Output Covariance Matrices Research Articles

Machine learning-based stochastic subspace identification method for structural modal parameters

Machine learning brings a new paradigm to the traditional structural modal parameter identification problem. In this study, we propose a novel machine learning method for stochastic subspace identification (SSI) problem. The proposed method embeds the mathematical characteristics of modal identification into a neural network and formalizes the modal identification into optimization problem of deep neural networks (DNN). The network optimization process is the process of obtaining modal parameters, which can be implemented in a relatively autonomous manner with little manual intervention. The designed modal identification network includes two sub-neural-networks: a model order determination neural network and modal identification neural network. In the model order determination neural network, the singular values of the Toeplitz matrix, which is constructed by output covariance matrices are fed into the network, and the designed network can automatically determine the model order by the designed loss function. In the modal identification neural network, the SSI principles are informed into the neural network, and the designed network is used to identify the modal parameters which optimizes the designed loss function to obtain the system matrix and output matrix. The examples of a numerical simulation and two actual bridges are used to illustrate the ability of the proposed method. Results show that the proposed method is capable of operating automatically to extract modal information from structural responses with stronger anti-interference ability and the identified number of accurate modes are obviously increased.

DOA estimation of the coherent signals using beamspace matrix reconstruction

The matrix reconstruction technique can effectively estimate the direction-of-arrival (DOA) of coherent signals with a relatively small computational complexity. However, the existing methods are affected by the phase perturbation or the fact that the eigenvalue ratio of the signal subspace to noise subspace is linearly related to the square of input signal-to-noise ratio (SNR). This results in a significant decrease in the DOA estimation performance for the cases with a low SNR. To address these problems, we propose a new method for DOA estimation of coherent signals based on the beamspace matrix reconstruction. The array is firstly divided into multiple subarrays, and the data received is transformed from the element space into the beamspace via beamforming, which can eliminate the phase perturbation caused by the mutual impact between the coherent signals and improve the SNR. Then, we add the output covariance matrices from several beam directions to realize the beamspace matrix reconstruction, this results in the eigenvalue ratio of the signal subspace to the noise subspace is the linear transformation of the input SNR in the beamspace domain, which can enhance the eigenvalue ratio of beamspace signal to noise at low SNRs. Finally, the DOAs can be resolved by combining it with the subspace-based methods. Theoretical analysis and simulation results verify the effectiveness of the proposed method at low input SNRs due to beamspace processing, even in the cases where the DOAs between the coherent signals are closely spaced and low snapshot number, our proposed method significantly provides better performance on estimation and resolution.

A Novel Approach to 3D-DOA Estimation of Stationary EM Signals Using Convolutional Neural Networks.

This paper proposes a novel three-dimensional direction-of-arrival (3D-DOA) estimation method for electromagnetic (EM) signals using convolutional neural networks (CNN) in a Gaussian or non-Gaussian noise environment. First of all, in the presence of Gaussian noise, four output covariance matrices of the uniform triangular array (UTA) are normalized and then fed into four neural networks for 1D-DOA estimation with identical parameters in parallel; then four 1D-DOA estimations of the UTA can be obtained, and finally, the 3D-DOA estimation could be obtained through post-processing. Secondly, in the presence of non-Gaussian noise, the array output covariance matrices are normalized by the infinity-norm and then processed in Gaussian noise environment; the infinity-norm normalization could effectively suppress impulsive outliers and then provide appropriate input features for the neural network. In addition, the outputs of the neural network are controlled by a signal monitoring network to avoid misjudgments. Comprehensive simulations demonstrate that in Gaussian or non-Gaussian noise environment, the proposed method is superior and effective in computation speed and accuracy in 1D-DOA and 3D-DOA estimations, and the signal monitoring network could also effectively control the neural network outputs. Consequently, we can conclude that CNN has better generalization ability in DOA estimation.

Realization and identification algorithm for stochastic LPV state-space models with exogenous inputs

In this paper, we present a realization and an identification algorithm for stochastic Linear Parameter-Varying State-Space Affine (LPV-SSA) representations. The proposed realization algorithm combines the deterministic LPV input output to LPV state-space realization scheme based on correlation analysis with a stochastic covariance realization algorithm. Based on this realization algorithm, a computationally efficient and statistically consistent identification algorithm is proposed to estimate the LPV model matrices, which are computed from the empirical covariance matrices of outputs, inputs and scheduling signal observations. The effectiveness of the proposed algorithm is shown via a numerical case study.

Direction Finding for Wideband Source Signals via Steered Effective Projection

A direction-of-arrival (DOA) estimation method for wideband source signals is proposed in the paper based on broadside steering. The steered effective noise subspace is constructed for each steering angle by collecting a certain number of subordinate eigenvectors of the steered array output covariance matrix according to the effective rank of its noise free version. The steered effective projection (STEP) based wideband direction finding then is realized as the steered effective noise subspace towards a true DOA of signal is shown to be: 1) orthogonal to a 1-D subspace spanned by an all-one vector with one single signal present and 2) approximately orthogonal to a 1-D subspace spanned by an all-one vector in the presence of multiple uncorrelated signals. The STEP method requires no preliminary DOA estimates for data focusing. It differs from the existing effective subspace based broad-band signal-subspace spatial spectrum (BASS-ALE) technique in three respects: 1) STEP employs the steered array output covariance matrices towards all the scanning angles while BASS-ALE takes into account only the (focused) array output covariance matrix; 2) STEP performs frequency independent effective subspace projections by constructing the steered effective noise subspace towards each scanning angle while BASS-ALE uses frequency dependent effective subspace projection by constructing only one (focused) effective noise subspace; and 3) STEP can be realized by spatial-only processing while BASS-ALE needs spatio-temporal joint processing to avoid ambiguity in frequency-angle pairs. The performance of the STEP method has been evaluated by extensive simulations, and compared with some current popular wideband DOA estimators.

A Robust Finite-Horizon Kalman Filter for Uncertain Discrete Time-Varying Systems with State-Delay and Missing Measurements

In this paper, a robust kalman filter is designed for the uncertainty time-varying discrete systems with state delay in process and output matrices combined with the possibility of missing measurements. The uncertainties are expected in the process, output and white noise covariance matrices. A formula for a candidate upper bound on the actual state estimation error variances for all admissible parameter uncertainties and possible missing measurements is obtained. The filter parameters are optimized to give a minimal upper bound on the state estimation error covariance for all admissible uncertainties and missing measurements.

Multivariate Control Performance Assessment and Control System Monitoring via Hypothesis Test on Output Covariance Matrices

Control loops widely exist in industrial processes, whose performance directly influences the efficiency, safety, and product quality of production plants. Therefore, control performance assessment (CPA) and control system monitoring (CSM) are critically important for industrial processing. In consideration of multivariate control systems, the covariance matrix of closed-loop outputs plays an important role in both CPA and CSM. Existing methods mainly focus on comparing traces or determinants of the output covariance matrices, which only utilize partial information contained in the matrices. As a result, the assessment and monitoring results may be misleading. In this paper, a multiobjective scheme is proposed for both CPA and CSM of multivariate control systems, which takes the entire covariance matrices into account by conducting a hypothesis test on the equality of the matrices. To fulfill the presupposition of such test, autoregressive moving-average (ARMA) filters are established to remove the autocorrelation contained in the closed-loop output data. The developed scheme can be divided into three aspects: CPA using a minimum variance (MV) benchmark, CPA using a user-specified benchmark, and CSM based on historical data. Case studies show that, compared with the conventional approaches, the proposed method provides more abundant information and achieves better results.

Optimal Forecasting Technique in Reducing Supply Chain Amplification

This paper investigates the optimal forecasting method in reducing supply chain amplification, a.k.a., the Bullwhip Effect. By using a simple replenishing policy and solving Stein Matrix Equations, the relationship between input and output covariance matrices is derived. Both analytical and simulational results support the opinion that proportional forecasting is superior in bullwhip mitigation. There exists trade-off in reducing variance amplifications in order and inventory. For different control objectives, we propose optimal proportional controllers.

Lutetia surface reconstruction and uncertainty analysis

Multiple views of Lutetia taken from OSIRIS NAC payload can be used to perform a metric reconstruction of its shape. In this work a general photogrammetric processing pipeline is described and a detailed uncertainty analysis is performed according with the standard metrological procedures.The uncertainty associated with the following quantities are highlighted and evaluated: intrinsic and extrinsic parameters of the multi-view system; the selected image feature detector and descriptor, which contribute to uncertainties associated with the used feature positions in each image plane; the lighting of the scene, which causes a not negligible uncertainty contribution to 2D positions in the image plane. The Bundle Adjustment, at the core of the reconstruction process, allows the assignment of the covariance of each input parameter and the estimation of derived 3D points covariance. The output covariance matrices represent the spatial uncertainty (magnitude and direction) of each reconstructed point and can be used to derive bounds on the uncertainty of other products as dense surface models and other physical parameters.Presented model of Lutetia is derived using 14 NAC images at the closest approach, 8042 features are tracked between consecutive frames and a final point cloud of 2590 points is produced. From the adjusted camera parameters a dense model with (approximatively) 1.5 million of points is derived using two views. The dense model has a resolution which is approximatively 120m/px and contains the surface topography up to 1km scale.

Solution and entanglement dynamics of a cavityless optomechanical system with Gaussian states

We use the symplectic transformation of the known linear optical elements to investigate the dynamical evolution of a three-mode cavityless optomechanical system and give explicit formulas for the input and output covariance matrices of the three mode fields when the initial state is Gaussian. Unlike the conventional approaches, the present one does not necessitate solution of the equation of motion of such a system. We study the dynamical behavior of bipartite entanglement in this system when the mirror vibrational mode is initially in a single-mode squeezed vacuum state and each of the two reflected optical sideband modes is in the vacuum state. It is found that the entanglement configuration alternates between a fully separable state and a continuous-variable entangled state during evolution.

Entanglement dynamics of multimode Gaussian states coupled to the same reservoir

We investigate the entanglement dynamics of a generic multimode Gaussian state interacting with a common environmental noise by means of the characteristic function method and the defined operators. We find that such operators obey the rather simple commutation relations. This enables us to exactly solve the Fokker-Planck equation and to establish the general form of the input and output covariance matrices of this state. As an application, we consider the separability and entanglement of three-mode squeezed Gaussian state in the common thermal and squeezed thermal bath.

A subarray-synthesis based 2D DOA estimation method

In some satellite communications, we need to perform Direction Of Arrival (DOA) angle estimation under the restriction that the number of receivers is less than that of the array elements in an array antenna. To solve the conundrum, a method named subarray-synthesis-based Two-Dimensional DOA (2D DOA) angle estimation is proposed. In the method, firstly, the array antenna is divided into a series of subarray antennas based on the total number of receivers; secondly, the subarray antennas’ output covariance matrices are estimated; thirdly, an equivalent covariance matrix is synthesized based on the subarray output covariance matrices; then 2D DOA estimation is performed. Monte Carlo simulations showed that the estimation method is effective.

A Convergent Algorithm for the Output Covariance Constraint Control Problem

This paper considers the optimal control problem of minimizing control effort subject to multiple performance constraints on output covariance matrices $Y_i$ of the form $Y_i \leq \overline{Y}_i$, where $\overline{Y}_i$ is given. The contributions of this paper are a set of conditions that characterize global optimality, and an iterative algorithm for finding a solution to the optimality conditions. This iterative algorithm is completely described up to a user-specified parameter. We show that, under suitable assumptions on problem data, the iterative algorithm converges to a solution of the optimality conditions, provided that this parameter is properly chosen. Both discrete- and continuous-time problems are considered.