ADAPTIVE FILTERING IN STRUCTURAL DYNAMICS

The Kalman filter has been shown to be ideally suited to both the state and parameter estimation problems in structural dynamics. However these exploratory works on the application of Kalman filtering to structural engineering problems, in general only give suboptimal results, relying on assumed statistics to describe the noise sequences. Optimality however can be achieved by adapting onto these statistics (or the filter gain), using output from the filter equations to feed the adaptive algorithm. The present paper details one recently developed adaptive approach which exhibits good computational and convergence properties. This is coupled with a correlation test to show the optimality or nonoptimality of the results in any given application. A seismically excited structure is used to illustrate the required problem formulation and estimation results.     

A semi-analytical particle filter for identification of nonlinear oscillators

Particle filters find important applications in the problems of state and parameter estimations of dynamical systems of engineering interest. Since a typical filtering algorithm involves Monte Carlo simulations of the process equations, sample variance of the estimator is inversely proportional to the number of particles. The sample variance may be reduced if one uses a Rao–Blackwell marginalization of states and performs analytical computations as much as possible. In this work, we propose a semi-analytical particle filter, requiring no Rao–Blackwell marginalization, for state and parameter estimations of nonlinear dynamical systems with additively Gaussian process/observation noises. Through local linearizations of the nonlinear drift fields in the process/observation equations via explicit Ito–Taylor expansions, the given nonlinear system is transformed into an ensemble of locally linearized systems. Using the most recent observation, conditionally Gaussian posterior density functions of the linearized systems are analytically obtained through the Kalman filter. This information is further exploited within the particle filter algorithm for obtaining samples from the optimal posterior density of the states. The potential of the method in state/parameter estimations is demonstrated through numerical illustrations for a few nonlinear oscillators. The proposed filter is found to yield estimates with reduced sample variance and improved accuracy vis-à-vis results from a form of sequential importance sampling filter.     

基于自适应滤波的锂电池隔膜卷绕系统张力估计

锂电池隔膜卷绕系统的电机转速、放卷辊的卷材卷径和放卷张力等实时信号都带有高斯白噪声,易形成较大的滞后,从而导致控制系统的稳定性和精度降低。现以协方差匹配技术为滤波发散判据,再结合对于指数加权系数的表达式限定记忆滤波的次数,提高噪声初始值的分配权重,来保持滤波的自适应程度,提出一种基于改进型SageHusa自适应滤波估计张力的方法,实现对系统噪声协方差阵与测量噪声协方差阵的自适应变化。实验结果表明,所提出的方法不仅能更准确、稳定地估计出锂电池隔膜卷绕系统放卷张力,还能在一定范围内使其不受给定的噪声协方差阵初值影响,而且有较高的精度和较强的实时性,优于一般的扩展卡尔曼滤波算法。     

基于神经网络的图像混合滤波及融合算法研究

当图像中同时存在高斯噪声和椒盐噪声时,单一的均值滤波或中值滤波很难达到最佳滤波效果。 分析了噪声特点和各种滤波方法的优势,提出了一种基于神经网络的图像混合滤波及融合算法:首先建立概率神经网络,检测椒盐噪声和高斯噪声点,并分别利用中值滤波和均值滤波去除噪声点,然后建立径向基函数神经网络,利用训练好的径向基函数神经网络融合 2 种不同滤波的图像,输出理想的融合图像。 Matlab 仿真实验结果表明,该算法有效去除混合噪声的同时,能很好地保护图像的边缘与细节,是一种有效的方法。     

Particle Filtering for State Estimation in Nonlinear Industrial Systems

State estimation is a major problem in industrial systems, particularly in industrial robotics. To this end, Gaussian and nonparametric filters have been developed. In this paper, the extended Kalman filter, which assumes Gaussian measurement noise, is compared with the particle filter, which does not make any assumption on the measurement noise distribution. As a case study, the estimation of the state vector of an industrial robot is used when measurements are available from an accelerometer that was mounted on the end effector of the robotic manipulator and from the encoders of the joints' motors. It is shown that, in this kind of sensor fusion problem, the particle filter outperforms the extended Kalman filter, at the cost of more demanding computations.     

Variational Bayesian Based IMM Robust GPS Navigation Filter

This paper investigates the navigational performance of Global Positioning System (GPS) using the variational Bayesian (VB) based robust filter with interacting multiple model (IMM) adaptation as the navigation processor. The performance of the state estimation for GPS navigation processing using the family of Kalman filter (KF) may be degraded due to the fact that in practical situations the statistics of measurement noise might change. In the proposed algorithm, the adaptivity is achieved by estimating the time-varying noise covariance matrices based on VB learning using the probabilistic approach, where in each update step, both the system state and time-varying measurement noise were recognized as random variables to be estimated. The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning. One of the two major classical adaptive Kalman filter (AKF) approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate (MMAE). The IMM algorithm uses two or more filters to process in parallel, where each filter corresponds to a different dynamic or measurement model. The robust Huber's M-estimation-based extended Kalman filter (HEKF) algorithm integrates both merits of the Huber M-estimation methodology and EKF. The robustness is enhanced by modifying the filter update based on Huber's M-estimation method in the filtering framework. The proposed algorithm, referred to as the interactive multi-model based variational Bayesian HEKF (IMM-VBHEKF), provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors, such as the multipath effect. Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.     

基于卡尔曼滤波的STFT域回声抵消算法

提出了一种低复杂度的短时傅里叶变换域卡尔曼滤波算法来解决声学回声抵消问题。首先在短时傅里叶变换域建立了基于频域卷积传递函数的观测方程,并利用一阶马尔科夫模型对频域回声路径进行建模,给出了精确的卡尔曼滤波方程,并讨论了过程噪声和观测噪声的估计问题。为降低算法计算复杂度,提出了低复杂度卡尔曼滤波算法。另外,在更新滤波器时加入远端信号邻近频点的信息来进一步提高回声抵消性能。实验结果表明,所提算法对近端干扰不敏感,不需要额外的双端对讲检测算法,且比传统的频域自适应滤波算法具有更快的收敛速度。     

一种结合时间轴滤波的视频消噪新方法

为了提高含噪视频图像的质量,提出了一种二维小波域自适应滤波与时域时间轴滤波相结合的视频图像消噪新方法。首先,对视频序列的各帧在二维小波域中进行自适应滤波,之后在时域中进行时间轴滤波。对于二维小波域滤波算法,提出了一种高效的自适应阈值选取方案;时间轴滤波器则是结合了运动检测和递归平均。实验结果表明,其消噪效果要优于单纯的二维小波域滤波方法。     

Study of the stability of a kalman-bucy filter subjected to correlated disturbances

The stability of a Kalman-Bucy filter that is optimal in the case of filtering of signals against a background of white Gaussian noise and of a filter that is optimal for nonwhite noise from measurements when subjected to the action of correlated disturbances is investigated. The “innovation process” correlation function is calculated and a noise decorrelator is synthesized and subsequently incorporated into the filter structure Translated from Izmeritel'naya Tekhnika, No. 8, pp. 27–29, August, 1997.     

A heuristic reference recursive recipe for adaptively tuning the Kalman filter statistics part-2: real data studies

In part-1 of this paper an adaptive filtering based on a reference recursive recipe (RRR) was developed and tested on a simulated dynamics of a spring, mass and damper with a weak nonlinear spring. In this paper the above recipe is applied to a more involved case of three sets of airplane data that have a larger number of state, measurements and unknown parameters. The flight tests cannot always be conducted in an ideal situation of the process noise and the measurement noises being white Gaussian as is generally assumed in the Kalman filter. The measurements may not be available with respect to the center of gravity and possess scale and bias factors, which will have to be modelled and estimated as well. The coupling between the longitudinal and lateral motion brings in added difficulty but makes the problem more interesting. It turns out that even a parameter that strongly affects the airplane dynamics is estimated which vary widely among the approaches. The RRR has been shown to be better than the earlier approaches in estimating the unknowns. The generalized cost functions that are introduced in the present work help identify definitive results from deceptive results.     

Nonlinear filtering for recognition of phase-encoded images

We investigate the use of Fourier plane nonlinear filtering for phase-encoded images. We investigate the performance of the nonlinear joint transform correlator and the nonlinearly transformed matched filter for phase-encoded images with different types of input noise. We use the peak-to-output-energy ratio, peak-to-sidelobe ratio, and discrimination ratio as the metrics for measuring the performances. We mathematically analyze the peak-to-output-energy ratio of the nonlinearly transformed matched filter for phase-encoded images with spatially nonoverlapping white noise. Computer simulations are provided to show the performance improvements of the nonlinear filtering techniques for the phase-encoded images. In comparison with linear filtering techniques, we find that the nonlinear filtering techniques substantially improve the performance metrics. From the computer-simulation results it can be seen that the nonlinear joint transform correlator performs better than the nonlinearly transformed matched filter in detecting phase-encoded targets in the presence of different types of noise, such as additive overlapping white noise, spatially nonoverlapping white background noise, spatially nonoverlapping colored background noise, and nontarget objects.     

小波变换与卡尔曼滤波结合的RLG降噪方法

针对激光陀螺随机游走噪声其非平稳和非正态分布的特性,提出了基于小波变换的卡尔曼滤波的RLG降噪方法,该方法既具有小波变换对自相似过程的去相关作用和多分辨分析的功能,同时又保持了卡尔曼滤波器对未知信号的线性无偏最小方差估计的特点,实现了激光陀螺随机游走噪声的实时多尺度分解和最优估计。实测激光陀螺零偏信号去噪的结果表明,基于小波变换的卡尔曼滤波器使随机游走噪声的标准差降低了10.3%,降噪效果优于传统的卡尔曼滤波器。     

基于多尺度Kalman数据融合滤波

本文通过分析基于小波变换的动态系统模型,提出一种基于小波多尺度的Kalman数据滤波方法,本文利用小波的多尺度特点,把初始估计序列多尺度分解,并在不同尺度层上进行Kalman滤波估计,再利用小波重构来融合各层的估计信息,把标准Kalman滤波只在单一尺度和时间轴上对状态估计值和误差协方差进行数据更新,改进为基于小波变换的尺度轴和时间轴上的双向数据更新,该算法将小波多尺度分解去噪和Kalman滤波相结合,对实际中含较强噪声的动态系统的状态估计效果较好.算法也可用于多分辨率多传感器数据融合.     

Multimodel Kalman filtering for adaptive nonuniformity correction in infrared sensors

We present an adaptive technique for the estimation of nonuniformity parameters of infrared focal-plane arrays that is robust with respect to changes and uncertainties in scene and sensor characteristics. The proposed algorithm is based on using a bank of Kalman filters in parallel. Each filter independently estimates state variables comprising the gain and the bias matrices of the sensor, according to its own dynamic-model parameters. The supervising component of the algorithm then generates the final estimates of the state variables by forming a weighted superposition of all the estimates rendered by each Kalman filter. The weights are computed and updated iteratively, according to the a posteriori-likelihood principle. The performance of the estimator and its ability to compensate for fixed-pattern noise is tested using both simulated and real data obtained from two cameras operating in the mid- and long-wave infrared regime.     

Stochastic linearization method with random parameters for SDOF nonlinear dynamical systems: prediction and identification procedures

This paper describes firstly, the calculation of the Power Spectral Density Function (PSDF) for the stationary response of SDOF nonlinear second-order dynamical systems excited by a white or a broad-band Gaussian noise, and secondly, the identification of a single-degree-of-freedom (SDOF) nonlinear dynamical second-order dynamical system driven by a broad-band or a colored Gaussian noise. The two aspects are based on the use of a stochastic linearization method with random parameters which is an efficient way of approximating the PSDF. The gain obtained by this method is shown on a SDOF nonlinear dynamical system. In addition, it is shown that the stochastic linearization method with random parameters is an efficient approach for identifying a SDOF nonlinear dynamical system.     

Kalman filter tracking in a Cherenkov neutrino telescope

The reconstruction of tracks in underwater Cherenkov neutrino telescopes is strongly complicated due to large background counting rate originates from ⁴⁰K beta decay and to the electromagnetic showers accompanying high energy muons together with the effects of light propagation in the water, in particular the photon scattering. These two effects lead to a non-linear problem with a non-Gaussian measurement noise. A method for track reconstruction based on Kalman filter approach in this situation is presented. We use Gaussian Sum Filter algorithm to take into account non-Gaussian process noise. While usual Kalman filter estimators based on linear least-square method are optimal in case all observations are Gaussian distributed, the Gaussian Sum Filter offers a better treatment of non-Gaussian process noise and/or measurement errors when these are modeled by Gaussian mixtures. As an example of the application, the results of muon track reconstruction in NEMO underwater neutrino telescope are presented as well as the comparison of its capability with other standard track reconstruction methods.     

Estimation Performance for the Cubature Particle Filter under Nonlinear/Non-Gaussian Environments

This paper evaluates the state estimation performance for processing nonlinear/non-Gaussian systems using the cubature particle filter (CPF), which is an estimation algorithm that combines the cubature Kalman filter (CKF) and the particle filter (PF). The CPF is essentially a realization of PF where the third-degree cubature rule based on numerical integration method is adopted to approximate the proposal distribution. It is beneficial where the CKF is used to generate the importance density function in the PF framework for effectively resolving the nonlinear/non-Gaussian problems. Based on the spherical-radial transformation to generate an even number of equally weighted cubature points, the CKF uses cubature points with the same weights through the spherical-radial integration rule and employs an analytical probability density function (pdf) to capture the mean and covariance of the posterior distribution using the total probability theorem and subsequently uses the measurement to update with Bayes’ rule. It is capable of acquiring a maximum a posteriori probability estimate of the nonlinear system, and thus the importance density function can be used to approximate the true posterior density distribution. In Bayesian filtering, the nonlinear filter performs well when all conditional densities are assumed Gaussian. When applied to the nonlinear/non-Gaussian distribution systems, the CPF algorithm can remarkably improve the estimation accuracy as compared to the other particle filter-based approaches, such as the extended particle filter (EPF), and unscented particle filter (UPF), and also the Kalman filter (KF)-type approaches, such as the extended Kalman filter (EKF), unscented Kalman filter (UKF) and CKF. Two illustrative examples are presented showing that the CPF achieves better performance as compared to the other approaches.     

Angular velocity estimation from measurement vectors of star tracker

In most spacecraft, there is a need to know the craft's angular rate. Approaches with least squares and an adaptive Kalman filter are proposed for estimating the angular rate directly from the star tracker measurements. In these approaches, only knowledge of the vector measurements and sampling interval is required. The designed adaptive Kalman filter can filter out noise without information of the dynamic model and inertia dyadic. To verify the proposed estimation approaches, simulations based on the orbit data of the challenging minisatellite payload (CHAMP) satellite and experimental tests with night-sky observation are performed. Both the simulations and experimental testing results have demonstrated that the proposed approach performs well in terms of accuracy, robustness, and performance.     

直角坐标系下的水下被动目标跟踪自适应卡尔曼滤波算法

针对纯方位被动目标跟踪中，直角坐标系下的扩展卡尔曼滤波器容易发散，导致滤波精度很差的情况，文章中提出了一种直角坐标系下自适应卡尔曼滤波算法，对虚拟噪声进行了估计，动态补偿观测模型的线性化误差，削减系统的观测误差，并对其滤波理论及其算法进行了研究和仿真，结果表明，该算法提高了滤波的稳定性、快速性和精确性，优于一般的扩展卡尔曼滤波算法。     

Finite element solution of Fokker–Planck equation of nonlinear oscillators subjected to colored non-Gaussian noise

Nonlinear oscillators subjected to colored Gaussian/non-Gaussian excitations are modelled through a set of three coupled first-order stochastic differential equations by representing the excitation as a first-order filtered white noise. A 3-D finite element (FE) formulation is developed to solve the corresponding 3-D Fokker Planck (FP) equations. The joint probability density functions of the state variables, obtained as a solution of the FP equation, are typically non-Gaussian and are used for computing the crossing statistics of the response – an essential metric for time variant reliability analysis. The method is illustrated through a noisy Lorenz attractor and a Duffing oscillator subjected to additive colored noise. The increase in state-space dimension when the Duffing oscillator is additionally excited with a parametric Gaussian noise is effectively handled by using stochastic averaging to reduce the state-space dimension. Investigations are carried out to examine the accuracy of the FE method vis-a-vis Monte Carlo simulations. The proposed method is observed to be computationally significantly cheaper for these three problems.