M-estimator based Chinese Remainder Theorem with few remainders using a Kroenecker product based mapping vector

The Chinese Remainder Theorem (CRT) explains how to estimate an integer-valued number from the knowledge of the remainders obtained by dividing such unknown integer by co-prime integers. As an algebraic theorem, CRT is the basis for several techniques concerning data processing. For instance, considering a single-tone signal whose frequency value is above the sampling rate, the respective peak in the DFT informs the impinging frequency value modulo the sampling rate. CRT is nevertheless sensitive to errors in the remainders, and many efforts have been developed in order to improve its robustness. In this paper, we propose a technique to estimate real-valued numbers by means of CRT, employing for this goal a Kroenecker based M-Estimation (ME), specially suitable for CRT systems with low number of remainders. Since ME schemes are in general computationally expensive, we propose a mapping vector obtained via Kroenecker products which considerably reduces the computational complexity. Furthermore, our proposed technique enhances the probability of estimating an unknown number accurately even when the errors in the remainders surpass 1/4 of the greatest common divisor of all moduli. We also provide a version of the mapping vectors based on tensorial n-mode products, delivering in the end the same information of the original method. Our approach outperforms the state-of-the-art CRT methods not only in terms of percentage of successful estimations but also in terms of smaller average error.     

基于M估计的非线性鲁棒检测卡尔曼滤波算法

针对传统鲁棒非线性滤波在观测噪声为非高斯强干扰噪声情况下,滤波性能下降的问题,提出一种利用卡方检测法预判断的非线性鲁棒检测滤波算法。该算法通过卡方检测设置门限,剔除突变野值,利用M估计修正量测更新。仿真实验对比了几种典型非线性滤波方法在不同观测噪声环境下的性能。所提算法在非高斯强干扰噪声情况下,比传统鲁棒滤波算法估计精度平均提高了25.5%;估计方差平均减少了18.3%。实验结果表明:所提算法可以抑制观测量非高斯强干扰噪声的影响,提高滤波精度及稳定性。     

PEAK-INSENSITIVE NON-PARAMETRIC SPECTRUM ESTIMATION

Abstract. We study the problem of non-parametric spectrum estimation of a stationary time series that might contain periodic components. In this case the periodogram ordinates have a significant amplitude at frequencies near the frequencies of the periodic components. These can be regarded as outliers in an asymptotically exponential sample. We develop a non-parametric estimator for the spectral density that is insensitive to these outliers in the frequency domain. This is done by robustifying the usual kernel estimator (smoothed periodogram) by means of M-estimation in the frequency domain. We propose to use data-tapered periodograms, which yield a drastic improvement of the procedure, typically for the contaminated situation. This is both shown theoretically and supported by means of simulation. We show consistency of the resulting estimator in the general case, and asymptotic normality in the special case of a Gaussian time series, whether contamination is present or not. Finally we illustrate the finite sample performance of the estimating procedure by some simulation results and by application to the Canadian lynx trappings data.     

一种深度图像中的表面曲率估计算法

曲率估计在深度图像分析中占有重要地位,传统的有限差分或局部拟合方法未考虑到表面上可能出现的不连续性,因而会不可避免地出现错误,为了得到有效可靠的曲率估计,本文提出了基于自适应局部表面拟合和鲁棒最大似然的估计的曲率估计算法,首先,提出曲面是分片光滑的假设,表面曲率需从该像素所属的光滑曲面片来估计,其次,定义了能量函数来度量拟合窗的平滑度,在局部表面拟合时,依据最小化能量函数的原则来自适应移动拟合窗的中心,以使拟合窗达到最“光滑”,最后,采用鲁棒最大似然估计以消除仍然存在的“局外点”的影响,理论分析和实验结果证明估计算法是稳健,可靠,有效的且计算复杂度小。     

长拖尾K分布杂波下雷达目标散射中心参数的稳健估计

实际条件下,在对基于衰减指数(DE)和模型的雷达目标散射中心参数估计和特征提取时,其噪声背景往往是非高斯的,分布密度函数表现出长拖尾性质。利用基于高斯假设条件下的估计方法进行参数估计时,往往不能得到较好的结果。针对这种情况,该文利用M估计方法来实现对长拖尾杂波下DE模型参数的稳健估计。首先分析了基于PRONY模型的M估计实现方法存在的不足,其次提出了两种较为有效的DE模型散射中心参数M估计的实现方法,并对这两种方法进行了分析和比较。仿真实验结果表明,在一类长拖尾K分布杂波条件下,与ESPRIT方法以及扩展PRONY估计方法相比,该文所提的两种方法均能得到较好的估计结果。     

应用改进迭代最近点方法的点云数据配准

提出了基于点云边界特征点的改进迭代最近点(ICP)方法来提高逆向工程中点云数据配准的效率和精度.首先,提出了基于点云边界特征点的初始配准方法.对点云最小包围盒进行三维空间划分,建立空间网格模型;运用边界种子网格识别及生长算法,从点云边界提取特征点,运用奇异值矩阵分解法(SVD)求出点云的变换矩阵,得到初始配准结果.然后,提出了改进的ICP精确配准方法.对点云对应点赋予权重,剔除权重大于阈值的点,通过对目标函数引入M-估计(M-estimation),剔除异常点.最后,在初始配准的基础上,运用改进的ICP方法精确配准.对经典ICP方法和改进ICF方法做对比实验,结果显示,改进方法的配准效率提高了70％以上,误差减小到0.02％.实验表明,本文方法大幅提高了点云配准的效率和精度.     

Robust panel unit root tests for cross-sectionally dependent multiple time series

Robust panel unit root tests are developed for cross-sectionally dependent multiple time series. The tests have limiting null distributions derived from standard normal distributions. A Monte Carlo experiment shows that the tests have better finite sample robust performance than existing tests. Some Latin American real exchange rates revealing many outlying observations are analyzed to check the purchasing power parity (PPP) theory.     

Robust window operators

It is a common practice in computer vision and image processing to convolve rectangular constant coefficient windows with digital images to perform local smoothing and derivative estimation for edge detection and other purposes. If all data points in each image window belong to the same statistical population, this practice is reasonable and fast. But, as is well known, constant coefficient window operators produce incorrect results if more than one statistical population is present within a window, for example, if a gray-level or gradient discontinuity is present. This paper shows one way to apply the theory of robust statistics to the data smoothing and derivative estimation problem. A robust window operator is demonstrated that preserves gray-level and gradient discontinuities in digital images as it smooths and estimates derivatives.     

M-Estimation for regressions with integrated regressors and arma errors

Abstract.  General M -estimation is developed for regression models with integrated regressors and autoregressive moving average (ARMA) errors, in which the ARMA parameters are jointly estimated with the regression parameters. The large sample distribution of the M -estimator is derived. Allowing the regressors to be dependent on the error terms, a parametric 'fully modified' (FM) M -estimator is proposed. In cases of ARMA errors, a Monte-Carlo experiment reveals superiority of the parametric estimators over the semiparametric FM M -estimator of Phillips Econometric Theory 11 (1995, p 912) in terms of empirical mean squared error.     

A novel robust Gaussian filtering method for the characterization of surface generation in ultra-precision machining

A lot of research work has been focused on the study of the surface generation mechanisms in order to predict the surface topography and provide the optimal machined parameters based on the experiential understanding of relationship of machined conditions and surface features. Although the formation of novel geometrical product specification (GPS) and verification framework system promotes the relevant research work to new characterization methods and draft of international standards, relative little research work was conducted on the application of surface characterization techniques to ultra-precision machining which is very important to evaluate the surface quality. In this paper, a novel robust Gaussian filtering method (RGF) is proposed and used to characterize the surface topography of ultra-precision machined surfaces. Cubic B-spline and M-estimation are used to make the method reliable and robust. Based on the property comparisons of classical weighting functions, a novel auto-developed robust weighting function (ADRF) is defined to improve the robustness of RGF. To verify the characterization feasibility of the proposed method, computer simulation is used and then the real ultra-precision machined surfaces are analyzed. The experimental results indicate that the RGF method cannot only separate the surface components effectively on the whole measured area and but also eliminates the influence of freak outliers.