考虑随机量测时滞和同步相关噪声的改进高斯滤波算法

经典高斯滤波算法存在量测信息实时获取,以及过程噪声和量测噪声相互独立的假设条件.然而,在工程实际应用中该假设条件有时难以满足.本文针对一类具有随机量测时滞和同步相关噪声的高斯系统的状态估计问题,设计了一种高斯滤波框架形式的最优估计算法,并给出了所设计算法的三阶球径容积法则的次优实现形式-考虑随机量测时滞和同步相关噪声的容积卡尔曼滤波器(CKF–RDSCN).其借助Bernoulli随机序列,来描述系统中可能存在的量测时滞现象,并利用高斯条件分布性质来解决噪声相关问题,在此基础上构建所提出的最优估计算法.仿真结果表明,相比于扩展卡尔曼滤波(EKF),无迹卡尔曼滤波(UKF)以及容积卡尔曼滤波(CKF),在含有随机量测时滞和噪声同步相关的状态估计问题中,CKF–RDSCN具有更高的精度和更好的数值稳定性.     

有色量测噪声下的改进求容积卡尔曼滤波器

为解决标准求容积卡尔曼滤波器在有色量测噪声条件下滤波精度退化的问题,提出改进求容积卡尔曼滤波器及其平方根形式.首先利用一阶马尔科夫模型白化非线性离散随机系统中有色量测噪声,将有色量测噪声下非线性离散随机系统转化为白噪声下非线性时滞系统.然后根据所得非线性时滞系统推导其高斯域的贝叶斯滤波框架,最后基于3度Spherical-Radial规则将该滤波框架近似为改进的求容积卡尔曼滤波器和其平方根形式.机动目标跟踪仿真试验结果表明两种改进求容积卡尔曼滤波算法在标准白噪声条件下与标准求容积卡尔曼滤波算法的估计精度相同,而在有色量测噪声背景下滤波精度和鲁棒性更优.     

具有一步随机滞后和多丢包的网络系统的最优线性估计

研究了具有随机时滞和丢包的网络系统的最优线性估计问题.本文通过两个满足 Bernoulli分布的随机变量来描述网络数据传输中可能存在的一步随机滞后和多丢包现象. 并基于新息分析方法,提出了线性最小方差下的最优线性状态滤波器、预报器和平滑器. 它们通过解一个Riccati方程和一个Lyapunov方程得到.最后,给出了稳态估值器存在的一个充分条件. 并通过仿真例子验证其有效性.     

有界随机测量时滞的网络控制系统的最优估计

在假设测量没有丢包的情况下, 研究了带有随机测量时滞的网络控制系统的最优估计问题. 利用已知的时 滞分布概率, 建立新的模型来描述随机时滞测量. 进一步将带有时滞的测量等价成每个通道是单时滞的多通道测 量, 从而利用新息重组方法, 通过求解黎卡提方程求解最优估计器. 最后给出仿真实例验证了该算法的有效性.     

有色量测噪声下的HCKF及其应用

针对高阶容积卡尔曼滤波（HCKF）算法在有色量测噪声条件下滤波精度下降的问题,提出了有色量测噪声下的HCKF算法。通过一阶马尔科夫模型将有色量测噪声进行白化,将带有色量测噪声的非线性离散随机系统转化为白噪声下的非线性时滞系统,并给出高斯域内针对非线性时滞系统的贝叶斯滤波框架。利用高阶容积准则对该滤波框架进行近似计算,进而得到有色量测噪声下的HCKF算法。将所提算法应用到机动目标跟踪系统中,仿真实验结果表明,量测噪声为白噪声时,所提算法与标准HCKF算法具有相同的估计性能;在量测噪声为有色噪声时,所提算法相比于标准HCKF具有更优的估计精度和鲁棒性。     

交互式容积卡尔曼滤波及其应用 交互式容积卡尔曼滤波及其应用

针对非线性系统模型参数未知情况下的状态估计问题, 提出一种融合极大后验估计的交互式容积卡尔曼滤波算法(InCKF). 该算法利用二阶斯特林插值公式和无迹变换对非线性函数的近似思想, 实现对模型未知参数的确定, 从而使滤波算法摆脱对模型参数精确已知的依赖, 并通过容积卡尔曼滤波算法完成状态估计和量测更新. 仿真结果表明, 相比于经典的参数扩维方法, InCKF 算法具有更高的精度和更强的数值稳定性.

     

改进的随机早期检测非线性算法

主动队列管理是目前的研究热点,随机早期检测(RED)算法是一种经典的队列管理算法。线性RED算法虽然简单且容易计算,但队列位于最小阈值和最大阈值附近时的丢包概率都不太合理。在论证了平均队列长度和丢包概率间为非线性性质后,提出了一种改进非线性RED算法——JRED。利用NS2对改进的算法进行仿真,结果表明,JRED算法提高了平均吞吐量,降低了丢包概率,增强了网络稳定性和可靠性。     

带多丢包和滞后随机不确定系统的最优线性估计

研究了带多丢包和滞后网络化随机不确定系统的最优线性估计问题. 通过白色乘性噪声来描述系统参数的随机不确定性. 通过一组满足Bernoulli分布的随机变量来描述数据传输过程中发生的丢包和滞后现象. 应用新息分析方法, 设计了线性最小方差意义下的最优线性估值器, 包括滤波器, 预报器和平滑器. 给出了稳态估值器存在的一个充分条件. 仿真例子验证了其有效性.     

非线性滞后Ito随机系统的滞后无关均方渐近稳定性

研究非线性滞后Ｉｔｏ随机系统的滞后无关均方渐近稳定性，将关于线性时滞不等式的Ｈａｌａｎａｙ不等式推广到非线性情形，用Ｌｙａｐｕｎｏｖ函数和关于时滞随机系统的比较原理，得到了非线性滞后Ｉｔｏ随机系统滞后无关均方渐近稳定性的一些判据。     

非线性滞后It(?)随机系统的滞后无关均方渐近稳定性

研究非线性滞后Ito随机系统的滞后无关均方渐近稳定性,将关于线性时滞不等式的Halanay不等式推广到非线性情形,用Lyapunov函数和关于时滞随机系统的比较原理,得到了非线性滞后Ito随机系统滞后无关均方渐近稳定性的一些判据。     

Adaptive Gaussian filters for nonlinear state estimation with one-step randomly delayed measurements

This paper proposes new algorithms of adaptive Gaussian filters for nonlinear state estimation with maximum one-step randomly delayed measurements. The unknown random delay is modeled as a Bernoulli random variable with the latency probability known a priori. However, a contingent situation has been considered in this work when the measurement noise statistics remain partially unknown. Due to unavailability of the complete knowledge of measurement noise statistics, the unknown measurement noise covariance matrix is estimated along with states following: (i) variational Bayesian approach, (ii) maximum likelihood estimation. The adaptation algorithms are mathematically derived following both of the above approaches. Subsequently, a general framework for adaptive Gaussian filter is presented with which variants of adaptive nonlinear filters can be formulated using different rules of numerical approximation for Gaussian integrals. This paper presents a few of such filters, viz., adaptive cubature Kalman filter, adaptive cubature quadrature Kalman filter with their higher degree variants, adaptive unscented Kalman filter, and adaptive Gauss–Hermite filter, and demonstrates the comparative performance analysis with the help of a nontrivial Bearing only tracking problem in simulation. Additionally, the paper carries out relative performance comparison between maximum likelihood estimation and variational Bayesian approaches for adaptation using Monte Carlo simulation. The proposed algorithms are also validated with the help of an off-line harmonics estimation problem with real data.     

Unscented Kalman Filtering for Nonlinear State Estimation with Correlated Noises and Missing Measurements

The unscented Kalman filtering problem is investigated for a class of nonlinear discrete stochastic systems subject to correlated noises and missing measurements. Here, a random variable obeying Bernoulli distribution with known conditional probability is introduced to depict the phenomenon of missing measurements occurring in a stochastic way. Due to taking the correlation of noises into account, a one-step predictor is designed by applying the innovative analysis and unscented transformation approach. And then, based on one-step predictor and the minimum mean square error principle, a new unscented Kalman filtering algorithm is proposed such that, for the correlated noises and missing measurements, the filtering error is minimized. By solving the recursive matrix equation, the filter gain matrices and the error covariance matrices can be obtained and the proposed results can be easily verified by using the standard numerical software. We finally provide a numerical example to show the performance of the proposed approach.     

Gaussian approximate filter for stochastic dynamic systems with randomly delayed measurements and colored measurement noises带随机延迟量测和有色量测噪声随机动态系统的高斯近似滤波器

In this paper, a new Gaussian approximate (GA) filter for stochastic dynamic systems with both one-step randomly delayed measurements and colored measurement noises is presented. For linear systems, a Kalman filter can be obtained to include one-step randomly delayed measurements and colored measurement noises. On the other hand, for nonlinear stochastic dynamic systems, different GA filters can be developed which exploit numerical methods to compute Gaussian weighted integrals involved in the proposed Bayesian solution. Existing GA filter with one-step randomly delayed measurements and existing GA filter with colored measurement noises are special cases of the proposed GA filter. The efficiency and superiority of the proposed method are illustrated in a numerical example concerning a target tracking problem.     

有限时间一致无迹Kalman滤波器

本文研究多个传感器测量非线性系统时的分布式无迹Kalman滤波器(Unscented Kalman filter, UKF)的设计问题.借助离散多智能体系统有限时间平均一致算法的思想, 针对无向通信和有向通信网络分别设计了两种不同的滤波算法.对于无向连通的通信拓扑, 利用节点存储的一致性算法的迭代值构造差向量, 由该差向量构成的Hankel矩阵的核来得到分布式无迹Kalman滤波器, 并通过利用误差协方差矩阵的逆来构造Lyapunov函数, 基于随机稳定性引理证明了该有限时间一致无迹Kalman滤波器的稳定性.对于有向强连通的通信拓扑, 结合比率一致和Hankal矩阵的核来设计分布式无迹Kalman滤波器, 该滤波器的稳定性与无向通信拓扑的滤波器相同.最后, 通过仿真例子来验证所提滤波器的跟踪效果.     

带一步随机延迟量测非线性序列贝叶斯估计的条件后验克拉美罗下界

为了解决带一步随机延迟量测非线性状态估计器可获得最优性能的评价问题,提出了一种适用于带一步随机延迟量测非线性系统的条件后验克拉美罗下界(Conditional posterior Cramr-Rao lower bound, CPCRLB),且现有的CPCRLB仅是所提出的CPCRLB在延迟概率为零时的一种特例. 为了递归地计算提出的CPCRLB,本文提出了一种带一步随机延迟量测的粒子滤波器(Particle filter, PF),继而推导了提出的CPCRLB 一般近似解和在高斯噪声情况下的特殊近似解. 单变量非平稳增长模型、纯方位跟踪和频率调制信号模型的数值仿真证明了本文提出方法与现有方法相比的有效性和优越性.     

Unscented Kalman filter for continuous‐time nonlinear fractional‐order systems with process and measurement noises

This study proposes the design of unscented Kalman filter for a continuous‐time nonlinear fractional‐order system involving the process noise and the measurement noise. The nonlinear fractional‐order system is discretized to get the difference equation. According to the unscented transformation, the design method of unscented Kalman filter for a continuous‐time nonlinear fractional‐order system is provided. Compared with the extended Kalman filter, the proposed method can obtain a more accurate estimation effect. For fractional‐order systems containing non‐differentiable nonlinear functions, the method proposed in this paper is still effective. The unknown parameters are also discussed by the augmented vector method to achieve the state estimation and parameter identification. Finally, two examples are offered to verify the effectiveness of the proposed unscented Kalman filter for nonlinear fractional‐order systems.     

量测随机延迟下带相关乘性噪声的非线性系统分布式估计

本文提出了乘性噪声和加性噪声相关下的量测随机延迟非线性系统分布式状态估计.在所考虑系统中,相关状态被多传感器簇构成的传感器网所观测.所得理想量测被传送到远程分布式处理网,并伴随服从一阶马尔可夫过程的随机延迟.在此基础上,本文提出了分布式高斯信息滤波(distributed Gaussian-information filter,DGIF),来实现估计精度与计算时间的折中.在单处理节点/单元中,以估计误差协方差最小化为准则,设计了相应的高斯递推滤波,并实现了延迟概率的在线递推估计.进一步地,在分布式处理网中,基于非线性量测方程的统计线性回归,结合一致性算法,给出了一种分布式信息滤波形式,有效实现了分布式融合.分别在单处理单元和分布式处理网中仿真验证了所提算法的有效性.     

State estimation for complex systems with randomly occurring nonlinearities and randomly missing measurements

This paper is concerned with the state estimation problem for the complex networked systems with randomly occurring nonlinearities and randomly missing measurements. The nonlinearities are included to describe the phenomena of nonlinear disturbances which exist in the network and may occur in a probabilistic way. Considering the fact that probabilistic data missing may occur in the process of information transmission, we introduce the randomly data missing into the sensor measurements. The aim of this paper is to design a state estimator to estimate the true states of the considered complex network through the available output measurements. By using a Lyapunov functional and some stochastic analysis techniques, sufficient criteria are obtained in the form of linear matrix inequalities under which the estimation error dynamics is globally asymptotically stable in the mean square. Furthermore, the state estimator gain is also obtained. Finally, a numerical example is employed to illustrate the effectiveness of the proposed state estimation conditions.     

Particle filter with one-step randomly delayed measurements and unknown latency probability

In this paper, a new particle filter is proposed to solve the nonlinear and non-Gaussian filtering problem when measurements are randomly delayed by one sampling time and the latency probability of the delay is unknown. In the proposed method, particles and their weights are updated in Bayesian filtering framework by considering the randomly delayed measurement model, and the latency probability is identified by maximum likelihood criterion. The superior performance of the proposed particle filter as compared with existing methods and the effectiveness of the proposed identification method of latency probability are both illustrated in two numerical examples concerning univariate non-stationary growth model and bearing only tracking.     

A skewed unscented Kalman filter

State estimation of nonlinear systems is a challenging task, especially when the Gaussian approximation fails. The unscented Kalman filter was proposed to deal with state estimation of nonlinear systems. We modify the traditional unscented Kalman filter to capture the third-order moment (skewness) of the state vector. Methods are also proposed to reduce the computation time of the suggested approach, and showing that the proposed algorithm is as fast as the unscented Kalman filter. Simulation results confirm that the method is better than, or at least as good as, the unscented Kalman filter.