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.     

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.     

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.     

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 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.     

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.     

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     

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 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.     

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     

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.     

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.     

An LMI approach to periodic discrete-time unbiased filtering

The problem of unbiased filtering for a discrete-time linear periodic system is faced by means of linear matrix inequality techniques. As leading case, we derive the synthesis conditions to obtain an unbiased filter and an unbiased fixed-lag smoother enforcing a bound on the H_∞ performance on the error dynamics.     

Instrumentation design based on optimal Kalman filtering

This paper presents a methodology for locating sensors in dynamic systems. It aims to maximize Kalman filtering performance by using accuracy as its main performance index. To accomplish this task, both the measurement noise and the observation matrices are manipulated. The method has been applied in two academic case studies and in the Tennessee Eastman Challenge Problem and has shown promising results.     

Knowledge-based approach to the optimal dock arrangement

A problem frequently encountered in ports is the sequencing of waiting ships for berthing to load or unload so that the total demurrage cost incurred is minimized. Here a knowledge-based approach is applied to solve this problem. The constraints of the port and the working rules adopted by the port are expressed as knowledge rules and embedded into the framework of the logic of dock arrangement. With the inference mechanism of a knowledge engineering language OPS5, the best arrangement of the docks can be inferred. Since the operation rules differ from port to port, the problem is confined to the material docks of the China Steel Corporation. A system entitled DOCK is designed to find the best three available alternatives. The idea can be applied and the DOCK system modified for use by other ports.     

A unified approach to optimal feature selection

The optimum finite set of linear observables for discriminating two Gaussian stochastic processes is derived using classical methods and distribution function theory. The results offer a new, accurate information-theoretic strategy and are superior to well-known conventional methods using statistical distance measures.