Search Results (42)

The eigen-decomposition of a covariance matrix is a key step in the Direction of Arrival (DOA) estimation algorithms such as subspace classes. Eigen-decomposition using the parallel Jacobi algorithm implemented on FPGA offers excellent parallelism and real-time performance. Addressing the high complexity and resource consumption of the traditional parallel Jacobi algorithm implemented on FPGA, this study proposes an improved FPGA-based parallel Jacobi algorithm for eigen-decomposition. By analyzing the relationship between angle calculation and rotation during the Jacobi algorithm decomposition process, leveraging parallelism in the data processing, and based on the concepts of time-division multiplexing and parallel partition processing, this approach effectively reduces FPGA resource consumption. The improved parallel Jacobi algorithm is then applied to the classic DOA estimation algorithm, the MUSIC algorithm, and implemented on Xilinx’s Zynq FPGA. Experimental results demonstrate that this parallel approach can reduce resource consumption by approximately 75% compared to the traditional method but introduces little additional time consumption. The proposed method in this paper will solve the problem of great hardware consumption of eigen-decomposition based on FPGA in DOA applications. Full article

The non-stationary clutter of space-based early warning radar (SBEWR) is more serious than that of airborne early warning radar. This phenomenon is primarily attributed to the Earth’s rotation and range ambiguity. The increase in clutter degrees of freedom (DOFs) and the significant widening of the clutter suppression notch are not conducive to moving target detection near main lobe clutter. This paper proposes an effective approach to suppress non-stationary clutter based on an interpulse multi-frequency mode for SBEWR. Using the orthogonality of the uniform stepping frequency signal, partial range ambiguity can be effectively suppressed, and the clutter DOFs will be reduced. Subsequently, joint pitch-azimuth-Doppler three-dimensional spacetime adaptive processing and slant range preprocessing are used to perform clutter suppression. This combination not only curtails the estimation error associated with the clutter covariance matrix but also enhances the overall detection capabilities of the system. The simulation results verify the effectiveness of the proposed approach. Full article

Motivated by a ternary generalization of the Pauli exclusion principle proposed by R. Kerner, we propose a notion of a ${\mathbb{Z}}_3$-skew-symmetric covariant $\mathrm{SO}\left(3\right)$-tensor of the third order, consider it as a 3-dimensional matrix, and study the geometry of the 10-dimensional complex space of these tensors. We split this 10-dimensional space into a direct sum of two 5-dimensional subspaces by means of a primitive third-order root of unity q, and in each subspace, there is an irreducible representation of the rotation group $\mathrm{SO}\left(3\right)\hookrightarrow \mathrm{SU}\left(5\right)$. We find two $\mathrm{SO}\left(3\right)$-invariants of ${\mathbb{Z}}_3$-skew-symmetric tensors: one is the canonical Hermitian metric in five-dimensional complex vector space and the other is a quadratic form denoted by $K(z,z)$. We study the invariant properties of $K(z,z)$ and find its stabilizer. Making use of these invariant properties, we define an $\mathrm{SO}\left(3\right)$-irreducible geometric structure on a five-dimensional complex Hermitian manifold. We study a connection on a five-dimensional complex Hermitian manifold with an $\mathrm{SO}\left(3\right)$-irreducible geometric structure and find its curvature and torsion. Full article

A space-time variational method is developed for retrieving upper-level vortex winds from geostationary satellite rapid infrared scans over hurricanes. In this method, new vortex-flow-dependent correlation functions are formulated for the radial and tangential components of the vortex wind. These correlation functions are used to construct the background error covariance matrix and its square root matrix. The resulting square root matrix is then employed to precondition the cost function, constrained by an advection equation formulated for rapidly scanned infrared image movements. This newly formulated and preconditioned cost function is more suitable for deriving upper-level vortex winds from GOES-16 rapid infrared scans over hurricanes than the cost function in the recently adopted optical flow technique. The new method was applied to band-13 (10.3 µm) brightness temperature images scanned every min from GOES-16 over Hurricanes Laura on 27 August 2020 and Hurricanes Ida on 29 August 2021. The retrieved vortex winds were shown to not only be much denser than operationally produced atmospheric motion vectors (AMVs) but also more rotational and better organized around the eyewall than the super-high-resolution AMVs derived from optical-flow technique. By comparing their component velocities (projected along radar beams) with limited radar velocity observations available near the cloud top, the vortex winds retrieved using the new method were also shown to be more accurate than the super-high-resolution AMVs derived from the optical-flow technique. The new method is computationally efficient for real-time applications and potentially useful for hurricane wind nowcasts. Furthermore, the combined use of VF-dependent covariance functions and imagery advection equation is not only novel but was also found to be critically important for the improved performance of the method. This finding implies that similar combined approaches can be developed with improved performance for retrieving vortex flows rapidly scanned using other types of remote sensing on different scales, such as tornadic mesocyclones rapidly scanned by phased-array radars. Full article

In radar array signal processing, weak nonstationary polarization signal direction of arrival (DOA) estimation is a challenging and significant issue when both strong and weak nonstationary signals coexist. Time-frequency (T-F) analysis is an effective method to deal with nonstationary signals. In the last decade, spatial time-frequency distributions (STFDs) have been proposed for multiple dual-polarization antenna arrays and efficaciously used for nonstationary signal DOA estimation. In this article, we introduced a novelty means for estimating weak nonstationary polarization signal DOA by utilizing spatial polarimetric time-frequency distributions (SPTFDs) of cross terms when there are strong nonstationary polarization interference signals and additive Gaussian white noise. The cross terms’ SPTFDs are considered via a replaceability matrix for data covariance in multiple signal classification (MUSIC) and the estimation of signal parameters using the rotational invariance technique (ESPRIT). Combining the STFDs of cross terms with polarization information about weak nonstationary signals improves signal DOA estimation accuracy. The combined MUSIC and ESPRIT are used in the algorithm to further ensure the success probability and accuracy of DOA estimation. Through simulation analyses, the proposed algorithm is more suitable for the required application scenarios than other algorithms and is superior to other algorithms. Full article

The use of a 3D range scanning device for autonomous object description or unknown environment mapping leads to the necessity of improving computer methods based on identical point pairs from different point clouds (so-called registration problem). The registration problem and three-dimensional transformation of coordinates still require further research. The paper attempts to guide the reader through the vast field of existing registration methods so that he can choose the appropriate approach for his particular problem. Furthermore, the article contains a regression method that enables the estimation of the covariance matrix of the transformation parameters and the calculation of the uncertainty of the estimated points. This makes it possible to extend existing registration methods with uncertainty estimates and to improve knowledge about the performed registration. The paper’s primary purpose is to present a survey of known methods and basic estimation theory concepts for the point cloud registration problem. The focus will be on the guiding principles of the estimation theory: ICP algorithm; Normal Distribution Transform; Feature-based registration; Iterative dual correspondences; Probabilistic iterative correspondence method; Point-based registration; Quadratic patches; Likelihood-field matching; Conditional random fields; Branch-and-bound registration; PointReg. The secondary purpose of this article is to show an innovative statistical model for this transformation problem. The new theory needs known covariance matrices of identical point coordinates. An unknown rotation matrix and shift vector have been estimated using a nonlinear regression model with nonlinear constraints. The paper ends with a relevant numerical example. Full article

The clutter becomes non-stationary for a space-based surveillance radar (SBSR), which is harmful for the moving targets detection due to the earth’s rotation. The non-stationarity will degrade the accuracy of clutter covariance matrix (CCM) estimation and increase the clutter degree of freedom (DOF), thereby degrading the performance of clutter suppression. To solve this problem, this paper proposes a novel non-stationary clutter suppression method using an elevation oblique subspace projection method. After analyzing the range ambiguity and non-stationarity of the clutter, the proposed method utilized the oblique projection matrix to project the signal onto the subspace spanned by the near-range and far-range clutter components along the subspace spanned by the main lobe clutter component. Then, the projected signal was used to estimate the elevation covariance matrix and calculate the optimal weight vector for the elevation adaptive filter. The proposed method can suppress the non-stationary clutter effectively with a higher improvement factor (IF) and a narrower main lobe width. Finally, the simulation results were given to verify the correctness and effectiveness of the proposed method. Full article

In bridge health monitoring, in order to closely monitor the structural state changes of the bridge under heavy traffic load and other harsh environments, the monitoring system is required to give the change process of structural modal parameters. Due to the symmetric variables of bridge monitoring during operation, the evaluation needs to be completed by the recursive identification of modal parameters based on environmental excitation, especially the recursive recognition of the random subspace method with high recognition accuracy. We have studied the recursive identification methods of covariance-driven and data-driven random subspace categories respectively, established the corresponding recursive format, and used the model structure of the ASCE structural health monitoring benchmark problem as a numerical example to verify the reliability of the proposed method. First, based on the similar interference environment of the observation data at the same time, a reference point covariance-driven random subspace recursive algorithm (IV-RSSI/Cov) based on the auxiliary variable projection approximation tracking (IV-PAST) algorithm is established. The recursive format of the system matrix and modal parameters is obtained. Based on Givens rotation, the rank-2 update form of the row space projection matrix is established, and the recursive format of the data-driven recursive random subspace method (RSSI/Data) under the PAST algorithm is obtained. Then, based on the benchmark problem of ASCE-SHM, the response of the model structure under environmental excitation is numerically simulated, the frequency, damping ratio and vibration mode of the structure are recursively tracked, and their reliability and shortcomings are studied. After improving the recursive method, the frequency tracking accuracy has been improved, with a maximum accuracy of 99.8%. Full article

To provide rapid direction finding (DF) for unmanned aerial vehicle (UAV) emitters in future wireless networks, a low-complexity direction of arrival (DOA) estimation architecture for massive multiple-input multiple-output (MIMO) receiver arrays is constructed. In this paper, we propose two strategies to address the extremely high complexity caused by eigenvalue decomposition of the received signal covariance matrix. Firstly, a rapid power iterative rotational invariance (RPI-RI) method is proposed, which adopts the signal subspace generated by power iteration to obtain the final direction estimation through rotational invariance between subarrays. RPI-RI causes a significant complexity reduction at the cost of a substantial performance loss. In order to further reduce the complexity and provide good directional measurement results, the rapid power iterative polynomial rooting (RPI-PR) method is proposed, which utilizes the noise subspace combined with the polynomial solution method to obtain the optimal direction estimation. In addition, the influence of initial vector selection on convergence in the power iteration is analyzed, especially when the initial vector is orthogonal to the incident wave. Simulation results show that the two proposed methods outperform the conventional DOA estimation methods in terms of computational complexity. In particular, the RPI-PR method achieves more than two orders of magnitude lower complexity than conventional methods and achieves performance close to the Cramér–Rao Lower Bound (CRLB). Moreover, it is verified that the initial vector and the relative error have a significant impact on the performance with respect to the computational complexity. Full article

In high-frequency (HF) radar systems, transient interference is a common phenomenon that dramatically degrades the performance of target detection and remote sensing. Up until now, various suppression algorithms of transient interference have been proposed. They mainly concentrate on the skywave over-the-horizon radar on the basis of the assumption that the interference is sparse in a coherent processing interval (CPI). However, HF surface wave radar (HFSWR) often faces more complex transient interference due to various extreme types of weather, such as thunderstorm and typhoon, etc. The above algorithms usually suffer dramatic performance loss when transient interference contaminates the enormously continuous parts of a CPI. Especially for the compact HFSWR, which suffers from severe beam broadening and fewer array degrees of freedom. In order to solve the above problem, this study developed a two-dimensional interference suppression algorithm based on space-time cascaded processing. First, according to the spatial correlation of the compact array, the statistical samples of the main-lobe transient interference are estimated using a rotating spatial beam method. Next, an adaptive selection strategy is developed to obtain the optimal secondary samples based on information geometry distance. Finally, based on a quadratic constraint approximation, a precise estimation method of the optimal weight is developed when the interference covariance matrix is singular. The experimental results of simulation and measured data demonstrate that the proposed approach provides far superior suppression performance. Full article

Multi-line LiDAR and GPS/IMU are widely used in autonomous driving and robotics, such as simultaneous localization and mapping (SLAM). Calibrating the extrinsic parameters of each sensor is a necessary condition for multi-sensor fusion. The calibration of each sensor directly affects the accurate positioning control and perception performance of the vehicle. Through the algorithm, accurate extrinsic parameters and a symmetric covariance matrix of extrinsic parameters can be obtained as a measure of the confidence of the extrinsic parameters. As for the calibration of LiDAR-GPS/IMU, many calibration methods require specific vehicle motion or manual calibration marking scenes to ensure good constraint of the problem, resulting in high costs and a low degree of automation. To solve this problem, we propose a new two-step self-calibration method, which includes extrinsic parameter initialization and refinement. The initialization part decouples the extrinsic parameters from the rotation and translation part, first calculating the reliable initial rotation through the rotation constraints, then calculating the initial translation after obtaining a reliable initial rotation, and eliminating the accumulated drift of LiDAR odometry by loop closure to complete the map construction. In the refinement part, the LiDAR odometry is obtained through scan-to-map registration and is tightly coupled with the IMU. The constraints of the absolute pose in the map refined the extrinsic parameters. Our method is validated in the simulation and real environments, and the results show that the proposed method has high accuracy and robustness. Full article

The Multiple Signal Classification (MUSIC) algorithm has become one of the most popular algorithms for estimating the direction-of-arrival (DOA) of multiple sources due to its simplicity and ease of implementation. Spherical microphone arrays can capture more sound field information than planar arrays. The collected multichannel speech signals can be transformed from the space domain to the spherical harmonic domain (SHD) for processing through spherical modal decomposition. The spherical harmonic domain MUSIC (SHD-MUSIC) algorithm reduces the dimensionality of the covariance matrix and achieves better DOA estimation performance than the conventional MUSIC algorithm. However, the SHD-MUSIC algorithm is prone to failure in low signal-to-noise ratio (SNR), high reverberation time (RT), and other multi-source environments. To address these challenges, we propose a novel joint spherical harmonic domain beam-space MUSIC (SHD-BMUSIC) algorithm in this paper. The advantage of decoupling the signal frequency and angle information in the SHD is exploited to improve the anti-reverberation property of the DOA estimation. In the SHD, the broadband beamforming matrix converts the SHD sound pressure to the beam domain output. Beamforming enhances the incoming signal in the desired direction and reduces the SNR threshold as well as the dimension of the signal covariance matrix. In addition, the 3D beam of the spherical array has rotational symmetry and its beam steering is decoupled from the beam shape. Therefore, the broadband beamforming constructed in this paper allows for the arbitrary adjustment of beam steering without the need to redesign the beam shape. Both simulation experiments and practical tests are conducted to verify that the proposed SHD-BMUSIC algorithm has a more robust adjacent source discrimination capability than the SHD-MUSIC algorithm. Full article

In this paper, we describe a rotation angle measurement system (RAMS) based on an inertial measurement unit (IMU) developed to measure the rotation angle of a movable surface. The existing IMU-based attitude (tilt) sensor can only accurately measure the rotation angle when the rotation axis of the movable surface is perfectly aligned with the X axis or Y axis of the sensor, which is always not possible in real-world engineering. To overcome the difficulty of sensor installation and ensure measurement accuracy, first, we build a model to describe the relationship between the rotation axis and the IMU. Then, based on the built model, we propose a simple online method to estimate the direction of the rotation axis without using a complicated apparatus and a method to estimate the rotation angle using the known rotation axis based on the extended Kalman filter (EKF). Using the estimated rotation axis direction, we can effectively eliminate the influence of the mounting position on the measurement results. In addition, the zero-velocity detection (ZVD) technique is used to ensure the reliability of the rotation axis direction estimation and is used in combination with the EKF as the switching signal to adaptively adjust the noise covariance matrix. Finally, the experimental results show that the developed RAMS has a static measurement error of less than 0.05° and a dynamic measurement error of less than 1° in the range of ±180°. Full article

The estimation of the covariance matrix is an important topic in the field of multivariate statistical analysis. In this paper, we propose a new estimator, which is a convex combination of the linear shrinkage estimation and the rotation-invariant estimator under the Frobenius norm. We first obtain the optimal parameters by using grid search and cross-validation, and then, we use these optimal parameters to demonstrate the effectiveness and robustness of the proposed estimation in the numerical simulations. Finally, in empirical research, we apply the covariance matrix estimation to the portfolio optimization. Compared to the existing estimators, we show that the proposed estimator has better performance and lower out-of-sample risk in portfolio optimization. Full article

For inverse synthetic aperture radar (ISAR) imaging of rapidly spinning targets, the large migration through range cells (MTRC) results in weak coherence between adjacent echoes, which makes the conventional envelope alignment method unable to be applied. By analyzing the correlation between the echoes, a translational motion compensation (TMC) method for rapidly spinning targets is proposed. Firstly, the rotation period of the target is estimated by the incoherent accumulation method for the echo signal after range compression. Secondly, Kalman filtering is performed on the shift values required to maximize the correlation coefficient of the echoes with one rotation period difference in azimuth time to obtain the relative translational motion of the radar and the target. Finally, a translational compensation function is constructed according to the results of Kalman filtering to compensate the phase items caused by translational motion. Furthermore, the covariance matrix of observation noise required by Kalman filtering is also provided. This method is used to achieve high-precision envelope alignment, and the effectiveness of the proposed method is validated by simulations. Full article