Polynomial approach to Wiener filtering

A rigorous derivation is given of the polynomial method for finding Wiener filters in both discrete-time and continuous-time. In each case the method involves one spectral factorization and the solution of one diophantine equation. The theory is applicable in multivariable situations but simple scalar examples are included here to compare the polynomial approach with the basic Wiener method.     

Limited memory optimal filtering

Linear and nonlinear optimal filters with limited memory length are developed. The filter output is the conditional probability density function and, in the linear Gaussian case, is the conditional mean and covariance matrix where the conditioning is only on a fixed amount of most recent data. This is related to maximum-likelihood least-squares estimation. These filters have application in problems where standard filters diverge due to dynamical model errors. This is demonstrated via numerical simulations.     

Specific optimal discrete filtering mechanizations

An optimization procedure is developed for obtaining the best discrete representation of a specified form for modeling a continuous, steady-state, Kalman filter. This technique is particularly useful for digital processors in real-time filtering applications. The generalized optimization format is developed, an optimal digital mechanization is obtained, and numerical comparisons are made with the Euler method and the second-order Runge-Kutta numerical integration formula. Significant improvements are shown for several fixed values of discretization intervals.     

An adaptive robustizing approach to kalman filtering

The performance of a linear Kalman filter will degrade when the dynamic noise is not Gaussian. A robust Kalman filter based on the m-interval polynomial approximation (MIPA) method for unknown non-Gaussian noise is proposed. Two situations are considered: (a) the state is Gaussian and the observation noise is non-Gaussian; (b) the state is non-Gaussian and the observation noise is Gaussian. It is shown, as compared with other non-Gaussian filters, the MIPA Kalman filter is computationally feasible, unbiased, more efficient and robust. For the scalar model, Monte Carlo simulations are given to demonstrate the ideas involved.     

A cascadic geometric filtering approach to subdivision

A new approach to subdivision based on the evolution of surfaces under curvature motion is presented. Such an evolution can be understood as a natural geometric filter process where time corresponds to the filter width. Thus, subdivision can be interpreted as the application of a geometric filter on an initial surface. The concrete scheme is a model of such a filtering based on a successively improved spatial approximation starting with some initial coarse mesh and leading to a smooth limit surface.

In every subdivision step the underlying grid is refined by some regular refinement rule and a linear finite element problem is either solved exactly or, especially on fine grid levels, one confines to a small number of smoothing steps within the corresponding iterative linear solver. The approach closely connects subdivision to surface fairing concerning the geometric smoothing and to cascadic multigrid methods with respect to the actual numerical procedure. The derived method does not distinguish between different valences of nodes nor between different mesh refinement types. Furthermore, the method comes along with a new approach for the theoretical treatment of subdivision.     

An optimization approach to adaptive Kalman filtering

In this paper, an optimization-based adaptive Kalman filtering method is proposed. The method produces an estimate of the process noise covariance matrix Q by solving an optimization problem over a short window of data. The algorithm recovers the observations h(x) from a system without a priori knowledge of system dynamics. Potential applications include target tracking using a network of nonlinear sensors, servoing, mapping, and localization. The algorithm is demonstrated in simulations on a tracking example for a target with coupled and nonlinear kinematics. Simulations indicate superiority over a standard MMAE algorithm for a large class of systems.     

A spatial filtering approach to texture analysis

A theory regarding the information processing strategies in human vision motivates the development of a texture feature space. The feature space is used in texture classification and segmentation problems. A statistic for determining the number of different textures in the image is developed and demonstrated.     

一种提高SVD滤波性能的新方法

提出一种提高SVD滤波性能的新方法。基于奇异值分解滤波可以有效地分析水平（垂直）方向的图像特性。根据图像的局部方向,自适应地调整待滤波区域的形状,使重采样后局部区域中的边缘垂直或水平,再对局部区域进行奇异值分解滤波;所得的结果加权平均,得到信号估计值。将这一算法应用于图像去噪,实验结果表明,新方法可以有效地提高SVD的滤波性能。     

A new martingale approach to Kalman filtering

A new derivation of continuous-time Kalman Filter equations is presented. The underlying idea has been previously used to derive the smoothing equations. A unified approach to filtering and smoothing problems has thus been achieved.     

On the optimal unbiased functional filtering

Presents a simple solution to the optimal unbiased reduced-order (or functional) filtering problem for linear time-varying systems. Necessary and sufficient conditions for the existence of the obtained filter are given. Stability and convergence conditions are developed for the time-invariant systems. Both continuous- and discrete-time cases are considered     

A new approach to optimal B-convergence

In this paper a new approach to derive optimalB-convergence results is presented; optimalB-convergence of order 2 for the implicit midpoint rule and the implicit trapezoidal rule and of order 1.5 for the two stage Lobatto IIIC scheme is then established.     

Hermite series approach to optimal control

A general expression for the operational matrix of integration, P, in the case of Hermite polynomials is derived. The structure of P is simple and it is therefore computationally attractive. Using this P, the optimal control with quadratic index problem and the singularly perturbed optimal control problem are studied. Some numerical examples are also included.     

A vegetarian approach to optimal parameterizations

According to a recent result by Farouki (1997), the optimal bilinear parameter transformation of an integral Bézier curve (which produces a rational parameterization whose parametric speed is as uniform as possible) can be computed by solving a quadratic equation. This note presents a simplified derivation of this result. In addition we outline its generalization to rational curves.     

A suffix tree approach to anti-spam email filtering

We present an approach to email filtering based on the suffix tree data structure. A method for the scoring of emails using the suffix tree is developed and a number of scoring and score normalisation functions are tested. Our results show that the character level representation of emails and classes facilitated by the suffix tree can significantly improve classification accuracy when compared with the currently popular methods, such as naive Bayes. We believe the method can be extended to the classification of documents in other domains. Editor: Tom Fawcett     

New approach to information fusion steady-state Kalman filtering

By the modern time series analysis method, based on the autoregressive moving average (ARMA) innovation model, a unified and general information fusion steady-state Kalman filtering approach is presented for the general multisensor systems with different local dynamic models and correlated noises. It can handle the filtering, smoothing, and prediction fusion problems for state or signal. The optimal fusion rule weighted by matrices is re-derived as a weighted least squares (WLS) fuser, and is reviewed. An optimal fusion rule weighted by diagonal matrices is presented, which is equivalent to the optimal fusion rule weighted by scalars for components, and it realizes a decoupled fusion. The new algorithms of the steady-state Kalman estimator gains are presented. In order to compute the optimal weights, the formulas of computing the cross-covariances among local estimation errors by Lyapunov equations are presented. The exponential convergence of the iterative solution of Lyapunov equation is proved. It is proved that the optimal fusion estimators under three weighted fusion rules are locally optimal, but are globally suboptimal. The proposed steady-state Kalman fusers can reduce the on-line computational burden, and are suitable for real-time applications. A simulation example for the 3-sensor steady-state Kalman tracking fusion estimators shows their effectiveness and correctness, and gives the accuracy comparison of the fusion rules.     

A generic approach to diffusion filtering of matrix-fields

Summary Diffusion tensor magnetic resonance imaging, is a image acquisition method, that provides matrix- valued data, so-called matrix fields. Hence image processing tools for the filtering and analysis of these data types are in demand. In this article, we propose a generic framework that allows us to find the matrix-valued counterparts of the Perona–Malik PDEs with various diffusivity functions. To this end we extend the notion of derivatives and associated differential operators to matrix fields of symmetric matrices by adopting an operator-algebraic point of view. In order to solve these novel matrix-valued PDEs successfully we develop truly matrix-valued analogs to numerical solution schemes of the scalar setting. Numerical experiments performed on both synthetic and real world data substantiate the effectiveness of our novel matrix-valued Perona–Malik diffusion filters. The Dutch Organization NWO is gratefully acknowledged for financial support. The German Organization DFG is gratefully acknowledged for financial support.     

A new approach to map-assisted Bayesian tracking filtering

This paper presents a new non-linear filter designed to track targets following a road network, taking advantage of the road map information. The algorithm is based on a Bayesian Multiple Hypotheses modelling of movement process, postulating and evaluating different hypotheses on the segments being followed by the target after road junctions. Then, the along-road tracking is carried out, for each hypothesis, by a longitudinal IMM filter capable of tracking target movements along straight roads, circular segments, and generic curvilinear segments defined through Bézier curves. The algorithm also includes a lateral drift estimator, which tracks the lateral motion of the target with respect to road axis, to be able to estimate target piloting error and especially to track targets in wide roads. The paper completely describes the filter and associated measurement preprocessing procedures, and also includes a comparative evaluation of the proposed filter with other filtering methods in the literature.     

A fuzzy approach to filtering interferometric SAR data

A new method is proposed for interferometric synthetic aperture radar (SAR) data filtering. Considering the overestimation of the correlation map and the reliability of the phases of the master and slave images after registration, the authors propose a new fuzzy filter, based on the weighted least square method and the improved median filter. This method can be employed to filter noise and to strongly reduce the number of residues. Using Pi‐SAR X‐band data from a volcano in Kaimon, Japan, the advantages of the new approach are demonstrated.