一种非本征光纤法布里-珀罗传感器的信号解调算法

给出了一种基于均方误差估计的非本征光纤法布里-珀罗(EFPI)传感器的腔长解调算法。在参量估计方面, 均方误差将估计子的方差和偏差结合在一起, 具有更高的估计精度和准确度。如果给出某一个真值的一系列估计子, 则具有最小均方误差的估计子比其他估计子更为有效。在非本征光纤法-珀传感器的腔长解调方面, 则实际腔长对应于腔长均方误差估计取最小值时的腔长估计子。对一个非本征光纤法-珀压力传感器的测试结果表明, 腔长解调分辨率为0.18 nm, 对应的压力分辨率可达2.99 kPa。与传统的解调算法相比, 通过该算法可在较宽的动态范围内获得高的解调分辨率, 并实现绝对腔长的解调。     

前后向子分段相位差频率估计法

为提高直接频率估计法的精度并推导出估计误差方差的闭合表达式,本文提出基于前后向子分段相位差的直接频率估计法. 该方法对样本的前向和后向两个子段做快速傅里叶变换,再提取这两个子段变换后的峰值谱相位差而获得频率估计. 本文证明了该估计器具有无偏性,并推导出其频率估计方差的闭合理论表达式. 仿真实验验证了该闭合表达式的正确性,故本文方法具有更高的测频精度和广泛的应用前景. 关键词： 频率估计 前后向子段 相位差 克拉美罗限     

Recovery-Based Error Estimator for Natural Convection Equations Based on Defect-Correction Methods

In this paper, we propose an adaptive defect-correction method for natural convection (NC) equations. A defect-correction method (DCM) is proposed for solving NC equations to overcome the convection dominance problem caused by a high Rayleigh number. To solve the large amount of computation and the discontinuity of the gradient of the numerical solution, we combine a new recovery-type posteriori estimator in view of the gradient recovery and superconvergent theory. The presented reliability and efficiency analysis shows that the true error can be effectively bounded by the recovery-based error estimator. Finally, the stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations.     

房间脉冲响应模拟法及混响时间盲估计应用

在构建混响语声数据集时,由于缺乏真实长混响房间脉冲响应且模拟的房间脉冲响应与真实不符,因而导致数据驱动的混响时间盲估计模型性能下降。提出了一种基于条件生成对抗网络的房间脉冲响应模拟法,该方法利用真实的房间脉冲响应训练条件生成对抗网络,可以根据指定的混响时间模拟更加真实的房间脉冲响应。使用不同方法模拟的房间脉冲响应构建训练集用于训练盲估计模型,通过声学实验评估模型性能。实验结果表明,由该方法模拟的房间脉冲响应训练的估计模型在不同信噪比下均具有最小的均方根误差且在长混响情况下显著优于其他模型。     

FREQUENCY DOMAIN ARX MODEL AND MULTI-HARMONIC FRF ESTIMATORS FOR NON-LINEAR DYNAMIC SYSTEMS

Non-linear dynamic systems respond at frequencies other than the excitation frequency; however, standard frequency response function estimators for linear systems do not accommodate this harmonic distortion. A new multi-harmonic frequency response function estimator that utilizes discrete frequency models for non-linear systems is introduced here. The multi-harmonic estimator relates the frequency response at each frequency to the input and output spectra within a given frequency band in the same way that autoregressive exogenous input models relate inputs and outputs at particular samples in the time domain. Overdetermined, least-mean-squares calculations are used to minimize model error throughout a frequency band rather than at a single frequency as in the corresponding linear estimators. The resulting multi-harmonic frequency response function models are non-parametric (e.g., vary with amplitude) when linear functions are used and parametric when non-linear functions are used. A new sensitive indicator for experimentally characterizing non-linearity is introduced.     

On Generalized Schürmann Entropy Estimators

We present a new class of estimators of Shannon entropy for severely undersampled discrete distributions. It is based on a generalization of an estimator proposed by T. Schürmann, which itself is a generalization of an estimator proposed by myself.For a special set of parameters, they are completely free of bias and have a finite variance, something which is widely believed to be impossible. We present also detailed numerical tests, where we compare them with other recent estimators and with exact results, and point out a clash with Bayesian estimators for mutual information.     

Selecting an Effective Entropy Estimator for Short Sequences of Bits and Bytes with Maximum Entropy

Entropy makes it possible to measure the uncertainty about an information source from the distribution of its output symbols. It is known that the maximum Shannon’s entropy of a discrete source of information is reached when its symbols follow a Uniform distribution. In cryptography, these sources have great applications since they allow for the highest security standards to be reached. In this work, the most effective estimator is selected to estimate entropy in short samples of bytes and bits with maximum entropy. For this, 18 estimators were compared. Results concerning the comparisons published in the literature between these estimators are discussed. The most suitable estimator is determined experimentally, based on its bias, the mean square error short samples of bytes and bits.     

Generalizing the Balance Heuristic Estimator in Multiple Importance Sampling

In this paper, we propose a novel and generic family of multiple importance sampling estimators. We first revisit the celebrated balance heuristic estimator, a widely used Monte Carlo technique for the approximation of intractable integrals. Then, we establish a generalized framework for the combination of samples simulated from multiple proposals. Our approach is based on considering as free parameters both the sampling rates and the combination coefficients, which are the same in the balance heuristics estimator. Thus our novel framework contains the balance heuristic as a particular case. We study the optimal choice of the free parameters in such a way that the variance of the resulting estimator is minimized. A theoretical variance study shows the optimal solution is always better than the balance heuristic estimator (except in degenerate cases where both are the same). We also give sufficient conditions on the parameter values for the new generalized estimator to be better than the balance heuristic estimator, and one necessary and sufficient condition related to χ2 divergence. Using five numerical examples, we first show the gap in the efficiency of both new and classical balance heuristic estimators, for equal sampling and for several state of the art sampling rates. Then, for these five examples, we find the variances for some notable selection of parameters showing that, for the important case of equal count of samples, our new estimator with an optimal selection of parameters outperforms the classical balance heuristic. Finally, new heuristics are introduced that exploit the theoretical findings.     

Cell Conservative Flux Recovery and a Posteriori Error Estimate of Vertex-Centered Finite Volume Methods

A cell conservative flux recovery technique is developed here for vertex-centered finite volume methods of second order elliptic equations. It is based on solving a local Neumann problem on each control volume using mixed finite element methods. The recovered flux is used to construct a constant free a posteriori error estimator which is proven to be reliable and efficient. Some numerical tests are presented to confirm the theoretical results. Our method works for general order finite volume methods and the recovery-based and residual-based a posteriori error estimators are the first result on a posteriori error estimators for high order finite volume methods.     

Maximum likelihood estimation of direction of arrival using an acoustic vector-sensor

A vector-sensor consisting of a monopole sensor collocated with orthogonally oriented dipole sensors is used for direction of arrival (DOA) estimation in the presence of an isotropic noise-field or internal device noise. A maximum likelihood (ML) DOA estimator is derived and subsequently shown to be a special case of DOA estimation by means of a search for the direction of maximum steered response power (SRP). The problem of SRP maximization with respect to a vector-sensor can be solved with a computationally inexpensive algorithm. The ML estimator achieves asymptotic efficiency and thus outperforms existing estimators with respect to the mean square angular error (MSAE) measure. The beampattern associated with the ML estimator is shown to be identical to that used by the minimum power distortionless response beamformer for the purpose of signal enhancement.     

Design of exponential state estimators for neural networks with mixed time delays

In this Letter, the state estimation problem is dealt with for a class of recurrent neural networks (RNNs) with mixed discrete and distributed delays. The activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. We aim at designing a state estimator to estimate the neuron states, through available output measurements, such that the dynamics of the estimation error is globally exponentially stable in the presence of mixed time delays. By using the Laypunov–Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions to guarantee the existence of the state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A simulation example is exploited to show the usefulness of the derived LMI-based stability conditions.     

Inferring a Property of a Large System from a Small Number of Samples

Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the knowledge of the prior distribution, and in many situations, it is not clear which prior should be used. Several estimators have been developed so far in which the proposed prior us individually tailored for each property of interest; such is the case, for example, for the entropy, the amount of mutual information, or the correlation between pairs of variables. In this paper, we propose a general framework to select priors that is valid for arbitrary properties. We first demonstrate that only certain aspects of the prior distribution actually affect the inference process. We then expand the sought prior as a linear combination of a one-dimensional family of indexed priors, each of which is obtained through a maximum entropy approach with constrained mean values of the property under study. In many cases of interest, only one or very few components of the expansion turn out to contribute to the Bayesian estimator, so it is often valid to only keep a single component. The relevant component is selected by the data, so no handcrafted priors are required. We test the performance of this approximation with a few paradigmatic examples and show that it performs well in comparison to the ad-hoc methods previously proposed in the literature. Our method highlights the connection between Bayesian inference and equilibrium statistical mechanics, since the most relevant component of the expansion can be argued to be that with the right temperature.     

Effect of noise and estimator type on bias for analysis of liver proton density fat fraction

PurposeProton-density fat-fraction (PDFF) is typically measured from PDFF maps by calculating the mean PDFF value within a region of interest (ROI). However, the mean estimator has been shown to result in bias when signal-to-noise ratio (SNR) is low, resulting from a skewed distribution of PDFF noise statistics. Thus, the purpose of this work was to determine the relative performance of three estimation methods (mean, median, maximum likelihood estimators (MLE)) for analysis of liver PDFF maps.MethodsObservational study of adult patients (n = 56) undergoing abdominal MRI. Both 2D-sequential CSE-MRI (‘low-SNR’) and 3D CSE-MRI (‘high-SNR’) acquisitions were obtained. Single-voxel MRS formed the independent reference measurement of hepatic PDFF. Intra-class correlation was tested on a subset of ‘low-SNR’ acquisitions. ROIs were semi-automatically co-registered across all acquisitions. Bland-Altman analysis and intra-class correlation coefficients were used for statistical analysis. A p-value of <0.05 was considered significant.ResultsFor in vivo low-SNR acquisitions, the mean estimator had a larger error than either the median or MLE values (bias ~ −1% absolute PDFF). The intra-class correlation coefficient was significantly greater for median and maximum likelihood estimators (0.992 and 0.993, respectively) compared to the mean estimator (0.973).ConclusionAlternative ROI analysis strategies, such as MLE or median estimators, are useful to avoid SNR-related PDFF bias. Median may be the most clinically practical strategy given its ease of calculation.     

Joint estimation of the lognormal-Rician atmospheric turbulence model by the generalized method of moments

The generalized method of moments (GMM) is introduced in the framework of estimating the lognormal-Rician parameters. This GMM approach provides a systematic procedure for finding the moment-based parameter estimators. The GMM estimator can estimate the two shaping parameters of the lognormal-Rician PDF jointly. The asymptotic performance of the GMM estimator is compared with Monte Carlo simulation results. The results show that the GMM approach can lead to estimators with satisfactory performance over a wide range of channel conditions. The proposed method can be easily applied to both noiseless and noisy environments.     

Monte Carlo-based tail exponent estimator

In this paper we propose a new approach to estimation of the tail exponent in financial stock markets. We begin the study with the finite sample behavior of the Hill estimator under α-stable distributions. Using large Monte Carlo simulations, we show that the Hill estimator overestimates the true tail exponent and can hardly be used on samples with small length. Utilizing our results, we introduce a Monte Carlo-based method of estimation for the tail exponent. Our proposed method is not sensitive to the choice of tail size and works well also on small data samples. The new estimator also gives unbiased results with symmetrical confidence intervals. Finally, we demonstrate the power of our estimator on the international world stock market indices. On the two separate periods of 2002-2005 and 2006-2009, we estimate the tail exponent.     

A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates

A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being computed based on hierarchical a posteriori error estimates. A global hierarchical error estimate is employed in this study to obtain reliable directional information of the solution. Instead of solving the global error problem exactly, which is costly in general, we solve it iteratively using the symmetric Gauß–Seidel method. Numerical results show that a few GS iterations are sufficient for obtaining a reasonably good approximation to the error for use in anisotropic mesh adaptation. The new method is compared with several strategies using local error estimators or recovered Hessians. Numerical results are presented for a selection of test examples and a mathematical model for heat conduction in a thermal battery with large orthotropic jumps in the material coefficients.     

Sparse Estimation Strategies in Linear Mixed Effect Models for High-Dimensional Data Application

In a host of business applications, biomedical and epidemiological studies, the problem of multicollinearity among predictor variables is a frequent issue in longitudinal data analysis for linear mixed models (LMM). We consider an efficient estimation strategy for high-dimensional data application, where the dimensions of the parameters are larger than the number of observations. In this paper, we are interested in estimating the fixed effects parameters of the LMM when it is assumed that some prior information is available in the form of linear restrictions on the parameters. We propose the pretest and shrinkage estimation strategies using the ridge full model as the base estimator. We establish the asymptotic distributional bias and risks of the suggested estimators and investigate their relative performance with respect to the ridge full model estimator. Furthermore, we compare the numerical performance of the LASSO-type estimators with the pretest and shrinkage ridge estimators. The methodology is investigated using simulation studies and then demonstrated on an application exploring how effective brain connectivity in the default mode network (DMN) may be related to genetics within the context of Alzheimer’s disease.     

Improving the accuracy of the n-dB method for determining damping of non-lightly damped systems

Damping measurements using the spectral magnitude remain popular and are studied here for non-lightly damped systems using the variable bandwidth n-dB method, which is advantageous for non-lightly damped systems. The most commonly used estimator (based on normalised bandwidth) provides significant errors for non-lightly damped systems. An existing more accurate method (using the squares of the frequencies used in the former method) is exact for hysteretic damping, but still provides significant error for viscous damping. Improved estimators are developed in order to correct either exactly, or to insignificant errors, measurements taken with existing estimators. Neither further data nor the individual frequencies are required; the previously calculated damping values are corrected. The application of the improved estimators is dependent upon the existing estimator used and the damping type; however a strategy is suggested to reduce errors if the latter is unknown.     

Asymptotic Properties of Estimators for Seasonally Cointegrated State Space Models Obtained Using the CVA Subspace Method

This paper investigates the asymptotic properties of estimators obtained from the so called CVA (canonical variate analysis) subspace algorithm proposed by Larimore (1983) in the case when the data is generated using a minimal state space system containing unit roots at the seasonal frequencies such that the yearly difference is a stationary vector autoregressive moving average (VARMA) process. The empirically most important special cases of such data generating processes are the I(1) case as well as the case of seasonally integrated quarterly or monthly data. However, increasingly also datasets with a higher sampling rate such as hourly, daily or weekly observations are available, for example for electricity consumption. In these cases the vector error correction representation (VECM) of the vector autoregressive (VAR) model is not very helpful as it demands the parameterization of one matrix per seasonal unit root. Even for weekly series this amounts to 52 matrices using yearly periodicity, for hourly data this is prohibitive. For such processes estimation using quasi-maximum likelihood maximization is extremely hard since the Gaussian likelihood typically has many local maxima while the parameter space often is high-dimensional. Additionally estimating a large number of models to test hypotheses on the cointegrating rank at the various unit roots becomes practically impossible for weekly data, for example. This paper shows that in this setting CVA provides consistent estimators of the transfer function generating the data, making it a valuable initial estimator for subsequent quasi-likelihood maximization. Furthermore, the paper proposes new tests for the cointegrating rank at the seasonal frequencies, which are easy to compute and numerically robust, making the method suitable for automatic modeling. A simulation study demonstrates by example that for processes of moderate to large dimension the new tests may outperform traditional tests based on long VAR approximations in sample sizes typically found in quarterly macroeconomic data. Further simulations show that the unit root tests are robust with respect to different distributions for the innovations as well as with respect to GARCH-type conditional heteroskedasticity. Moreover, an application to Kaggle data on hourly electricity consumption by different American providers demonstrates the usefulness of the method for applications. Therefore the CVA algorithm provides a very useful initial guess for subsequent quasi maximum likelihood estimation and also delivers relevant information on the cointegrating ranks at the different unit root frequencies. It is thus a useful tool for example in (but not limited to) automatic modeling applications where a large number of time series involving a substantial number of variables need to be modelled in parallel.     

Delay-coordinates embeddings as a data mining tool for denoising speech signals

In this paper, we utilize techniques from the theory of nonlinear dynamical systems to define a notion of embedding estimators. More specifically, we use delay-coordinates embeddings of sets of coefficients of the measured signal (in some chosen frame) as a data mining tool to separate structures that are likely to be generated by signals belonging to some predetermined data set. We implement the embedding estimator in a windowed Fourier frame, and we apply it to speech signals heavily corrupted by white noise. Our experimental work suggests that, after training on the data sets of interest, these estimators perform well for a variety of white noise processes and noise intensity levels.