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Detecting targets in dynamically changing clutter environments has always been challenging for radar techniques. The innovative matrix information geometry-based (MIG) detector, which equips with different geometric distances to discriminate the target and clutter on the Hermitian positive-definite manifold, treats the detection issue from a geometric point of view, however, the current geometric distances do not always perform satisfactory under the changing environment. To address this problem, this article proposes an adaptive log-Euclidean (LE) metric on the manifold to properly match the actual clutter environment and achieve satisfactory performance. Specifically, the adaptive LE metric is developed on a dimension-reduced manifold by deriving a discriminative manifold transformation, and the determination of the transformation is formulated as a joint optimization problem between the cell under test and the clutter centroid. In this study, manifold-based methods and an eigen-decomposition-based method are proposed to solve the optimization problem. Moreover, an adaptive LE metric-based MIG detector is designed, and its bounded constant false alarm rate property is analyzed. At last, both simulated data and real radar data are utilized to validate the performance of the proposed method. Particularly, in the unmanned aerial vehicle target detection experiment, the results show that the strong clutter is effectively suppressed and the target is simultaneously highlighted without any prior knowledge.

In recent years, electromagnetic (EM) vortex imaging has emerged as a novel technique in the field of radar super-resolution imaging. This approach fundamentally differs from conventional methods by the relative lateral motion between the target and the platform. Although super-resolution azimuthal imaging can be achieved, different orbital angular momentum (OAM) modes should be modulated in different signal pulses. In contrast, a new OAM modulation and monopulse imaging method is proposed in this article, which involves multiplexing OAM modes based on frequency diversity in one pulse and can considerably improve imaging efficiency. By introducing tiny frequency offsets among the elements of a uniform circular frequency diverse array (UC-FDA), the OAM multiplexing beams are generated. Subsequently, the EM vortex imaging model for the coherent UC-FDA is established, and the imaging method is proposed. The theoretical performance analyses of spatial azimuthal resolution and efficiency are derived. Finally, the results demonstrate that the proposed method exhibits comparable imaging performance to the conventional EM vortex imaging method, even when only a single pulse is transmitted.

Capture of trace benzene is an important and challenging task. Metal–organic framework materials are promising sorbents for a variety of gases, but their limited capacity towards benzene at low concentration remains unresolved. Here we report the adsorption of trace benzene by decorating a structural defect in MIL-125-defect with single-atom metal centres to afford MIL-125-X (X = Mn, Fe, Co, Ni, Cu, Zn; MIL-125, Ti8O8(OH)4(BDC)6where H2BDC is 1,4-benzenedicarboxylic acid). At 298 K, MIL-125-Zn exhibits a benzene uptake of 7.63 mmol g−1at 1.2 mbar and 5.33 mmol g−1at 0.12 mbar, and breakthrough experiments confirm the removal of trace benzene (from 5 to <0.5 ppm) from air (up to 111,000 min g−1of metal–organic framework), even after exposure to moisture. The binding of benzene to the defect and open Zn(II) sites at low pressure has been visualized by diffraction, scattering and spectroscopy. This work highlights the importance of fine-tuning pore chemistry for designing adsorbents for the removal of air pollutants.

The aim of this study was to determine the osteogenic activity and mechanism of soybean peptide VVELLKAFEEKF (SOP) and the potential relationship between SOP and transforming growth factor-β1 (TGF-β1). The results show that SOP promotes MC3T3-E1 cell proliferation by altering cell progression. SOP induced cell differentiation and mineralization in a dose-dependent manner at 0.7–7 μM. Moreover, SOP stimulates osteoblast differentiation, which may be achieved through the activation of p38-MAPK and Smad2/3 signaling pathways. Furthermore, treatment with a TβRI inhibitor (SB525334) inhibited the phosphorylation levels of p38 and Smad2/3, which indicates the involvement of TβRI in the process of osteoblast differentiation caused by SOP. Besides, in non-FBS-cultured MC3T3-E1 cells, SOP and TGF-β1 promoted the phosphorylation of Smad2/3 and alkaline phosphatase (ALP) activity, but the effect was lost when SOP was incubated separately, indicating that SOP stimulated osteoblast differentiation by promoting TGF-β1 activity. In vivo, SOP significantly restores bone mineral density loss and behavioral deficits in a model of glucocorticoid-induced osteoporosis (GIOP) in zebrafish. These results suggest that SOP may have the function of promoting bone remodeling and may be used as a potential active factor for functional food development to prevent osteoporosis.

Porous solids can accommodate and release molecular hydrogen readily, making them attractive for minimizing the energy requirements for hydrogen storage relative to physical storage systems. However, H2adsorption enthalpies in such materials are generally weak (−3 to −7 kJ/mol), lowering capacities at ambient temperature. Metal–organic frameworks with well-defined structures and synthetic modularity could allow for tuning adsorbent–H2interactions for ambient-temperature storage. Recently, Cu2.2Zn2.8Cl1.8(btdd)3(H2btdd = bis(1H-1,2,3-triazolo-[4,5-b],[4′,5′-i])dibenzo[1,4]dioxin; CuI-MFU-4l) was reported to show a large H2adsorption enthalpy of −32 kJ/mol owing to π-backbonding from CuIto H2, exceeding the optimal binding strength for ambient-temperature storage (−15 to −25 kJ/mol). Toward realizing optimal H2binding, we sought to modulate the π-backbonding interactions by tuning the pyramidal geometry of the trigonal CuIsites. A series of isostructural frameworks, Cu2.7M2.3X1.3(btdd)3(M = Mn, Cd; X = Cl, I; CuIM-MFU-4l), was synthesized through postsynthetic modification of the corresponding materials M5X4(btdd)3(M = Mn, Cd; X = CH3CO2, I). This strategy adjusts the H2adsorption enthalpy at the CuIsites according to the ionic radius of the central metal ion of the pentanuclear cluster node, leading to −33 kJ/mol for M = ZnII(0.74 Å), −27 kJ/mol for M = MnII(0.83 Å), and −23 kJ/mol for M = CdII(0.95 Å). Thus, CuICd-MFU-4lprovides a second, more stable example of optimal H2binding energy for ambient-temperature storage among reported metal–organic frameworks. Structural, computational, and spectroscopic studies indicate that a larger central metal planarizes trigonal CuIsites, weakening the π-backbonding to H2.

Nanoporous materials have attracted great attention for gas storage, but achieving high volumetric storage capacity remains a challenge. Here, by using neutron powder diffraction, volumetric gas adsorption, inelastic neutron scattering and first-principles calculations, we investigate a magnesium borohydride framework that has small pores and a partially negatively charged non-flat interior for hydrogen and nitrogen uptake. Hydrogen and nitrogen occupy distinctly different adsorption sites in the pores, with very different limiting capacities of 2.33 H2and 0.66 N2per Mg(BH4)2. Molecular hydrogen is packed extremely densely, with about twice the density of liquid hydrogen (144 g H2per litre of pore volume). We found a penta-dihydrogen cluster where H2molecules in one position have rotational freedom, whereas H2molecules in another position have a well-defined orientation and a directional interaction with the framework. This study reveals that densely packed hydrogen can be stabilized in small-pore materials at ambient pressures.

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In this assay, based on the terminal protection of small-molecule-linked DNA, a new ultrasensitive real-time fluorescence strategy combined with an isothermal exponential amplification reaction (IEXPAR) has been established for protein assay. By the clever design of DNA, terminal protection is combined with efficient IEXPAR. The target protein explicitly binds to small molecules attached to the template DNA, protecting the template DNA from exonuclease I (Exo I) degradation. The added DNA primer hybridizes with the protected template DNA and triggers the following IEXPAR. IEXPAR has a super amplification efficiency of 106–109times. The IEXPAR yields numerous double-stranded DNA (dsDNA) molecules. The fluorescence dye SYBR Green I (SG), which is sensitive to dsDNA, is used to determine the real-time fluorescence of the IEXPAR. Conversely, without the target protein, the template DNA is hydrolyzed by Exo I, failing to trigger the IEXPAR. The intriguing combination of IEXPAR and terminal protection realizes the ultrasensitive detection of protein. As low as 100 fmol L−1SA and 200 pg mL−1folic acid (FR) are accurately detected.

Last-mile delivery has gained much popularity in recent years, it accounts for about half of the whole logistics cost. Unlike container transportation, companies must hire significant number of employees to deliver packages to the customers. Therefore, many companies are studying automated methods such as robotic delivery to complete the delivery work to reduce the cost. It is undeniable that the security issue is a huge challenge in such a system. In this article, we propose an AI-driven robotic delivery system, which consists of two modules. A multilevel cooperative user authentication module for delivering parcel using both PIN code and biometrics verification, i.e., voiceprint and face verification. Another noncooperative user identification module using face verification which detects and verifies the identification of the customer. In this way, the robot can find the correct customer and complete the delivery task automatically. Finally, we implement the proposed system on a Turtlebot3 robot and analyze the performance of the proposed schema. Experimental results show that our proposed system has a high accuracy and can complete the delivery task securely.

Conversion of plastic wastes to valuable carbon resources without using noble metal catalysts or external hydrogen remains a challenging task. Here we report a layered self-pillared zeolite that enables the conversion of polyethylene to gasoline with a remarkable selectivity of 99% and yields of >80% in 4 h at 240 °C. The liquid product is primarily composed of branched alkanes (selectivity of 72%), affording a high research octane number of 88.0 that is comparable to commercial gasoline (86.6). In situ inelastic neutron scattering, small-angle neutron scattering, solid-state nuclear magnetic resonance, X-ray absorption spectroscopy and isotope-labelling experiments reveal that the activation of polyethylene is promoted by the open framework tri-coordinated Al sites of the zeolite, followed by β-scission and isomerization on Brönsted acids sites, accompanied by hydride transfer over open framework tri-coordinated Al sites through a self-supplied hydrogen pathway to yield selectivity to branched alkanes. This study shows the potential of layered zeolite materials in enabling the upcycling of plastic wastes.

In this article, the power spectrum information geometry (PSIG) detector, which inherits the performance advantages of matrix information geometry (MIG) detectors in heterogeneous clutter backgrounds, is proposed. The PSIG detector can address two urgent problems in applications of MIG detectors, which are the expensive computation expense and unavailable acquisition ability of target velocity. Specifically, the PSIG detector utilizes power spectra (PSs) instead of high-dimensional covariance matrices to characterize sample data and employs subband filter bank to extend the detection from range cells to range-Doppler cells; thus, it requires less computation expense and can obtain the target velocity information according to the Doppler cell. Experiments based on the real data show the advantages of the proposed PSIG detectors in comparison with competitive methods. Especially, in the experiments with the real-recorded airborne radar data, the proposed method can effectively suppress the heterogeneous main-lobe clutter without any prior knowledge and provides detection probability improvement of more than 30% to the competitive methods with low false-alarm ratios.

For the target in the radar forward-looking sight, only the range-history phase information can be exhibited when the plane electromagnetic (EM) wave illuminating. For traditional approaches, the reconstruction of target azimuthal information requires antennas configured at both ends of the long baseline to implement multi-angle observation, usually leading to a baseline length burden. In contrast, the target’s azimuth information, related to the orbital angular momentum (OAM), is directly modulated in the new-dimensional echo phase by the antenna radiating the vortex EM wave, which provides a new foundation for target azimuth reconstruction. In this article, a novel forward-looking target reconstruction methodology with EM vortex interferometry is proposed, and the target 3-D imaging with different OAM modes interferometry strategies is achieved as well. The developed approach can improve the target azimuthal reconstruction error performance without increasing the length of short baseline and image registration. Comprehensive results of simulated data and real-world measured data are performed to validate the effectiveness and anti-noise robustness of the proposals.

Long-duration storage of hydrogen is necessary for coupling renewable H2with stationary fuel cell power applications. In this work, aluminum formate (ALF), which adopts the ReO3-type structure, is shown to have remarkable H2storage performance at non-cryogenic (>120 K) temperatures and low pressures. The most promising performance of ALF is found between 120 K and 160 K and at 10 bar to 20 bar. The study illustrates H2adsorption performance of ALF over the 77 K to 296 K temperature range using gas isotherms, in situ neutron powder diffraction, and DFT calculations, as well as technoeconomic analysis (TEA), illustrating ALF’s competitive performance for long-duration storage versus compressed hydrogen and leading metal–organic frameworks. In the TEA, it is shown that ALF’s storage capacity, when combined with a temperature/pressure swing process, has advantages versus compressed H2at a fraction of the pressure (15 bar versus 350 bar). Given ALF’s performance in the 10 bar to 20 bar regime under moderate cooling, it is particularly promising for use in safe storage systems serving fuel cells.

Rapid and accurate antimicrobial prescriptions are critical for bloodstream infection (BSI) patients, as they can guide drug use and decrease mortality significantly. The traditional antimicrobial susceptibility testing (AST) for BSI is time-consuming and tedious, taking 2–3 days. Avoiding lengthy monoclonal cultures and shortening the drug sensitivity incubation time are keys to accelerating the AST. Here, we introduced a bacteria separation integrated AST (BSI-AST) chip, which could extract bacteria directly from positive blood cultures (PBCs) within 10 min and quickly give susceptibility information within 3 h. The integrated chip includes a bacteria separation chamber, multiple AST chambers, and connection channels. The separator gel was first preloaded into the bacteria separation chamber, enabling the swift separation of bacteria cells from PBCs through on-chip centrifugation. Then, the bacteria suspension was distributed in the AST chambers with preloaded antibiotics through a quick vacuum-assisted aliquoting strategy. Through centrifuge-assisted on-chip enrichment, detectable growth of the phenotype under different antibiotics could be easily observed in the taper tips of AST chambers within a few hours. As a proof of concept, direct AST from artificial PBCs with Escherichia coliagainst 18 antibiotics was performed on the BSI-AST chip, and the whole process from bacteria extraction to AST result output was less than 3.5 h. Moreover, the integrated chip was successfully applied to the diagnosis of clinical PBCs, showing 93.3% categorical agreement with clinical standard methods. The reliable and fast pathogen characterization of the integrated chip suggested its great potential application in clinical diagnosis.

Proton-exchange membrane fuel cells enable the portable utilization of hydrogen (H2) as an energy resource. Current electrolytic materials have limitation, and there is an urgent need to develop new materials showing especially high proton conductivity. Here, we report the ultra-fast proton conduction in a novel metal–organic framework, MFM-808, which adopts an unprecedented topology and a unique structure consisting of two-dimensional layers of {Zr6}-clusters. By replacing the bridging formate with sulfate ligands within {Zr6}-layers, the modified MFM-808-SO4exhibits an exceptional proton conductivity of 0.21 S·cm–1at 85 °C and 99% relative humidity. Modeling by molecular dynamics confirms that proton transfer is promoted by an efficient two-dimensional conducting network assembled by sulfate–{Zr6}-layers. MFM-808-SO4also possesses excellent photocatalytic activity for water splitting to produce H2, paving a new pathway to achieve a renewable hydrogen-energy cycle.

Underwater target detection has been a significant challenge in environment aware. In this letter, an underwater target detection scheme is proposed by measuring the water-surface vibrations caused by acoustic waves with a millimeter-wave radar. First, the power of the water-surface vibration due to the reflection of acoustic waves by the target is derived, which gives a quantitative relationship between the perturbations on water-surface vibration and the position of the target. Then, the signal model to accurately measure the water-surface vibration with millimeter-wave radar is established. A method to estimate the power spectrum of the phase of water-surface vibrations is proposed, based on which a test statistic for underwater target detection is formulated. Finally, the effectiveness of the proposed scheme is validated by water-tank experiments using a frequency modulated radar with a center frequency of 77 GHz.

ABSTRACTThe sparse array imaging radar could largely reduce the system complexity, but it also suffers from poor azimuthal resolution due to the limited aperture length and incomplete observation caused by non-uniform array configuration. In this letter, a radar forward-looking imaging method with improved imaging quality and reduced system complexity is proposed. Firstly, the matrix completion method is utilized to recover the missing signals of sparse array. Then, based on the plane-wave assumption, a fast 2-dimensional atomic norm minimization (ANM) is adopted to solve the positions and amplitudes of scatterers. As a continues compressed sensing method, the result of ANM-based method earns sharper main-lobes and much lower-level side-lobes compared to the fast Fourier transform -based method. Although the resolution of proposed method is still limited by Rayleigh resolution, the imaging quality can be greatly improved by emphasizing main-lobes and avoiding the perturbation of side-lobes. Simulations and experiments are carried out to demonstrate the performance of the proposed method.

The high volatility in wind power and uncertainty of ramp events has brought significant hidden hazards to maintain the stable and safe operation of the power system. In this paper, a two-stage prediction framework is proposed, taking the measurement of the probability density curve and the judgment of ramp-up mode. Aiming at the issue of limited prediction information and the sensitivity of prediction values at extreme points, an uncertainty prediction model for wind power based on a gated recurrent unit quantile regression network is proposed to realize the screening and judgment of ramps based on the prediction results and the divergence measurement of probability density distribution. Faced with notoriously unpredictable ramps and the small-samples poor learning performance, this paper proposes a ramp pattern discrimination model based on a gradient boosting decision tree, which describes the events in a future period from their magnitude and duration. Compared with state-of-the-art ramp forecasting methods, our proposed framework yields highly outstanding performances and realizes the adaptive detection for wind power ramps.

Wildfires in transmission line passages are a severe threat to power security. Two wildfire detection models, which are based on the YOLOv5, are proposed in this paper. Due to the limited computing power of embedded terminals, the proposed models simplify the network structure of YOLOv5. Specifically, one is that only the overall structure of the neck and head parts in the original network structure is simplified, and the second method is based on the first method to delete the modules of backbone, which greatly reduces the number of parameters of the model. The experimental results show that the proposed lightweight models can achieve real-time monitoring in embedded devices while the accuracy and recall remain high.

Cubic energy materials such as thermoelectrics or hybrid perovskite materials are often understood to be highly disordered1,2. In GeTe and related IV–VI compounds, this is thought to provide the low thermal conductivities needed for thermoelectric applications1. Since conventional crystallography cannot distinguish between static disorder and atomic motions, we develop the energy-resolved variable-shutter pair distribution function technique. This collects structural snapshots with varying exposure times, on timescales relevant for atomic motions. In disagreement with previous interpretations3–5, we find the time-averaged structure of GeTe to be crystalline at all temperatures, but with anisotropic anharmonic dynamics at higher temperatures that resemble static disorder at fast shutter speeds, with correlated ferroelectric fluctuations along the <100>cdirection. We show that this anisotropy naturally emerges from a Ginzburg–Landau model that couples polarization fluctuations through long-range elastic interactions6. By accessing time-dependent atomic correlations in energy materials, we resolve the long-standing disagreement between local and average structure probes1,7–9and show that spontaneous anisotropy is ubiquitous in cubic IV–VI materials.

The mass production of plastic waste has caused an urgent worldwide public health crisis. Although government policies and industrial innovation are the driving forces to meet this challenge, trying to understand public attitudes may improve the efficiency of this process. Social media has become the main ways for the public to obtain information and express opinions and feelings. This motivated us to mine the perceptions and behavioral responses towards plastic usage using social media data. In this paper, we proposed a framework for data collection and analysis based on mainstream media in the UK to obtain public opinions on plastics. An unsupervised machine learning model based on Latent Dirichlet Allocation (LDA) has been employed to analyse and cluster the topics to deal with the lack of annotation of the data contents. An additional dictionary method was then proposed to evaluate the sentiment of the comments. The framework also provides tools to visualise the model and results to stimulate insightful understandings. We validated the framework's effectiveness by applying it to analyse three mainstream social media, where 6 first-level topic categories and 13 second-level topic categories from the comment texts related to plastics have been identified. The results show that public sentiment towards plastic products is generally stable. The spatiotemporal distribution of each topic's sentiment is highly correlated with the number of occurrences.

We developed a bent-capillary-centrifugal-driven (BCCD) monodisperse droplet generator, which could achieve a perfect combination of driving and segmentation for the dispersed phase only using a rotating bent capillary immersed in the continuous phase (mineral oil). The sample could flow continuously to the bent-capillary outlet to form the droplet precursors, which were segmented into homogeneous droplets in the continuous phase. Through the investigation of influence factors on droplet size and stability, we found that the droplet size could be conveniently controlled by the rotational speed of the bent capillary. The droplet volumes could be adjusted with the range from 34 pL to 1 μL, and the coefficient variations (CVs) were less than 3%. Meanwhile, the BCCD droplet generator could realize the controllable droplet output with a high-efficiency sample utilization of 99.75 ± 1.15%, which offered a significant advantage in reducing the waste of precious samples in the droplet generation process. We validated this system with a digital loop-mediated isothermal amplification (dLAMP) assay for the absolute quantification of Mycobacterium tuberculosiscomplex nucleic acids. The results demonstrated that the BCCD droplet generator was easy to build, was of low cost, and was convenient to operate, as well as avoided sample loss and cross-contamination by coupling with a 96-well plate. Overall, the present platform, as a simple chip-free droplet generator, will provide an especially valuable droplet generation solution for biochemical applications based on droplets.

This article addresses the problem of detecting radar targets submerged in a strong sea-clutter background. In this study, a novel type of detection method based on matrix information geometry (MIG) is developed. The filtering process and manifold projection are incorporated into the detector design. First, a filtering scheme for correlation coefficients is established via subband decomposition, such that a subband Hermitian positive definite (HPD) manifold constructed by a set of subband HPD matrices is formulated. Accordingly, the detection is performed by discriminating the target and the clutter on the subband HPD manifold. Then, in order to enhance the discriminative power between the target and the strong clutter, a manifold projection method that maps the HPD manifold into a lower-dimensional and more discriminative one is devised. In this study, the manifold projection is formulated as an optimization problem on a Stiefel manifold according to the principle of maximizing signal-to-clutter ratio (SCR). Subsequently, a manifold projection-based subband MIG detector is proposed. Extensive experiments based on simulated data and real radar data are carried out to verify the effectiveness of the proposed method. The experimental results demonstrate that the proposed method can efficiently suppress the strong sea clutter and achieve better detection performance than the competitors.

Vortex electromagnetic (EM) wave carrying orbital angular momentum (OAM) has been exploited in radar imaging realms in recent years. However, the radiation energy pattern caused by the Bessel amplitude modulation limits the OAM-based applications in the long distance. To solve the radiation energy divergence problem in radar realms, the imaging method based on waveform diversity (WD) and rotational array is developed in this article. The energy hollow along the beam axis is avoided by the orthogonal waveform design during the radar illumination process. Then, the echo demodulation approach is proposed, and the corresponding imaging model is established. Furthermore, a highly efficient imaging scheme based on rotational array is designed, where the OAM multiplexing approach is proposed and large OAM index can be used for imaging by virtual synthesis. Both simulation results and experimental results in an anechoic chamber are provided to demonstrate the effectiveness. This work can promote the application of OAM technology in realistic scenarios.

To treat the slow-moving fluctuating target detection issues, the information geometry-based track-before-detect algorithms, which combines the performance advantages of information geometry detectors and the multi-frame information integration ability of dynamic programming algorithm, are proposed in this article. The proposed methods are based on the Hermitian positive definite (HPD) manifold and power spectrum (PS) manifold, that the geometric properties of the target feature track and clutter track on the HPD or PS manifold are exploited for the integration of inter-frame target information. Specifically, the IG-based scoring function is designed to evaluate the candidate trajectories, and a general IG-based DP algorithm is deduced to obtain the trajectories with the maximum integration of scoring functions. Moreover, to avoid the performance degradation resulting from the illegal candidate trajectories, a stricter constraint for the trajectories of slow-moving target is established, and a corresponding efficient IG-based DP algorithm is deduced by utilizing the skipping transition. Experimentally, the superiority of the proposed methods have been validated with the real-recorded ship target echo data and sea clutter data. The experimental results show that the proposed methods can provide a signal-to-clutter ratio improvement of approximately 5.5 dB.

In this letter, an effective parametric IF estimation method based on piece-wise sparse representation (PWSR) is proposed to enhance the precision of conventional time-frequency distribution (TFD)-based estimators. Firstly, the signal is divided into a series of short-time segments according to the piece-wise quadratic frequency modulation (QFM) model. Then, the corresponding QFM parameters of each segment are accurately estimated by solving a sparse representation (SR) problem. Moreover, a construction scheme enabling the QFM dictionary to vary adaptively with the analyzed short-time signal is also provided. Finally, the IF of each segment is reconstructed according to the SR solution individually and combined together to generate the complete IF estimates. A radar imaging example verifies that the proposed method achieves a notable improvement in estimation accuracy as compared to existing TFD-based approaches.

This article deals with the problem of detecting maritime targets embedded in nonhomogeneous sea clutter, where the limited number of secondary data is available due to the heterogeneity of sea clutter. A class of linear discriminant analysis (LDA)-based matrix information geometry (MIG) detectors is proposed in the supervised scenario. As customary, Hermitian positive-definite (HPD) matrices are used to model the observational sample data, and the clutter covariance matrix of the received dataset is estimated as the geometric mean of the secondary HPD matrices. Given a set of training HPD matrices with class labels, which are elements of a higher dimensional HPD matrix manifold, the LDA manifold projection learns a mapping from the higher dimensional HPD matrix manifold to a lower dimensional one subject to maximum discrimination. In this study, the LDA manifold projection, with the cost function maximizing between-class distance while minimizing within-class distance, is formulated as an optimization problem in the Stiefel manifold. Four robust LDA-MIG detectors corresponding to different geometric measures are proposed. Numerical results based on both simulated radar clutter with interferences and real IPIX radar data show the advantage of the proposed LDA-MIG detectors against their counterparts without using LDA and the state-of-the-art maritime target detection methods in nonhomogeneous sea clutter.

To improve target detection performance in non-Gaussian backgrounds, the joint design of transmit sequence and receive filter for multiple-input–multiple-output (MIMO) radar is studied. By approximating the probability density function of observed non-Gaussian data with the Gaussian mixture model (GMM), a Riemannian manifold of Gaussian mixture distribution is developed to depict the complicated background first. Then, maximizing the geometric distance on manifolds, which is converted by maximizing the discrimination between the target and clutter, is proposed as the criterion for the joint design of transmit sequence and receive filter. Thereby, under the constant-modulus constraint, the joint design problem can be transformed into an optimization problem. However, the proposed optimization problem is nonconvex and constrained. To solve this problem, a Riemannian optimization framework is provided. By taking the advantage of the underlying geometric and algebraic structure of the constraint space, the original constrained optimization problem in Euclidean space can be transformed into the unconstraint optimization problem over Riemannian product manifolds. Moreover, to obtain the global optimal solution, the Riemannian gradient of the geometric distance cost is derived for the conjugate gradient algorithm. Experiments demonstrate that the proposed method shows advantages in detection performance compared with competitive methods.