With the wide application of convolutional neural networks (CNNs), a variety of ship detection methods based on CNNs in synthetic aperture radar (SAR) images were proposed, but there are still two main challenges: (1) Ship detection requires high real-time performance, and a certain detection speed should be ensured while improving accuracy; (2) The diversity of ships in SAR images requires more powerful multi-scale detectors. To address these issues, a SAR ship detector called Duplicate Bilateral YOLO (DB-YOLO) is proposed in this paper, which is composed of a Feature Extraction Network (FEN), Duplicate Bilateral Feature Pyramid Network (DB-FPN) and Detection Network (DN). Firstly, a single-stage network is used to meet the need of real-time detection, and the cross stage partial (CSP) block is used to reduce the redundant parameters. Secondly, DB-FPN is designed to enhance the fusion of semantic and spatial information. In view of the ships in SAR image are mainly distributed with small-scale targets, the distribution of parameters and computation values between FEN and DB-FPN in different feature layers is redistributed to solve the multi-scale detection. Finally, the bounding boxes and confidence scores are given through the detection head of YOLO. In order to evaluate the effectiveness and robustness of DB-YOLO, comparative experiments with the other six state-of-the-art methods (Faster R-CNN, Cascade R-CNN, Libra R-CNN, FCOS, CenterNet and YOLOv5s) on two SAR ship datasets, i.e., SSDD and HRSID, are performed. The experimental results show that the AP50 of DB-YOLO reaches 97.8% on SSDD and 94.4% on HRSID, respectively. DB-YOLO meets the requirement of real-time detection (48.1 FPS) and is superior to other methods in the experiments.

In conformal array radar, due to the directivity of antennas, the responses of the echo signals between different antennas are distinct, and some antennas cannot even receive the target echo signal. These phenomena significantly affect the accuracy of direction-of-arrival (DOA) estimation. To implement accurate DOA estimation in a conformal uniform circular array (UCA) composed of directional antennas, the two-stage fast DOA estimation algorithm is proposed. In the pre-processing stage, multi-target decoupling and target detection are mainly used to obtain the targets’ range bin indexes set; in the rough-precise DOA estimation stage, the amplitude and phase information of each antenna are used for rough DOA estimation and precise DOA estimation, respectively. Based on simulation and actual anechoic chamber radar experiments, and through quantitative analyses of the accuracy, validity and elapsed time of the two-stage fast DOA estimation algorithm compared with the directional antenna MUSIC (DA-MUSIC), sub-array MUSIC (S-MUSIC) and Capon-like algorithms, results indicate that the two-stage fast DOA estimation algorithm can rapidly and accurately estimate DOAs in a multi-target scenario without the range-angle pair-matching procedure. Lower computational complexity and superior estimation accuracy provide the two-stage fast DOA estimation algorithm a broader application prospect in the practical engineering field.

A direct and analytical algorithm for pose estimation of single space circle in the context of monocular machine vision is proposed. Circular feature with detected centre in the image is used to find two special diameters, one is primarily found for estimating the location of space circle, the other is for estimating the normal vector. The proposed algorithm formulates the problem with solving equations instead of matrix transformation; by solving the equations efficiently, it obtains the single‐valued true solution automatic without choosing the process. Experiments on real images prove that the proposed algorithm can achieve high accuracy. Automatic, efficiency and accuracy together make the proposed algorithm applicable especially in real‐time system.

High-accuracy and dependable prediction of the bias of space-borne atomic clocks is extremely crucial for the normal operation of the satellites in the case of interrupted communication. Currently, the clock bias prediction for the Chinese BeiDou Navigation Satellite System (BDS) remains still a huge challenge. To develop a high-precision approach for forecasting satellite clock bias (SCB) in allusion to analyze the shortcomings of the exponential smoothing (ES) model, a modified ES model is proposed hereof, especially for BDS-2 satellites. Firstly, the basic ES models and their prediction mechanism are introduced. As the smoothing coefficient is difficult to determine, this leads to increasing fitting errors and poor forecast results. This issue is addressed by introducing a dynamic “thick near thin far (TNTF)” principle based on the sliding windows (SW) to optimize the best smoothing coefficient. Furthermore, to enhance the short-term forecasted accuracy of the ES model, the gray model (GM) is adopted to learn the fitting residuals of the ES model and combine the forecasted results of the ES model with the predicted results of the GM model from error learning (ES + GM). Compared with the single ES models, the experimental results show that the short-term forecast based on the ES + GM models is improved remarkably, especially for the combination of the three ES model and GM model (ES3 + GM). To further improve the medium-term prediction accuracy of the ES model, the new algorithms in ES with GM error learning based on the SW (ES + GM + SW) are presented. Through examples analysis, compared with the single ES2 (ES3) model, results indicate that (1) the average forecast precision of the new algorithms ES2 + GM + SW (ES3 + GM + SW) can be dramatically enhanced by 49.10% (56.40%) from 5.56 ns (6.77 ns) to 2.83 ns (2.95 ns); (2) the average forecast stability of the new algorithms ES2 + GM + SW (ES3 + GM + SW) is also observably boosted by 53.40% (49.60%) from 8.99 ns (16.13 ns) to 4.19 ns (8.13 ns). These new coupling forecast models proposed in this contribution are more effective in clock bias prediction both forecast accuracy and forecast stability.

Solving linear time-varying equations is a classic problem in science and engineering. With the development of the neural network, some recurrent neural networks are presented, such as Zhang neural network (ZNN) and gradient neural network (GNN), to obtain the solutions with high precision and fast convergence speeds. In this paper, we use a recently new method named as gradient-Zhang neural network (GZNN) by combining the GNN and ZNN, and build the corresponding GZNN model (named as GZNN-L) to solve the linear time-varying equations. For adapting to digital-circuit implementation and numerical algorithm development, four discretization formulas are applied, such as Euler forward formula, Taylor-Zhang discretization formula, five-instant discretization formula, and eight-instant discretization formula on the GZNN-L model. Then, four discretization GZNN-L algorithms are obtained. At last, we perform some numerical experiments to validate the correctness of the discretization GZNN-L algorithms and discuss the factors that influence the solution convergence.

The spaceborne interferometric synthetic aperture radar (InSAR) is expected to measure the sea surface height (SSH) with high accuracy over a wide swath. Since centimeter-level accuracy is required to monitor the ocean sub-mesoscale dynamics, the high accuracy implies that the altimetric errors should be totally understood and strictly controlled. However, for the dynamic waves, they move randomly all the time, and this will lead to significant altimetric errors. This study proposes an analytical method for the dynamic wave-related errors of InSAR SSH measurement based on the wave spectrum and electromagnetic scattering model. Additionally, the mechanisms of the dynamic wave-related errors of InSAR altimetry are analyzed, and the detailed numerical model is derived. The proposed analytical method is validated with NASA’s Surface Water and Ocean Topography (SWOT) project error budget, and the Root-Mean-Square Errors (RMSEs) are in good agreement (0.2486 and 0.2470 cm on a 0.5 km² grid, respectively). Instead of analysis for a typical project, the proposed method can be applied to different radar parameters under multiple sea states. The RMSEs of Ka-band under low sea state, moderate sea state, and high sea state are 0.2670, 1.3154, and 6.6361 cm, respectively. Moreover, the RMSEs of X-band and Ku-band are also simulated and presented. The experimental results demonstrate that the dynamic wave-related errors of InSAR altimetry are not sensitive to the frequencies but are sensitive to the sea states. The error compensation method is necessary for moderate and higher sea states for centimetric accuracy requirements. This can provide feasible suggestions on system design and error budget for the future interferometric wide-swath altimeter.