带模型误差系统自适应Kalman滤波的虚拟噪声补偿技术

本文讨论了带模型误差系统的自适应 Kalman 滤波问题。通过引入虚拟噪声,应用带未知时变噪声统计系统的自适应 Kalman 滤波器,提出了补偿模型误差、改进滤波器性能的虚拟噪声补偿新技术。三个不同类型的数值仿真例子证明了本文结果的有效性。     

基于自然梯度的噪声自适应变分贝叶斯滤波算法

考虑到运动目标跟踪系统机动、隐身等人为对抗特征以及非视距、干扰、遮挡等环境因素, 其系统建模、估计与辨识过程中越来越无法回避非线性、非高斯以及参数未知等复杂系统特征的影响. 针对过程噪声先验信息不准确以及量测噪声非高斯环境下运动目标的非线性状态估计问题, 提出一种基于自然梯度的噪声自适应变分贝叶斯(Variational Bayes, VB)滤波算法. 首先, 利用指数族分布具有统一表达形式的优势, 构建参数化逆威沙特(Inverse-Wishart, IW)分布作为状态一步预测误差协方差的共轭先验分布, 同时选取学生t分布重构因量测随机缺失导致的具有非高斯特点的似然函数; 其次, 在变分贝叶斯优化框架下采用平均场理论将状态变量联合后验分布近似分解为独立的变分分布, 在此基础上, 结合坐标上升方法更新各变量的变分分布参数; 进而, 结合 Fisher 信息矩阵推导置信下界最大化关于状态估计及其估计误差协方差的自然梯度, 使非线性状态后验分布的近似分布沿梯度下降, 以实现对状态后验概率密度函数(Probability density function, PDF)的“紧密”逼近. 理论分析和仿真实验表明: 相对传统的非线性滤波方法, 本文算法对噪声不确定问题具有较好的自适应能力, 并且能够获得较高的状态估计精度.     

基于不确定模型误差系统的变分贝叶斯STCKF

强跟踪容积卡尔曼滤波器在对含有模型误差和时变噪声的非线性系统进行滤波时, 容易出现性能降低甚至发散. 鉴于此, 提出一种基于变分贝叶斯的强跟踪容积卡尔曼滤波算法. 该算法运用虚拟噪声法补偿模型误差, 假设虚拟噪声均值非零, 且满足高斯分布, 虚拟噪声方差服从逆gamma分布, 在强跟踪容积卡尔曼滤波器估计状态的同时, 采用变分贝叶斯推理估计虚拟噪声参数. 仿真结果表明, 所提出算法对含模型误差与时变噪声的非线性系统具有较好的估计精度, 相比于自适应算法具有更强的鲁棒性.     

具有参数自适应的交互式多模型算法

动态多模型估计（SMME）广泛应用于结构和参数的不确定／变化的估计问题中,比如目标跟踪和故障诊断与隔离,然而由先验信息选定的滤波参数是模式切换与模式未切换情况下的折衷,针对SMME,本文通过在每个滤波循环开始处起始多个状态预测器实时辨识滤波参数,包括模式切换概率和基于模型的过程噪声方差,考虑到交互式多模型（IMM）是SMME中比较有效的方法,我们将上述的参数辨识与IMM相结合,提出了一种自适应IMM（AIMM）,在跟踪一个机动目标的仿真中,AIMM表现出了比IMM更高的估计精度。     

一种具有噪声干扰的MIMO非线性时变系统自适应控制

针对含噪声多输入多输出不确定非线性时变系统,提出一种基于多维泰勒网(MTN)的自适应控制方案,其中两个MTN分别用来实现优化控制和非线性滤波.首先,提出多维泰勒网控制器(MTNC)以实现实时跟踪控制.将滤波输出与期望值之间的闭环误差作为MTNC的输入,根据系统不确定因素引起的误差,基于稳定的学习率,设计线性再励的自适应变步长算法以快速更新MTNC权值.其次,提出多维泰勒网滤波器(MTNF)以消除测量噪声.由于定义了测量值与MTNF输出之间误差的Lyapunov函数,自适应MTN滤波系统兼具基于Lyapunov理论的自适应滤波(LAF)和MTN的特有性质.最后,通过在Lyapunov意义下选取适当的权值更新律,可使MTNF输出渐近地收敛到期望信号,并证明了滤波器的收敛性和稳定性.仿真结果验证了所提出方案的有效性.     

CCD扫描噪声建模及自适应滤波算法

为去除图像因扫描引入的电荷耦合器件(CCD)噪声,提出一种基于变窗口的自适应滤波算法。分析CCD主要噪声：散粒,固有和输出噪声的噪声特性,建立CCD扫描噪声模型,根据噪声和边缘处理方式的不同设计了局部和全局自适应滤波器。实验结果表明,该算法具有较好的信噪分离能力,在充分抑制噪声的同时,很好地保持了边缘,提高对比度,视觉效果良好。     

基于自适应神经网络滤波的噪声消除

设计的自适应神经网络噪声抵消系统不需要关于输入信号的先验知识,非线性映射能力强,具有自学习能力、计算量小、实时性好。利用该系统对含噪声的非线性信号建模,达到消除噪声的目的。通过LMS算法,对不同信噪比(SNR)的含噪信号进行滤波。仿真结果表明,该滤波器能有效地抑制噪声。     

基于异步IMM融合滤波的网络化系统故障诊断

针对一类带随机丢包的异步多传感器网络化系统,提出了基于网络化异步交互式多模型（Interacting multiple model,IMM）融合滤波的故障诊断方法.考虑不同传感器通道具有不同丢包概率的情况,将未知的故障幅值看作扩维的系统状态,利用提出的网络化异步IMM融合滤波算法对由系统正常模型和各种可能的故障模型构成的模型集进行滤波,根据模型概率进行故障检测和定位,同时得到故障幅值和系统状态的联合估计.提出的方法避免了传统IMM故障诊断方法模型集设计中故障大小难以确定的问题,适用于具有任意采样速率和任意初始采样时刻的异步多传感器网络化系统,并且通过融合多个传感器的信息提高了故障诊断的准确性.仿真实例验证了所提出方法的可行性和有效性.     

消除噪声引起的自适应滤波偏差

在自适应滤波中，如何消除有色噪声引起的估计偏差一直是人们关心的重要问题。为了解决此问题，本文提出了一种偏差补偿的自适应滤波算法（ＢＥＬＳＡＦ）。理论分析和仿真实验表明，本文所提出的算法是收敛的，并且它可在不对噪声建模的情况下去除噪声对滤波的影响。     

混合式自适应Kalman滤波算法

采用虚拟噪声补偿模型误差和有偏的噪声方差估值器、滤波器收敛性判据相结合的方法来解决自适应Kalman滤波发散的问题。首先若模型不准确,则引入虚拟噪声对模型误差进行虚拟补偿,然后采用有偏的噪声方差估值器、滤波器收敛性判据对噪声方差估计值进行监控,阻止滤波器发散。采用混合式自适应Kalman滤波算法对Gill公司的风向风速仪实时采集的数据进行处理,实验结果表明,该方法能有效的提高性能、抑制滤波发散,具有较强的实用性、自适应能力。     

用于带有量测噪声系统的新型扩张状态观测器

提出了扩张状态观测器的一种新的形式,用于处理量测环节带有噪声干扰时的情况.ESO可以对不确定系统中的内外扰动进行观测,并以此为基础构成自抗扰控制器.但其性能会受量测噪声的影响.本文利用滤波器消除噪声的影响,并把已知的滤波器方程扩展到原有的ESO中,以补偿滤波器对实际输出信号的偏移作用.数字仿真表明,该方法可以有效的解决输出噪声对扩张状态观测器的影响.     

不确定噪声下基于轴对称盒空间滤波的非线性系统状态估计

针对不确定噪声下的非线性系统状态估计问题, 本文提出了一种基于轴对称盒空间滤波的状态估计方法. 首先, 利用轴对称盒空间包裹线性化过程带来的误差项, 将状态函数线性化误差轴对称盒空间与噪声轴对称盒空间求取闵可夫斯基和, 得到干扰误差轴对称盒空间; 随后, 利用状态量、线性误差和测量噪声的轴对称盒空间的闵可夫斯基和, 得到系统状态预测集; 进而, 利用轴对称盒空间边界正交的性质, 将盒空间拆分为多组超平面, 构造测量更新的约束条件并得到集员包裹. 本文所提方法相比传统的椭球滤波方法而言, 降低了算法的复杂度, 减少了包裹状态可行集和线性化过程带来的余, 获得了更加紧致精确的系统状态集. 最后, 采用非线性弹簧–质量–阻尼器系统验证了本文所提算法的有效性.     

A filter for a state space model with fractional Gaussian noise

A filter for estimating the hidden signal and parameters in a state space model, where the noise in the observations is fractional Gaussian noise, is obtained.     

一种影像测量系统中自适应混合噪声滤波方法

介绍了影像测量系统中的噪声来源以及常用的滤波方法。针对均值滤波器和中值滤波器在滤除高斯噪声和脉冲噪声时各自表现出良好的性能,设计了一种针对待测零件图像中混合噪声的自适应滤波方法,系统根据噪声类别灵活选择滤波方法。实验证明改进的滤波策略能获得比传统滤波方法更高的信噪比改善因子。     

An adaptive noise smoothing filter for remotely-sensed images with microphonic noise

Abstract

In this paper we consider the restoration of airborne scanner images with microphonic noise. According to the practical generation process of micro-phonic noise, the noise can be assumed multiplicative and to be a stationary Markov random sequence. An adaptive noise smoothing filter, based on the Kalman filter and NMNV (non-stationary mean and non-stationary variance) image model, is developed. The microphonic noise in airborne scanner images can be effectively filtered out by this adaptive filter. Results of the algorithm on simulation and realistic images are shown.     

Bayesian adaptive filter for tracking with measurements of uncertain origin

The probabilistic data association filter (PDA) estimates the state of a target in the presence of source uncertainty and measurement inaccuracy. This suboptimal procedure assumes that variances of process and measurement noises are known. The aim of this paper concerns the research of an adaptive probabilistic data association filter (APDAF). This Bayesian method estimates the state of a target in a cluttered environment when the noise statistics are unknown. Simulation results on target tracking using experimental data are presented.     

Direct data-driven filter design for uncertain LTI systems with bounded noise

This paper investigates the filter design problem for linear time-invariant dynamic systems when no mathematical model is available, but a set of initial experiments can be performed where also the variable to be estimated is measured. Instead of using the initial experimental data to identify a model on the basis of which a filter is designed, these data are used to directly design a filter. Assuming norm-bounded disturbances and noises, a Set Membership formulation is followed. For classes of filters with exponentially decaying impulse response, approximating sets are determined that guarantee to contain all the solutions to the optimal filtering problem, where the aim is the minimization of the induced norm from disturbances to the estimation error. A method is proposed for designing almost-optimal linear filters with finite impulse response, whose worst-case filtering error is at most twice the lowest achievable one. In the H_∞ SISO case, an efficient technique is presented, that allows the evaluation of bounds on the guaranteed worst-case filtering error of the designed filter. Numerical examples illustrate the effectiveness of the proposed solution.     

Interacting multiple model estimation-based adaptive robust unscented Kalman filter

The unscented Kalman filter (UKF) is a promising approach for the state estimation of nonlinear dynamic systems due to its simple calculation process and superior performance in highly nonlinear systems. However, its solution will be degraded or even divergent when the system model involves uncertainty. This paper presents an interacting multiple model (IMM) estimation-based adaptive robust UKF to address this problem. This method combines the merits of the adaptive fading UKF and robust UKF and discards their demerits to inhibit the disturbance of system model uncertainty on the filtering solution. An adaptive fading UKF for the case of process model uncertainty and a robust UKF for the case of measurement model uncertainty are established based on the principle of innovation orthogonality. Subsequently, an IMM estimation is developed to fuse the adaptive fading UKF and robust UKF as sub-filters according to the mode probability. The system state estimation is achieved as a probabilistic weighted sum of the estimation results from the two sub-filters. Simulations, experiments and comparison analysis validate the efficacy of the proposed method.     

带不确定参数和噪声方差的鲁棒观测融合Kalman滤波器

对带不确定参数和噪声方差的多传感器定常系统,引入虚拟白噪声补偿不确定参数,可将其转化为带已知参数和不确定噪声方差系统.应用极大极小鲁棒估值原理和加权最小二乘法,基于带噪声方差保守上界的最坏情形保守系统,提出了鲁棒加权观测融合Kalman滤波器,并证明了它与集中式融合鲁棒Kalman滤波器是等价的,且融合器的鲁棒精度高于每个局部滤波器鲁棒精度.一个Monte-Carlo仿真例子说明了如何寻求不确定参数的鲁棒域和如何搜索保守性较小的虚拟噪声方差上界.     

Optimal LQG control for discrete time-varying system with multiplicative noise and multiple state delays

This paper is concerned with the optimal linear quadratic Gaussian (LQG) control problem for discrete time-varying system with multiplicative noise and multiple state delays. The main contributions are twofolds. First, in virtue of Pontryagin’s maximum principle, we solve the forward and backward stochastic difference equations (FBSDEs) and show the relationship between the state and the costate. Second, based on the solution to the FBSDEs and the coupled difference Riccati equations, the necessary and sufficient condition for the optimal problem is obtained. Meanwhile, an explicit analytical expression is given for the optimal LQG controller. Numerical examples are shown to illustrate the effectiveness of the proposed algorithm.