MW in transmitted power) such as Jicamarca, ALTAIR, Arecibo, and others [Mathews et al., 2001; Close et al., 2002; Dyrud et al., 2002; Janches et al., 2000; Oppenheim et al., 2008]. In this paper, we use radar data from an intermediate power (30 kW) radar system, the University of Illinois Portable Radar, to test the proposed detection and classification algorithm. As discussed in detail by Urbina et al. , the radar antenna consisted of two antenna subarrays with a 50 m east-west separation and overlapping beam patterns pointed with aθ = 49° zenith angle in the geomagnetic meridian plane. The instrument was deployed at Campamento Santiago near the town of Salinas (17.9985°N, 66.2851°W) on the southern coast of Puerto Rico, and operated at a frequency of 49.8 MHz.
 The system monitored the ionosphere continuously between sunset and sunrise on a daily basis to make observations of meter-scale E-region plasma density irregularities in support of the NASA Coqui 2 rocket campaign, from February 16 to April 5, 1998 [Urbina et al., 2000].
 On three nights of April 3–5, 1998, the two arrays of the Coqui 2 radar were split, with one directed perpendicular to the Earth's magnetic field B and the other directed off perpendicular to B. Radar echoes observations were conducted using 11-baud Barker-coded pulses with 1.05-km baud length. The interpulse period (IPP) was 4 ms and 96 ranges were sampled at 1.05-km intervals starting at 120 km range. The radar detected specular, nonspecular trail reflections, a small number of head echoes, and other midlatitude ionospheric phenomena [Urbina et al., 2000, 2004]. Since head echoes are from fast moving meteoroids, they can be detected effectively using Doppler spectra [Wen et al., 2004]. However, we focus only on the meteor trail reflections in this work because the radar was unable to detect a meaningful number of head echoes due to its low sensitivity.
 Currently, most meteor trail detection algorithms generally look for periods when the signal power exceeds a threshold (usually 3 dB above the noise floor) and the subsequent decay after the immediate signal rise typical signature of specular reflections [Hocking et al., 2001; Holdsworth et al., 2004]. The Doppler signature is then easily retrieved from these echoes in order to study the dynamics of the MLT region while rejects all other types of echoes, which are needed to characterize the meteor flux. The purpose of this paper is to offer a machine learning approach to classify these set of reflections in real-time to better quantify the meteor flux into the Earth. Insection 2 we describe the characteristics of the meteor reflections and the corresponding signal analysis. In section 3we discuss the detection and classification algorithm in detail including the implementation of time-frequency waveform detector, feature extraction, the support vector machine classifier, performance analysis and data visualization. Conclusions and future work are given insection 4.
2. Meteor Signal Analysis
 Algorithm development for detection of underdense, overdense, and nonspecular echoes requires an understanding of their reflection mechanisms. In this section, differences between various radar echo types are characterized and key features that are utilized by the classifier are discussed.
 In underdense trails, the electron density is very low and the plasma frequency of the trail is lower than the probing radar frequency so that the radio waves penetrate the trail without attenuation. Each electron scatters the incoming wave individually, and the total signal received from the trail is the sum of the signal from all individual electrons [Ceplecha et al., 1998]. Immediately after the trail is formed, the electrons and ions start diffusing into the surrounding atmosphere, which causes the received signal to decay with time. This feature can be seen in the underdense meteor trail depicted in Figure 1, the signal plots of data collected with the Coqui 2 radar system. These figures show that the power of an underdense echo rises rapidly and it is followed by a quasi-exponential decay, which can be modeled as a complex damped sinusoidal signal [Ceplecha et al., 1998]:
Figure 2 shows the curve fitting, using equation (1), to the underdense example shown on Figure 1. Starting from the peak power, an exponentially decaying sinusoidal signal is applied to fit the underdense echo. The data are read from the peak power until the SNR drops to 3 dB. The maximum amplitude of the signal “A” is estimated as square root of the peak power and the initial phase “ϕ0” can be considered as the phase of the first data point of the event. The Doppler frequency “fd” is estimated by applying the fast Fourier transform (FFT) of the signal. The average of a few power data around the middle of the signal is computed to estimate the decay coefficient “α” with the relation of = . These parameters are used to construct the fitting function and are optimized with least squares. The normalized fitting mean square error (MSE) is one of the features we use to characterize underdense echoes.
 In overdense trails, the electron density of the trail is so high that radio waves cannot penetrate the central part of the trail. In classical theory, the meteor trail is approximated by a reflecting cylinder. Total reflection takes place on the cylinder in the trail for which the electron density is higher than the critical density. If the radio wavelength is small compared to the cylinder radius, the power scattered in the normal direction is directly proportional to the radius of the cylinder [Ceplecha et al., 1998]. Figure 3 shows an overdense trail example from Coqui 2 radar data.
 Notice that the power of the overdense trail echo also shows a steep rise similar to that of underdense trail echoes. Then the amplitude remains fairly constant for approximately 0.3 s. During this period, the reflection is almost independent of the electron density, which indicates that the reflection happens from the overdense core of the trail [Ceplecha et al., 1998]. As the ionization diffuses, the overdense part gradually vanishes and only an underdense trail is left. Then the received power starts to decay exponentially like an underdense trail echo. Figures 4 and 5 show the I, Q, and power plots of a long lasting overdense trail echo.
 Nonspecular trail echoes are attributed to coherent radio scatter from field-aligned irregularities (FAI) in electron density that have been generated from Farley-Buneman/gradient drift (FBGD) instabilities [Dyrud et al., 2002]. Nonspecular trails can be exclusively detected when the radar k vector is oriented perpendicular to the Earth's magnetic field B. The most important difference between specular and nonspecular echoes in our data is that specular echoes typically occur in only one or two range bins whereas nonspecular trail echoes usually span more than three range bins and last much longer than specular ones as shown in Figure 6. Notice that only the west antenna (Figure 6, top) shows a strong nonspecular meteor trail since it is oriented perpendicular to the Earth's magnetic field B but the east antenna (Figure 6, bottom) is oriented off-perpendicular toBon April 5, 1998. The extremely weak event shown on the east array is due to antenna sidelobe contamination. One of the difficulties with detecting nonspecular echoes, however, is that other nonmeteor reflections also occur in many range bins. Though the duration of those echoes are significantly longer than the nonspecular trails, their signal power are many times weak and quasi-oscillatory, which can appear as several individual short meteor trail echoes to the detector. When these events are stronger as depicted inFigures 7 and 8, the detector is able to handle these events with no problem since the duration of these echoes and nonspecular trails differ by an order of magnitude. The event shown in Figure 7is a quasi-periodic event (QP) that is caused by plasma irregularities developed at E-region heights [Urbina et al., 2004] while the event shown in Figure 8 is known as tidal ion layer reflection (TIL). This type of echo has relatively long duration and is produced by slowly descending electron density layers observed in the 90–100 km altitude range. Back scatter from tidal ion layers is due to a volume filling distribution of the Bragg scale structures that is either a homogeneous distribution or more likely short scale structuring in zonal direction [Urbina et al., 2000]. When these ionospheric reflections are weak and unstable, the echoes can be detected as several shorter echoes as stated before, which causes detection difficulties to nonspecular trails. In this case, additional information may be used. The received power of a nonspecular echo has a general trend of decay as time elapses, whereas the TIL remains constant for a period of time and the QP shows a periodic structure. This evolving differences are incorporated in our detector as attributes for recognizing the nonspecular echoes in addition to range and duration features.
3. Multilayer Classification Process
 The process includes both detection and classification and is summarized in Figure 9. Notice that this figure contains two stages of preprocess (before detection is applied) of the radar data: decoding (of the Barker code) and cleaning (due to sidelobes saturation of the Barker code). The sidelobes of the decoded data are eliminated by recursively cleaning a portion of the signal power on each side of the peak value. The cleaning process can be varied accordingly in order to achieve the best detection rate [Urbina, 2002]. The cleaned data are then transferred to the input of the time-frequency waveform detector [Kang and Palo, 2007], which produces a mapping output that contains only useful signals. Low SNR threshold values in this detector are chosen to achieve a high probability of detection. The algorithm then scans the data along the time axis and records information of all the events. For each event, the time and range are recorded so that the raw in-phase and quadrature data can be retrieved for feature extraction, classification and further analysis. Notice that the discriminator stage mentioned in the work ofKang and Palo is not considered in this manuscript because it does not identify uniquely each type of ionospheric echo that occurs in nature. The goal of our work is to introduce learning machine techniques as described below to classify each type of radar reflection automatically and in real-time.
 The time-frequency waveform detector is designed to detect a single damped sinusoidal signal in an unknown additive white Gaussian noise background. Since almost every echo has a damped part, this detector is actually capable of detecting all types of echoes in our data with higher SNR than the threshold values.
where μk and δk2 are frequency domain statistics to detect narrow band signals and μn is time domain statistic to detect highly damped signals. These values are determined by
z(m) can represent the received signal y(n) or its Fourier transform, Y(k). Notice that m = −L, .L is the series of samples generalized from n = 0, 1, ., N − 1 and k = 0, 1, ., N − 1. Since it can be shown that ∑m=-LLP(m) = 1, P(m) can be interpreted as a probability density function of variable m. Notice that P(m) is invariant to the scaling of z(m), which makes it invariant to the noise variance.
 In this detector, a and b are thresholds that can be determined from Monte Carlo simulation. Threshold curves calculated for different time series lengths are shown in Figure 10. The best thresholds for our data were estimated according to the plot and then adjusted following a few trials. More specific details about the time-frequency waveform detector are given byKang and Palo .
 After processing the radar data through the time-frequency waveform detector, the algorithm scans this selected data created by this detector along the time axis. For each IPP, it identifies the number of detected events by looking at both continuous and noncontinuous ranges. Signals detected in adjacent ranges are considered as one event. Once an event/s is/are identified within one IPP, the algorithm takes this IPP as a reference and searches the next IPP but with wider ranges and centered around the previous detected event/s. After the length and number of ranges of the event/s are determined, the data of the event/s are cleared so that the algorithm does not record the same event/s repeatedly. This approach enables the detection of all simultaneous events. During this process, time and range information are recorded and features are extracted for each type of meteor and nonmeteor echoes.Table 1 lists in detail each extracted attribute from the echoes, which are constructed with the following criteria.
Table 1. Complete List of Attributes Extracted From Radar Echoes
number of ranges
10 (5 for echoes less than 2.5 s) evenly selected power data (integration of 64 IPP) in each echo
average of 8 power data (integration of 64 IPP) before each echo
average of 8 power data (integration of 64 IPP) after each echo
normalized mean square-error of damped sinusoidal fitting
 1. Number of ranges and duration. These two attributes are used to discriminate specular echoes from nonspecular and range-spread ionospheric reflections. Since nonspecular trail echoes are relatively long, the duration information obtained from the time-frequency waveform detector was used if the detected echo length was longer than 1.2 s (each of the data block is 0.25 s). For specular trail echoes (detected echoes with length shorter than 1.2 s), the duration was determined by finding the maximum power point and scanning backward and afterward for 3dB SNR point, and adding the two parts together.
 2. Maximum signal-to-noise ratio (SNR). As stated before, we choose low threshold values in the time-frequency waveform detector, thus the SNR and duration can be used to further discard noise and weak echoes.
 3. Evenly selected power data in each echo. This attribute is used to capture the feature of decay in nonspecular echoes as opposed to the invariance and periodic characteristics in other echoes such as QP and TIL. Considering the echoes with weak power, we use incoherent integration to avoid the impact of noise for long duration echoes. A total number of 10 integrated power data (each with an integration of 64 IPP) are selected for long echoes (greater than 2.5 s), and 5 integrated power data for short duration echoes (less than 2.5 s); we used values of 1 to pad this vector to 10.
 4. Data before and after each detected echo. Since all the echoes decay gradually to the noise background, at the end of some echoes, the detected signals are very weak and break into noncontinuous signals. These signals are still above the detection threshold but they are not individual echoes. Thus, the information before and after each detected echo may be used to judge a truly independent echo. Here we average a total of 8 power data (integration of 64 IPP) before/after each echo. This is based on the observation that most nonspecular trail echoes in our data have fading time not exceeding 2 s, which fall below the detection threshold before they stage a comeback.
 After feature extraction, the data is now characterized with 16 dimensions in total which can be used to compose a training data set and a testing data set. A total of 270 echoes were examined and labeled with values of 0,1,2,3,4; corresponding to noise, specular underdense, specular overdense, nonspecular trails, and QP/TIL. The training/testing spread is a N × 17 matrix, where N = 136 is the number of samples used for training and N = 134 is the number of testing samples which are further subdivided into 5 subsets for generalization testing. Each row corresponds to a subject (echo) and each column corresponds to an attribute. The last column contains the class labels. This new formatted data are then used to train and test a support vector machine classifier.
 The support vector machine (SVM) is a classification technique that transforms data into a high-dimensional space so that complex classification problems (with complex decision surfaces) can be converted into simpler problems that can use linear discriminant functions (http://en.wikipedia.org/wiki/Support_vector_machine). The SVM approaches the classification problem through the concept of the margin, which is defined to be the smallest distance between the decision boundary and any of the samples. In support vector machine the decision boundary is chosen to be the one for which the margin is maximized and the points that lie on the maximum margin hyperplanes in feature space are called support vectors. An important property of support vector machines is that the determination of the model parameters corresponds to a convex optimization problem, and so any local solution is also a global optimum.
 The support vector machine require the solution of the following optimization problem [Bishop, 2006]:
 Here training vectors xn are mapped into a higher dimensional space by the function ϕ. Then SVM finds a linear separating hyperplane with the maximal margin in this higher dimensional space. C > 0 is the penalty parameter of the error term, which allows some of the training set data points to be misclassified, because exact separation of the training data may lead to poor generalization. K(x, x′) ≡ ϕ(x)Tϕ(x′) is the kernel function. ω and b are weight vector and bias parameter of the linear model, which are optimized by maximizing the margin.
 1. Conduct simple scaling on the data. Scaling each feature to the range [0, 1] can avoid features in greater numeric ranges dominate those in smaller numeric ranges and avoid numerical difficulties during the calculation.
 2. Choose the radial basis function (RBF) kernel K(xn, xm) = exp(−γ∥xn − xm∥2), γ ≥ 0. The RBF kernel nonlinearly maps samples into a higher dimensional space so it can handle the case when the relation between class labels and attributes is nonlinear.
 3. Use fivefold cross-validation to find the best parameterC and γ. A coarse grid search is applied first. After identifying a better region on the grid, a finer grid search on that region is conducted. Exponentially growing sequences of C and γ is used to identify good parameters. The grid searches and resulting values are illustrated in Figures 11 and 12 in a log2γ versus a log2C.
 4. Train the support classifier using the optimal values of C and γ.
 5. Apply the classifier to the testing samples to test its performance.
Table 2 shows the training and testing results. The average classification rate is above 80%. The detection and classification algorithm is developed in MATLAB with the libSVM toolbox [Chang and Lin, 2001]. To process an hour of radar data, it takes approximately 10 min.
Table 2. Support Vector Machine Classification Accuracy
Testing subset 1
Testing subset 2
Testing subset 3
Testing subset 4
Testing subset 5
 We also tested with randomly selecting 75% of the labeled data as training samples and the rest 25% as testing samples. This division is chosen based on the general estimate to avoid overfitting and insufficient training. This process and the SVM training were repeated 10 times and a best model with the best testing accuracy was obtained. The averaged accuracy for training is 89.9% ± 4.0% and the averaged accuracy for testing is 78.2% ± 4.3%. The training and testing confusion matrices are presented in Tables 3 and 4. Each row of the table represents the class predicted by the algorithm, while each column represents the actual class. As it can be seen from the result, a large number of overdense trails are stillmisclassified. This results occurs because the features chosen to characterize overdense trails are a first order approximation. Overdense echoes are highly variable in amplitude and their precise classification requires further tuning to our approach in order to classify them correctly, which will be subject of future work. The strength of this classification approach is that it is a machine learning algorithm and it can automatically learn to recognize types of meteor trails and make classification decisions based on data. The weakness is that it needs good features to create accurate result and the success of feature extraction depends largelyon the performer's experience.
Table 3. Support Vector Machine Training Classification Accuracya
Average total accuracy: 89.9% ± 4.0%. Best total accuracy: 86.7%.
Table 4. Support Vector Machine Testing Classification Accuracya
Average total accuracy: 78.2% ± 4.3%. Best total accuracy: 86.5%.
 To better understand the meteor flux and its effect on the upper atmosphere, there is a need to take continuous observations of all types of meteor reflections. Consequently, this requires better detection routine to access the large data set. In this paper, we have presented the first classification algorithm with pattern recognition technique to automatically identify both specular and nonspecular meteor trails from a VHF radar. The complete process consists of preprocessing, detection, training/testing, and final classification. Preprocessing includes decoding of Barker-coded data and the sidelobe cleaning. Detection is mainly a time-frequency waveform detector which serves to remove the noise background. The selection of low threshold values in the detector guarantees a high probability of detection. Next, all the events are recorded and features are extracted based on the echo power, duration, and number of ranges. The data is subsequently divided in training and testing subsets, and a support vector machine classifier is constructed to perform final classification of the detected echoes. Fivefold cross-validation and two-level grid search were used for model selection. The overall performance is promising, achieving a best testing accuracy of about 85%; however, a number of overdense trails are still misclassified. One possible solution to increase the classification rate higher is to add a rejection option to separate all the difficult echoes from the training data set. With this output, a large training data set can be separated into small parts, and with a smaller number of echoes in each part, they can be classified by the SVM more easily using a distinct set of weights and biases; therefore, it can control the recognizing rejection and reduce the error rate. The performance of the algorithm can also be improved further by exploring the data and extracting more features that can be utilized by the classifier. When many features are extracted, a feature selection is necessary to select the best subset from the input space. With feature selection, the best features can be found, which may not only improve the performance of the classification, but also bring insight to the understanding of the data. Another wayis to try other kernels in SVM or to try other classification techniques such as Bayesian classifiers, k-nearest neighbors, and neural network. The incorporation of these additional strategies in our algorithm will be subjects of future work. It is also necessary to use data that span an entire year since both the atmosphere and meteor events vary greatly with the season. Once a good trained model is produced, the approach can be further developed as a real-time detection routine so that the newest meteor data can be accessed regularly.
 Siming Zhao's, Julio Urbinas, and Ryan Seal's work was supported by NSF grants ATM-0638624 and ATM-0457156, and Lars Dyruds work was supported by NSF grant ATM-1032334.