A parametric and feasibility study for data sampling of the dynamic mode decomposition: range, resolution, and universal convergence states

Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The dynamic mode decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear systems into periodically distinct constituents on reduced-order subspaces. As a novel mathematical hatchling, the DMD bears vast potentials yet an equal degree of unknown. This effort investigates the nuances of DMD sampling with an engineering-oriented emphasis. It aimed at elucidating how sampling range and resolution affect the convergence of DMD modes. We employed the most classical nonlinear system in fluid mechanics as the test subject—the turbulent free-shear flow over a prism—for optimal pertinency. We numerically simulated the flow by the dynamic-stress Large-Eddies Simulation with Near-Wall Resolution. With the large-quantity, high-fidelity data, we parametrized and identified four global convergence states: Initialization, Transition, Stabilization, and Divergence with increasing sampling range. Results showed that Stabilization is the optimal state for modal convergence, in which DMD output becomes independent of the sampling range. The Initialization state also yields sufficient accuracy for most system reconstruction tasks. Moreover, defying popular beliefs, over-sampling causes algorithmic instability: as the temporal dimension, n, approaches and transcends the spatial dimension, m (i.e., m < n), the output diverges and becomes meaningless. Additionally, the convergence of the sampling resolution depends on the mode-specific dynamics, such that the resolution of 15 frames per cycle for target activities is suggested for most engineering implementations. Finally, a bi-parametric study revealed that the convergence of the sampling range and resolution are mutually independent.

An Efficient Maritime Target Joint Detection and Imaging Method with Airborne ISAR System

In this paper, a joint maritime moving target detection and imaging approach, referred to as the fast inverse synthetic aperture radar (ISAR) imaging approach, based on the multi-resolution space−time adaptive processing (STAP), is proposed to improve the target detection performance and the target imaging efficiency in an airborne radar system. In the target detection stage, the sub-band STAP is introduced to improve the robustness of clutter suppression and to enhance the target output power with the decreased range resolution, by which the coarse estimation of target range-Doppler (R-D) location is obtained as the prior knowledge. In the following target imaging stage, the ISAR imaging is applied in the localized R-D zone surrounding with the target location. However, it is difficult to directly apply ISAR imaging with the conventional R-D algorithm because the slow-moving maritime target cannot be separated from the clutter interference in the Doppler frequency dimension. In this regard, the full-band STAP is applied in the R-D two-dimensional frequency domain for the simultaneous clutter suppression and high-resolution ISAR imaging, in which the envelope alignment and phase compensation are achieved by adaptive match filtering with the target Doppler frequency coarse estimation. Moreover, the reduced-dimension STAP applied in the target-surrounded localized Doppler frequency zone gives facilities for alleviating the computation burden. Simulation results corroborate the effectiveness of the proposed method.

Architecture Exploration of a Backprojection Algorithm for Real-Time Video SAR

This paper explores novel architectures for fast backprojection based video synthetic aperture radar (BP-VISAR) with multiple GPUs. The video SAR frame rate is analyzed for non-overlapped and overlapped aperture modes. For the parallelization of the backprojection process, a processing data unit is defined as the phase history data or range profile data from partial synthetic-apertures divided from the full resolution target data. Considering whether full-aperture processing is performed and range compression or backprojection are parallelized on a GPU basis, we propose six distinct architectures, each having a single-stream pipeline with a single GPU. The performance of these architectures is evaluated in both non-overlapped and overlapped modes. The efficiency of the BP-VISAR architecture with sub-aperture processing in the overlapped mode is accelerated further by filling the processing gap from the idling GPU resources with multi-stream based backprojection on multiple GPUs. The frame rate of the proposed BP-VISAR architecture with sub-aperture processing is scalable with the number of GPU devices for large pixel resolution. It can generate 4096 × 4096 video SAR frames of 0.5 m cross-range resolution in 23.0 Hz on a single GPU and 73.5 Hz on quad GPUs.

An Inter-Subband Processing Algorithm for Complex Clutter Suppression in Passive Bistatic Radar

Clutter suppression is a challenging problem for passive bistatic radar systems, given the complexity of actual clutter scenarios (stationary, time-varying and fractional-order clutter). Such complex clutter induces intense sidelobes in the entire range-Doppler plane and thus degrades target-detection performance, especially for low-observable targets. In this paper, a novel method, denominated as the batch version of the extensive cancellation algorithm (ECA) in the frequency domain (ECA-FB), is presented for the first time, to suppress stationary clutter and its sidelobes. Specifically, in this method, the received signal is first divided into short batches in the frequency domain to coarsen the range resolution, and then the clutter is removed over each batch via ECA. Further, to suppress the time-varying clutter, a Doppler-shifted version of ECA-FB (ECA-FBD) is proposed. Compared with the popular ECA and ECA-B methods, the proposed ECA-FB and ECA-FBD obtained superior complex clutter suppression and slow-moving target detection performance with lower computational complexity. A series of simulation and experimental results are provided to demonstrate the validity of the proposed methods.

Fine-Scale Velocity Measurement on the Wirewalker Wave-Powered Profiler

The Wirewalker (WW) ocean-wave-powered vertical profiling system allows the collection of high-resolution oceanographic data due to its rapid profiling, hydrodynamically quiet operation, and long endurance. We have assessed the potential for measuring fine-scale ocean velocities from the Wirewalker platform using commercially available acoustic velocimeters. Although the vertical profiling speed is relatively steady, platform motion affects the velocity measurements and requires correction. We present an algorithm to correct our velocity estimates using platform motion calculated from the inertial sensors – accelerometer, gyroscope, and magnetometer – on a Nortek Signature1000 Acoustic Doppler Current Profiler. This correction, carried out ping-by-ping, was effective in removing the vehicle motion from the measured velocities. The motion-corrected velocities contain contributions from surface wave orbital velocities, especially near the surface, and the background currents. To proceed, we use an averaging approach that leverages both the vertical platform profiling of the system and the ~15-20 m vertical profiling range resolution of the down-looking ADCP to separate the surface wave orbital velocities and the background flow. The former can provide information on the wave conditions. From the latter, we are able to estimate fine-scale velocity and shear with spectral wavenumber roll-off at vertical scales around 3 m, a vertical resolution several times finer than that possible from modern shipboard or fixed ADCPs with similar profiling range, and similar to recent glider measurements. When combined with a continuous time-series of buoy drift calculated from the onboard GPS, a highly-resolved total velocity field is obtained, with a unique combination of space and time resolution.

A Novel Composite Coding Method for Incoherent Scatter Radar

Many modern ionospheric studies rely on incoherent scatter radars (ISR) since this kind of radar is able to detect various ionospheric parameters over very long ranges. The performance of ISR significantly depends on its coding system. In recent decades, a new type of coding system, which is the so-called composite coding, was presented. It used to be constructed by using a certain code to modulate alternating code to achieve better detection resolution and anti-noise performance for ISRs. In the present study, a new composite coding system was presented, which is constructed based on complementary codes and alternating codes. In this paper, the performance of the new composite code will be compared with that of several traditional codes to show that the new composite code can help to improve the detection performance of the ISR. According to the analysis based on the ambiguity function, the present composite coding system helps to improve the range resolution and detection range for ISR detections. In addition, numerical tests on anti-noise performance show that the complementary composite coding system has a good anti-noise performance and helps to reduce the necessary times of incoherent integration. As a result, the composite coding system can improve the time resolution.

Photon-counting distributed free-space spectroscopy

Spectroscopy is a well-established nonintrusive tool that has played an important role in identifying and quantifying substances, from quantum descriptions to chemical and biomedical diagnostics. Challenges exist in accurate spectrum analysis in free space, which hinders us from understanding the composition of multiple gases and the chemical processes in the atmosphere. A photon-counting distributed free-space spectroscopy is proposed and demonstrated using lidar technique, incorporating a comb-referenced frequency-scanning laser and a superconducting nanowire single-photon detector. It is suitable for remote spectrum analysis with a range resolution over a wide band. As an example, a continuous field experiment is carried out over 72 h to obtain the spectra of carbon dioxide (CO2) and semi-heavy water (HDO, isotopic water vapor) in 6 km, with a range resolution of 60 m and a time resolution of 10 min. Compared to the methods that obtain only column-integrated spectra over kilometer-scale, the range resolution is improved by 2–3 orders of magnitude in this work. The CO2 and HDO concentrations are retrieved from the spectra acquired with uncertainties as low as ±1.2% and ±14.3%, respectively. This method holds much promise for increasing knowledge of atmospheric environment and chemistry researches, especially in terms of the evolution of complex molecular spectra in open areas.

ISAR Signal Tracking and High-Resolution Imaging by Kalman Filtering

In a short observation time, after the range alignment and phase adjustment, the motion of a target can be approximated as a uniform rotation. The radar observing process can be simply described as multiplying an observation matrix on the ISAR image, which can be thought of as a linear system. It is known that the longer observation time is, the higher cross-range resolution is. In order to deal with the conflict between short observation time and high cross-range resolution, we introduce Kalman filtering (KF) into the ISAR imaging and propose a novel method to reconstruct a high-resolution image with short time observed data. As KF has excellent reconstruction performance, it leads to a good application in ISAR image reconstruction. At each observation aperture, the reconstructed image denotes the state vector in KF at the aperture time. It is corrected by a two-step KF process: prediction and update. As iteration continues, the state vector is gradually corrected to a well-focused high-resolution image. Thus, the proposed method can obtain a high-resolution image in a short observation time. Both simulated and real data are applied to demonstrate the performance of the proposed method.

Contactless Simultaneous Breathing and Heart Rate Detections in Physical Activity Using IR-UWB Radars

Vital signs monitoring in physical activity (PA) is of great significance in daily healthcare. Impulse Radio Ultra-WideBand (IR-UWB) radar provides a contactless vital signs detection approach with advantages in range resolution and penetration. Several researches have verified the feasibility of IR-UWB radar monitoring when the target keeps still. However, various body movements are induced by PA, which lead to severe signal distortion and interfere vital signs extraction. To address this challenge, a novel joint chest–abdomen cardiopulmonary signal estimation approach is proposed to detect breath and heartbeat simultaneously using IR-UWB radars. The movements of target chest and abdomen are detected by two IR-UWB radars, respectively. Considering the signal overlapping of vital signs and body motion artifacts, Empirical Wavelet Transform (EWT) is applied on received radar signals to remove clutter and mitigate movement interference. Moreover, improved EWT with frequency segmentation refinement is applied on each radar to decompose vital signals of target chest and abdomen to vital sign-related sub-signals, respectively. After that, based on the thoracoabdominal movement correlation, cross-correlation functions are calculated among chest and abdomen sub-signals to estimate breath and heartbeat. The experiments are conducted under three kinds of PA situations and two general body movements, the results of which indicate the effectiveness and superiority of the proposed approach.