With the continuous advancement of target detection technology in remote sensing, target detection technology in images captured by drones has performed well. However, object detection in drone imagery is still a challenge under rainy conditions. Rain is a common severe weather condition, and rain streaks often degrade the image quality of sensors. The main issue of rain streaks removal from a single image is to prevent over smoothing (or underclearing) phenomena. Aiming at the above problems, this paper proposes a deep learning (DL)-based rain streaks removal framework called GSDerainNet, which properly formulates the single image rain streaks removal problem; rain streaks removal is aptly described as a Gaussian Shannon (GS) filter-based image decomposition problem. The GS filter is a novel filter proposed by us, which consists of a parameterized Gaussian function and a scaled Shannon function. Two-dimensional GS filters exhibit high stability and effectiveness in dividing an image into low- and high-frequency parts. In our framework, an input image is first decomposed into a low-frequency part and a high-frequency part by using the GS filter. Rain streaks are located in the high-frequency part. We extract and separate the rain features of the high-frequency part through a deep convolutional neural network (CNN). The experimental results obtained on synthetic data and real data show that the proposed method can better suppress the morphological artifacts caused by filtering. Compared with state-of-the-art single image rain streaks removal methods, the proposed method retains finer image object structures while removing rain streaks.

Effective noise management and control of periodic fluctuations in spaceborne atomic clocks are essential for the accuracy and reliability of Global Navigation Satellite Systems. Time-varying periodic terms can impact both the performance evaluation and prediction accuracy of satellite clocks, making it crucial to mitigate these influences in the clock bias. We propose methods based on the Fourier dictionary and basis pursuit, namely the Fourier basis pursuit (FBP) spectrum and the Fourier basis pursuit bandpass filter (FBPBPF), to analyze and extract periodic terms in the satellite clock bias. The FBP method minimizes the L1-norm to improve spectral quality, while the FBPBPF reduces boundary effects and noise. Our experimental results show that the FBP spectrum has a more obvious main lobe and reduces spectral leakage compared to traditional windowed Fourier transforms. In simulation experiments, the FBPBPF achieves periodic term extraction with errors reduced by 6.81% to 26.55% compared to traditional signal processing methods, and boundary extraction errors reduced by up to 63.67%. Using the BeiDou Navigation Satellite System’s precise clock bias for verification, the FBP-based prediction method has significantly improved the prediction accuracy compared to the spectral analysis model. For 6, 12, 18, and 24 h predictions, the average root mean square error of the FBP prediction method is reduced by 15.85%, 11.04%, 6.45%, and 4.01%, respectively.

An ocean target electric field signal is an effective approach for analyzing the ocean environment and is widely used for detecting ocean targets, extracting their features, and tracking them. Low-frequency analysis and recording (LOFAR) is a commonly used time–frequency analysis tool that provides the time–frequency spectrum of a signal; however, its reliance on the Fourier transform (FT) results in a low frequency resolution and signal-to-noise ratio (SNR), which limits its target detection capabilities. To address this problem, we propose a method called low-frequency analysis and recording based on basis pursuit (LOFAR-BP) for analyzing and detecting ocean target electric field signals. LOFAR-BP uses basis pursuit (BP) with the L1 norm for frequency analysis, whereas LOFAR utilizes the FT. We demonstrate that the FT is the L2 norm mathematically. LOFAR-BP generates the time–frequency spectrum in the same way that LOFAR does. By extracting characteristic values from the time–frequency spectrum, targets can be detected using an appropriate threshold. Both simulation and ocean experiments showed that LOFAR-BP effectively enhances target signals and suppresses noise. Compared with LOFAR, LOFAR-BP improved the frequency resolution by 60% in both experiments and increased the SNR by 54.82 dB in the simulation experiment and by 39.59 dB in the ocean experiment. When applied to target detection, LOFAR-BP can detect targets 6 s earlier than LOFAR can.

Satellite clock bias exhibits complex, time-varying periodic characteristics due to environmental disturbances. Accurate modeling and prediction of periodic terms play a crucial role in improving the precision and stability of short-term predictions. Traditional models such as spectral analysis model (SAM) estimate the frequency, amplitude, and phase of periodic terms through global fitting, which limits their ability to adapt to abrupt changes at the prediction boundary. To address this limitation, this paper proposes an improved spectral analysis model (IM-SAM) based on the inaction method (IM). The model employs IM to extract the instantaneous frequency, amplitude, and phase parameters of periodic terms precisely at the data endpoint, and utilizes the parameters of periodic terms at the data endpoint for prediction, effectively suppressing periodic fluctuations in prediction errors. Experimental results based on real GPS clock bias data demonstrate that the root mean square (RMS) of IM-SAM prediction errors is reduced by 19.14%, 14.39%, and 10.48% for 3 h, 6 h, and 12 h prediction tasks, respectively, compared with SAM. Furthermore, a kinematic precise point positioning experiment was performed using IM-SAM-predicted clock products and compared with the predicted half of IGS ultra-rapid clock products. The RMS of position error was reduced by 14.3%, 12.6%, and 7.9% in the east, north, and up directions, respectively. These results demonstrate the practical effectiveness and accuracy of IM-SAM in real-time clock prediction and GPS positioning applications.