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Multi-rotor aircraft have the advantages of a simple structure, low cost, and flexible operation in the unmanned aerial vehicle (UAV) family, and have developed rapidly in recent years. Radar surveillance and classification of the growing number of multi-rotor aircraft has become a challenging problem due to their low-slow-small (LSS) characteristics. Estimation of the blade number is an important step in distinguishing LSS targets. However, most of the current research on micro-motion parameters estimation has focused on the analysis of rotational frequency, length, and the initial phase of blades with a prior of blade number, affecting its ability to identify LSS targets. In this article, a micro-motion parameters estimation method for multi-rotor targets without a prior is proposed. On the basis of estimating the flashing frequency of the blades, a validation function is constructed through spectral analysis to judge the number of blades, and then the rotational frequency is estimated. The blade length is calculated by estimating the maximum Doppler shift. Moreover, the variational mode decomposition (VMD)-based atomic scaling orthogonal matching pursuit (AS-OMP) method is jointly applied to estimate the blade length when suffering from the low PRF and insufficient SNR conditions. Extensive experiments on the simulated and measured data demonstrate that the proposed method outperforms robust micro-motion parameter estimation capability in low PRF and insufficient SNR conditions compared to the traditional time-frequency analysis methods.

In the realm of ballistic target analysis, micro-motion attributes, such as warhead precession, nutation, and decoy oscillations, play a pivotal role. This paper addresses these critical aspects by introducing an advanced analytical model for assessing the Doppler power spectra of convex quadric revolution bodies during precession. Our model is instrumental in calculating the Doppler shifts pertinent to both precession and swing cones. Additionally, it extends to delineate the Doppler power spectra for configurations involving cones and sphere–cone combinations. A key aspect of our study is the exploration of the effects exerted by geometric parameters and observation angles on the Doppler spectra, offering a comparative perspective of various micro-motion forms. The simulations distinctly demonstrate how different micro-motion patterns of a cone influence the Doppler power spectra and underscore the significance of geometric parameters and observational angles in shaping these spectra. This research not only contributes to enhancing LIDAR target identification methodologies but also lays a groundwork for future explorations into complex micro-motions like nutation.

Space target classification based on micro-motion characteristics has become a subject of great interest in the field of radar, particularly when using deep learning techniques. However, in practical applications, the ability of deep learning is hampered by the available radar datasets. As a result, obtaining a sufficient amount of the training dataset is a daunting challenge. To address this issue, this paper presents a novel framework for space target classification, consisting of three distinct modules: dataset generation, the kinematically sifted module, and classification. Initially, the micro-motion model of cone-shaped space targets is constructed to analyze target characteristics. Subsequently, the dataset generation module employs a complex-valued generative adversarial network (CV-GAN) to generate a large number of time-range maps. These maps serve as the foundation for training the subsequent modules. Next, the kinematically sifted module is introduced to eliminate images that do not align with the micro-motion characteristics of space targets. By filtering out incompatible images, the module ensures that only relevant and accurate dataset is utilized for further analysis. Finally, the classification model is constructed using complex-valued parallel blocks (CV-PB) to extract valuable information from the target. Experimental results validate the effectiveness of the proposed framework in space micro-motion target classification. The main contribution of the framework is to generate a sufficient amount of high-quality training data that conforms to motion characteristics, and to achieve accurate classification of space targets based on their micro-motion signatures. This breakthrough has significant implications for various applications in space target classification.

Radar micro-motion signatures help to judge the target’s motion state and threat level, which plays a vital role in space situational awareness. Most of the existing micro-motion feature extraction methods derived from time-frequency (TF) representation cannot simultaneously satisfy the requirements of high resolution and multiple component representation, which has limitations on processing intersected multi-component micro-motion signals. Meanwhile, as the micro-motion features extracted from the TF spectrograms only focus on the global characteristics of the targets and ignore the physical properties of micro-motion components, it leads to poor performance in micro-motion discrimination. To address these challenges, we empirically observed a decrease in the probability of intersection between the components within the time-frequency-frequency rate (TFFR) space, where components appeared as separated and non-intersecting spatial trajectories. This observation facilitates the extraction and association of multiple components. Given the differences in modulation laws among various micro-motions in the TFFR space, we introduced a novel micro-motion identification method based on scatterer-level TFFR representation. Our experimental evaluations of different targets and micro-motion types demonstrate the efficacy and robustness of this proposed method. This method not only underscores the separability of signal components but also expands the scope of micro-motion discrimination within the TFFR domain.

Spectrum aliasing occurs in signal echoes when the sampling frequency does not comply with the Nyquist Sampling Theorem. In this scenario, the extraction of micro-motion parameters becomes challenging. This paper proposes a spectral de-aliasing method for micro-motion signals based on a complex-valued U-Net network. Zero interpolation is employed to insert zeros into the echo, effectively increasing the sampling frequency. After zero interpolation, the micro-motion signal contains both real micro-motion signal frequency components and new frequency components. Short-Time Fourier Transform (STFT) is then applied to transform the zero-interpolated echo from the time domain to the time–frequency domain. Furthermore, a complex-valued U-Net training model is utilized to eliminate redundant frequency components generated by zero interpolation, thereby achieving the frequency reconstruction of micro-motion signal echoes. Finally, the training models are employed to process the measured data. The theoretical analysis, simulations, and experimental results demonstrate that this method is robust and feasible, and is capable of addressing the problem of micro-motion signal echo spectrum aliasing in narrowband radar.

Radar cross section (RCS) sequences, an easy-to-obtain target feature with small data volume, play a significant role in radar target classification. However, radar target classification based on RCS sequences has the shortcomings of limited information and low recognition accuracy. In order to overcome the shortcomings of RCS-based methods, this paper proposes a spatial micro-motion target classification method based on RCS sequences encoding and convolutional neural network (CNN). First, we establish the micro-motion models of spatial targets, including precession, swing and rolling. Second, we introduce three approaches for encoding RCS sequences as images. These three types of images are Gramian angular field (GAF), Markov transition field (MTF) and recurrence plot (RP). Third, a multi-scale CNN is developed to classify those RCS feature maps. Finally, the experimental results demonstrate that RP is best at reflecting the characteristics of the target among those three encoding methods. Moreover, the proposed network outperforms other existing networks with the highest classification accuracy.

A problem with synthetic aperture radars (SARs) is that due to the poor penetrating action of electromagnetic waves within solid bodies, the ability to see through distributed targets is precluded. In this context, indeed, imaging is only possible for targets distributed on the scene surface. This work describes an imaging method based on the analysis of micro-motions present in volcanoes and generated by the Earth’s underground heat. Processing the coherent vibrational information embedded in a single SAR image, in the single-look-complex configuration, the sound information is exploited, penetrating tomographic imaging over a depth of about 3 km from the Earth’s surface. Measurement results are calculated by processing a single-look-complex image from the COSMO-SkyMed Second Generation satellite constellation of Vesuvius. Tomographic maps reveal the presence of the magma chamber, together with the main and the secondary volcanic conduits. This technique certainly paves the way for completely new exploitation of SAR images to scan inside the Earth’s surface.

It is of great significance to detect drones in airspace due to the substantial increase and regrettable misuse in the consumer market. In this paper, we establish a micro-motion theoretical model of a drone and analyze the micro-Doppler signature of rotor targets and the flicker mechanisms of the multi-rotor targets. Hence, for the target recognition problem of multi-rotor drones, a multi-rotor target micro-Doppler parameter estimation method is proposed. Firstly, a signal frequency domain segmentation method is proposed based on the complex variational mode decomposition (CVMD) to separate the high-frequency part of the high-frequency flicker in the frequency domain. Secondly, for the signal after frequency domain segmentation, a flicker time domain position method based on singular value decomposition (SVD) is proposed. Finally, by integrating CVMD frequency domain segmentation and SVD time domain positioning, the reconstruction of multi-rotor target scintillation at different speeds is realized, and the micro-motion parameters of rotor blades are successfully estimated. The simulation results show that the method has high accuracy in estimating the micro-motion parameters of a multi-rotor, which makes up for the shortage of the traditional method in estimating the micro-motion parameters of the multi-rotor target.

Aiming at the difficult problem of the classification between flying bird and rotary-wing drone by radar, a micro-motion feature classification method is proposed in this paper. Using K-band frequency modulated continuous wave (FMCW) radar, data acquisition of five types of rotor drones (SJRC S70 W, DJI Mavic Air 2, DJI Inspire 2, hexacopter, and single-propeller fixed-wing drone) and flying birds is carried out under indoor and outdoor scenes. Then, the feature extraction and parameterization of the corresponding micro-Doppler (m-D) signal are performed using time-frequency (T-F) analysis. In order to increase the number of effective datasets and enhance m-D features, the data augmentation method is designed by setting the amplitude scope displayed in T-F graph and adopting feature fusion of the range-time (modulation periods) graph and T-F graph. A multi-scale convolutional neural network (CNN) is employed and modified, which can extract both the global and local information of the target’s m-D features and reduce the parameter calculation burden. Validation with the measured dataset of different targets using FMCW radar shows that the average correct classification accuracy of drones and flying birds for short and long range experiments of the proposed algorithm is 9.4% and 4.6% higher than the Alexnet- and VGG16-based CNN methods, respectively.

Micro-motion parameters extraction is crucial in recognizing ballistic missiles with a wideband radar. It is known that the phase-derived range (PDR) method can provide a sub-wavelength level accuracy. However, it is sensitive and unstable when the signal-to-noise ratio (SNR) is low. In this paper, an improved PDR method is proposed to reduce the impacts of low SNRs. First, the high range resolution profile (HRRP) is divided into a series of segments so that each segment contains a single scattering point. Then, the peak values of each segment are viewed as non-stationary signals, which are further decomposed into a series of intrinsic mode functions (IMFs) with different energy, using the ensemble empirical mode decomposition with the complementary adaptive noise (EEMDCAN) method. In the EEMDCAN decomposition, positive and negative adaptive noise pairs are added to each IMF layer to effectively eliminate the mode-mixing phenomenon that exists in the original empirical mode decomposition (EMD) method. An energy threshold is designed to select proper IMFs to reconstruct the envelop for high estimation accuracy and low noise effects. Finally, the least-square algorithm is used to do the ambiguous phases unwrapping to obtain the micro-curve, which can be further used to estimate the micro-motion parameters of the warhead. Simulation results show that the proposed method performs well with SNR at −5 dB with an accuracy level of sub-wavelength.