Optimal Covariance Matrix Research Articles

Quantifying the information lost in optimal covariance matrix cleaning

Quantifying the information lost in optimal covariance matrix cleaning

Seizure Detection Algorithm Based on Multidimensional Covariance Matrix and Binary Harris Hawks Optimization With Cauchy–Gaussian Mutation

Seizure Detection Algorithm Based on Multidimensional Covariance Matrix and Binary Harris Hawks Optimization With Cauchy–Gaussian Mutation

Sensorless HSPMSM Control of an Improved SMC and EKF Based on Immune PSO

Here, for controlling a high-speed flywheel permanent magnet synchronous motor (HSPMSM), a position sensorless control method for estimation of motor rotor position and speed is proposed to address the problems faced by mechanical position sensors of high cost, large size, and poor interference immunity. The extended Kalman filter (EKF) has difficulty obtaining the optimal covariance matrix when performing state estimation. Therefore, the particle swarm algorithm (PSO) with an immune mechanism is used to optimize the covariance matrix of the EKF. However, the EKF algorithm makes the system less robust due to its delay effect. Based on the traditional sliding mode control rate, the exponential convergence law is improved, and the continuous function sat(s) is used instead of the symbolic function sgn(s). This improves the convergence law and proves the asymptotic stability of the designed sliding mode variable structure controller based on Lyapunov’s stability theorem. Then, the novel control law is applied to the sliding mode surface (SMS). An ordinary sliding mode controller (OSMC) using a linear sliding mode controller (LSMC), a global sliding mode controller (GSMC) using a global sliding mode surface (GSMS), and an integral sliding mode controller (ISMC) using an integral sliding mode surface (ISMS) are designed for improving control. Joint simulation in MATLAB and Simulink verifies that the optimized EKF based on the immune PSO can improve precision and accuracy for controlling the electronic rotor position and speed. Comparing the new sliding mode controller with a traditional PI controller reveals that the proposed system has stronger resistance to load disturbance and better robustness.

Speed Estimation Strategy for Closed-Loop Control of PMSM Based on PSO Optimized KF Series Algorithms

In this paper, solving the problem of the noise covariance matrix parameters tuning of the extended Kalman filter (EKF) and unscented Kalman filter algorithms (UKF) is difficult. A speed estimation strategy for a permanent magnet synchronous motor (PMSM) based on particle swarm optimization (PSO) optimized Kalman filter (KF) series algorithms is proposed. By using MATLAB/Simulink, in this paper, 20 effective simulation experiments on the noise covariance matrix parameter optimization process are conducted to obtain the optimal covariance matrix parameters of the extended Kalman filter and unscented Kalman filter. Moreover, EKF, PSO-EKF, UKF, and PSO-UKF are also compared to verify the effectiveness of the particle swarm optimization algorithm in optimizing the systems using the extended Kalman filter and unscented Kalman filter. For the error of speed estimation, taking 4000 rpm as a reference, the system using PSO-EKF has improved by 2.125% compared to that using EKF, and the system applying PSO-UKF has improved by 0.55% compared to the system applying UKF. For the error of electrical angle estimation, taking the system errors of original algorithms as references, the system adopting PSO-EKF has decreased by 60% compared to that adopting EKF, and the system using PSO-UKF has decreased by 47% compared to the system using UKF.

An Improved DCC Model Based on Large-Dimensional Covariance Matrices Estimation and Its Applications

The covariance matrix estimation plays an important role in portfolio optimization and risk management. It is well-known that portfolio is essentially a convex quadratic programming problem, which is also a special case of symmetric cone optimization. Accurate covariance matrix estimation will lead to more reasonable asset weight allocation. However, some existing methods do not consider the influence of time-varying factor on the covariance matrix estimations. To remedy this, in this article, we propose an improved dynamic conditional correlation model (DCC) by using nonconvex optimization model under smoothly clipped absolute deviation and hard-threshold penalty functions. We first construct a nonconvex optimization model to obtain the optimal covariance matrix estimation, and then we use this covariance matrix estimation to replace the unconditional covariance matrix in the DCC model. The result shows that the loss of the proposed estimator is smaller than other variants of the DCC model in numerical experiments. Finally, we apply our proposed model to the classic Markowitz portfolio. The results show that the improved dynamic conditional correlation model performs better than the current DCC models.

Optimization Method of Airborne LiDAR Individual Tree Segmentation Based on Gaussian Mixture Model

Forests are the main part of the terrestrial ecosystem. Airborne LiDAR is fast, comprehensive, penetrating, and contactless and can depict 3D canopy information with a high efficiency and accuracy. Therefore, it plays an important role in forest ecological protection, tree species recognition, carbon sink calculation, etc. Accurate recognition of individual trees in forests is a key step to various application. In real practice, however, the accuracy of individual tree segmentation (ITS) is often compromised by under-segmentation due to the diverse species, obstruction and understory trees typical of a high-density multistoried mixed forest area. Therefore, this paper proposes an ITS optimization method based on Gaussian mixture model for airborne LiDAR data. First, the mean shift (MS) algorithm is used for the initial ITS of the pre-processed airborne LiDAR data. Next, under-segmented samples are extracted by integrated learning, normally segmented samples are classified by morphological approximation, and the approximate distribution uncertainty of the normal samples is described with a covariance matrix. Finally, the class composition among the under-segmented samples is determined, and the under-segmented samples are re-segmented using Gaussian mixture model (GMM) clustering, in light of the optimal covariance matrix of the corresponding categories. Experiments with two datasets, Trento and Qingdao, resulted in ITS recall of 94% and 96%, accuracy of 82% and 91%, and F-scores of 0.87 and 0.93. Compared with the MS algorithm, our method is more accurate and less likely to under-segment individual trees in many cases. It can provide data support for the management and conservation of high-density multistoried mixed forest areas.

Optimal covariance matrix estimation for high-dimensional noise in high-frequency data

We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the random vector are observed at the same time and the measurement errors are latent variables, leading to major challenges besides high data dimensionality. We propose a new covariance matrix estimator in this context with appropriate localization and thresholding, and then conduct a series of comprehensive theoretical investigations of the proposed estimator. By developing a new technical device integrating the high-frequency data feature with the conventional notion of α-mixing, our analysis successfully accommodates the challenging serial dependence in the measurement errors. Our theoretical analysis establishes the minimax optimal convergence rates associated with two commonly used loss functions; and we demonstrate with concrete cases when the proposed localized estimator with thresholding achieves the minimax optimal convergence rates. Considering that the variances and covariances can be small in reality, we conduct a second-order theoretical analysis that further disentangles the dominating bias in the estimator. A bias-corrected estimator is then proposed to ensure its practical finite sample performance. We also extensively analyze our estimator in the setting with jumps, and show that its performance is reasonably robust. We illustrate the promising empirical performance of the proposed estimator with extensive simulation studies and a real data analysis.

A Modified Method for Beam-Forming Using Covariance Matrix in MIMO Radar System

A MIMO radar provides solution for beamforming, since transmit beampattern synthesis is well proven method for stimulating the antenna array to develop the beampattern. It is close to the desired one which can give minimum error between these two. A covariance matrix in beamforming contains the direction of invariable data and magnitude distribution in multidimensional space which decides the closeness with the desired beampattern. Here, selection of an optimal covariance matrix is constrained optimization problem with minimization of cost function. In high directivity radar systems, the antenna beam is needed to be steered to cover a large area for detection. In this proposed work, minimization of convex function and transmit beampattern synthesis is carried out with modifications of the covariance matrix ‘Rcov’ for minimum and maximum transmission power utilization constraints. The beampattern design problem is reformulated here, as semi-definite programming optimization problem and solved using convex optimization, with MATLAB simulation platform. The results show that the beampattern generated using this modified covariance matrix is optimally close to desired pattern.

Capacity Characterization for Reconfigurable Intelligent Surfaces Assisted Multiple-Antenna Multicast

The reconfigurable intelligent surface (RIS), which consists of a large number of passive and low-cost reflecting elements, has been recognized as a revolutionary technology to enhance the performance of future wireless networks. This paper considers an RIS assisted multicast transmission, where a base station (BS) with multiple-antenna multicasts common message to multiple single-antenna mobile users (MUs) under the assistance of an RIS. An equivalent channel model for the considered multicast transmission is analyzed, and then an optimization problem for the corresponding channel capacity is formulated to obtain the optimal covariance matrix and phase shifts. In order to solve the above non-convex and non-differentiable problem, this paper first exploits the gradient descent method and alternating optimization, to approach the locally optimal solution for any number of MUs. Then, this paper considers a special case, which can obtain the global optimal solution, and shows the sufficient and necessary condition for this special case. Finally, the order growth of the maximal capacity is obtained when the numbers of the reflecting elements, the BS antennas, and the MUs go to infinity.

Shrinkage estimation of large covariance matrices: Keep it simple, statistician?

Under rotation-equivariant decision theory, sample covariance matrix eigenvalues can be optimally shrunk by recombining sample eigenvectors with a (potentially nonlinear) function of the unobservable population covariance matrix. The optimal shape of this function reflects the loss/risk that is to be minimized. We solve the problem of optimal covariance matrix estimation under a variety of loss functions motivated by statistical precedent, probability theory, and differential geometry. A key ingredient of our nonlinear shrinkage methodology is a new estimator of the angle between sample and population eigenvectors, without making strong assumptions on the population eigenvalues. We also introduce a broad family of covariance matrix estimators that can handle all regular functional transformations of the population covariance matrix under large-dimensional asymptotics. In addition, we compare via Monte Carlo simulations our methodology to two simpler ones from the literature, linear shrinkage and shrinkage based on the spiked covariance model.

Underlying Topography Inversion Using TomoSAR Based on Non-Local Means for an L-Band Airborne Dataset

The underlying topography is an important part of the three-dimensional structure of forests, and is used for a variety of applications, such as hydrology and water resource management, civil engineering projects, and forest resource surveying. Due to the three-dimensional imaging ability and strong penetration, the tomographic synthetic aperture radar (TomoSAR) with a long wavelength has been shown to be a useful tool to estimate the underlying topography. At present, most of the current methods use the local means method to estimate the sample covariance matrix, in which the vertical backscattering power is estimated. However, these methods cannot easily obtain high-precision underlying topography, and often lose some detailed information. In this paper, to solve this problem, a non-local means method is introduced to estimate the optimal covariance matrix by combining weighted neighborhood pixels. To validate the feasibility and effectiveness of this proposed method, a BioSAR 2008 campaign L-band dataset acquired from the northern forests of Sweden was used to inverse the underlying topography. The results show that the accuracy of the underlying topography retrieved by the proposed method is improved by more than 30% when compared with the traditional method.

Common-covariance based person re-identification model

Abstract This paper develops a new covariance-matrix based person re-identification model. It takes each person as a Gaussian distribution with a common covariance matrix. The learning process is to find an optimal covariance matrix among all the distributions. This paper has two major contributions: (1) It proves the statistical meaning of Mahalanobis matrix as a common covariance matrix among all related classes; (2) The intra-class distance is measured using the determinant of the common covariance matrix. The proposed model largely reduces the computational cost. Moreover, it automatically avoids imbalanced computations between the distances for inter-class images and the distances for intra-class images. Experimental results demonstrate that the proposed model is more efficient than many state-of-the-art methods in both accuracy and time cost.

Intelligent Reflecting Surface Assisted Secure Wireless Communications With Multiple- Transmit and Multiple-Receive Antennas

In this paper, we propose intelligent reflecting surfaces (IRS) assisted secure wireless communications with multi-input and multi-output antennas (IRS-MIMOME). The considered scenario is an access point (AP) equipped with multiple antennas communicates with a multi-antenna enabled legitimate user in the downlink at the present of an eavesdropper configured with multiple antennas. Particularly, the joint optimization of the transmit covariance matrix at the AP and the reflecting coefficients at the IRS to maximize the secrecy rate for the IRS-MIMOME system is investigated, with two different assumptions on the phase shifting capabilities at the IRS, i.e., the IRS has the continuous reflecting coefficients and the IRS has the discrete reflecting coefficients. For the former case, due to the non-convexity of the formulated problem, an alternating optimization (AO)-based algorithm is proposed, i.e., for given the reflecting coefficients at the IRS, the successive convex approximation (SCA)-based algorithm is used to solve the transmit covariance matrix optimization, while given the transmit covariance matrix at the AP, alternative optimization is used again in individually optimizing of each reflecting coefficient at the IRS with other fixed reflecting coefficients. For the individual reflecting coefficient optimization, the closed-form or an interval of the optimal solution is provided. Then, the proposed algorithm is extended to the discrete reflecting coefficient model at the IRS. Finally, some numerical simulations have been done to demonstrate that the proposed algorithm outperforms other benchmark schemes.

User-centric harvested energy-efficiency maximisation for secure SWIPT transmissions

ABSTRACTIn this paper, simultaneous wireless information and power transfer (SWIPT) transmissions with multiple-input single-output transceiver pairs are considered. In each pair, a multi-antenna transmitter sends data and energy to a single-antenna receiver with a signal-splitting structure and a non-linear energy harvesting model. Each transceiver pair tries to achieve high individual harvested energy efficiency, and uses artificial noise (AN) to protect the information from being overheard by other users that cooperate like a virtual eavesdropper. The weighted sum user-centric harvested energy-efficiency maximisation problem is formulated under constraints on the required signal-to-interference-plus-noise ratio (SINR) at each receiver, plus a limited SINR for virtual eavesdroppers and limited transmit power at each transmitter. The optimal precoding beamforming, AN, and signal-splitting factors are obtained by two proposed algorithms. The first solution exploits semidefinite relaxation and sequential parametric convex approximation techniques to convert the non-convex problem to a series of convex subproblems with matrix variables. We obtain optimal beamforming vectors along with an optimal covariance matrix for AN. The second solution directly utilizes beamforming approximation and obtains a low complexity solution for the convex subproblem. Moreover, we need to apply the feasible point pursuit method. Finally, numerical evaluations are provided in comparison with some benchmark schemes.

Optimal Multi-Antenna Transmission With Multiple Power Constraints

We determine the capacity-optimal transmission strategy for a multiple-input-multiple-output (MIMO) Gaussian channel under multiple power constraints, namely joint sum power constraint (SPC), per group power constraints (PGPC), and per antenna power constraints (PAPC). First, we focus on cases where we can analytically determine the optimal transmit strategy under joint SPC-PGPC-PAPC. We obtain results for the following cases: 1) $n_{t} \times 1$ multiple-input-single-output (MISO); 2) MIMO channel with full column rank and full rank optimal covariance matrix; and 3) $2 \times n_{r}$ MIMO channel. These results generalize some recent results for the special cases of PAPC only and joint SPC-PAPC. Then, we propose a projected factored gradient descent (PFGD) algorithm for the general MIMO Gaussian channel under joint SPC-PGPC-PAPC including the possibility of additional rank constraints. This algorithm matches the solution of standard convex optimization tools with lower complexity. The algorithm also overcomes the limitations of existing algorithms, in terms of accuracy and applicability to low rank channels.

Robust Beamforming and Power Allocation in CR MISO Networks with SWIPT to Maximize the Minimum Achievable Rate

In this paper, a new method is presented to maximize the minimum achievable rate of the users in a cognitive radio multiple input single output network. The secondary system provides simultaneous wireless information and power transfer (SWIPT) for energy harvesting receivers. Considering random Gaussian vector for the estimation error of the channel state information (CSI), we impose some outage constraints to guarantee the quality of service of the network. Outage constraints on the received power and the information leakage at the energy harvesting users are imposed to assure SWIPT. We introduce new convex inequalities to replace the original non-convex constraints and write the objective function as the minimization of the maximum of some fractional functions. This new objective function and convex inequalities result in a new quasi-convex general fractional programming problem. The new quasi-convex optimization problem is written in such a way that the computational costs to solve this problem are as low as possible. We develop an algorithm to obtain the optimal beamforming weights and artificial noise covariance matrix. All stochastic constraints are rewritten for the special case that the covariance matrices of error in the estimation of CSI are a factor of identity matrix. This reformulation results in less computation costs to obtain optimal beamforming weights and AN covariance matrix. Simulation results confirm that, all stochastic constraints are satisfied with certain probability. In comparison with the previous robust related work, the proposed method achieves higher rates which confirms superiority of our method.

Shrinkage Estimation of Large Covariance Matrices: Keep it Simple, Statistician?

Under rotation-equivariant decision theory, sample covariance matrix eigenvalues can be optimally shrunk by recombining sample eigenvectors with a (potentially nonlinear) function of the unobservable population covariance matrix. The optimal shape of this function reflects the loss/risk that is to be minimized. We solve the problem of optimal covariance matrix estimation under a variety of loss functions motivated by statistical precedent, probability theory, and differential geometry. A key ingredient of our nonlinear shrinkage methodology is a new estimator of the angle between sample and population eigenvectors, without making strong assumptions on the population eigenvalues. We also introduce a broad family of covariance matrix estimators that can handle all regular functional transformations of the population covariance matrix under large-dimensional asymptotics. In addition, we compare via Monte Carlo simulations our methodology to two simpler ones from the literature, linear shrinkage and shrinkage based on the spiked covariance model.

A Robust and Efficient Algorithm for Coprime Array Adaptive Beamforming

Coprime array offers a larger array aperture than uniform linear array with the same number of physical sensors, and has a better spatial resolution with increased degrees of freedom. However, when it comes to the problem of adaptive beamforming, the existing adaptive beamforming algorithms designed for the general array cannot take full advantage of coprime feature offered by the coprime array. In this paper, we propose a novel coprime array adaptive beamforming algorithm, where both robustness and efficiency are well balanced. Specifically, we first decompose the coprime array into a pair of sparse uniform linear subarrays and process their received signals separately. According to the property of coprime integers, the direction-of-arrival (DOA) can be uniquely estimated for each source by matching the super-resolution spatial spectra of the pair of sparse uniform linear subarrays. Further, a joint covariance matrix optimization problem is formulated to estimate the power of each source. The estimated DOAs and their corresponding power are utilized to reconstruct the interference-plus-noise covariance matrix and estimate the signal steering vector. Theoretical analyses are presented in terms of robustness and efficiency, and simulation results demonstrate the effectiveness of the proposed coprime array adaptive beamforming algorithm.

Transmit Signal Design in Colocated MIMO Radar Without Covariance Matrix Optimization

In this paper, the problem of the waveform design for colocated multiple-input multiple-output (MIMO) radars is considered in two parts. In the first part, we design transmit waveform in order to approximate the desired beampattern with low number of samples in the transmitter. Unlike the traditional waveform design methods, in our solution, waveforms are designed for a specific number of samples. Also, the constant envelope constraint that is an important practical constraint is considered. In the second part, we jointly design the transmit waveform and receive filter by a sequential algorithm, considering a priori information of target and interference angle locations. We have evaluated the performance of the proposed algorithms via numerical simulations and shown that the proposed algorithm in the first part is able to approximate the desired beampattern with low number of samples. Also, our method in the second part achieves better signal-to-interference-plus-noise ratio performance compared with the existing active sensing array methods (e.g., phased-array and correlated MIMO radars).

Optimal Network Control With Stochastic Link Variations and Indefinite Quadratic Constraints

In this paper, we consider the problem of optimal control of a network with stochastic links modeled as multiplicative noise with given second moments and arbitrary probability distributions. Additional quadratic constraints are imposed, where the quadratic forms may be indefinite and, thus, not necessarily convex. We show that the problem can be transformed to a semidefinite program. The optimization problem is over a certain variable serving as the covariance matrix of the state and the controller. We show that affine controllers are optimal and depend on the optimal covariance matrix. Furthermore, we show that optimal controllers are linear if all of the quadratic forms are convex in the control variable. The solutions are presented for the finite and infinite horizon cases. We give a necessary and sufficient condition for mean square stabilizability of the dynamical system with additive and multiplicative noise. The condition is a Lyapunov-like condition whose solution is again given by the covariance matrix of the state and the control variable. The results are illustrated with an example.