Limiting optimal adaptive filtering with unknown disturbance covariance

The accuracy of estimating the variance of the Kalman-Bucy filter depends essentially on disturbance covariance matrices and measurement noise. The main difficulty in filter design is the lack of necessary statistical information about the useful signal and the disturbance. Filters whose parameters are tuned during active estimation are classified with adaptive filters. The problem of adaptive filtering under parametric uncertainty conditions is studied. A method for designing limiting optimal Kalman-Bucy filters in the case of unknown disturbance covariance is presented. An adaptive algorithm for estimating disturbance covariance matrices based on stochastic approximation is described. Convergence conditions for this algorithm are investigated. The operation of a limiting adaptive filter is exemplified.     

Multiresolutional Maneuvering Target Tracking Fusion Algorithm Based on Singular Sensor and Multipale Models

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正交小波变换的向量空间算法

本文揭示了一个事实，小波不仅可构成Ｌ２空间中的正交基，小波分解与重构滤波还可产生Ｎ维空间中的正交基．在本文提出修改的小波变换算法之下，Ｎ点信号的小波变换等价于Ｎ维空间中的正交变换．用该算法进行信号或图象压缩，无需对信号或图象进行周期延拓，可严格地在Ｎ维空间中进行．     

利用非线性提升的信号去噪

本文提出了一种基于非线性滤波和提升格式进行信号去噪的算法。利用提升格式设计的灵活性取非线性滤波为预测算子 ,数值算例表明该方法的去噪效果优于仅使用非线性滤波去噪。     

Comparison of adaptive filters for gas turbine performance monitoring

Kalman filters are widely used in the turbine engine community for health monitoring purpose. This algorithm has proven its capability to track gradual deterioration with a good accuracy. On the other hand, its response to rapid deterioration is either a long delay in recognising the fault, and/or a spread of the estimated fault in several components. The main reason of this deficiency lies in the transition model of the parameters that assumes a smooth evolution of the engine’s condition. The aim of this contribution is to compare two adaptive diagnosis tools that combine a Kalman filter and a secondary system that monitors the residuals. This auxiliary component implements on one hand a covariance matching scheme and on the other hand a generalised likelihood ratio test to improve the behaviour of the diagnosis tool with respect to abrupt faults.     

Extended Kalman filters using explicit and derivative-free local linearizations

We propose three variants of the extended Kalman filter (EKF) especially suited for parameter estimations in mechanical oscillators under Gaussian white noises. These filters are based on three versions of explicit and derivative-free local linearizations (DLL) of the non-linear drift terms in the governing stochastic differential equations (SDE-s). Besides a basic linearization of the non-linear drift functions via one-term replacements, linearizations using replacements through explicit Euler and Newmark expansions are also attempted in order to ensure higher closeness of true solutions with the linearized ones. Thus, unlike the conventional EKF, the proposed filters do not need computing derivatives (tangent matrices) at any stage. The measurements are synthetically generated by corrupting with noise the numerical solutions of the SDE-s through implicit versions of these linearizations. In order to demonstrate the effectiveness and accuracy of the proposed methods vis-à-vis the conventional EKF, numerical illustrations are provided for a few single degree-of-freedom (DOF) oscillators and a three-DOF shear frame with constant parameters.     

Vibration testing for anomaly detection

In this paper we propose an efficient method to reconstruct a small inclusion buried inside a body using the perturbation of modal parameters measured on the boundary of the body. We design a reconstruction algorithm based on the asymptotic expansions of the eigenvalue perturbations obtained by Ammari and Moskow (Math. Meth. Appl. Sci. 2003; 26 :67–75). We then implement this algorithm and demonstrate its viability and limitations. Copyright © 2008 John Wiley & Sons, Ltd.     

基于单传感器多模型的多分辨目标跟踪融合算法

Multiresolutional signal processing has been employed in image processing and computer vision to achieve improved performance that cannot be achieved using conventional signal processing techniques at only one resolution level[1,2,5,6]. In this paper,we have associated the thought of multiresolutional analysis with traditional Kalman filtering and proposed A new fusion algorithm based on singular Sensor and Multipale Models for maneuvering target tracking.     

通带可调相位 FIR 数字滤波器及其设计

常见的 FIR 数字滤波器大致可分为两类:一类是线性相位滤波器;另一类是极小相位滤波器,这两种类型的滤波器,其相位响应均不可调.第一种滤波器,其群延迟为((N-1)T)/2,其中 N 为滤波器长度,T 为采样周期.以 N=60,T=0.2秒的线性相位滤波器为例,它的相位响应为     

Integer solution of a set of bilinear equations

An efficient method for a design of transmultiplexer filters is suggested. The perfect reconstruction conditions lead to the bilinear equations for FIR filters coefficients. The method of solving these equations results from the presented theorem. Usefulness of the algorithm in fixed-point arithmetic is the crucial issue. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A dynamical systems framework for intermittent data assimilation

We consider the problem of discrete time filtering (intermittent data assimilation) for differential equation models and discuss methods for its numerical approximation. The focus is on methods based on ensemble/particle techniques and on the ensemble Kalman filter technique in particular. We summarize as well as extend recent work on continuous ensemble Kalman filter formulations, which provide a concise dynamical systems formulation of the combined dynamics-assimilation problem. Possible extensions to fully nonlinear ensemble/particle based filters are also outlined using the framework of optimal transportation theory.     

基于截断加权基追踪模型的迭代支撑探测算法

迭代支撑探测算法是基于截断的基追踪(Basis Pursuit,BP)模型的一种l_1最小化信号重构算法,它可以实现信号的快速重构并且所需要的观测值比经典的L1算法以及迭代加权L1算法更少.本文针对非零元具有快速退化分布性质的稀疏信号,提出了一种改进算法一一基于截断的加权BP模型的迭代支撑探测算法.在迭代的过程中,改进的算法探测原信号支撑集中元素的同时调整重构模型的权值,使得重构模型更有利于实现信号的精确重构.根据所考虑的信号的非零元具有快速退化分布性质这样的先验信息,利用阈值法则探测原信号支撑集中的元素.最后通过Matlab数值实验实现了算法,验证了基于截断的加权BP模型的迭代支撑探测算法比迭代加权L1算法需要的观测值更少,并且比迭代加权L1算法以及传统的迭代支撑探测算法需要更少的重构时间就可以实现信号的精确重构.     

Stochastic independent modal-space control of distributed-parameter systems

A method capable in theory of estimating and controlling all the modes of a distributed-parameter system is presented. A linear distributed estimator using a distributed Kalman function is defined. It is shown that a particular choice of the Kalman function, in conjunction with the independent modal-space control method, leads to an infinite set of independent second-order modal-space Kalman filters cascaded with spatial modal filters. Independent modal-space Kalman filters experience no computational difficulties, regardless of the order of the system, and closed-form solutions for the modal Kalman gain matrices can be obtained with relative ease, making real-time implementation feasible. It is also shown that the independent modal-space Kalman filters are theoretically free of observation spillover.This work was supported in part by NSF Grant No. PFR-80-20623.     

A novel approach using parallel Kalman filters in time and frequency estimation

In the present information based knowledge society, accurate knowledge of time and frequency plays a fundamental role. For many applications, real time estimates of the clocks time and frequency error are required. We have developed a novel approach for estimating time and frequency errors based on an assembly of clocks of varying quality. By using parallel Kalman filters we utilize all available measurements in the estimation. As these measurements are available with different delays, the Kalman filter produces estimates of different quality. One filtermay produce real-time estimates while another filter waits for delayed measurements. When new information becomes available, the parallel Kalman filters exchange information in order to keep the state matrices updated with the most recent information. In Kalman filtering, accurate modelling of the measurement system is fundamental. All the contributing clocks, as well as the time transfer methods, are modelled as stochastic processes. By using this methodology and by correctly modelling the contributing clocks, we obtain minimum mean square error estimators (MMSE) of the time and frequency errors of a specific clock at every epoch. In addition, we also determine the uncertainty of each time and frequency error estimate. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An exact minimum variance filter for a class of discrete time systems with random parameter perturbations

An exact, closed-form minimum variance filter is designed for a class of discrete time uncertain systems which allows for both multiplicative and additive noise sources. The multiplicative noise model includes a popular class of models (Cox-Ingersoll-Ross type models) in econometrics. The parameters of the system under consideration which describe the state transition are assumed to be subject to stochastic uncertainties. The problem addressed is the design of a filter that minimizes the trace of the estimation error variance. Sensitivity of the new filter to the size of parameter uncertainty, in terms of the variance of parameter perturbations, is also considered. We refer to the new filter as the ‘perturbed Kalman filter’ (PKF) since it reduces to the traditional (or unperturbed) Kalman filter as the size of stochastic perturbation approaches zero. We also consider a related approximate filtering heuristic for univariate time series and we refer to filter based on this heuristic as approximate perturbed Kalman filter (APKF). We test the performance of our new filters on three simulated numerical examples and compare the results with unperturbed Kalman filter that ignores the uncertainty in the transition equation. Through numerical examples, PKF and APKF are shown to outperform the traditional (or unperturbed) Kalman filter in terms of the size of the estimation error when stochastic uncertainties are present, even when the size of stochastic uncertainty is inaccurately identified.     

How to Get the Original Discrete Approximation for the Pyramid Algorithm of Multiresolution Decomposition

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The extended Kalman Filter and the unscented Kalman Filter for Material Parameter Identification with Application in Tunneling

We present in this work the use of the extended Kalman filter (EKF) and unscented Kalman filter (UKF) for identification of constitutive material parameters with application in mechanized tunneling. Although both filters are based on the principle of recursive least squares estimation, one differs from another in terms of where approximation is made. Whereas in the EKF first-order Taylor series expansion is used to approximate the nonlinear modeling equation, in the UKF approximation of the probability density of the state is made using a small number of well defined points. To validate the methods, we performed parameter identification of the Hardening Soil constitutive model used for describing the soil behavior in an tunnel excavation model. Both methods showed fast and stable convergence of the considered soil parameters - the four parameters of the Hardening Soil model. Although the EKF requires less number of forward calculations of the numerical model, the UKF is favored since it does not require calculation of the derivatives of the observables with respect to the identifying parameters. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A linearly convergent algorithm for sparse signal reconstruction

For the sparse signal reconstruction problem in compressive sensing, we propose a projection-type algorithm without any backtracking line search based on a new formulation of the problem. Under suitable conditions, global convergence and its linear convergence of the designed algorithm are established. The efficiency of the algorithm is illustrated through some numerical experiments on some sparse signal reconstruction problem.     

State of charge estimation for lithium-ion batteries based on adaptive dual Kalman filter

Accurate estimation of the battery state of charge (SOC) is of great significance for enhancing its service life and safety. In this study, based on the fractional-order equivalent circuit model of lithium-ion battery, the SOC estimation methods using dual Kalman filter (DKF) and dual extended Kalman filter (DEKF) are simulated and compared, in terms of model accuracy and SOC estimation accuracy. Then, combining the advantages of the DKF and DEKF algorithms, an SOC estimation algorithm based on adaptive double Kalman filter is proposed. This algorithm uses the recursive least squares (RLS) method to update the battery model parameters online in real time, and employs the DKF algorithm to filter the SOC twice to reduce the interferences from the battery model error and the current measurement error. In the experimental studies, the measured SOC values are compared with the estimated SOC values produced by the proposed algorithm. The comparison results show that SOC estimation error of the proposed algorithm is within the range of ±0.01 under most test conditions, and it can automatically correct SOC to true value in the presence of system errors. Thus, the validity, accuracy, robustness and adaptability of the proposed algorithm under different operation conditions are verified.     

固定时间梯度流在l1-l2范数中的稀疏重构

压缩感知（compressed sensing,CS）是一种全新的信号采样技术,对于稀疏信号,它能够以远小于传统的Nyquist采样定理的采样点来重构信号。在压缩感知中, 采用动态连续系统,对l₁-l₂范数的稀疏信号重构问题进行了研究。提出了一种基于固定时间梯度流的稀疏信号重构算法,证明了该算法在Lyapunov意义上的稳定性并且收敛于问题的最优解。最后通过与现有的投影神经网络算法的对比,体现了该算法的可行性以及在收敛速度上的优势.