Nonlinear Filtering Method Research Articles

Accuracy of sensor bias estimation and its relationship with Allan variance

The paper discusses the relationship between Allan variance and error variance of sensor bias estimate obtained by averaging over a certain period. Allan variance is shown to coincide with this variance in some cases. Bias estimation accuracy can be improved using nonlinear filtering methods in the conditions of uncertain error model.

Recent developments in accuracy and stability improvement of nonlinear filter methods for DNS and LES of compressible flows

Recent developments in accuracy and stability improvement of nonlinear filter methods for DNS and LES of compressible flows

Control of DC–DC Converter and DC Motor Dynamics Using Differential Flatness Theory

The article proposes a method for nonlinear control of the dynamical system that is formed by a DC–DC converter and a DC motor, making use of differential flatness theory. First it is proven that the aforementioned system is differentially flat which means that all its state vector elements and its control inputs can be expressed as differential functions of primary state variables which are defined to be the system’s flat outputs. By exploiting the differential flatness properties of the model its transformation to a linearized canonical (Brunovsky) form becomes possible. For the latter description of the system one can design a stabilizing feedback controller. Moreover, estimation of the nonmeasurable state vector elements of the system is achieved by applying a new nonlinear Filtering method which is known as Derivative-free nonlinear Kalman Filter. This filter consists of the Kalman Filter recursion applied on the linearized equivalent model of the system and of an inverse transformation that is based on differential flatness theory and which enables to obtain estimates of the initial nonlinear state-space model. Moreover, to compensate for parametric uncertainties and external perturbations the filter is redesigned as a disturbance observer. By estimating the perturbation inputs that affect the joint model of the DC–DC converter and of the DC motor their compensation becomes possible. The efficiency of the proposed control scheme is further confirmed through simulation experiments.

Method of image filtering using singular decomposition and the surrogate data technology

A method for nonlinear filtering of additive noise on digital image has been proposed. This method is based on presenting the image by its matrix singular decomposition and applying the surrogate data technology to components of the image. The proposed method ensures a superior resolution as compared to most common methods of window filtering that is corroborated by the results of simulation modeling.

Impact load identification for composite structures using Bayesian regularization and unscented Kalman filter

In structural health monitoring of composite structures, one important task is to detect and identify the low-velocity impact events, which may cause invisible internal damages. This paper presents a novel approach for simultaneously identifying the impact location and reconstructing the impact force time history acting on a composite structure using dynamic measurements recorded by a sensor network. The proposed approach consists of two parts: (1) an inner loop to reconstruct the impact force time history and (2) an outer loop to search for the impact location. In the inner loop, a newly developed inverse analysis method with Bayesian inference regularization is employed to solve the ill-posed impact force reconstruction problem using a state-space model. In the outer loop, a nonlinear unscented Kalman filter (UKF) method is used to recursively estimate the impact location by minimizing the error between the measurements and the predicted responses. The newly proposed impact load identification approach is illustrated by numerical examples performed on a composite plate. Results have demonstrated the effectiveness and applicability of the proposed approach to impact load identification. Copyright © 2016 John Wiley & Sons, Ltd.

A New Estimation at Completion of Project’s Time and Cost Approach Based on Particle Filter

Estimation at completion is an important tool for supervising the performance and risk of each project, in order to estimate the project completion time and final cost. This calculation is one of the most important goals of project managing. In this paper, a new estimation at completion approach is presented for estimation of finishing time and final cost of the project. The innovation of this paper can be organized as using particle filter as one of the strong nonlinear filtering methods for next estimation state of the system by using smoothed data which is done by filter itself, based on autoregressive fitted model. After estimating next states, it will be possible to predict system’s reaction in later seconds and the time and cost of finishing the project are estimated for comparing the performance and efficiency of invented method. The simulation results demonstrate the performance of proposed scheme in comparison with older approach.

A robust dynamic state estimation for droop controlled islanded microgrids

This paper proposes a nonlinear particle filter (PF) method for dynamic state estimation in droop-controlled islanded microgrids (IMGs). The PFs are normally applied to systems that (1) have highly nonlinear system dynamics, and (2) do not require the additive process or observation noise to be Gaussian. This flexibility allows the PFs to handle noisy measurements from a range of varied distributions, thereby increasing its robustness. To that end, a nonlinear dynamic state model has been developed in this work for droop-controlled IMGs. Additive noise has been incorporated into the state model to account for the error in its accuracy. Monte Carlo simulations have been conducted to verify that the PF accurately tracks the IMG state variables in spite of using significantly corrupted state and observation values. A comparison between the PF and unscented Kalman filter (UKF) has been carried out to test the effectiveness and robustness of the proposed methodology.

New advances in visual computing for intelligent processing of visual media and augmented reality

Visual imagery constitutes the most important sensory information for humans. The entire field of acquiring, analyzing and synthesizing visual data by means of computers is called visual computing. It has an extraordinarily wide range of applications, including for example: industrial quality control, street view and driver assistance systems, robot navigation, multimedia systems, and computer games. Visual computing comprises four key areas: computer vision and image processing, computer graphics, virtual and augmented reality, and visualization. It requires deep, interdisciplinary scientific knowledge, in particular in computer science, mathematics, physics, engineering, and cognitive sciences. It tackles high level tasks such as editing and composition of visual content [1] and recognition of sematic content [2–5], as well as basic low level problems such as denoising [6,7] and decomposing [8,9] images, video and 3D shapes. Denosing is often a first step to provide high quality inputs to more complicated tasks such as panoramic image stitching to construct a street view database, and image understanding in computer vision. The object of image denoising is to reduce the noise level, while preserving edges and textures as much as possible. The necessary processing may be done in the image domain, or frequency domain using FFT or wavelets. Recent studies have considered how to represent contour information in images using ridgelets, curvelets and contourlets, as well as finding suitable threshold schemes to remove noise [6]. There is also corresponding work on mesh denosing, which finds structures in terms of positional and normal features [7]. Image decomposition concerns the splitting of an image into two or more components. A fundamental goal in image analysis and computer vision is to extract meaningful components from an image, for tasks such as scene understanding, generation of visual media and many intelligent applications of visual content. Various image decomposition strategies exist. One approach is cartoon and texture decomposition: ref. [9] gave a good survey on the existing decomposition models and extended the nonlinear filter method to decompose an image into three components: the cartoon component, i.e. the main geometric structures, the oscillatory component, or texture, and noise. An image can also be decomposed into a lighting image and a reflectance image known as the intrinsic image. Automatic intrinsic image decomposition remains a significant challenge, particularly for real-world scenes. Recent advances to this longstanding problem are data-driven methods based on large scale datasets of ground truth data. For example, ref. [8] built a dataset of more than 5000 labeled intrinsic images as a basis for a decomposition algorithm, as demonstrated in Figure 1. Computer understanding of scenes or objects within them is a fundamental problem in computer vision, and is crucial to intelligent applications based on visual content. For example, efficient recognition of objects and scene understanding of a live video captured by cameras on a car allows a driver assistance system to instantly feed appropriate information to the driver, or to the cars controls directly.

Real-time rendering of refracting transmissive objects with multi-scale rough surfaces

This paper presents an efficient approach to render refracting transmissive objects with multi-scale surface roughness, under distant illumination. To correctly capture both fine-scale surface details and large-scale appearances, and enable real-time processing at various viewing resolutions, we first divide the surface roughness into three levels, namely, micro-scale, meso-scale and macro-scale. Each scale of roughness is modeled and evaluated using different strategies, and the overall roughness is approximated by their spherical convolution. Then, this representation is incorporated into a microfacet-based BTDF model, and multi-scale rough refractions are simulated on both front and back sides of an object as light enters and exits the object. In particular, non-linear filtering methods are applied to both macro-scale geometries and meso-scale bumps to reduce aliasing when viewed across a range of distances. Finally, experimental results illustrate that our approach produces resolution-dependent refraction effects that match super-sampled ground truth, while achieving a speed up of several orders of magnitude with hardware acceleration.

Nonlinear Feedback Control of Three-Phase Inverter Systems Using the Derivative-Free Nonlinear Kalman Filter

The use of three-phase voltage inverters (DC to AC converters) is frequently met in the electric power system, such as in the connection of photovoltaics with the rest of the grid. The paper proposes a nonlinear feedback control method for three-phase inverters, which is based on differential flatness theory and a new nonlinear filtering method under the name Derivative-free nonlinear Kalman Filter. First, it is shown that the inverter’s dynamic model is a differentially flat one. This means that all its state variables and the control inputs can be written as functions of a single algebraic variable which is the flat output. By exploiting differential flatness properties it is shown that the inverter’s model can be transformed to the linear canonical (Brunovsky’s) form. For the latter description the design of a state feedback controller becomes possible, e.g. using pole placement methods. Moreover, to estimate the non-measurable state variables of the linearized equivalent of the inverter, the Derivative-free nonlinear Kalman Filter is used. This consists of the Kalman Filter recursion applied on the linearized inverter’s model and of an inverse transformation that is based on differential flatness theory, which enables to compute estimates of the state variables of the initial nonlinear system. Furthermore, by redesigning the aforementioned filter as a disturbance observer it becomes also possible to estimate disturbance terms that affect the inverter and subsequently to compensate for them. The performance and disturbance rejection capability of the proposed nonlinear feedback control scheme is evaluated through simulation experiments.

Fire Localization Based On Range-Range-Range Model for Limited Interior Space

Fire localization problem is studied based on temperature data taken by wireless sensor arrays and a novel range-range-range (RRR) model is proposed to overcome shortcomings, which exists in the current range-point-range (RPR) model in this paper. For a single sensor array composed of four sensors deployed with a square, three angle estimates on fire bearing can be obtained using far-field localization technology. These angle estimates are used to get their statistical mean and variance at a single time. Based on the statistical features, we propose two fire localization methods under the RRR frame, which are angle bisector and nonlinear filtering methods. For the angle bisector method, a recursive formula of the mean and variance is presented in time series so that global angle estimates can be used. Furthermore, a fire coordinate estimate, which is actually the center of estimated-range circle, can be taken by use of intersecting two angle bisectors from two sensor arrays. Moreover, the estimation of a radius for the estimated fire region is also realized. In order to improve localization accuracy and robustness of fire estimation to non-Gaussian noise component, the fire localization is taken as a nonlinear bearing-only tracking issue for the case where the covariance of measurement noise is unknown and a specific variational Bayesian adaptive square-cubature Kalman filter is proposed to estimate the coordinate of the center. These proposed algorithms not only provide some new points of view on the fire localization for limited interior space, but are helpful for practical fire fighting applications.

Numerical analysis of rating transition matrix depending on latent macro factor via nonlinear particle filter method

We propose a new nonlinear filtering model for a better estimation of credit rating transition matrix consistent with the hypothesis that rating transition intensities as well as dynamics of financial asset prices depend on some unobservable macroeconomic factor. We attempt a branching particle filter method to numerically obtain the conditional distribution of the latent factor. For an illustration, we analyze a rating transition history of Japanese enterprises. As a result, we realize that our model can capture some contagion effect of credit events and an interpolative role of financial market information on the rating transition intensities.

Nonlinear Filter Smoothing for Aeromagnetic Vertical First-Order Derivative Contour Mapping on the Scale of 1:250,000

By the analysis of two filter smooth method principle on the platform of Oasis Montaj software,the author of the thesis selected one dimension nonlinear filter method to remove the noise signal of aeromagnetic vertical first-order derivative data, not only smoothing the contour but also enhancing the geological structure edge signal effectively.

Water Distribution System Burst Detection Using a Nonlinear Kalman Filter

AbstractA water distribution system burst from a sudden pipe failure results in water loss and disruption of customer service. Artificial neural networks, state estimation, and statistical process control (SPC) have been applied to detect bursts. However, system operational condition changes such as the set of operating pumps and valve closures greatly complicates the detection problem. Thus, to date applications have been limited to networks that are supplied by gravity or under consistent operation conditions. This study seeks to overcome these limitations using a nonlinear Kalman filter (NKF) method to identify system condition, estimate system state, and detect bursts.

Image Restoration Based on Morphological Operations

Image processing including noise suppression, feature extraction, edge detection, image segmentation, shape recognition, texture analysis, image restoration and reconstruction, image compression etc uses mathematical morphology which is a method of nonlinear filters. It is modulated from traditional morphology to order morphology, soft mathematical morphology and fuzzy soft mathematical morphology. This paper is covers 6 morphological operations which are implemented in the matlab program, including erosion, dilation, opening, closing, boundary extraction and region filling.

A modified optical flow algorithm based on bilateral-filter and multi-resolution analysis for PIV image processing

Particle Image Velocimetry (PIV) technology is an efficient and powerful testing method to investigate the characteristics of flow field. The topic of PIV post-processing techniques has roused researchers׳ wide concern for its great influence on the success of flow field measurement. The traditional correlation algorithms have their innate defects. In the present study, a modified optical flow algorithm is proposed to overcome these deficiencies based on bilateral-filter and multi-resolution analysis of PIV image processing. The algorithm is designed based on the principle of multilayer segments, in which the isotropic diffusion method is employed to calculate the low-resolution layer of the image and the nonlinear filtering method is used to process the high-resolution layer. This new algorithm can reduce image noise effectively and maintain the details of the image boundary. In addition, the design of nonlinear filter makes the optical flow equation simpler, and the optimal velocity mapping factor method needs less iteration and reduces the computational load. The algorithm is first tested on synthetic time-resolved channel flow images, and the computational results from the simulated particle images are found to be in reasonable agreement with the given simulated data. The algorithm is then applied to images of actual up-channel flow, and the results also confirmed that the algorithm proposed in the present study has good performance and reliability for post-processing PIV images.

Nonlinear estimation of the navigation parameters of an object based on the integration of satellite and tracker measurements

The problem of the high-precision estimation of the navigation parameters of a mobile object by eliminating the most significant measurement noise in the process of integration of satellite and tracker navigation measurements and the application of nonlinear filtering methods is solved.

一种基于多尺度分析和非线性滤波的光流算法

PIV后处理技术对于PIV流场实验测量的结果有着重要的影响而成为研究热点。传统的互相关算法有着许多先天缺陷，本文提出的基于多尺度分析和非线性滤波的修正光流算法能够克服这些的缺陷，该算法以多层细化理论为基础，对低分辨率序列采用同性扩散算法，而高分辨率序列采用非线性扩散方法。同时，该算法被应用到实际测量的二维向上槽道流PIV图像中，结果表明该算法对于PIV图像的后处理具有良好的性能和可靠性。 PIV post-processing techniques have a great influence on the success of flow field measurement and have aroused the researchers’ wide concern. The traditional correlation algorithms have their congenital defects. In the present study, a modified optical flow algorithm is proposed to overcome these deficiencies based on bilateral-filter and multi-resolution analysis for PIV image processing. The algorithm is designed on the basis of the principle of multilayer segments, in which the isotropic diffusion method is employed to calculate the low-resolution layer of the image and the nonlinear filtering method is used to process the high-resolution layer. This new algorithm can reduce image noise effectively and maintain the details of the image boundary. The algorithm is applied to images of actual up-channel flow, and the results also confirmed that the algorithm proposed in the present study has good performance and reliability for post-processing PIV images.

Comparative Study of Three High Order Schemes for LES of Temporally Evolving Mixing Layers

AbstractThree high order shock-capturing schemes are compared for large eddy simulations (LES) of temporally evolving mixing layers for different convective Mach numbers ranging from the quasi-incompressible regime to highly compressible supersonic regime. The considered high order schemes are fifth-order WENO (WENO5), seventh-order WENO (WENO7) and the associated eighth-order central spatial base scheme with the dissipative portion of WENO7 as a nonlinear post-processing filter step (WENO7fi). This high order nonlinear filter method of Yee & Sjögreen is designed for accurate and efficient simulations of shock-free compressible turbulence, turbulence with shocklets and turbulence with strong shocks with minimum tuning of scheme parameters. The LES results by WENO7fi using the same scheme parameter agree well with experimental results compiled by Barone et al., and published direct numerical simulations (DNS) work of Rogers & Moser and Pantano & Sarkar, whereas results by WENO5 and WENO7 compare poorly with experimental data and DNS computations.

Bayesian Quickest Detection in Sensor Arrays

We study Bayesian quickest detection problems with sensor arrays. An underlying signal is assumed to gradually propagate through a network of several sensors, triggering a cascade of interdependent change-points. The aim of the decision maker is to centrally fuse all available information to find an optimal detection rule that minimizes Bayes risk. We develop a tractable continuous-time formulation of this problem focusing on the case of sensors collecting point process observations and monitoring the resulting changes in intensity and type of observed events. Our approach uses methods of nonlinear filtering and optimal stopping and lends itself to an efficient numerical scheme that combines particle filtering with a Monte Carlo–based approach to dynamic programming. The developed models and algorithms are illustrated with plenty of numerical examples.