Optimal Covariance Research Articles

Co‐Design of Watermarking and Controller for Reducing Detection Delay of Replay Attacks

ABSTRACTThis paper investigates the problem of reducing the detection delay of the replay attacks by co‐designing the watermarking signal and the controller parameters. Based on the dynamic encryption‐decryption scheme, we propose a cumulative sum test, which utilizes the sensor measurements and watermarking signals to detect the replay attacks, and derive the relationship between the detection delay and the watermarking signal covariance. Then, we analyze the control performance loss caused by the watermarking signal added to the sensor measurements to expose the replay attacks. Furthermore, to reduce the detection delay, an optimization problem is formulated to design the optimal covariance of the watermarking signal with a tolerable control performance loss. Finally, we reformulate another optimization problem of co‐designing the watermarking signal and the controller parameters to simultaneously reduce the detection delay and the control performance loss. A numerical example is provided to verify the effectiveness of theoretical results.

Quantifying the information lost in optimal covariance matrix cleaning

Obtaining an accurate estimate of the underlying covariance matrix from finite sample size data is challenging due to sample size noise. In recent years, sophisticated covariance-cleaning techniques based on random matrix theory have been proposed to address this issue. Most of these methods aim to achieve an optimal covariance matrix estimator by minimizing the Frobenius norm distance as a measure of the discrepancy between the true covariance matrix and the estimator. However, this practice offers limited interpretability in terms of information theory. To better understand this relationship, we focus on the Kullback–Leibler divergence to quantify the information lost by the estimator. Our analysis centers on rotationally invariant estimators, which are state-of-art in random matrix theory, and we derive an analytical expression for their Kullback–Leibler divergence. Due to the intricate nature of the calculations, we use genetic programming regressors paired with human intuition. Ultimately, using this approach, we formulate a conjecture validated through extensive simulations, showing that the Frobenius distance corresponds to a first-order expansion term of the Kullback–Leibler divergence, thus establishing a more defined link between the two measures.

Optimal innovation-based attacks against remote state estimation with side information and historical data

This work investigates the attack strategy design problem of the false data injection attack against the cyber-physical system. Distinct from the relevant results which utilise the current intercepted data or additionally consider side information, a more universal attack model is proposed which combines historical data and side information with the current intercepted data to synergistically deteriorate the system estimation performance. In order to quantify the impact resulting from the proposed attack strategy, the optimisation objective is characterised by deriving the error covariance matrix under the attacks, which becomes more intricate since the proposed attack model introduces more decision variables and coupled terms. Take the stealthiness which is characterised by Kullback-Leibler divergence as the constraints, the problem investigated in this work is equivalently transformed into the constrained multi-variable non-convex optimisation problems, which are not able to be solved directly by the methods in the relevant results. By utilising the Lagrange multiplier method, the structural characteristic of the optimal mean and the optimal covariance which only related to the Lagrange multiplier are derived, such that the optimal distribution of the modified innovation is able to be obtained by a simple search procedure. Following that, the design of the optimal attack strategy is completed by using semi-definite programming to derive the optimal attack matrices. Finally, the simulation examples are given such that the validity of the results is verified.

Optimal Covariance Steering for Continuous-Time Linear Stochastic Systems With Martingale Additive Noise

Optimal Covariance Steering for Continuous-Time Linear Stochastic Systems With Martingale Additive Noise

Theoretical and Practical Analysis of MIMO Simultaneous Wireless Information and Power Transfer Over Inductively Coupled Circuits

The number of wireless devices continues to increase, and this growth will be further fueled by the Internet of Things (IoT). There is an urgent need to develop new techniques to both wirelessly transfer power to and communicate with these devices. Recently, inductive power transfer has gained much attention as a potentially efficient wireless powering solution for short and medium distance charging scenarios. In this paper, we consider multiple-input multiple-output (MIMO) simultaneous wireless information and power transfer (SWIPT) using inductive coupling. While an analysis of SWIPT requires a model that correctly captures transmit power, harvested power, and information capacity, the vast majority of previous studies have overlooked the relationship between the mathematical signal representations and the real-world physical quantities. To overcome this challenge, we propose a framework in which signals and channels are represented by traveling waves and scattering parameters. The optimal covariance matrices of the transmit traveling waves are derived for three different working scenarios. We propose a simple estimation procedure to determine unknown scattering parameters and noise distribution. The rate-energy regions and the magnetic field strengths are computed for two inductively-coupled MIMO models based on the finite element method.

Optimal Covariance Steering for Continuous-Time Linear Stochastic Systems With Multiplicative Noise

Optimal Covariance Steering for Continuous-Time Linear Stochastic Systems With Multiplicative Noise

Joint design of transmit precoding and antenna selection for multi-user multi-target MIMO DFRC

Dual-function radar and communications (DFRC) systems based on multiple-input multiple-output (MIMO) arrays have received considerable attention in recent years due to their excellent ability to alleviate spectrum congestion. The MIMO DFRC systems enable high-resolution detection of multiple targets while communicating with multiple users simultaneously. However, MIMO arrays require numerous radio frequency (RF) units and suffer a strong mutual coupling among antennas, resulting in significant system overhead and performance degradation, respectively. In light of this, this paper investigates the joint optimization of transmit precoding and antenna selection for MIMO DFRC systems, aiming to improve the angular ambiguity function with a guaranteed communication quality of service (QoS) using a small number of antennas. To address the resultant non-convex optimization problem, both the indirect and direct precoding methods are proposed. In the former, the waveform covariance and antenna selection vector are first jointly optimized via a promoted sparsity along the covariance diagonal, followed by the precoding matrix indirectly derived from the optimal covariance. In the latter, the precoding matrix is directly optimized via an imposed group sparsity under the communication QoS and power constraints. Simulation results demonstrate that the proposed sparse MIMO DFRC system with fewer active antennas can achieve comparable dual-functional performance to that of the full array system.

Stochastic linear quadratic optimal control problem with terminal state constraints

AbstractThis paper addresses the stochastic linear quadratic (LQ) control problem with first‐ and second‐order moment constraints on the terminal state. The problem is a modified version of the optimal covariance control problem, where the terminal state is steered to a given probability distribution. Studying a multiplicative‐noise stochastic system rather than an additive‐noise system is a salient feature. Unlike the existing ideas in the optimal steering, by using the Lagrange multipliers method and establishing the stochastic maximum principle, our problem is converted into solving forward–backward stochastic difference equations (FBSDEs), which is a special stochastic two‐point boundary‐value problem (TPBVP). We provide the optimal closed‐loop controller and necessary and sufficient solvability conditions by developing a nonhomogeneous relationship between the optimal state and costate in FBSDEs. Finally, numerical examples are given to demonstrate our results.

Optimal covariance cleaning for heavy-tailed distributions: Insights from information theory.

In optimal covariance cleaning theory, minimizing the Frobenius norm between the true population covariance matrix and a rotational invariant estimator is a key step. This estimator can be obtained asymptotically for large covariance matrices, without knowledge of the true covariance matrix. In this study, we demonstrate that this minimization problem is equivalent to minimizing the loss of information between the true population covariance and the rotational invariant estimator for normal multivariate variables. However, for Student's t distributions, the minimal Frobenius norm does not necessarily minimize the information loss in finite-sized matrices. Nevertheless, such deviations vanish in the asymptotic regime of large matrices, which might extend the applicability of random matrix theory results to Student's t distributions. These distributions are characterized by heavy tails and are frequently encountered in real-world applications such as finance, turbulence, or nuclear physics. Therefore, our work establishes a connection between statistical random matrix theory and estimation theory in physics, which is predominantly based on information theory.

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.

A data-driven LQG method for linear time-varying systems to monitor the controller performance in the batch process

PurposeThe flexibility of batch process enables its wide application in fine-chemical, pharmaceutical and semi-conductor industries, whilst its complexity necessitates control performance monitoring to ensure high operation efficiency. This paper proposes a data-driven approach to carry out controller performance monitoring within batch based on linear quadratic Gaussian (LQG) method.Design/methodology/approachA linear time-varying LQG method is proposed to obtain the joint covariance benchmark for the stochastic part of batch process input/output. From historical golden operation batch, linear time-varying (LTV) system and noise models are identified based on generalized observer Markov parameters realization.FindingsOpen/closed loop input and output data are applied to identify the process model as well as the disturbance model, both in Markov parameter form. Then the optimal covariance of joint input and output can be obtained by the LQG method. The Hotelling's Tˆ2 control chart can be established to monitor the controller.Originality/value(1) An observer Markov parameter approach to identify the time-varying process and noise models from both open and closed loop data, (2) a linear time-varying LQG optimal control law to obtain the optimal benchmark covariance of joint input and output and (3) a joint input and output multivariate control chart based on Hotelling's T2 statistic for controller performance monitoring.

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.

Bayesian control variates for optimal covariance estimation with pairs of simulations and surrogates

ABSTRACT Predictions of the mean and covariance matrix of summary statistics are critical for confronting cosmological theories with observations, not least for likelihood approximations and parameter inference. Accurate estimates require running costly N-body and hydrodynamics simulations. Approximate solvers, or surrogates, greatly reduce the computational cost but introduce biases, especially in the non-linear regime of structure growth. We propose ‘CARPool Bayes’ to solve the inference problem for both the means and covariances using a combination of simulations and surrogates. Our approach allows incorporating prior information for the mean and covariance. We derive closed-form solutions for maximum a posteriori covariance estimates that are efficient Bayesian shrinkage estimators, guarantee positive semidefiniteness, and can optionally leverage analytical covariance approximations. We discuss choices of the prior and propose a procedure for obtaining optimal prior hyperparameter values with a small set of test simulations. We test our method by estimating the covariances of clustering statistics of gadget-iiiN-body simulations at redshift z = 0.5 using surrogates from a 100–1000× faster particle-mesh code. Taking the sample covariance from 15 000 simulations as the truth, and using an empirical Bayes prior with diagonal blocks, our estimator produces nearly identical Fisher matrix contours for ΛCDM parameters using only 15 simulations of the non-linear dark matter power spectrum. In this case, the number of simulations is so small that the sample covariance is degenerate. We show cases where even with a naïve prior our method improves the estimate. Our framework is applicable to a wide range of cosmological problems where fast surrogates are available.

Transmit Design for Joint MIMO Radar and Multiuser Communications With Transmit Covariance Constraint

In this paper, we consider the waveform design of a multiple-input multiple-output (MIMO) transmitter which simultaneously functions as a MIMO radar and a base station for downlink multiuser communications. In addition to a power constraint, we require the covariance of the transmit waveform be equal to a given optimal covariance for MIMO radar, to guarantee the radar performance. With this constraint, we formulate and solve the signal-to-interference-plus-noise ratio (SINR) balancing problem for multiuser transmit beamforming via convex optimization. Considering that the interference cannot be completely eliminated with this constraint, we introduce dirty paper coding (DPC) to further cancel the interference, and formulate the SINR balancing and sum rate maximization problem in the DPC regime. Although both of the two problems are non-convex, we show that they can be reformulated to convex optimizations via the Lagrange and downlink-uplink duality. In addition, we propose gradient projection based algorithms to solve the equivalent dual problem of SINR balancing, in both transmit beamforming and DPC regimes. The simulation results demonstrate significant performance improvement of DPC over transmit beamforming, and also indicate that the degrees of freedom for the communication transmitter is restricted by the rank of the covariance.

Real time obstacle motion prediction using neural network based extended Kalman filter for robot path planning

Navigation in dynamic environments for mobile robots is a difficult problem as it involves estimating the path of moving obstacles. The measured data usually contains a bias and noise in addition to its true value. Based on a stacked denoising autoencoder (SDAE), the enhanced Kalman filter developed in this paper can estimate the obstacle position from any type of noisy input. The extended Kalman filter's ability to predict an error-free path is impacted by the measurement noise covariance matrix employed. The SDAE is a neural network topology based on deep learning that can be used to determine the optimum covariance matrix. Both Adam and stochastic gradient learning algorithms are used to train the neural network. The robot's path is re-planned based on the predicted obstacle path to ensure safe navigation. MATLAB-based numerical simulations are used to demonstrate the utility and superiority of the proposed method over the traditional Kalman filter and Particle filter methodologies. The simulation results show that in the presence of any sort of noise, the proposed technique is exceptionally durable and reliable. The simulation findings also reveal that when it comes to denoising the measured data, the stacked denoising autoencoder with Adam optimizer is more efficient than the stochastic approach. The performance of the developed algorithm is validated in MATLAB simulated environments, and it can be extended for navigation tasks. In terms of computation time and robustness in closely spaced obstacles, simulation experiments demonstrated that the path planning using the proposed algorithm outperforms the hybrid A star, artificial potential field, and decision algorithms.

Unscrambling spectral interference and matrix effects in Vitis vinifera Vis-NIR spectroscopy: Towards analytical grade ‘in vivo’ sugars and acids quantification

• Unscrambling interference and matrix effects in spectroscopy for ’in situ’ non-dominant absorbance constituents quantification. • Covariance mode search methodology - finding optimal covariance eigenvector with equivalence to the Beer–Lambert law. • State-of-the-art figures of merit review and benchmark against covariance mode search. • Spectral bands interpretation and relationship with tissue maturation. • Enabling analytical-grade ’in situ’ quantifications of sugars and acids in grapes. Analytical grade ’in vivo’ plant metabolic quantification using spectroscopy is a key enabling technology for precision agriculture.Current methods such as PLS, ANN and LS-SVM are non-optimal for resolving spectral interference and matrix effects to provide similar results to the analytical chemistry laboratory. This research presents a new self-learning artificial intelligence (SL-AI) method based on the search of covariance modes. These isolate the different modes of interference present in spectral data, allowing the consistent quantification of constituents. A review of the state-of-the-art methods with the figures of merit mean absolute standard error percentage (MASEP) and Pearson correlation coefficient (R) is presented for comparison and discussion. 707 grapes were quantified for glucose, fructose, malic and tartaric acids in five wine-making and one table grape varieties, and used to benchmark the new method against the state-of-the-art methodologies: partial least squares, local partial least squares, artificial neural networks and least squares support vector machines. SL-AI provides consistent quantifications, whereas previous methods exhibit data-driven performance dependence. Pearson correlations of 0.93 to 0.99 and MASEP of 3.70% to 7.33% were obtained with the new methodology. Local partial least squares, the method with the best benchmarks from literature, achieved correlations of 0.81 to 0.94 and MASEP of 8.00% to 13.4%. The covariance mode isolates a particular interference, providing a direct relationship between spectral inference and constituent concentrations, consistent with the Beer–Lambert law. Such quantifies non-dominant absorbance constituents (e.g. sugars and acids), which is a significant step towards ’in vivo’ plant physiology-based precision agriculture.

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.