Elsevier

Neurocomputing

Volume 418, 22 December 2020, Pages 314-325
Neurocomputing

One-dimension hierarchical local receptive fields based extreme learning machine for radar target HRRP recognition

https://doi.org/10.1016/j.neucom.2020.08.050Get rights and content

Abstract

Radar automatic target recognition (RATR) aims at extracting meaningful target features from the electromagnetic echo signal and utilizing the features to automatically recognize the target types. The high-resolution range profile (HRRP) plays an important role in RATR field, HRRP is the amplitude of the echo summation for target scattering centers in each range cell of wideband radar. Using deep neural networks for HRRP radar target recognition encounters the problem of storage overhead and slow convergence rate, to resolve those issues, we propose a one-dimension local receptive fields based extreme learning auto-encoder (1D ELM-LRF-AE) network for HRRP local structures and meaningful representations learning. ELM-LRF-AE consists of an input layer, a random convolution layer, a pooling layer, several local connected layers and an output layer, it reconstructs the input with a greedy strategy that the input feature vectors are divided into several subgroups and the i-th pooling feature vector is used to reconstruct the i-th grouping input feature vector. Then we use the learned pooling feature vectors to replace the random pooling feature vectors as the learned representations. We also stack several 1D ELM-LRF-AEs to build 1D hierarchical local receptive fields based extreme learning machine (1D H-ELM-LRF) for high level HRRP abstract representations learning and recognition. Experimental results on simulated HRRP data set demonstrate the superior high recognition performance and high computational efficiency of our algorithm.

Introduction

A high-resolution range profile (HRRP) is the amplitude of the coherent summations of the complex returns from target scattering centers in each range cell, which represents the projection of the complex returned echoes from the target scattering centers along the radar line-of-sight (LOS) [1], [2], [3], so it reflects the distribution of radar scattering centers and contains abundant target geometric structural signatures [4], such as target size, distribution of radar cross section (RCS) along the observation direction of the radar, the structure and intensity of the scattering centers, etc. Compared with the two-dimensional high-resolution synthetic aperture radar (SAR) or inverse synthetic aperture radar (ISAR) images (ISAR), HRRP has the advantages of easy acquisition and easy processing, so radar automatic target recognition based on HRRP has received intensive attentions in the community of radar automatic target recognition [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20].

Many researchers have explored various feature learning methods for HRRP recognition. Some researchers built complicated statistic models to extract features from HRRP raw data that have specific physical meaning [5], [6], such as the target size, the center of gravity, the number of peaks. Some transformation features of raw HRRP data were also been extracted for HRRP recognition, including FFT magnitude feature [7], [8], spectrum feature [9], [10], [11], high-order spectra feature [10], polarization feature [11], [12] and so on. Some other researchers investigated feature selection methods to extract subspace discriminant features of the HRRP, including PCA based feature subspace learning [13], manifold learning [14], factor analysis [8], [15], and dictionary learning [2], [16]. However, those features are hand-crafted and rely on the personal experiences, those feature learning methods build linear and shallow architectures to extract the HRRP features, which limit their capability to represent the complicated HRRP data.

Deep learning algorithms [21] can learn hierarchical feature representations from raw data automatically, they don’t require any target domain information. Therefore, the deep learning techniques shield a light on the traditional RATR field in last few years, many successful researches of deep neural networks have been applied in HRRP based RATR. Because the HRRP is a one-dimension feature vector, most of the methods focus on employing the deep full connected network for HRRP recognition, such as deep belief network (DBN) [17], stacked auto-encoder(SAE) [18], and recurrent neural network (RNN) [19]. Pan et al. [17] proposed a framework for unbalanced HRRP data recognition, they utilized t-SNE and synthetic sampling method to provide well segmented and balanced HRRP data, then explored discriminant deep belief network (DDBN) for HRRP recognition. Feng et al. [18] proposed a stacked corrective auto-encoder to yield more abstract and useful hierarchical features for HRRP target recognition, where the average profile of the HRRP was used as a corrective output for a stacked auto-encoder, and the covariance matrix of each HRRP frame was also considered for establishing an effective loss function under the Mahalanobis distance criterion. Zhao et al. [19] explored stacked auto-encoder to extract abstract and useful hierarchical features and used the extreme learning machine to classify the HRRP, which can greatly improve the learning speed and generalization performance of the model. Duet et al. [20] proposed a factorized discriminative conditional variational auto-encoder framework for radar HRRP target recognition, the proposed method introduced the label information into conditional variational auto-encoder to guide the model to learn the discriminative latent representations, and factorized the parameters to effectively reduce model parameters. Xu et al. [1] divided each HRRP into multiple overlapping sequential as input of recurrent neural network to encode the HRRP sequence into hidden states, and weighted the hidden state at each timestep so as to focus on the discriminative regions data-dependently with the help of attention strategy.

However, above deep models are fully-connected networks, the number of weight parameters to be learned exponentially increases as the number of nodes and layers increases, having too many weights in a network can lead to huge computational complexity and storage overhead; Besides, deep fully connected networks may not capture the structural information of HRRP layer by layer. Since HRRP reflects the distribution of scatters of target along the range dimension, the local respective field of CNN can learn local structural of data samples and weight sharing can reduce the parameters of deep models, so some researchers employed the 1D CNN to extract the geometric structural signatures of HRRP [22], [23], [24]. Guo et al. [22] designed a one-dimensional residual-inception network for HRRP recognition, the residual-inception CNN could greatly reduce the parameters and improve the generalization performance of the model. In [23], a radar HRRP target recognition method based on feature pyramid fusion CNN was proposed to fully utilize the features extracted by each depthwise separable convolutional feature extraction block. Wan et al. [24] also used one-dimensional CNN to handle HRRP recognition problems. Besides, they found that the spectrogram of HRRP recorded the amplitude feature and characterizes the phase information compared with the time domain representations, so they further devised a two-dimensional CNN model for the spectrogram feature recognition. The features extracted by the CNN model have the characteristics of translation invariance and rotation invariance, which are suitable to solve problem of translation sensitivity and aspect sensitivity of the HRRP.

Thought CNN can reduce the parameters of deep model, but it is trained with gradient descent based algorithms [40], and it still has the problem of slow convergence rate, which can’t meet the demand of high real-time for radar target recognition. In the past years, extreme learning machine [25], [26], [27] has attracted increasing attentions in machine learning community. In general, ELM is a feed forward neural network, the parameters of hidden layer are randomly generated and fixed, and then the output weights are analytically calculated without iteratively tuning, so it has very extremely faster learning speed than conventional neural network training with gradient-based learning algorithms. ELM have also been extended to ELM based auto-encoder (ELM-AE) for high level abstract representation learning [28]. Due to its high efficiency, ELM have been applied for radar target recognition to meet the demand of high real-time [19], [29]. Zhao et al. [19] used extreme learning machine to classify the HRRP representation extracted from stacked auto-encoder. Avci et al. [29] proposed a combination method of wavelet signal processing and extreme learning machine to efficiently extract features from the real radar target echo signals and classification for target recognition among different targets.

To utilize ELM for images processing directly, Huang et al. [30] proposed a local receptive field based extreme learning machine (ELM-LRF), where random convolutional nodes and pooling structure were implemented for learning local and translational invariance structures, and the output weights were calculated analytically, so ELM-LRF provided a simple deterministic solution. The ELM-LRF is designed to operate exclusively on 2D data, such as images and videos [30], [31], it involves no gradient-descent steps and the training is remarkably efficient. Because HRRP contains abundant target geometric structural signatures, the local receptive field of ELM-LRF can learn the local structures and generate more meaningful representations. Therefore, we think that the 1D ELM-LRF is suitable for HRRP data processing and recognition, but 1D ELM-LRF is a shallow model, we intend to use deep model to process HRRP. So in this paper, we design a one-dimension ELM-LRF based auto-encoder (1D ELM-LRF-AE) module to extract the HRRP structure features and stack ELM-LRF-AE to construct deep ELM-LRF for HRRP recognition. The main contributions of the proposed method are summarized as follows:

  • 1)

    Inspired by ideas of the ELM-LRF and ELM-AE, we investigate a 1D ELM-LRF-AE network, which aims at learning local structures and generating meaningful representations of HRRP based on the encoder-decoder paradigm. ELM-LRF-AE consists of an input layer, a random convolution layer, a pooling layer, several local connected layers and an output layer (shown as Fig. 5, Fig. 6). When using ELM-LRF-AE to processing data, we divide the input feature vectors into several subgroups, because each pooling feature vector is the combination transformation of all input feature vectors, it contains enough information to reconstruct each grouping feature vector, so we use i-th pooling feature vector to reconstruct the i-th grouping feature vector. Then we use the learned pool feature vectors to replace the random pooling feature vectors as the learned representations. This is a greedy strategy, once each grouping feature vector is reconstructed, all input feature vectors are reconstructed. Our greedy strategy is very computational efficiency and effective, because both the dimension of the i-th pooling feature vector and i-th grouping feature vector reconstruction target are low.

  • 2)

    We stack several 1D ELM-LRF-AEs to build 1D hierarchical ELM-LRF (1D H-ELM-LRF) for high level HRRP abstract representations learning and recognition. The 1D H-ELM-LRF can obtain deep essential characteristics and further contribute to the recognition performance.

  • 3)

    We carry out comparative analysis about the HRRP recognition performances of our method with many shallow and deep neural networks. Extensive empirical results demonstrate the superior performance of our algorithm.

The remainder of this paper is organized as follows. Section 2 introduces some preliminary related works, consisting of the basic theories of ELM, extreme learning machine based auto-encoder and local receptive fields based extreme learning machine. Section 3 presents our proposed 1D H-ELM-LRF framework in detail. Section 4 presents quantitative performance analyses on HRRP data. Finally, we draw the conclusion of this paper in Section 5.

Section snippets

ELM and ELM based auto-encoder

  • 1)

    Extreme learning machine

ELM was originally proposed by Huang et al. [25], [26], [27] in 2006, it is a single hidden layer feed forward neural network. Different from that the traditional neural networks are optimized with gradient descent based algorithms [40], the weights and biases in hidden layer of ELM can be assigned randomly without tuning and they are independent of the training data, while the parameters of output layer are determined analytically by the least-square method. So it can

Hierarchical local receptive fields based extreme learning machine

A HRRP is a 1D signal data, it contains abundant target geometric structural signatures, the local receptive field in CNN can learn the local structures and generate more meaningful representations, such as in [22], [23], [24], the 1D CNN extracts the geometric structural signatures of HRRP, greatly reduces the parameters and improves the generalization performance of the model. Resembling 1D CNN, 1D ELM-LRF is suitable for HRRP recognition, a simple 1D ELM-LRF with L feature vectors is shown

Introduction of the simulated HRRP data

In this paper, we focus on ballistic missiles (BM) HRRP target recognition. Generally, a BM trajectory can be divided into three parts [32]: boost phase, which comprises the powered flight portion; midcourse phase, which comprises the free-flight portion; and the re-entry phase wherein the warhead re-enters the earth’s atmosphere to approach the target. In the midcourse phase, the missile releases the warhead and some decoys to confuse the defense systems, the missile also releases massive

Conclusions

In this paper, we propose a one-dimension local receptive fields based extreme learning auto-encoder network for HRRP local structures and meaningful representations learning. ELM-LRF-AE reconstructs the input with a greedy strategy that divides the input feature vectors into several subgroups and uses i-th pooling feature vector to reconstruct the i-th grouping feature vector. Then we use the learned pooling feature vectors to replace the random pooling feature vectors as the learned

CRediT authorship contribution statement

Xiaodan Wang: Methodology, Supervision, Project administration. Rui Li: Conceptualization, Writing - original draft, Software. Jian Wang: Supervision, Data curation, Visualization, Resources. Lei Lei: . Yafei Song: Software, Validation, Investigation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work is supported by National Natural Science Foundation of China under Grant 61806219, Grant 61876189, Grant 61503407, Grant 61703426 and Grant 61273275. This work is also supported by Young Talent fund of University Association for Science and Technology in Shaanxi, China, NO z. 20190108.

Xiaodan Wang was born in Hanzhong, Shanxi, China in 1967. She received her Ph.D. in computer science from North Western Polytechnical University of China. She is now a professor and Ph.D. advisor at the College of Air and Missile Defense, Air Force Engineering University. Her research interest covers pattern recognition, machine learning, computer vision, and artificial intelligence. As a professor, she has published more than 100 papers in international conferences and journals.

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    Xiaodan Wang was born in Hanzhong, Shanxi, China in 1967. She received her Ph.D. in computer science from North Western Polytechnical University of China. She is now a professor and Ph.D. advisor at the College of Air and Missile Defense, Air Force Engineering University. Her research interest covers pattern recognition, machine learning, computer vision, and artificial intelligence. As a professor, she has published more than 100 papers in international conferences and journals.

    Rui Li was born in Xinzhou, Shanxi, China in 1992. He received the B.S. degree in 2014 and the M.S. degree in 2017 from Air Force Engineering University. He is now pursuing the Ph.D. degree at the College of Air and Missile Defense, Air Force Engineering University. His research interest covers pattern recognition, machine learning, and artificial intelligence.

    Jian Wang was born in Xian, Shanxi, China in 1983. He received his Ph.D. in 2013 from Air Force Engineering University. He is now a professor he College of Air and Missile Defense, Air Force Engineering University. Her research interest covers pattern recognition, intelligent information processing,

    Lei Lei was born in Nanchong, Sichuan, China in 1988. She received his Ph.D. in 2015 from Air Force Engineering University. She is now a lecturer at the College of Air and Missile Defense, Air Force Engineering University. Her research interest covers pattern recognition, intelligent information processing.

    Yafei Song, member of IEEE, was born in Henan, China in 1988. He received his Ph.D. in 2015 from Air Force Engineering University. He is now a lecturer at the College of Air and Missile Defense, Air Force Engineering University. He is working as a postdoctoral researcher in Air Force Engineering University since April 2017. His research interest covers pattern recognition, intelligent information processing, and evidential reasoning.

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