Optimum decoding-based smoothing algorithm for dynamic systems

A new smoothing algorithm for discrete models is presented. For the disturbance noise and the observation noise, only independency is assumed. Moreover the models’ functions are not limited to continuous functions, i.e. they can be non-continuous. This algorithm estimates the states by first quantizing them and then using the Viterbi decoding algorithm. Simulation results have shown that for some non-linear models the new algorithm performs better than the extended Kalman filter algorithm, while it performs almost as well as the Kalman filter algorithm for linear models with gaussian noise.     

基于多元插值的DD型滤波算法仿真研究

DD型滤波是一种基于Striling多元插值方法,将函数按多项式近似展开的非线性滤波算法.相对于扩展卡尔曼滤波而言,它不需要对非线性函数进行微分运算,具有滤波精度高、数值稳定性好和适用范围广的优点,其运算量却与扩展卡尔曼滤波相当.对DD型滤波算法进行了深入分析,并将该算法应用于状态估计领域.对一多传感器目标跟踪问题进行了仿真计算,仿真结果表明了DD型滤波算法的有效性和实用性.     

Continuous Finite-Dimensional Locally Optimal Filtering of Jump Diffusions

This paper considers continuous-time state estimation for a dynamic system with Gaussian and Poisson white noise. We design a finite-dimensional filter with a lower computational cost than the extended Kalman–Bucy filter: its order is the dimension of the estimated part of the system state vector. The nonlinear structure of the filter is selected using the mean squared optimal unbiased estimation for each infinitesimal period of time. We develop an algorithm to find the structural functions of the filter that is based on the Kolmogorov–Feller equation for the density function. A numerical method to calculate them a priori by sequential Monte Carlo trials is presented, which requires the histograms of the desired functions. Due to its cumbersome form, some numerical and analytical approximations of the suggested filter are also given. They structurally coincide with the corresponding nonlinear extensions of the Kalman–Bucy filter but have a considerably smaller order and calculable parameters.     

基于粒子滤波的机动目标跟踪算法仿真研究

针对非线性多目标模型,应用粒子滤波算法,这种方法不受模型线性和Gauss假设的约束,是一种处理非线性非高斯动态系统状态递推估计的有效算法。在粒子滤波的基础上融合扩展卡尔曼滤波算法和无迹卡尔曼滤波算法。融合后的新算法在计算提议概率密度分布时,粒子的产生充分考虑当前时刻的量测,使得粒子的分布更加接近状态的后验概率分布,再用平滑算法处理滤波的结果。仿真结果表明,算法有较好的跟踪效果。     

双目视觉基于修正卡尔曼滤波器的运动估计

研究了目标物体的远程运动估计.首先,建立了一种双目视觉系统的基于卡尔曼滤波器的目标物体运动估计的运动学模型,并且证明了双目视觉系统同步的各自连续两帧图像中至少三个对应图像点能完全确定刚性物体的运动参数和空间位置;然后,通过对状态向量中的速度分量进行再估计,提出了一种修正卡尔曼滤波器对目标物体远程运动估计的算法,与直接卡尔曼滤波器的远程运动估计相比,提高了估计的精度.将该方法运用到一种实时预测的实验中,其结果证明了该算法的有效性.     

一类空间连接系统的分布式状态估计及其收敛性分析

针对一类一维空间连接系统, 提出了一种分布式递推状态估计算法, 给出了其收敛的充要条件. 与集总式Kalman滤波算法相比, 该算法可大幅度降低计算的时间复杂度和内存占用量, 并具有可简单地实现并行计算的特点. 这一算法还可直接推广到多维空间连接系统. 数值仿真结果表明, 该算法通常只牺牲少量的滤波精度.     

Robust Kalman filter for linear discrete-time system with gaussian sum noises

This paper considers the filtering problem for discrete-time linear systems where the distributions of the process and observation noises are of gaussian sum distributions. Since the gaussian sum noise can be considered to be a sample from one of the gaussian distributions forming the gaussian sum, we define the distribution selection parameters that specify sample noises from the gaussian sum distribution. By using the maximum a posteriori (MAP) estimates of the selection parameters, a robust state estimation algorithm combined with the Kalman filter is developed. Simulation studies are also included to show the effectiveness of the present algorithm.     

含有分数阶有色关联噪声的分数阶系统的卡尔曼滤波器设计

提出基于Tustin生成函数的分数阶卡尔曼滤波器设计方法,以解决含有相互关联的分数阶有色过程噪声和分数阶有色测量噪声的连续时间线性分数阶系统的状态估计问题.通过Tustin生成函数方法,对连续时间线性分数阶系统进行离散化,将分数阶系统的微分方程转化为差分方程.利用增广向量法,将分数阶状态方程和分数阶有色噪声作为新的增广...     

基于Kalman滤波器的非视距误差抑制算法

针对蜂窝网定位中影响定位精度的非视距传播误差问题,提出一种基于Kalman滤波器的非视距(NLOS)误差抑制算法,将到达时间(TOA)测量值及非视距误差作为Kalman滤波器的状态变量,根据TOA测量值的结构特点和NLOS误差的统计特性,确定Kalman滤波器过程方程的状态转移矩阵。以NLOS误差服从指数分布的情况为例进行仿真,结果表明,该算法在精度估计和算法计算量方面具有明显优势。     

Alternative state estimation from nongaussian observation

An alternative state estimation scheme to extract gaussian message from nongaussian observation was proposed. The filter consists of a modification of Kalman filter to include a prefilter instead Kalman gain scheme. This prefilter is a conection in paralell of three branches: the first one, constant, has certain control over the transient; the second one, is basically a sum operator that “gaussianizes” the output estimation error; and a third one, a difference operator, is sensible to output estimation error bias. The three branches give an aspect of the PID structure on the prefiltering of the innovation process. An analysis, by simulation, and comparison with other structures is presented.     

基于模糊卡尔曼滤波器的网络控制系统状态估计

针对基于T S模糊模型的网络控制系统提出了一种卡尔曼滤波器的设计方法．先运用卡尔曼滤波理论给每个子系统设计出子滤波器，然后通过这些子滤波器的模糊融合得出全局滤波器．本文证明此全局滤波器可实现无偏状态估计，并给出了其稳定的条件．最后用仿真实例验证了所提出的卡尔曼滤波器的有效性．     

A parallel processing solution to the adaptive Kalman filtering problem with vector measurements

The adaptive Kalman filtering problem with vector measurements is considered. A computational algorithm is derived which gives estimates of the state of a linear dynamic system driven by additive white Gaussian noise with unknown covariance Q and observed by a linear function of the state contaminated by additive white Gaussian noise with unknown covariance R. The computational algorithm is inherently parallel in nature and it is noted that the algorithm should be implemented in a special purpose parallel processing digital computer made up of a number of filters similar to steady state Kalman filters each with a different gain. It is shown that the estimates of the state and the estimates of the unknown covariances Q and R can be made arbitrarily close to the optimal nonlinear Bayesian estimates by an appropriate choice for the number of parallel paths in the computer. When the filtering algorithm is implemented in a parallel processing computer the total processing time for state estimation in the unknown noise environment is only slightly increased over that required for a steady state Kalman filter. A numerical example with a five dimensional state and two dimensional measurement vector is presented.     

An adaptive unscented Kalman filter approach to secure state estimation for wireless sensor networks

Wireless sensor networks are vulnerable to false data injection attacks, which may mislead the state estimation. To solve this problem, this paper presents a chi-square test-based adaptive secure state estimation (CTASSE) algorithm for state estimation and attack detection. Taking advantage of Kalman filters, attack signal together with process noise or measurement noise are described as total white Gaussian noise with uncertain covariance matrix. The chi-square test method is used in the adaptation of the total noise covariance and attack detection. Then, a standard adaptive unscented Kalman filter (UKF) is used for the state estimation. Finally, simulation results show that the proposed CTASSE algorithm performs better than other UKFs in state estimation and is also effective in real-time attack detection.     

状态缺失多变量系统的极大似然辨识方法

提出一种极大似然辨识方法,用于解决状态缺失多变量系统的参数估计问题。通过构造以输入-输出序列为条件概率的似然函数 表达式,以及分析数据缺失程度对参数估计的影响,设计适用于状态缺失情况的卡尔曼状态估计器,在此基础上提出极大化似然函数的参数计算方法。数值仿真结果证明了该方法的有效性。     

基于模糊卡尔曼滤波的信息融合算法

应用自适应模糊逻辑系统（AFLS）原理,研究了一种基于卡尔曼滤波器的信息融合算法;AFLS通过在线监视融合数据新息是否为零均值白噪音,然后根据模糊规则调整融合滤波器的指数加权值,从而保证了滤波器的最优估计性能;仿真结果证明该方法在高噪声环境中具有良好的信息融合能力,能有效跟踪研究对象的状态变化。     

A comparison of simultaneous state and parameter estimation schemes for a continuous fermentor reactor

This article proposes a maximum likelihood algorithm for simultaneous estimation of state and parameter values in nonlinear stochastic state-space models. The proposed algorithm uses a combination of expectation maximization, nonlinear filtering and smoothing algorithms. The algorithm is tested with three popular techniques for filtering namely particle filter (PF), unscented Kalman filter (UKF) and extended Kalman filter (EKF). It is shown that the proposed algorithm when used in conjunction with UKF is computationally more efficient and provides better estimates. An online recursive algorithm based on nonlinear filtering theory is also derived and is shown to perform equally well with UKF and ensemble Kalman filter (EnKF) algorithms. A continuous fermentation reactor is used to illustrate the efficacy of batch and online versions of the proposed algorithms.     

基于量测迭代更新集合卡尔曼滤波的机动目标跟踪算法

在机动目标跟踪中,用于模型辨识和状态估计的非线性滤波器的合理选择和优化是提升滤波精度的关键.融合量测迭代更新集合卡尔曼滤波和交互式多模型(interacting multiple models,IMM)方法,本文提出了基于量测迭代更新集合卡尔曼滤波的机动目标跟踪算法.通过迭代更新思想的引入构建了一种量测迭代更新下集合卡尔曼滤波的实现结构,并将其作为IMM的模型滤波器实现对于目标运动模式和状态的辨识与估计.针对算法结合过程中滤波精度和计算量的平衡,设计了用于输入交互环节的状态估计样本,同时简化输入交互环节和输出交互环节中滤波误差协方差矩阵的交互过程.理论分析和仿真结果验证了算法的可行性和有效性.     

基于正交变换的改进CKF算法

为了解决容积卡尔曼滤波(CKF)算法在处理高维问题时出现的非局部采样问题,提出基于采样点正交变换的改进CKF算法(TCKF).从数值积分近似角度导出无迹卡尔曼滤波(UKF)和CKF两种近似滤波算法,并指出CKF只是UKF的一个特例;基于多元Taylor级数展开分析,揭示CKF在克服UKF数值不稳定性问题的同时,引入非局部采样问题;对Cubature点集进行正交变换得到TCKF算法,并从理论上证明,在高维、强非线性等非局部采样问题突出的滤波模型中,TCKF具有比CKF更高的估计精度.仿真实例验证了所提出算法的有效性.     

基于鲁棒H∞滤波的蓄电池荷电状态估计

针对蓄电池系统的荷电状态(SOC)受蓄电池材料及加工制作、工作温度、充放电大小及频率等因素的影响,是一个典型的非线性时变系统,相应的状态估计模型在测量过程中存在噪声干扰引起模型参数不确定性的特征。以安时法为基础,建立SOC的状态方程并应用鲁棒H∞滤波算法预测SOC估计值。仿真研究表明,提出的鲁棒H∞滤波算法在有色噪声干扰下比卡尔曼滤波(Kalman filter)有更好的估计精度;在白噪声情况下,鲁棒H∞滤波算法可通过调节其参数达到和卡尔曼滤波器相同的估计精度。     

基于Kalman滤波的通用和统一的白噪声估计方法

用射影理论,基于Kalman滤波提出了通用和统一的白噪声估计方法,可统一解决带非零均值相关噪声的线性离散时变随机控制系统的白噪声滤波、平滑和预报问题.提出了输入白噪声估值器和观测白噪声估值器,最优和稳态白噪声估值器,固定点、固定滞后和固定区间白噪声平滑器,白噪声新息滤波器和Wiener滤波器.它可应用于石油地震勘探信号处理和状态估计,为解决信号和状态估计问题,提供了新的途径和工具.关于Bernoulli-Gaussian白噪声估值器的仿真例子说明了其有效性.