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We present a non‐Gaussian ensemble data assimilation method based on the maximum‐likelihood ensemble filter, which allows for any combination of Gaussian, lognormal, and reverse lognormal errors in both the background and the observations. The technique is fully nonlinear, does not require a tangent linear model, and uses a Hessian preconditioner to minimise the cost function efficiently in ensemble space. When the Gaussian assumption is relaxed, the results show significant improvements in the analysis skill within two atmospheric toy models, and the performance of data assimilation systems for (semi)bounded variables is expected to improve. [ABSTRACT FROM AUTHOR]

Magnetic resonance fingerprinting (MRF) is a novel quantitative MR technique that simultaneously provides multiple tissue property maps. When optimizing MRF scans, modeling undersampling errors and field imperfections in cost functions for direct measurement of quantitative errors will make the optimization results more practical and robust. However, optimizing such cost function is computationally expensive and impractical for MRF optimization with tens of thousands of iterations. Here, we introduce a fast MRF simulator to simulate aliased images from actual scan scenarios including undersampling and system imperfections, which substantially reduces computational time and allows for direct error estimation of the quantitative maps and efficient sequence optimization. We evaluate the performance and computational speed of the proposed approach by simulations and in vivo experiments. The simulations from the proposed method closely approximate the signals and MRF maps from in vivo scans, with 158 times shorter processing time than the conventional simulation method using Non-uniform Fourier transform. We also demonstrate the power of applying the fast MRF simulator in MRF sequence optimization. The optimized sequences are validated with in vivo scans to assess the image quality and accuracy. The optimized sequences produce artifact-free T1 and T2 maps in 2D and 3D scans with equivalent mapping accuracy as the human-designed sequence but at shorter scan times. Incorporating the proposed simulator in the MRF optimization framework makes direct estimation of undersampling errors during the optimization process feasible, and provide optimized MRF sequences that are robust against undersampling artifacts and field inhomogeneity. [ABSTRACT FROM AUTHOR]

A sampling error‐based finite‐set predictive current control (FS‐PCC) is proposed in this article for the open‐end winding induction motor (OEWIM) drive. The proposed scheme controls the zero‐sequence current (ZSC) alongside the stator currents. In a model‐free approach, this method predicts the future of ZSC and stator current components by the stator current and voltage sampling errors. In this way, the parameters of the OEWIM are not utilised in the prediction algorithm of the FS‐PCC. So, the proposed method is robust against the variation of the parameter. Moreover, this article presents a simple vector selection technique for the FS‐PCC of the OEWIM. The proposed technique has two cost functions and a simple algebraic equation to put the voltage vectors (VVs) in the prediction algorithm. The first cost function uses VVs that do not have the zero‐sequence voltage component. Then, the algebraic equation determines VVs that must be utilised in the second cost function. Finally, the optimum VV is selected by the second cost function. In the proposed scheme, the prediction algorithm is iterated 14 times instead of 27 iterations of the conventional predictive algorithm. So, besides establishing a novel model‐free prediction algorithm, the proposed method has almost 50% fewer calculations. The validity of the proposed sampling error‐based FS‐PCC and the simplified vector selection technique has been verified through experimental tests. [ABSTRACT FROM AUTHOR]

Summary: In this article, an event‐based intelligent critic algorithm is developed to address the optimal tracking control problem for a type of discrete‐time nonlinear systems. The nonlinear optimal tracking control design is replaced by solving the optimal regulation problem of the error system. Then, the generalized value iteration algorithm is employed to obtain the admissible tracking control law with off‐line learning. Next, a novel triggering condition is designed to reduce the update times of the controller and improve the resource utilization. It is emphasized that this triggering condition is established based on the iteration of the time‐triggered mechanism. Moreover, in order to realize the cost guarantee of the error system, the real cost function is proved to possess a predetermined upper bound. By analysis, it is shown that the error system is asymptotically stable while the tracking error and the sampling signal are uniformly ultimately bounded during the process of training neural networks. Finally, two examples are conducted to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A local data assimilation method, Local DA, is introduced. The proposed algorithm aims to perform hybrid and multiscale analyses simultaneously yet independently for each grid, vertical column or column group and aims to flexibly perform analyses with or without ensemble perturbations. To achieve these goals, an error sample matrix is constructed by explicitly computing the localized background error correlation matrix of model variables that are projected onto observation-associated grids (e.g., radar velocity) or columns (e.g., precipitable water vapor). This error sample matrix allows Local DA to apply the conjugate gradient (CG) method to solve the cost function and to perform localization in the model-variable space, the observation-variable space, or both spaces (double-space localization). To assess the Local DA performance, a typhoon case is simulated, and a multiscale observation network comprising sounding, wind profiler, precipitable water vapor, and radar data is built; additionally, a time-lagged ensemble is employed. The results show that experiments using the hybrid covariance and double-space localization yield smaller analysis errors than experiments without the static covariance and experiments without double-space localization. Moreover, the hybrid covariance plays a more important role than does localization when a poor time-lagged ensemble is used. The results further indicate that applying the CG method for each local analysis does not result in a discontinuity issue, and the wall clock time of Local DA implemented in parallel is halved as the number of cores doubles. [ABSTRACT FROM AUTHOR]

Efficient and robust facial landmark localisation is crucial for the deployment of real-time face analysis systems. This paper presents a new loss function, namely Rectified Wing (RWing) loss, for regression-based facial landmark localisation with Convolutional Neural Networks (CNNs). We first systemically analyse different loss functions, including L2, L1 and smooth L1. The analysis suggests that the training of a network should pay more attention to small-medium errors. Motivated by this finding, we design a piece-wise loss that amplifies the impact of the samples with small-medium errors. Besides, we rectify the loss function for very small errors to mitigate the impact of inaccuracy of manual annotation. The use of our RWing loss boosts the performance significantly for regression-based CNNs in facial landmarking, especially for lightweight network architectures. To address the problem of under-representation of samples with large pose variations, we propose a simple but effective boosting strategy, referred to as pose-based data balancing. In particular, we deal with the data imbalance problem by duplicating the minority training samples and perturbing them by injecting random image rotation, bounding box translation and other data augmentation strategies. Last, the proposed approach is extended to create a coarse-to-fine framework for robust and efficient landmark localisation. Moreover, the proposed coarse-to-fine framework is able to deal with the small sample size problem effectively. The experimental results obtained on several well-known benchmarking datasets demonstrate the merits of our RWing loss and prove the superiority of the proposed method over the state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

The performance of an assimilation system is strongly dependent on the quality of the error statistics used. A number of error statistics estimation and tuning methods have previously been developed to better assess and determine these statistics. Many of these are a posteriori methods which make use of quantities calculated during the assimilation procedure, while other a priori methods do not require information from the assimilation. In this study, we develop a conceptual framework that relates these methods when applied to error variance determination, where each method is associated with the minimization of a particular cost function. The minimization of these cost functions describes a fitting procedure that fits parts of the prescribed modelled innovation covariance to its observed values. Each method must in some way separate the innovation covariance into its contributions from the background and the observations, which are then used in the fitting procedure. It is shown that the examined a posteriori methods use the analysis filter to make this separation and that the minimization of their associated cost functions is done implicitly within the tuning procedure. Analytical expressions for the expectation value and variance of estimates for error variance scaling parameters are determined for each method. The expressions for the expectation values of these estimates show that the accuracy of each method is dependent on its ability to separate the background from the observation contributions to the innovation covariance. This separability is quantified by use of the Frobenius inner product between the background‐ and observation‐error covariances, which additionally allows for geometric interpretations of the covariances to be made. Comparisons between variance parameter estimates from different methods are made for the case of a 1D periodic domain. [ABSTRACT FROM AUTHOR]

This paper proposes an effective sliding mode controller (SMC) for a grid-connected 7-level packed U-cell (PUC7) inverter. The aim is to design a simple controller that deals effectively with the complex control problem of the PUC7 inverter (multiobjective control problem). The selection of the control actions is achieved according to the system state error at every sampling time, regardless of the previous values, which makes the control technique model-independent. The control algorithm evaluates online two cost functions (one for each state error), which are derived on the basis of sliding mode theory, and it selects the optimal control input in order to satisfy the reaching conditions of the two cost functions. Compared with the existing solutions, the proposed SMC technique ensures lower average switching frequency by tuning the hysteresis bandwidth of the capacitor-voltage error. The fast implementation, needless of gains tuning, and simple design procedure are the main features of the proposed algorithm. Simulation and experimental results are presented to prove the effectiveness of the proposed technique in controlling the PUC7 inverter with high dynamic performance and robustness against disturbances and parameters mismatch. [ABSTRACT FROM AUTHOR]

Some versions of weighted (twin) support vector machines have been developed to handle the contaminated data. However, the weights of samples are generally obtained from the prior knowledge of data in advance. This article develops an adaptively weighted twin support vector machine via Bregman divergences. To better handle the contaminated data, we employ an insensitive loss function to control the fitting error of the samples in one class and introduce the weight (fuzzy membership) of each sample into the proposed model. The alternating optimization technique is utilized to solve the proposed model due to the characteristics of the model. The accelerated version of first-order methods is used to solve a quadratic programming problem, and the fuzzy membership of each sample is achieved analytically in the case of Bregman divergences. Experiments on some data sets have been conducted to show that our method gains better classification performance than previous methods, especially for the open set experiment. [ABSTRACT FROM AUTHOR]

In order to identify the network attack elements better, and solve the nonlinear data multi-classification problem of the network attack elements, this paper presents a classification model and training method based on radial basis neural network. The model uses the training sample error to construct the cost function to solve the minimum value of the cost function and improve the classification accuracy. In the training process of the model, the K-mean algorithm is improved by constructing the average difference between the samples, the number of the hidden layer nodes and the initial value of the basis function center are determined, and the influence of the hidden layer structure on the classification accuracy is reduced. The learning rate in the gradient algorithm is optimized by Q learning method, and the interference of the learning rate to the training of the network parameters is reduced. The OLS algorithm is used to adjust the weights of the hidden layer to the output layer to improve the accuracy of the model classification output. The simulation results show that the model can solve the nonlinear classification problem of network attack well, and the average accuracy rate is improved by about 9% compared with the existing classification methods. [ABSTRACT FROM AUTHOR]

In this paper, we develop an upper bound for the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) estimation error in a general scheme, i.e., when the cost function is strongly convex and the regularized norm is decomposable for a pair of subspaces. We show how this general bound can be applied to a sparse regression problem to obtain an upper bound of the estimation error for the traditional l 1 SPARSEVA problem. Numerical results are used to illustrate the effectiveness of the suggested bound. [ABSTRACT FROM AUTHOR]

In a recent work by the authors the concept of Fading Gaussian Deterministic filter was investigated. The algorithm is based on a set of equations derived from the minimization of a cost function where earlier data are progressively de-weighted by a fading factor. In such a way, the estimation was proved to be less prone to problem unknowns. A tuning procedure was proposed that allows the resulting globally best estimator to evaluate the covariance of an effective measurement noise and the true estimation error, without any a-priori assumption. In the present paper, a general formulation is derived where the observed system is influenced by a control input. Also, a proof is derived for the proposed tuning criterion, which is shown to provide, under certain assumptions, the fading factor that best dampens the modeling errors with respect to measurement noise. The validity of the proposed approach is investigated by means of both numerical simulations and an experimental campaign, where height estimation is performed by fusing information from MEMS accelerometers and a barometric altimeter. [ABSTRACT FROM AUTHOR]

This paper proposes a novel adaptive observer for Lipschitz nonlinear systems and dissipative nonlinear systems in the presence of disturbances and sensor noise. The observer is based on anH∞observer that can estimate both the system states and unknown parameters by minimising a cost function consisting of the sum of the square integrals of the estimation errors in the states and unknown parameters. The paper presents necessary and sufficient conditions for the existence of the observer, and the equations for determining observer gains are formulated as linear matrix inequalities (LMIs) that can be solved offline using commercially available LMI solvers. The observer design has also been extended to the case of time-varying unknown parameters. The use of the observer is demonstrated through illustrative examples and the performance is compared with extended Kalman filtering. Compared to previous results on nonlinear observers, the proposed observer is more computationally efficient, and guarantees state and parameter estimation for two very broad classes of nonlinear systems (Lipschitz and dissipative nonlinear systems) in the presence of input disturbances and sensor noise. In addition, the proposed observer does not require online computation of the observer gain. [ABSTRACT FROM AUTHOR]

In this paper, a single-channel speech enhancement method based on Bayesian decision and spectral amplitude estimation is proposed, in which the speech detection module and spectral amplitude estimation module are included, and the two modules are strongly coupled. First, under the decisions of speech presence and speech absence, the optimal speech amplitude estimators are obtained by minimizing a combined Bayesian risk function, respectively. Second, using the obtained spectral amplitude estimators, the optimal speech detector is achieved by further minimizing the combined Bayesian risk function. Finally, according to the detection results of speech detector, the optimal decision rule is made and the optimal spectral amplitude estimator is chosen for enhancing noisy speech. Furthermore, by considering both detection and estimation errors, we propose a combined cost function which incorporates two general weighted distortion measures for the speech presence and speech absence of the spectral amplitudes, respectively. The cost parameters in the cost function are employed to balance the speech distortion and residual noise caused by missed detection and false alarm, respectively. In addition, we propose two adaptive calculation methods for the perceptual weighted order p and the spectral amplitude order β concerned in the proposed cost function, respectively. The objective and subjective test results indicate that the proposed method can achieve a more significant segmental signal-noise ratio (SNR) improvement, a lower log-spectral distortion, and a better speech quality than the reference methods. [ABSTRACT FROM AUTHOR]

We study the sensitivity of the control cost for a linear stationary object with discrete time to estimation errors in spectral densities of the perturbances. We establish that the cost functional defined on sufficiently massive classes of spectral densities with standard metrization is irregular. We propose a regularization for the cost functional with a change in metric that lets us justify the price description with the substitution method. [ABSTRACT FROM AUTHOR]

This study concerns the unscented Kalman filter (UKF) for the non-linear dynamic systems with error statistics following non-Gaussian probability distributions. A novel robust unscented Kalman filter (NRUKF) is proposed. In the NRUKF the measurement information (measurements or measurements noise) is reformulated using Huber cost function, then the standard unscented transformation (UT) is applied to exact non-linear measurement equation. Compared with the conventional Huber-based unscented Kalman filter (HUKF) which is derived by applying the Huber technique to modify the measurement update equations of the standard UKF, the NRUKF, without linear (statistical linear) approximation, has much-improved performance and versatility with maintaining the robustness. Then the NRUKF is applied to the target tracking problem. The validity of the algorithm is demonstrated through numerical simulation study. [ABSTRACT FROM AUTHOR]

A novel Huber M-estimator based proportionate affine projection algorithm (APA) is proposed for echo cancellation. The Huber objective function is minimised as the cost function and results in Huber M-estimator based APA. Moreover, the cutoff value of Huber objective function is updated according to the correlation between the error signal and the far-end input signal. It is shown that the proposed algorithm can achieve faster convergence and better robustness against double-talk than conventional robust algorithms. [ABSTRACT FROM AUTHOR]