Selection Of Filter Parameters Research Articles

A UD factorization‐based nonlinear adaptive set‐membership filter for ellipsoidal estimation

AbstractThe extended set‐membership filter (ESMF) for nonlinear ellipsoidal estimation suffers from numerical instability, computation complexity as well as the difficulty in filter parameter selection. In this paper, a UD factorization‐based adaptive set‐membership filter is developed and applied to nonlinear joint estimation of both time‐varying states and parameters. As a result of using the proposed UD factorization, combined with a new sequential and selective measurement update strategy, the numerical stability and real‐time applicability of conventional ESMF are substantially improved. Furthermore, an adaptive selection scheme of the filter parameters is derived to reduce the computation complexity and achieve sub‐optimal estimation. Simulation results have shown the efficiency and robustness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.

Herschel-Bulkley diffusion filtering: non-Newtonian fluid mechanics in image processing

We consider certain nonlinear diffusion filters of TV-type, which have a physical analogy as a visco-plastic fluid model. By separating timescales and spatial scales of the image and noise, we develop an energy inequality that governs the evolution of the noise on a local sub-domain of 4k 2 pixels. Subtracting the local mean of the noise we derive an inequality that bounds the decay of the L 2 norm of the noise, minus its local mean. We thus produce estimates for the decay of the noise to its local mean. We show that the noise decays to its local mean in a finite time and give an expression for this stopping time. We show that our stopping time estimate is valid for a range of filter parameters and show how to properly select filter parameters in a consistent way. Finally, we show how the noise decay can be improved by making our filter parameters locally defined, according to the underlying image.

Regional–residual Gravity Field Separation in the Central Andes using Global Geopotential Models

Traditional methods of regional?residual gravity field separation typically involve high-pass filtering, low-order polynomial fitting or computations using isostatic models. All of these methods are susceptible to ambiguity and subjectivity in the selection of filter parameters, polynomial degree and isostatic model. Global Geopotential Models (GGMs), on the other hand, provide long-wavelength gravity data that are based on observations. Therefore, they have the potential to be used to more objectively define the regional gravity field and to give residual anomalies with reduced ambiguity. We have examined residual gravity anomalies in the Central Andes computed using a regional field defined by the recent EIGEN?GRACE01S satellite-only GGM. The resulting residual anomalies show significant correlations with the active volcanic arc and the geometry of the subducting Nazca plate. These results suggest that GGMs have a place in regional gravity interpretation, but the advantages over existing techniques remain to be thoroughly tested.

On the estimation of random unobserved signals by maximization of target likelihoods and its application to blind timing and phase recovery

Many important problems in signal processing can be reduced to the adequate selection of the parameters of a (possibly nonlinear) filter in order to obtain an output signal that complies with some desired properties. In this work, we analyze a novel criterion for selecting filter parameters that relies on the ability to characterize the desired filter output in terms of a target probability density function (pdf). This target pdf can be handled as a likelihood function to be maximized, thus we refer to the new criterion as maximum target-likelihood (MTL). We present a very general signal model where the MTL criterion can be applied and derive necessary and sufficient conditions for asymptotic convergence of the method. The relationship and differences between MTL and standard maximum likelihood (ML), minimum Kullback-Leibler divergence (MKLD), and minimum entropy (ME) methods are explored. Finally, as an example, we apply the novel criterion to the problem of blind timing and phase recovery in a digital transmission system and show that the resulting algorithm is competitive with existing non-data-aided ML-based algorithms.

Composite filters for inverse synthetic aperture radar classification of small ships

Pattern recognition of small ship inverse synthetic aperture radar (ISAR) images is considered. This represents a formidable new distortion-invariant pattern recognition problem. New weighted correlation range alignment and weighted multiple-scatterer motion compensation variations to standard image formation steps were developed and used. A new algorithm to determine if an input image is useful was developed and found to be necessary for small ship ISAR data. Initial recognition results using distortion-invariant (composite) filters are presented. These provide new concepts including: use of a validation set and a goodness measure to select filter parameters, use of new output criteria for which a filter in a bank of filters is best for class determination, rejection of decisions on some poor test input images, and use of voting over a time sequence of test inputs.

An unsupervised texture segmentation algorithm with feature space reduction and knowledge feedback

This paper presents an unsupervised texture segmentation algorithm based on feature extraction using multichannel Gabor filtering. It is shown that feature contrast, a criterion derived for Gabor filter parameter selection, is well suited for feature coordinate weighting in order to reduce the feature space dimension. The central idea of the proposed segmentation algorithm is to decompose the actual segmented image into disjunct areas called scrap images and use them after lowpass filtering as additional features for repeated k-means clustering and minimum distance classification. This yields a classification of texture regions with an improved degree of homogeneity while preserving precise texture boundaries.

Fixed-gain two-stage estimators for tracking maneuvering targets

The two-stage alpha-beta-gamma estimator is proposed as an alternative to adaptive gain versions of the alpha, beta and alpha, beta, and gamma filters for tracking maneuvering targets. The aim is to achieve fixed-gain, variable dimension filtering. The two-stage alpha-beta-gamma estimator is derived from the two-stage Kalman estimator, and the noise variance reduction matrix and steady-state error covariance matrix are given as a function of the steady-state gains. A procedure for filter parameter selection is also given along with a technique for maneuver response and a gain scheduling technique for initialization. The kinematic constraint for constant speed targets is also incorporated into the two-stage estimator to form the two-stage alpha-beta-gamma-lambda estimator. Simulation results are given to compare the performances of other estimators with that of the alpha-beta-gamma filter. >

High resolution spectral estimation using a specially constrained adaptive notch filter

Abstract This paper presents a high resolution spectral estimation technique using a specially constrained adaptive notch filter to estimate and resolve two closely spaced dominant frequencies buried in noise. The notch filter parametrization is an autoregressive moving average model which is implemented in cascaded form. A computationally simple gradient-based adaptive algorithm was applied and found to provide a robust solution to the problem of parameter estimation. Error surface analysis is included and clearly indicates that the algorithm has guaranteed convergence. In addition the analysis provides valuable insights into the appropriate filter and adaption coefficient parameter selection. Extensive experimental testing has been undertaken and results indicate superior performance over existing techniques such as the fast Fourier transform. Typical results are included to demonstrate the capabilities of the proposed technique.

Comparison of Some Parameter Estimation Methods for Continuous-time Models

Seven parameter estimation methods have been tested and compared using continuous–time models considering different error definitions to estimate the performance of these methods. The identified processes were simulated on an analog computer. It was found, that the total least squares method in recursive form (RTLS) showed the best performance, followed by the square root algorithms (DSFI and DSFC). Before ca.paring the different methods, the selection of excitation, sampling time and state variable filter parameters was investigated. The comparison itself was done with different signal–to–noise ratios.

On the Concept of Varying Influence Radii for a Successive Corrections Objective Analysis

There has been a long-standing concept by those who use successive corrections objective analysis that the way to obtain the most accurate objective analysis is first, to analyze for the long wavelengths and then to build in details of the shorter wavelengths by successively decreasing the influence of the more distant observations upon the interpolated values. Using the Barnes method. we compared the filter characteristics for families of response curves that pass through a common point at a reference wavelength. It was found that the filter cutoff is a maximum if the filter parameters that determine the influence of observations are unchanged for both the initial and correction passes. This information was used to define and test the following hypothesis. If accuracy is defined by how well the method retains desired Wavelengths and removes undesired wavelengths, then the Barnes method gives the most accurate analyses if the filter parameters on the initial and correction passes are the same. This hypothesis does not follow the usual conceptual approach to successive corrections analysis. Theoretical filter response characteristics of the Barnes method were compared for filter parameters set to retrieve the long wavelengths and then build in the short wavelengths with the method for filter parameters set to retrieve the short wavelengths and then build in the long wavelengths. The theoretical results and results from analyses of regularly spaced data show that the customary method of first analyzing for the long wavelengths and then building in the shorter wavelengths is not necessary for the stride correction pass version of the Barnes method. Use of the same filter parameters for initial and correction passes improved the analyses from a fraction of a percent for long wavelengths to about ten percent for short but resolvable wavelengths. However, the more sparsely and irregularly distributed the data, the less the results are in accord with the predictions of theory. Use of the same filter parameters gave better overall fit to the wavelengths shorter than eight times the minimum resolvable wave and slightly degraded fit to the longer wavelengths. Therefore, in the application of the Barnes method to irregularly spaced data, successively decreasing the influence of the more distant observations is still advisable if longer wavelengths are present in the held of data. It also was found that no single selection of filter parameters for the two-pass method gives the best analysis for all wavelengths. A three-pass hybrid method is shown to reduce this problem.

Efficient recursive realizations of FIR filters

Recursive filter structures have been found for FIR filters with piecewisepolynomial or piecewise-(polynomial · sinusoid) impulse responses. The amount of arithmetic required for these filters is proportional to the number of piecewise sections in their impulse responses rather than the actual filter lengths. In this paper, it is shown that these impulse response expressions are quite good approximations to many practical filters. Low-pass filters, high-pass filters, narrowband, band-pass, and band-stop filters, Hilbert transformers, and differentiators all have impulse responses which can be approximated by these forms, and a long filter impulse response consists of only a few piecewise sections with greatly reduced arithmetic requirements. Though this technique is based on time-domain approximation, a frequency-domain optimization to select filter parameters is presented with excellent results.

Production of thin CT sections and coronal and sagittal images by spatial filtering.

A method for the production of thin axial transverse sections, coronal views, and sagittal views from overlapped thick computed tomography (CT) scans has been developed. Thin slices are produced by spatially filtering the overlapped CT data using a filter that is a combination of square waves in the spatial domain. Resolution recovery and noise properties have been examined in phantomas and patients for a selection of filter parameters. Sample results of these studies are presented. The method has been applied to data from several hundred patient studies. Several of these cases are shown to illustrate the method.

Digital notch filter design procedure

An analytical procedure for designing a linear digital notch filter is presented. The resultant filter is sixth-order and is implemented by cascading three second-order filters so as to avoid instability which may arise from computer coefficient truncation. The procedure outlined is straightforward, requires only simple algebraic steps, and gives filter parameter selection criteria for reducing the effects of computer coefficient truncation. Notch filters have utility in situations where a desired signal is corrupted by an additive sinusoidal pickup. One thus must process the noisy signal so as to remove the sinusoid without significantly distorting the desired signal.