# Multi-Source HRRP Target Fusion Recognition Based on Time-Step Correlation
## 1 Introduction  
The high-resolution range profile is a one-dimensional projection of target scattering points along the radar line of sight. It contains rich information such as target scattering fluctuation characteristics, geometry, and attitude. Compared with SAR images, HRRP is easy to obtain, store and process quickly [1]. Therefore, using the HRRP for target recognition has attracted wide attention in the field of RATR [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. Extracting stable and easily distinguishable features from HRRP data is the key technique of RATR, which has become a research hotspot for domestic and foreign scholars. [PERSON] et al. [1], [PERSON] et al. [2] and [PERSON] et al. [11] started from the spectrum of the HRRP to extract features that are easy to identify. The recognition accuracy of these methods largely depends on manual extraction of spectral features, which is not conducive to engineering promotion. In order to weaken the influence of this artificial factor, [PERSON] et al. [12] applied Principal Component Analysis (PCA) to extract HRRP features by minimizing reconstruction errors. [PERSON] et al. [13] used dictionary learning to approximate sparse signals to extract HRRP features. [PERSON] et al. [14] proposed a radar HRRP model based on a hidden Markov model, combined with time domain features and spectral features, and achieved good results. In recent years, the rapid development of deep learning has provided a new approach for radar automatic target recognition. Extracting stable features that are easy to distinguish from HRRP data through neural networks and machine learning algorithms has become a popular research direction. The literature [15; 16; 17] used RNNs in recurrent neural networks, Long Short-Term Memory (LSTM), and a Gated Recurrent Unit (GRU) to classify HRRP targets and combined them with attention mechanisms to achieve good results. The literature [18] used a Convolutional Neural Network (CNN) to construct a deep model for classification and rejection of HRRP targets by convolution and deconvolution operations on convolutional kernels of different sizes. [9], a Stacked Corrective Autoencoder (SCAE) is proposed on the basis of a Stacked Autoencoder (SAE), and through a series of stacked Corrective Autoencoders (CAEs). The recognition effect of HRRP is improved by stackinga series of Corrective Autoencoders (CAEs). All of the above methods use a single HRRP for target classification, and the quality of the data directly affects the effectiveness of recognition. In today's modern warfare, the use of different radars to collaborate on target recognition is the trend of early warning detection system development, and multi-source target fusion recognition has been developed in this context. Multi-source target fusion methods are divided into decision-level fusion methods and feature-level fusion methods. The decision-level fusion methods are as follows: the literature [19] uses the decision template of each target obtained by training, compares the decision results of the sample with the decision templates of various targets, and determines the target category by similarity. The literature [20; 21] introduced the decision-level fusion recognition method based on the D-S evidence theory, and further improved the traditional D-S theory based on the discount principle to make it more suitable for radar target data. The feature-level fusion methods are as follows: the literature [22] fuses several typical features of low-resolution radar and classifies targets by a Support Vector Machine (SVM). Refs. [23; 24], a fusion algorithm based on Canonical Correlation Analysis (CCA) is used to select features by correlation size, which not only retains the useful information of the target, but also eliminates redundant information, and realizes the effective fusion of multiple features. Refs.