Discrete Filter Research Articles

Control Performance Monitoring of State-Dependent Nonlinear Processes

This paper presents a novel approach to monitor control performance of nonlinear processes that can be described as state-dependent models (SDMs). A discrete Kalman filter (KF) is established to estimate the SDM parameters. A covariance control formulation is introduced to split the system closed-loop variance/covariance into two terms, one term to account for the minimum expected quadratic loss bound (equivalent to the minimum variance performance bound but in state space formulation), and another to account for performance deviations from the minimum variance bound. Simulation studies have been conducted on several nonlinear process systems including a cold rolling mill model with roll eccentricity and a steel making system with real time oxyfuel slab reheating furnace control data. The case study results demonstrate the computational efficiency of the proposed strategy in real time monitoring and control of systems with fast, nonlinear and time-varying dynamics.

The Filter Design Technique for Trend Change Detection of Random Process in Real Time

A filter for non-stationary processes, which allows receiving real-time filtering result without edge effects and delay, was proposed. Designed filtering algorithm can be used for continuous monitoring of technological processes of production conducted in order to prevent emergency situations and/or output of the process beyond the technological limitations. Built filtration system includes a Kalman filter and optimum discrete filter for random time series with stationary increments.

Multiscale analysis of discrete functions with a given number of filters

The method of discrete wavelet transforms at oriented basis that is constructed by use discrete spectral transform of the functions with modular argument is considered and generalized. Unlike traditional wavelet transforms (like classical Haar’s wavelet) this mathematical approach allows getting more information about the details and behavior of original signal due to more amount of discrete filters that are used for its decomposition. In Haar’s and other wavelet methods there are only two discrete filters are used to decompose initial signal – one low-frequency filter and one high-frequency filter. Low-frequency wavelet coefficients (marked as s-coefficients) give the compressed and approximated version of the initial signal (called trend), and high-frequency wavelet coefficients (marked as d-coefficients) give the high-frequency oscillations around the trend. Such decomposition and calculation of wavelet coefficients is realized at each level of wavelet analysis. While using wavelet transform at oriented basis, there are more than one type of high-frequency wavelet coefficients (marked as d(1)-, d(2)-,…, d(m)-coefficients) where m is defined by the type of spectral transform at oriented basis (dimension of the matrix of basic function). Number of decomposition levels is defined by the length of initial signal’s interval. In the case of Haar’s wavelet transform this length is determined as N=2n, and in the case of wavelet transform at oriented basis this length is determined as N=mn. While selecting the value m equal to three it gives some advantages in calculation volume and consequently, in the speed of wavelet analysis that could be very useful for the processing of the signals with large interval of definition and non-stationery signals. As an interesting example, time dependence of discrete function that describes electrical energy consumption in MicroGrid system could be considered as an object for compressing and removing of casual high-frequency oscillations with the help of wavelet analysis. The use of wavelet transforms with more than two high-frequency filters makes it possible to increase the quantity of data about signal fluctuations and to better localize its characteristic intervals compared with traditional discrete wavelets that operates with one low-frequency and one high-frequency filters. The principle of wavelet transform is based on a multiscale analysis. Basic functions are scaled and shifted along the time axis and by amplitude. A feature of the represented wavelet transform is the using of basic functions of new spectral transforms. These are functions of a symmetric transform on finite intervals and transform at oriented basis. The system of these functions is orthogonal and contains Np discrete functions of different shapes. One of these functions is a low-pass filter, and all the others are high-pass filters. Sphere of application of wavelet transforms with N basic functions is diagnostics of semiconductor converters, predictive energy-efficient control of energy consumption, analysis of bio-telemetric signals, processing and transmission of images and video signals.Ref. 7, fig. 1, tabl. 3.

Explicit and implicit LES closures for Burgers turbulence

In this work, we perform an aposteriori error analysis on implicit and explicit large eddy simulation closure models for solving the Burgers turbulence problem. Our closure modeling efforts include both functional and structural models equipped with various low-pass filters. We introduce discrete binomial smoothing filters and an enhanced version of the Van Cittert algorithm to accelerate the convergence of approximate deconvolution processes including regularization and relaxation filtering approaches. Our implicit modeling efforts consist of various high-order schemes including compact and non-compact fifth-order upwind schemes as well as weighted essential non-oscillatory (WENO) and compact reconstructed WENO (CRWENO) schemes, and the resulting schemes are shown to effectively converge to the direct numerical simulation (DNS) for increasing resolutions. Comparing with DNS and underresolved DNS computations, our numerical assessments illustrate the ability of these methods to capture the energy content near grid cut-off scale.

Implementation of fractional order filters discretized by modified Fractional Order Darwinian Particle Swarm Optimization

Digital systems are placed at the core of information technology and they are used extensively in electronics. The digital filter realization has become a central topic of signal processing studies. This paper presents a discrete IIR filter design method for approximate realization of fractional order continuous filters in digital systems. For this purpose, Fractional Order Darwinian Particle Swarm Optimization (FODPSO) method is modified to provide better fitting of a discrete IIR filter function to a fractional order continuous filter and we implemented a hybrid version of FODPSO method, where the initial particle generation is carried out by arithmetical candidate point selection technique of the Base Optimization Algorithm (BaOA). This modification expands the search range of the FODPSO and thus the optimized discrete IIR filter can provide better approximation to amplitude response of fractional order continuous filter functions. In the paper, several illustrative examples are presented to demonstrate the performance of proposed methods.

A Review to the Stability of Discrete Time State-Space Filters using Saturation Non-Linearity

A Review to the Stability of Discrete Time State-Space Filters using Saturation Non-Linearity

Accurate continuous–discrete unscented Kalman filtering for estimation of nonlinear continuous-time stochastic models in radar tracking

This paper presents a new state estimation technology grounded in the unscented Kalman filtering for nonlinear continuous-time stochastic systems. The resulting accurate continuous–discrete unscented Kalman filter is based on adaptive solvers with automatic global error control for treating numerically the moment differential equations arising in the mean and covariance calculation of propagated Gaussian density. It is intended for an accurate and robust state estimation in nonlinear continuous–discrete stochastic systems of various sorts, including in radar tracking models. This new filter is examined in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn. The latter is considered to be a challenging one for testing nonlinear filtering algorithms. For comparison, we also examine such efficient state estimators as the accurate continuous–discrete extended Kalman filter, the continuous–discrete unscented Kalman filter and the mixed-type accurate continuous–discrete extended-unscented Kalman filter designed earlier, but further modified in the present study. The comparison is fulfilled in terms of accuracy and efficiency of estimating the state in the mentioned air traffic control scenario.

Design of Optimized Minimum Inductor Bandpass Filters

A design methodology for optimized minimum inductor bandpass filters (BPFs) is presented. Design curves are provided to determine the filter order for a required out-of-band rejection as a function of bandwidth (BW). Coefficients for BWs from 10% to 100% in steps of 10% for different filter orders and two different transmission zero placements are provided. For both cases, the required in-band return loss is larger than 10 dB. Using the derived coefficients, filters with required rejections can be designed for a given center frequency. To validate the design methodology, five discrete element filters with different BWs are designed and fabricated at a center frequency of 1.5 GHz. Furthermore, to show the application of the minimum inductor filters in complementary metal–oxide–semiconductor (CMOS), an S-band BPF in 0.13- $\mu \text{m}$ CMOS, with 60% BW, is designed and fabricated. The out-of-band rejection of the fabricated filter is larger than 50 dB.

Curvature Filters Efficiently Reduce Certain Variational Energies.

In image processing, the rapid approximate solution of variational problems involving generic data-fitting terms is often of practical relevance, for example in real-time applications. Variational solvers based on diffusion schemes or the Euler-Lagrange equations are too slow and restricted in the types of data-fitting terms. Here, we present a filter-based approach to reduce variational energies that contain generic data-fitting terms, but are restricted to specific regularizations. Our approach is based on reducing the regularization part of the variational energy, while guaranteeing non-increasing total energy. This is applicable to regularization-dominated models, where the data-fitting energy initially increases, while the regularization energy initially decreases. We present fast discrete filters for regularizers based on Gaussian curvature, mean curvature, and total variation. These pixel-local filters can be used to rapidly reduce the energy of the full model. We prove the convergence of the resulting iterative scheme in a greedy sense, and we show several experiments to demonstrate applications in image-processing problems involving regularization-dominated variational models.

Automated Detection and Tracking of Cell Clusters in Time-Lapse Fluorescence Microscopy Images

Fluorescence microscopy imaging of live cells has drawn the attention of many researchers in the past decade. Because of the large amount of image data produced by a fluorescence microscope, automated cell detection and tracking algorithms have become an emerging need to help cell biologists visualize and analyze cell kinematics such as changes in cell population caused by proliferation, attachment, and differentiation. This study uses the adaptive background subtraction technique to detect cell clusters in time-lapse fluorescence microscopy images and the discrete Kalman filter to track the position, motion, merging and splitting of these clusters. A set of two-dimensional (2D) time-series images from mouse embryonic stem cells obtained using wide-field microscopy and a set of three-dimensional (3D) time-series from HeLa cells obtained using confocal microscopy are used to demonstrate that biologists can visualize various quantitative measures such as motion, merging and splitting, centroids, areas, and growth rates of cell clusters to acquire useful information through 2D and 3D interfaces.

Применение метода Пикара для вычисления ковариационных матриц в дискретных фильтрах Калмана

Применение метода Пикара для вычисления ковариационных матриц в дискретных фильтрах Калмана

고속에서 동작하는 이산 루프필터를 가진 PLL

고속에서 동작하는 이산 루프필터를 가진 PLL

Estimating the Positive and Negative Jumps of Asset Returns Via Kalman Filtering. The Case of Nasdaq Index

The daily asset (log) return is considered to consist of two parts, the positive and negative jump. These jumps are determined by the arrival of positive and negative news in the market, are not observable and their differences define the asset returns. In order to estimate the jumps, the basic discrete time-homogeneous linear Kalman filter is applied, in which all the noises are assumed to be normally distributed. Then, under the assumption that the estimated jumps have to be non-negative, the method of their pdfs’ truncation, according to the non-negativity constraints, is used, and it is accompanied by appropriate scaling. The fitting of the model is justified by examining the fitting of the estimated returns to the empirical ones. For that purpose, the daily Nasdaq returns during the three year period 2006-2008 are used.

Improved inverse filter for the correction of distorted measured cutting forces

The cutting forces sampled from machining processes may be distorted by the dynamic response of measuring system. Traditional methods, whether discrete inverse filter or Kalman filter, may result in accuracy loss due to inaccurate approximation of transfer function. This paper proposes an improved inverse filter to achieve accurate and efficient correction of the distorted cutting forces. Failure behaviors of traditional methods are analyzed in-depth first, and then, a spline curve-based interpolation scheme is proposed to approximate the transfer function of the measuring system. The transfer function corresponding to the frequencies of the measured cutting forces obtained by this method can be close to the actual response of the cutting system to the most degree. As a result, the corrected cutting forces can well reflect the actual physical response of the machining processes. To show the advantage of the proposed method, both the improved inverse filter and traditional Kalman filter are utilized to correct the cutting forces measured from three tests. Thorough comparison implies that both methods can give good and consistent corrected results in most cases, while Kalman filter will lose correction accuracy if the transfer function cannot be fitted so well to be sufficiently close to the measured result. Especially, calculation procedure turns out that the improved inverse filter is better in efficiency than Kalman filter.

Feasibility of filter‐based NIR spectroscopy for the routine measurement of olive oil fruit ripening indices

The aim of this work was to apply and validate a NIR spectrometer based on a discrete filter system for the rapid measurement of the moisture, oil, sugar, and phenolic compounds contents of olive oil fruits. The batches of olive oil fruits were collected during seven crop seasons from several farms located in Tuscany and then they were crushed into olive paste. The water content was measured gravimetrically, oil content was measured using the Soxhlet method, sugar content was measured enzymatically and phenolic compound content was measured by HPLC. NIR spectra were recorded from 1400 to 2400 nm at 19 selected wavelengths. Calibration and validation models were processed using PLS regression. In PLS models built for moisture, oil, and sugar contents, the r2 in calibration ranged between 0.90 and 0.93 with low standard error of calibration (SEC) values (i.e. 2.5, 3.6 and 4.0, respectively). For these parameters the standard error of prediction (SEP) and the standard error of laboratory (SEL) values proved to be comparable (i.e. 2.4 vs. 3.2, 6.0 vs. 4.4, and 6.7 vs. 4.7, respectively). Instead, the calibration and validation results concerning the phenolic compounds were not satisfactory, probably because the necessary wavelengths in the section of absorbance from 1100 to 1400 nm were not covered.Practical applications: NIR spectrometers based on discrete filter systems may be interesting since they are cost‐saving compared to the more sophisticated FT‐NIR and NIR‐AOTF instruments (i.e. the cost is approximately half). Our study also showed that with this instrument it was possible to build some effective models for predicting moisture, oil, and sugar contents in olive paste. The results obtained for moisture and oil contents are comparable with those obtained with other spectrometers, and a predictive model was obtained for sugar content for the first time. Instead the tool did not prove suitable for obtaining predictive models for total phenolic compounds or oleuropein contents. The additional use of a filter‐based NIR spectrometer is therefore to be suggested to rapidly monitor olive fruit ripening on the basis of moisture, oil, and sugar contents.The used filter‐based NIR spectrometer, relevant spectra, and calibration‐validation results.

An efficient implementation of a high-order filter for a cubed-sphere spectral element model

A parallel-scalable, isotropic, scale-selective spatial filter was developed for the cubed-sphere spectral element model on the sphere. The filter equation is a high-order elliptic (Helmholtz) equation based on the spherical Laplacian operator, which is transformed into cubed-sphere local coordinates. The Laplacian operator is discretized on the computational domain, i.e., on each cell, by the spectral element method with Gauss–Lobatto Lagrange interpolating polynomials (GLLIPs) as the orthogonal basis functions. On the global domain, the discrete filter equation yielded a linear system represented by a highly sparse matrix. The density of this matrix increases quadratically (linearly) with the order of GLLIP (order of the filter), and the linear system is solved in only O(Ng) operations, where Ng is the total number of grid points. The solution, obtained by a row reduction method, demonstrated the typical accuracy and convergence rate of the cubed-sphere spectral element method. To achieve computational efficiency on parallel computers, the linear system was treated by an inverse matrix method (a sparse matrix–vector multiplication). The density of the inverse matrix was lowered to only a few times of the original sparse matrix without degrading the accuracy of the solution. For better computational efficiency, a local-domain high-order filter was introduced: The filter equation is applied to multiple cells, and then the central cell was only used to reconstruct the filtered field. The parallel efficiency of applying the inverse matrix method to the global- and local-domain filter was evaluated by the scalability on a distributed-memory parallel computer. The scale-selective performance of the filter was demonstrated on Earth topography. The usefulness of the filter as a hyper-viscosity for the vorticity equation was also demonstrated.

Vision-based Markov localization for long-term autonomy

Lifelong autonomous operation has gained much attention in the field of mobile robotics in recent years. In the context of robot navigation based on vision, lifelong applications include scenarios with substantial perceptual changes due to changes in season, illumination and weather. In this paper, we present an approach to localize a mobile robot, equipped with a low frequency camera, with respect to an image sequence recorded in a different season. Our approach employs a discrete Bayes filter with a sensor model based on whole image descriptors. We compute a similarity matrix over all image descriptors and leverage the sequential nature of typical image streams with a flexible transition scheme in the Bayes filter framework. Since we compute a probability distribution over the entire state space, our approach can handle complex trajectories that may include same season loop-closures as well as fragmented sub-sequences. Furthermore, we show that decorrelating the similarity matrix results in an improved localization performance. Through an extensive experimental evaluation on challenging datasets we demonstrate that our approach outperforms state-of-the-art techniques.

Joint interpolation for LTE downlink channel estimation in very high‐mobility environments with support vector machine regression

In this study, the estimation of fast-fading long term evolution (LTE) downlink channels in high-speed applications of LTE advanced is investigated by the authors. A robust channel estimation and interpolation algorithm is essential in order to adequately track the fast time-varying channel response. In this contribution, the multipath fast-fading channel is modelled as a discrete, tapped-delay and finite impulse response filter. Using support vector machine regression (SVR), they develop an extended algorithm to jointly estimate the complex-valued channel frequency response in time and frequency domains, in the presence of fading and non-linear noise from the transmission of known pilot symbols. Furthermore, the channel estimates at the known pilot symbols are interpolated to the unknown data symbols by using the non-linear SVR approach exploiting kernel features. This study integrates both channel estimation at pilot symbols and interpolation at data symbol into the complex SVR interpolation method. The bit error rate and mean square error performances of the authors’ fast-fading channel estimation scheme is demonstrated via simulation for LTE downlink with 64-QAM modulation and 500 km/h velocity under non-linearities.

Optimal continuous-discrete nonlinear finite memory filter with a discrete predictions

We consider the following problem: using the discrete time measurements of the state variables of a continuous stochastic object and obtain the most precise estimate of these variables. To accelerate the estimating process, we synthesize the optimal structure of a discrete final-dimensional nonlinear filter with a piecewise-constant prediction, remembering the last few measurements in its state vector. The dimension of this vector (i.e., the filter memory volume) can be selected arbitrarily to balance the desired measurement precision and available processing speed for the measurements. We obtain the mean-square optimal structure functions of the filter expressed via the corresponding probability distributions and a chain of Fokker—Planck—Kolmogorov equations to find those distributions. We describe the procedure to obtain the structural functions of the filter numerically by means of the Monte-Carlo method. Also, we provide simple numeric-analytic approximations to the proposed filters: they are compared with approximations to the known filters. An example of the construction of such approximations is considered.

СИНТЕЗ НЕРЕКУРСИВНЫХ ДИСКРЕТНЫХ ФИЛЬТРОВ ВО ВРЕМЕННОЙ ОБЛАСТИ

СИНТЕЗ НЕРЕКУРСИВНЫХ ДИСКРЕТНЫХ ФИЛЬТРОВ ВО ВРЕМЕННОЙ ОБЛАСТИ