Optimal Estimation of High-Dimensional Covariance Matrices with Missing and Noisy Data

The estimation of covariance matrices is very important in many fields, such as statistics. In real applications, data are frequently influenced by high dimensions and noise. However, most relevant studies are based on complete data. This paper studies the optimal estimation of high-dimensional covariance matrices based on missing and noisy sample under the norm. First, the model with sub-Gaussian additive noise is presented. The generalized sample covariance is then modified to define a hard thresholding estimator , and the minimax upper bound is derived. After that, the minimax lower bound is derived, and it is concluded that the estimator presented in this article is rate-optimal. Finally, numerical simulation analysis is performed. The result shows that for missing samples with sub-Gaussian noise, if the true covariance matrix is sparse, the hard thresholding estimator outperforms the traditional estimate method.

Stochastic Optimal Estimation with Fuzzy Random Variables and Fuzzy Kalman Filtering

By constructing a mcan-square performance index in the case of fuzzy random variable, the optimal estimation theorem for unknown fuzzy state using the fuzzy observation data are given. The state and output of linear discrete-time dynamic fuzzy system with Gaussian noise are Gaussian fuzzy random variable sequences. An approach to fuzzy Kalman filtering is discussed. Fuzzy Kalman filtering contains two parts： a real-valued non-random recurrence equation and the standard Kalman filtering.

An improved constraint method in optimal estimation of CO2 from GOSAT SWIR observations

We propose an algorithm that combines a pre-processing step applied to the a priori state vector prior to retrievals, with the modified damped Newton method （MDNM）, to improve convergence. The initial constraint vector pre-processing step updates the initial state vector prior to the retrievals if the algorithm detects that the initial state vector is far from the true state vector in extreme cases where there are CO2 emissions. The MDNM uses the Levenberg-Marquardt parameter ~,, which ensures a positive Hessian matrix, and a scale factor a, which adjusts the step size to optimize the stability of the convergence. While the algorithm iteratively searches for an optimized solution using observed spectral radiances, MDNM adjusts parameters ）, and a to achieve stable convergence. We present simulated retrieval samples to evaluate the performance of our algorithm and comparing it to existing methods. The standard deviation of our retrievals adding random noise was less than 3.8 ppmv. After pre-processing the initial estimate when it was far from the true value, the CO2 retrieval errors in the boundary layers were within 1.2 ppmv. We tested the MDNM algorithm＇s performance using GOSAT Llb data with cloud screening. Our preliminary validations comparing the results to TCCON FTS measurements showed that the average bias was less than 1.8 ppm and the correlation coefficient was approximately 0.88, which was larger than for the GOSAT L2 product.

Retrievals of aerosol optical depth and total column ozone from Ultraviolet Multifilter Rotating Shadowband Radiometer measurements based on an optimal estimation technique

A Bayesian optimal estimation （OE） retrieval technique was used to retreive aerosol optical depth （AOD）, aerosol single scattering albedo （SSA）, and an asymmetry factor （g） at seven ultraviolet wavelengths, along with total column ozone （TOC）, from the measurements of the UltraViolet Multifilter Rotating Shadowband Radiometer （UV-MFRSR） deployed at the Southern Great Plains （SGP） site during March through November in 2009. The OE technique specifies appropriate error covariance matrices and optimizes a forward model （Tropospheric ultraviolet radiative transfer model, TUV）, and thus provides a supplemental method for use across the network of the Department of Agriculture UV-B Monitoring and Research Program （USDA UVMRP） for the retrieval of aerosol properties and TOC with reasonable accuracy in the UV spectral range under various atmo- spheric conditions. In order to assess the accuracy of the OE technique, we compared the AOD retreivals from this method with those from Beer＇s Law and the AErosol RObotic Network （AERONET） AOD product. We also examine the OE retrieved TOC in comparison with the TOC from the U.S. Department of Agriculture UV-B Monitoring and Research Program （USDA UVMRP） and the Ozone Monitoring Instrument （OMI） satellite data. The scatterplots of the estimated AOD from the OE method agree well with those derived from Beer＇s law and the collocated AERONET AOD product, showing high values of correlation coefficients, generally 0.98 and 0.99, and large slopes, ranging from 0.95 to 1.0, as well as small offsets, less than 0.02 especially at 368 nm. The comparison of TOC retrievals also indicates the promising accuracy of the OE method in that the standard deviations of the difference between the OE derived TOC and other TOC products are about 5 to 6 Dobson Units （DU）. Validation of the OE retrievals on these selected dates suggested that the OE technique has its merits and can serve as a supplemental tool in further analyzing UVMRP data.

Methodology for Obtaining Optimal Sleeve Friction and Friction Ratio Estimates from CPT Data

Cone penetration testing (CPT) is a cost effective and popular tool for geotechnical site characterization. CPT consists of pushing at a constant rate an electronic penetrometer into penetrable soils and recording cone bearing (qc), sleeve friction (fc) and dynamic pore pressure (u) with depth. The measured qc, fs and u values are utilized to estimate soil type and associated soil properties. A popular method to estimate soil type from CPT measurements is the Soil Behavior Type (SBT) chart. The SBT plots cone resistance vs friction ratio, Rf [where: Rf = (fs/qc)100%]. There are distortions in the CPT measurements which can result in erroneous SBT plots. Cone bearing measurements at a specific depth are blurred or averaged due to qc values being strongly influenced by soils within 10 to 30 cone diameters from the cone tip. The qcHMM algorithm was developed to address the qc blurring/averaging limitation. This paper describes the distortions which occur when obtaining sleeve friction measurements which can in association with qc blurring result in significant errors in the calculated Rf values. This paper outlines a novel and highly effective algorithm for obtaining accurate sleeve friction and friction ratio estimates. The fc optimal filter estimation technique is referred to as the OSFE-IFM algorithm. The mathematical details of the OSFE-IFM algorithm are outlined in this paper along with the results from a challenging test bed simulation. The test bed simulation demonstrates that the OSFE-IFM algorithm derives accurate estimates of sleeve friction from measured values. Optimal estimates of cone bearing and sleeve friction result in accurate Rf values and subsequent accurate estimates of soil behavior type.

Optimal State Estimation and Fault Diagnosis for a Class of Nonlinear Systems

This study proposes a scheme for state estimation and,consequently,fault diagnosis in nonlinear systems.Initially,an optimal nonlinear observer is designed for nonlinear systems subject to an actuator or plant fault.By utilizing Lyapunov's direct method,the observer is proved to be optimal with respect to a performance function,including the magnitude of the observer gain and the convergence time.The observer gain is obtained by using approximation of Hamilton-Jacobi-Bellman(HJB)equation.The approximation is determined via an online trained neural network(NN).Next a class of affine nonlinear systems is considered which is subject to unknown disturbances in addition to fault signals.In this case,for each fault the original system is transformed to a new form in which the proposed optimal observer can be applied for state estimation and fault detection and isolation(FDI).Simulation results of a singlelink flexible joint robot(SLFJR)electric drive system show the effectiveness of the proposed methodology.

Study on optimal state estimation strategy with dual distributed controllers based on Kalman filtering

Considering dual distributed controllers, a design of optimal state estimation strategy is studied for the wireless sensor and actuator network(WSAN). In particular, the optimal linear quadratic(LQ) control strategy with estimated plant state is formulated as a non-cooperative game with network-induced delays. Then, using the Kalman filter approach, an optimal estimation of the plant state is obtained based on the information fusion of the distributed controllers. Finally, an optimal state estimation strategy is derived as a linear function of the current estimated plant state and the last control strategy of multiple controllers. The effectiveness of the proposed closed-loop control strategy is verified by the simulation experiments.

The First Global Map of Atmospheric Ammonia(NH_(3)) as Observed by the HIRAS/FY-3D Satellite

Atmospheric ammonia(NH_(3)) is a chemically active trace gas that plays an important role in the atmospheric environment and climate change. Satellite remote sensing is a powerful technique to monitor NH_(3) concentration based on the absorption lines of NH_(3) in the thermal infrared region. In this study, we establish a retrieval algorithm to derive the NH_(3)column from the Hyperspectral Infrared Atmospheric Sounder(HIRAS) onboard the Chinese Feng Yun(FY)-3D satellite and present the first atmospheric NH_(3) column global map observed by the HIRAS instrument. The HIRAS observations can well capture NH_(3) hotspots around the world, e.g., India, West Africa, and East China, where large NH_(3) emissions exist. The HIRAS NH_(3) columns are also compared to the space-based Infrared Atmospheric Sounding Interferometer(IASI)measurements, and we find that the two instruments observe a consistent NH_(3) global distribution, with correlation coefficient(R) values of 0.28–0.73. Finally, some remaining issues about the HIRAS NH_(3) retrieval are discussed.

OPTIMAL ERROR ESTIMATES OF A DECOUPLED SCHEME BASED ON TWO-GRID FINITE ELEMENT FOR MIXED NAVIER-STOKES/DARCY MODEL

Although the two-grid finite element decoupled scheme for mixed Navier-Stokes/ Darcy model in literatures has given the numerical results of optimal convergence order, the theoretical analysis only obtain the optimal error order for the porous media flow and a non-optimal error order for the fluid flow. In this article, we give a more rigorous of the error analysis for the fluid flow and obtain the optimal error estimates of the velocity and the pressure.

Re-adhesion control strategy based on the optimal slip velocity seeking method

In the railway industry, re-adhesion control plays an important role in attenuating the slip occurrence due to the low adhesion condition in the wheel-rail inter- action. Braking and traction forces depend on the normal force and adhesion coefficient at the wheel-rail contact area. Due to the restrictions on controlling normal force, the only way to increase the tractive or braking effect is to maximize the adhesion coefficient. Through efficient uti- lization of adhesion, it is also possible to avoid wheel-rail wear and minimize the energy consumption. The adhesion between wheel and rail is a highly nonlinear function of many parameters like environmental conditions, railway vehicle speed and slip velocity. To estimate these unknown parameters accurately is a very hard and competitive challenge. The robust adaptive control strategy presented in this paper is not only able to suppress the wheel slip in time, but also maximize the adhesion utilization perfor- mance after re-adhesion process even if the wheel-rail contact mechanism exhibits significant adhesion uncer- tainties and/or nonlinearities. Using an optimal slip velocity seeking algorithm, the proposed strategy provides a satisfactory slip velocity tracking ability, which was demonstrated able to realize the desired slip velocity without experiencing any instability problem. The control torque of the traction motor was regulated continuously to drive the railway vehicle in the neighborhood of the opti- mal adhesion point and guarantee the best traction capacity after re-adhesion process by making the railway vehicle operate away from the unstable region. The results obtained from the adaptive approach based on the second- order sliding mode observer have been confirmed through theoretical analysis and numerical simulation conducted in MATLAB and Simulink with a full traction model under various wheel-rail conditions.

A novel hybrid estimation of distribution algorithm for solving hybrid flowshop scheduling problem with unrelated parallel machine

The hybrid flow shop scheduling problem with unrelated parallel machine is a typical NP-hard combinatorial optimization problem, and it exists widely in chemical, manufacturing and pharmaceutical industry. In this work, a novel mathematic model for the hybrid flow shop scheduling problem with unrelated parallel machine(HFSPUPM) was proposed. Additionally, an effective hybrid estimation of distribution algorithm was proposed to solve the HFSPUPM, taking advantage of the features in the mathematic model. In the optimization algorithm, a new individual representation method was adopted. The(EDA) structure was used for global search while the teaching learning based optimization(TLBO) strategy was used for local search. Based on the structure of the HFSPUPM, this work presents a series of discrete operations. Simulation results show the effectiveness of the proposed hybrid algorithm compared with other algorithms.

DOA estimation via sparse recovering from the smoothed covariance vector

A direction of arrival（DOA） estimation algorithm is proposed using the concept of sparse representation. In particular, a new sparse signal representation model called the smoothed covariance vector（SCV） is established, which is constructed using the lower left diagonals of the covariance matrix. DOA estimation is then achieved from the SCV by sparse recovering, where two distinguished error limit estimation methods of the constrained optimization are proposed to make the algorithms more robust. The algorithm shows robust performance on DOA estimation in a uniform array, especially for coherent signals. Furthermore, it significantly reduces the computational load compared with those algorithms based on multiple measurement vectors（MMVs）. Simulation results validate the effectiveness and efficiency of the proposed algorithm.

Mathematical Analysis of Two Approaches for Optimal Parameter Estimates to Modeling Time Dependent Properties of Viscoelastic Materials

Mathematical models for phenomena in the physical sciences are typically parameter-dependent, and the estimation of parameters that optimally model the trends suggested by experimental observation depends on how model-observation discrepancies are quantified. Commonly used parameter estimation techniques based on least-squares minimization of the model-observation discrepancies assume that the discrepancies are quantified with the L2-norm applied to a discrepancy function. While techniques based on such an assumption work well for many applications, other applications are better suited for least-squared minimization approaches that are based on other norm or inner-product induced topologies. Motivated by an application in the material sciences, the new alternative least-squares approach is defined and an insightful analytical comparison with a baseline least-squares approach is provided.

Estimation of Parameters of Boundary Value Problems for Linear Ordinary Differential Equations with Uncertain Data

In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed here that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax mean square or guaranteed estimates. We establish that the minimax mean square estimates are expressed via solutions of some systems of differential equations of special type and determine estimation errors.

Technique for Estimating the Cone Bearing Smoothing Parameters

Cone penetration testing (CPT) is an extensively utilized and cost effective tool for geotechnical site characterization. CPT consists of pushing at a constant rate an electronic cone into penetrable soils and recording the resistance to the cone tip (qc value). The measured qc values (after correction for the pore water pressure) are utilized to estimate soil type and associated soil properties based predominantly on empirical correlations. The most common cone tips have associated areas of 10 cm2 and 15 cm2. Investigators also utilized significantly larger cone tips (33 cm2 and 40 cm2) so that gravelly soils can be penetrated. Small cone tips (2 cm2 and 5 cm2) are utilized for shallow soil investigations. The cone tip resistance measured at a particular depth is affected by the values above and below the depth of interest which results in a smoothing or blurring of the true bearing values. Extensive work has been carried out in mathematically modelling the smoothing function which results in the blurred cone bearing measurements. This paper outlines a technique which facilitates estimating the dominant parameters of the cone smoothing function from processing real cone bearing data sets. This cone calibration technique is referred to as the so-called CPSPE algorithm. The mathematical details of the CPSPE algorithm are outlined in this paper along with the results from a challenging test bed simulation.

Optimized Robust Filter for Uncertain Discrete Time System and Its Application to Flight Test

An optimized robust filtering algorithm for uncertain discrete-time systemsis presented. To get a series of computational equations, the uncertain part generated by theuncertain systematic matrix in the expression of the error-covariance matrix of time update stateestimation is optimized and the least upper bound of the uncertain part is given. By means of theseresults, the equivalent systematic matrix is obtained and a robust time update algorithm is builtup. On the other hand, uncertain parts generated by the uncertain observation matrix in theexpression of the error-covariance matrix of measurement update state estimation are optimized, andthe largest lower bound of the uncertain part is given. Thus both the time update and measurementupdate algorithms are developed. By means of the matrix inversion formula, the expression structuresof both time update and measurement update algorithms are all simplified. Moreover, the convergencecondition of a robust filter is developed to make the results easy to application. The results offlight data processing show that the method presented in this paper is efficient.

Error estimates of H^1-Galerkin mixed finite element method for Schrdinger equation

An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.

A LOCKING-FREE ANISOTROPIC NONCONFORMING FINITE ELEMENT FOR PLANAR LINEAR ELASTICITY PROBLEM

The main aim of this article is to study the approximation of a locking-free anisotropic nonconforming finite element for the pure displacement boundary value problem of planar linear elasticity. The optimal error estimates are obtained by using some novel approaches and techniques. The method proposed in this article is robust in the sense that the convergence estimates in the energy and L^2-norms are independent-of the Lame parameter λ.

A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS

In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order Crouzeix- Raviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.

Numerical solutions to regularized long wave equation based on mixed covolume method

The mixed covolume method for the regularized long wave equation is devel- oped and studied. By introducing a transfer operator γh, which maps the trial function space into the test function space, and combining the mixed finite element with the finite volume method, the nonlinear and linear Euler fully discrete mixed covolume schemes are constructed, and the existence and uniqueness of the solutions are proved. The optimal error estimates for these schemes are obtained. Finally, a numerical example is provided to examine the efficiency of the proposed schemes.