An analysis of the effects of spectral uncertainty on wiener filtering

A representative selection of results from an extensive study of the performance of Wiener filtering under spectral uncertainty is presented. For a variety of spectral uncertainty models the Wiener filter is shown to have undesirable sensitivity to even small deviations from those signal and noise spectral densities which were used to design the filter. Performance of a robust filter (designed to have the best possible performance when the uncertainty is worst) is also examined. In most cases the robust filter's insensitivity to spectral uncertainty makes it preferable to the traditional Wiener filter.     

Robust filtering under stochastic parametric uncertainties

This paper is concerned with a polynomial approach to robust deconvolution filtering of linear discrete-time systems with random modeling uncertainties. The modeling errors appear in the coefficients of the numerators and denominators of both the input signal and system transfer function models in the form of random variables with zero means and known upper bounds of the covariances. The robust filtering problem is to find an estimator that minimizes the maximum mean square estimation error over the random parameter uncertainties and input and measurement noises. The key to our solution is to quantify the effect of the random parameter uncertainties by introducing two fictitious noises for which a simple way is given to calculate their covariances. The optimal robust estimator is then computed by solving one spectral factorization and one polynomial equation as in the standard optimal estimator design using a polynomial approach. An example of signal detection in mobile communication is given to illustrate the effectiveness of our approach.     

Weiner and Kalman filters for systems with random parameters

A linear stationary optimal filtering problem is considered in which the plant dynamics and noise covariances are incompletely known. Unknown plant parameters in the plant model, such as gains and time constants, are treated as random variables with specified means and variances. Generalized Wiener and Kalman-Bucy filters are derived on the basis of transfer-function matrix or state-space representations of the plant, respectively. An application of the generalized filter to the linear quadratic optimal control of plants with unknown disturbances is also described and a certainty equivalence principle is shown to apply.     

An RBFN–Wiener hybrid filter using higher order signal statistics

In this paper we propose a radial basis function network (RBFN) based nonlinear filter with a basic framework of a linear Wiener filter. In addition, in order to improve the filtering performance, we further propose a novel nonlinear filter, which is synthesized by a hybridization of an RBFN filter and a linear Wiener filter. The proposed filters are realized with a least mean square error scheme using higher order statistics of a target signal and an observation noise.The validity and the effectiveness of the proposed filters have been verified by applying them to the actual filtering problems of the noisy images.     

A Novel Adaptive Kalman Filter Based on Credibility Measure

It is quite often that the theoretic model used in the Kalman filtering may not be sufficiently accurate for practical applications, due to the fact that the covariances of noises are not exactly known. Our previous work reveals that in such scenario the filter calculated mean square errors(FMSE) and the true mean square errors(TMSE) become inconsistent, while FMSE and TMSE are consistent in the Kalman filter with accurate models. This can lead to low credibility of state estimation regardless o...     

时域Wiener状态滤波新方法

基于稳态Kalman滤波器和射影理论,提出了统一和通用的时域Wiener状态滤波新方法,用它得到带非零均值相关噪声线性随机系统的渐近稳定的Wiener状态估值器和解耦Wiener状态估值器.它可统一处理状态滤波、预报和平滑问题.发现了Kalman滤波器和Wiener滤波器之间的变换关系,Wiener状态估值器可由Kalman估值器通过自回归滑动平均(ARMA)新息模型得到.一个仿真例子说明了其有效性.     

基于Kalman滤波的统一的Wiener状态滤波器

对于带相关噪声系统 ,基于稳态Kalman滤波器和自回归滑动平均 (ARMA)新息模型 ,提出了统一的渐近稳定的Wiener状态滤波器 ,可统一处理状态滤波 ,平滑和预报问题 .它们构成了一种新的时域Wiener滤波算法 .揭示了Kalman滤波器与Wiener滤波器之间的关系 .一个目标跟踪系统的仿真例子说明了它们的有效性     

用时域方法设计多通道Wiener去卷滤波器

基于ＡＲＭＡ 新息模型和Ｗｉｅｎｅｒ状态估值器,提出多通道Ｗｉｅｎｅｒ去卷滤波器设计的一种新的时域方法,给出了渐近稳定的递推Ｗｉｅｎｅｒ去卷滤波器,可统一处理去卷滤波、平滑和预报问题。同频域上的多项式方法相比,避免了求解Ｄｉｏｐｈａｎｔｉｎｅ方程,且便于实时应用。仿真例子说明了其有效性     

基于维纳滤波的超声增强实现方法

超声在传播时,由于受到材质不均匀、材料内部杂质等的影响而使接收信号受到噪声的干扰,这种干扰有时会淹没所检测的裂纹信号,因此必须要经过增强处理。声学增强处理常用的方法是维纳滤波。本文提出维纳滤波用于超声增强的具体实现方法,即首先统计平均无脉冲段的初始噪声功率谱,然后自适应计算带干扰超声段功率谱,最后进行维纳滤波。超声数据在不同信噪比下的维纳滤波实验表明了所提方法的有效性,超声维纳去噪方法与谱减法一样能够降低超声回波中的噪声,且更加有效。     

Minimax linear observers and regulators for stochastic systems with uncertain second-order statistics

The problem of minimax design of linear observers and regulators for linear time-varying multivariable stochastic systems with uncertain models of their second-order statistics is treated in this paper. General classes of allowable covariance matrices and means of the process and observation noises and of the random initial condition are considered. A game formulation of the problem is adopted and it is shown that the optimal filter for the least favorable set of covariances is minimax robust for each of the filtering situations analyzed. Conditions satisfied by the saddle-point solutions are given, and their utility for finding the worst case covariances is illustrated by way of several examples of uncertainty classes of practical interest.     

不带Diophantine方程的多通道最优去卷滤波器

用时域上的现代时间序列分析方法,基于ARMA新息模型和白噪声估值器,分别提出 了在ARMA新息滤波器形式下和在Wiener滤波器形式下的新的渐近稳定的多通道最优去卷 滤波器.它们避免了求解Diophantine方程,可统一处理去卷滤波、平滑和预报问题.还给出了 ARMA新息滤波器和Wiener去卷滤波器之间的关系.仿真例子说明了它们的有效性.     

Robust Wiener filtering with non-parametric spectral uncertainty

In this article, robust least-squares filtering problems are considered for non-parametric multivariate spectral uncertainty defined by the so-called spectral band and generalised-moment constraints. Its major aim is to provide a basis for computing approximate solutions to worst-case, Wiener-filtering optimisation problems involving causal filters and multivariate signals. It hinges upon associating upper and lower bounds on the minimum worst-case performance achievable with causal filters with linear-cost/linear matrix inequality (LC/LMI)-constraint optimisation problems. On the basis of a Lagrangean duality formulation for the worst-case, least-squares performance of a given filter, upper bounds on it are obtained as the optimal values of LC/LMI problems. Then, for linearly parameterised classes of filter transfer functions, a causal filter which optimises such an upper bound on worst-case performance can also be obtained from an LC/LMI optimisation problem. To estimate the amount of conservatism incurred when relying on such upper bounds, optimal, nominal, least-squares performance for a given pair of power spectral densities (for the information and noise signal) is maximised over finite-dimensional, linearly parameterised classes of the latter. Again, such problems are shown to be equivalent to LC/LMI problems and the corresponding optimal values are lower bounds on the minimum worst-case, least-squares error achievable in the original robust filtering problem (say, μ_*). Finally, two simple numerical examples are presented to illustrate how causal filters can be obtained whose worst-case, least-squares performance is quite close to the optimal one (i.e. μ_*).     

FIR方法在维纳滤波器设计中的应用与仿真

基于最小均方误差准则,得到维纳-霍夫方程,并利用FIR(有限冲击响应)方法求解,进而得到维纳滤波器的传递函数。在MatLab环境下,基于一阶AR(自回归)模型生成原始信号,对维纳滤波器进行设计和仿真,并分析抽样点数、AR模型参数、信噪比和滤波器阶数对滤波效果的影响。仿真结果表明,增大抽样点数和信噪比以及减小AR模型参数,滤波效果增强;增大滤波器阶数,滤波效果先增强后减弱。     

Hole-spectrum representation and model-based optimal morphological restoration of binary images degraded by subtractive noise

A shape-based image representation grounded on the distribution of holes within an image is developed, and the manner in which this representation can be used to design optimal morphological filters to restore images suffering from subtractive-noise degradation is investigated. The image and noise models are predicated on the existence of some class of shape primitives into which both image and noise can be decomposed (relative to union), and this decomposition is developed within the framework of a general algebraic paradigm for component-based filtering that does not depend on the linear-space structure typically used in spectral representations. Both deterministic and nondeterministic models are considered, and in each case the necessary model constraints are fully explored. Moreover, the type of filters that are naturally compatible with the image-noise models are analyzed. Specifically, optimal morphological filter design is studied in terms of the shape-based hole spectrum (as linear filter design is studied in terms of the frequency spectrum). Various forms of a design algorithm are discussed, the particulars depending on a symmetric-difference error analysis yielding approximate error expressions in terms of the spectral decomposition and the geometry of the underlying shape primitives. Finally, the statistical estimation procedures required for practical implementation of the entire spectrum-filter paradigm are explained.     

Nonlinear filtering structure for image smoothing in mixed-noise environments

This paper introduces a new nonlinear filtering structure for filtering image data that have been corrupted by both impulsive and nonimpulsive additive noise. Like other nonlinear filters, the proposed filtering structure uses order-statistic operations to remove the effects of the impulsive noise. Unlike other filters, however, nonimpulsive noise is smoothed by using a maximum a posteriori estimation criterion. The prior model for the image is a novel Markov random-field model that models image edges so that they are accurately estimated while additive Gaussian noise is smoothed. The Markov random-field-based prior is chosen such that the filter has desirable analytical and computational properties. The estimate of the signal value is obtained at the unique minimum of the a posteriori log likelihood function. This function is convex so that the output of the filter can be easily computed by using either digital or analog computational methods. The effects of the various parameters of the model will be discussed, and the choice of the predetection order statistic filter will also be examined. Example outputs under various noise conditions will be given.     

Computational noise effects on adaptive filter algorithms

Finite word length arithmetic roundoff noise in adaptive filter algorithms results in statistical variations in the filter weight vector about the infinite precision arithmetic weight vector. These roundoff errors may be modeled as a statistically non stationary driving noise affecting weight mean and covariance convergence. Mean and covariance expressions and bounds are desired for word lengths in fixed-point arithmetic by making use of multiplication roundoff error models. The adaptive filter algorithms consist of the LMS algorithm, the Widrow-Hoff LMS algorithm, pilot-vector algorithm and clipped vector algorithm. All of these algorithms can be implemented on-line and real-time. However, only the behavior of the LMS algorithm is reported here. The implementation of the adaptive filter algorithms in finite word length arithmetic is most evident in minicomputer, microprocessor, and dedicated digital signal processors for on-line real-time signal identification and parameter estimation in many disciplines. Radar signal processing, adaptive beam forming, acoustic signal identification, communication channel enhancement have a definite need for advanced filtering concepts. Our adaptive algorithms are typically employed in these filter configurations. These filters can also be employed in phase distortion equalizers. A particular advantage of these filters is that they can be trained to equalize a variety of distortions. Should a particular distortion scenario change in time, the filters can be made to easily adapt to the new problem.     

带丢失观测和不确定噪声方差系统改进的鲁棒协方差交叉融合稳态Kalman滤波器

对带丢失观测和不确定噪声方差的线性定常多传感器系统,引入虚拟噪声将原系统转化为仅带不确定噪声方差的系统.根据极大极小鲁棒估值原理,用Lyapunov方程方法提出局部鲁棒稳态Kalman滤波器及其实际方差最小上界,并利用保守的局部滤波误差互协方差,提出一种改进的鲁棒协方差交叉(covariance intersection,CI)融合稳态Kalman滤波器及其实际方差最小上界.证明了所提出的鲁棒局部和融合滤波器的鲁棒性,并证明了改进的CI融合器鲁棒精度高于原始CI融合鲁棒精度,且高于每个局部滤波器的鲁棒精度.一个仿真例子验证所提出结果的正确性和有效性.     

Nonlinear restoration of noisy images

The restoration of images degraded by an additive white noise is performed by nonlinearly filtering a noisy image. The standard Wiener approach to this problem is modified to take into account the edge information of the image. Various filters of increasing complexity are derived. Experimental results are shown and compared to the standard Wiener filter results and other earlier attempts involving nonstationary filters.     

Speech enhancement with an adaptive Wiener filter

This paper proposes an adaptive Wiener filtering method for speech enhancement. This method depends on the adaptation of the filter transfer function from sample to sample based on the speech signal statistics; the local mean and the local variance. It is implemented in the time domain rather than in the frequency domain to accommodate for the time-varying nature of the speech signals. The proposed method is compared to the traditional frequency-domain Wiener filtering, spectral subtraction and wavelet denoising methods using different speech quality metrics. The simulation results reveal the superiority of the proposed Wiener filtering method in the case of Additive White Gaussian Noise (AWGN) as well as colored noise.     

Robust Limits of Risk Sensitive Nonlinear Filters

Deterministic filter models are considered, and a criterion for a deterministic filter to be robust is introduced. Among the candidates for robust deterministic filters are so-called minimax estimators. In the second part of the paper, a risk sensitive stochastic approach to nonlinear filtering is considered, in which the traditional expected mean squared error criterion is replaced by an expected exponential-of-mean squared error. Minimax filters are obtained as totally risk averse limits of risk sensitive filters. Date received: July 22, 1999. Date revised: June 19, 2000.