Accurate recognition and parameter estimation of frequency hopping (FH) signals remain challenging in FH signal-based transmission systems. This study proposes a scheme combining time-frequency analysis (TFA) and deep learning (DL)-based image processing algorithms to alleviate the degradation of recognition accuracy and estimation performance caused by complex electromagnetic interference (EMI). A short-time Fourier transform (STFT) was used to obtain the signal spectrogram, which reflects the signal energy in a concentration-dependent manner. Then, a CenterNet-based deep network was employed to identify the shape and position of the FH signal, which reduces the computational burden via a lightweight neural network while maintaining high recognition accuracy. Inverse mapping from the coordinates to the spectrogram was used to perform parameter estimation in the time-frequency (TF) domain. The estimation error was reduced by precisely locating the centroid of the signal energy using CenterNet. The simulation results demonstrate that the proposed scheme can accurately estimate the FH signal at a low signal-to-noise ratio (SNR) with complex EMI. Furthermore, appropriately determining the optimal parameters of CenterNet to ensure the estimator performance provides a novel approach for integrating DL into signal detection in complex EMI environments.

Traditional orthogonal matching pursuit (OMP) algorithms for direction of arrival (DOA) estimation suffer from poor angular resolution and noise suppression. In this paper, we analyze the reason why the OMP algorithm has difficulties in resolving closely separated DOAs and conclude that it lies in the rules of support detection. Moreover, we propose a solution to this problem via developing the connection between the sparse reconstruction class algorithm and the subspace algorithm from the structure of the redundant dictionary. Based on the framework of the matching pursuit (MP) algorithm, the effective information of the signal and noise subspaces is integrated, and a noise subspace reprojection orthogonal matching pursuit (NSRomp) algorithm for DOA estimation is proposed. By adopting signal subspaces to reconstruct the original signal, the proposed NSRomp can reduce both the influence of noise on the selection of the support set and the computing time. By implementing the minimum norm method to optimize the noise subspace into a vector, which corrects the selection rules of the support set during each iteration, the angular resolution of the proposed algorithm is improved. From the simulation results, when the signal to noise ratio (SNR) is lower than or near 0, the angular resolution can be improved by > 15° using OMP algorithms to by > 5° using the proposed NSRomp algorithm.

In this paper, the concept and definitions of the Fractional Order Moment (FOM) and Fractional Order Cumulant (FOC) are proposed, which is based on the fractional derivative of the fractional order Moment-generating function and the fractional order Cumulant-generating function of stochastic processes. The moment and cumulant are defined on an expanded set from positive integer to the whole positive real. This development not only provides a new technology for signal processing, also complements the existing theory in the field. The properties of the FOC have been derived, and their uniformity and particularity with the High Order Cumulant are compared and commented. In addition, the transformation between the FOM and the FOC are derived and discussed in detail. As one of the applications of the new concept to the α and Gaussian processes, a new method of suppressing α and Gaussian noise is proposed. Furthermore, a FOC-based parameter estimation algorithm is developed for the non-minimum phase ARMA processes in α and/or Gaussian noise. Simulation examples are used to demonstrate the effectiveness of the proposed parameter estimation algorithm.

A new method of fault detection and fault-tolerant control is proposed in this article for mechanical systems and aeronautical systems. The faults to be estimated and diagnosed are malfunctions that occurred within the control loops of the systems, rather than some static faults, such as gearbox fault, component cracks, and so on. In the proposed method, two neural networks are used as online estimators, the fault will be accurately estimated when the estimators are adapted online with the post-fault dynamic information. Furthermore, the estimated values of faults are used to compensate for the impact of the faults, so that the stability and performance of the system with the faults are maintained until the faulty components to be repaired. The sliding mode control is used to maintain system stability under the post-fault dynamics. The control law and the neural network learning algorithms are derived using the Lyapunov method, so that the neural estimators are guaranteed to converge to the fault to be diagnosed, while the entire closed-loop system stability is guaranteed with all variables bounded. The main contribution of this article to the knowledge in this field is that the proposed method can not only diagnose and tolerant with constant fault but also diagnose and tolerant with the time-varying faults. This is very important because most faults occurred in industrial systems are time varying in nature. A simulation example is used to demonstrate the design procedure and the effectiveness of the method. The simulation results are compared with the two existing methods that can cope with constant faults only, and the superiority is demonstrated.

We propose a hybrid Convolutional Graph Neural Network (C-GNN) for direction-of-arrival (DOA) estimation in sparse sensor arrays under low-snapshot conditions. The C-GNN architecture combines 1D convolutional layers for local spatial feature extraction with graph convolutional layers for global structural learning, effectively capturing both fine-grained and long-range array dependencies. Leveraging the difference coarray technique, the sparse array is transformed into a virtual uniform linear array (VULA) to enrich the spatial sampling; real-valued covariance matrices derived from the array measurements are used as the network’s input features. A final multi-layer perceptron (MLP) regression module then maps the learned representations to continuous DOA angle estimates. This approach capitalizes on the increased degrees of freedom offered by the virtual array while inherently incorporating the array’s geometric relationships via graph-based learning. The proposed C-GNN demonstrates robust performance in noisy, low-data scenarios, reliably estimating source angles even with very limited snapshots. By focusing on methodological innovation rather than bespoke architectural tuning, the framework shows promise for data-efficient DOA estimation in challenging practical conditions.