一种新的带白噪声估值器的固定滞后Kalman平滑器

本文基于经典Kalman滤波器和Mendel的输入白噪声估值器，应用射影理论，提 出了一种新的带白噪声估值器的最优固定滞后Kalman平滑器，且给出了平滑增益阵和平滑误 差方差阵新算法，避免了计算滤波和预报误差方差阵的逆矩阵，减少了计算负担．还提出了 相应的稳态次优固定滞后Kalman平滑器，它具有渐近稳定性．仿真例子说明了所提出的结果 的有效性．     

Iterative learning Kalman filter for repetitive processes

In this paper, a discrete-time iterative learning Kalman filter scheme is proposed for repetitive processes to reject repeatable disturbances as well as random noises. The proposed state estimator scheme integrates Kalman filter with iterative learning control. The estimation process contains two stages: a conventional Kalman filter is applied in the first stage; the second stage refines the estimates in an iterative learning fashion, leading to a gradual improvement on the estimation performance. According to the estimates that the first stage feeds to the second stage, the optimal design includes two types – posterior type and priori type. In order to reduce the memory and computation load of the optimal design, two suboptimal estimators are provided as well. The stability of the both suboptimal estimators is also studied. Furthermore, a lower bound is given to estimate the ultimate estimation performance before implementing any estimation. Finally, an illustrative example of injection molding is given to verify the performance of the four estimators developed.     

基于次优区间卡尔曼滤波的机器鱼跟踪方法

目前,自主水下航行器(Autonomous Underwater Vehicle,AUV)研究的重点集中在跟踪定位、精确制导和返坞等领域。机器鱼已成为AUV在智能教育、民用与军事等方面的应用热点。从非线性跟踪分析中发现,区间卡尔曼滤波算法虽然包含了一切可能的滤波结果,但范围比较宽,也比较保守,而且区间数据向量在实现之前是不确定的。文中提出了一种次优区间卡尔曼滤波优化算法。次优区间卡尔曼滤波方案用区间矩阵的逆 代替 其最坏逆,比标准区间卡尔曼滤波更逼近状态方程和测量方程的非线性过程,提高了标称动态系统模型的精确度,改善了跟踪系统的速度与精度。蒙特卡洛仿真实验结果表明,次优区间卡尔曼滤波算法的最优轨迹优于区间卡尔曼滤波方法及标准的卡尔曼滤波方法。     

U-D分解的前向固定区间平滑新算法

本文提出了两种前向固定区间平滑新算法以解决工程问题.为了确保算法的数值稳定 性并提高计算效率,两种算法中的协方差矩阵传播均使用了U-D分解形式.计算量分析结果 表明,两种新算法与Keigo Watanabe前向平滑算法相比较,计算量减少40%以上;状态维数 较高时,计算效率提高3倍以上.     

基于抗差扩展卡尔曼滤波器的永磁同步电机转速估计策略

通过分析粗差对扩展卡尔曼滤波器(extended Kalman filte,EKF)状态估计的影响,对无速度传感器矢量控制的永磁同步电机的转速,提出了一种基于抗差扩展卡尔曼滤波器(robust extended Kalman filter,REKF)的估计方法.建立了永磁同步电机的REKF模型,探讨了永磁同步电机在粗差干扰下引入REKF能否获得优于EKF的估计性能这一问题,比较了REKF与EKF在遇到外部粗差干扰或内部估算粗差干扰时转速和磁链的变化.仿真和实验结果表明REKF较EKF而言具有更好的抗粗差性能,使系统遇到干扰时能更快收敛.     

White noise estimators for networked systems with packet dropouts

This paper studies the optimal and suboptimal deconvolution problems over a network subject to random packet losses, which are modeled by an independent identically distributed Bernoulli process. By the projection formula, an optimal input white noise estimator is first presented with a stochastic Kalman filter. We show that this obtained deconvolution estimator is time-varying, stochastic, and it does not converge to a steady value. Then an alternative suboptimal input white-noise estimator with deterministic gains is developed under a new criterion. The estimator gain and its respective error covariance-matrix information are derived based on a new suboptimal state estimator. It can be shown that the suboptimal input white-noise estimator converges to a steady-state one under appropriate assumptions.     

极点配置固定区间Kalman平滑器和Wiener平滑器

基于稳态Kalman滤波器和白噪声估值器,根据控制理论中的极点配置原理,提出了极 点配置固定区间稳态Kalman平滑器和Wiener平滑器.它们避免了计算最优平滑初值,且通过配 置平滑器的极点,可快速消除初始平滑估值的影响,因而它们具有在有限固定区间上的实用稳定 性,仿真例子说明了它们的有效性.     

U－D分解的前向固定区间平滑新算法

本文提出了两种前向固定区间平滑新算法以解决工程问题．为了确保算法的数值稳定性并提高计算效率，两种算法中的协方差矩阵传播均使用了Ｕ－Ｄ分解形式．计算量分析结果表明，两种新算法与ＫｅｉｇｏＷａｔａｎａｂｅ前向平滑算法相比较，计算量减少４０％以上；状态维数较高时，计算效率提高３倍以上．     

Estimation using a multirate filter

This note presents both optimal and suboptimal filtering algorithms for estimating state variables based on measurements sampled at two different data rates. The optimal algorithm consists of two parallel Kalman filters; one processes the fast rate measurement and is of reduced-order, and the other processes the residuals from the first filter along with the slow rate measurement. This algorithm is used to design a suboptimal algorithm that has decreased computational requirements with only a small performance penalty.     

Linear estimation for random delay systems

This paper is concerned with the linear estimation problems for discrete-time systems with random delayed observations. When the random delay is known online, i.e., time-stamped, the random delayed system is reconstructed as an equivalent delay-free one by using measurement reorganization technique, and then an optimal linear filter is presented based on the Kalman filtering technique. However, the optimal filter is time-varying, stochastic, and does not converge to a steady state in general. Then an alternative suboptimal filter with deterministic gains is developed under a new criteria. The estimator performance in terms of their error covariances is provided, and its mean square stability is established. Finally, a numerical example is presented to illustrate the efficiency of proposed estimators.     

Bathymetric and oceanographic applications of Kalman filtering techniques

Ocean currents and seamounts (underwater mountains) can be mapped by analyzing data from satellite radar altimeters. This paper describes the application of Kalman filtering techniques to the analysis of such data acquired during the SEASAT mission. The altimeter data are modeled as samples from autoregressive random processes. Based on these models, matched filters are used to detect the characteristic nonstationarities in the altimeter data caused by seamounts and ocean currents such as the gulf stream. The geostrophic velocities of detected ocean currents are then estimated using Kalman smoothers. A useful formula is derived, which expresses the error power spectrum of the optimal fix lag smoother as a function of the lag and the error spectra of the optimal filter and the optimal infinite-lag smoother.     

未知探测概率下多目标PHD 跟踪算法

针对未知探测概率下多目标跟踪问题, 提出一种基于时变滤波算法的多目标概率假设密度(PHD) 滤波器. 算法推导了未知探测概率PHD递推式, 提出了将未知探测概率转化为目标的丢失与接收事件, 并依此建立了目标跟 踪的马尔科夫模型, 给出了该模型下时变卡尔曼滤波最优解, 进而在高斯混和PHD(GMPHD) 框架下推导了算法闭集解. 仿真实验表明, 所提出算法在未知且随时间变化的探测概率情形下, 仍能实时地跟踪各目标, 具有良好的工程应用前景.     

Non-linear filtering—the link between Kalman and extended Kalman filters

The problem of developing practical suboptimal filters for non-linear systems is treated using a different, approach. The filter developed (El-F) is found to fill in the gap between Kalman and extended Kalman filters. A numerical experiment to test the performance of the developed filter is conducted and the results are shown,     

不确定离散系统的最优鲁棒滤波

本文对一类含有范数有界参数不确定的离散线性系统的滤波问题进行了研究,了有限时域时变以及无限时域时不变两种情形,给出了一个对所有可容许参数不确定都能满足的估计误差方差上界,得到了使得该上界达到最小的最优鲁棒滤波器形式及其存在的充要条件,数值结果表明：当系统存在参数不确定时,本文所得到的滤波器优于标准的Ｋａｌｍａｎ滤波器以及文（４）中的鲁棒滤波器。     

Development of soft sensor by incorporating the delayed infrequent and irregular measurements

Originated from challenging industrial applications, this paper addresses a soft sensor development problem for linear systems with two types of measurements. One is fast, regular and delay-free measurements. The other is infrequent, irregular measurements with time-varying delays. The approach to be taken is based on the Kalman filter and data fusion technique, avoiding running the full augmented state Kalman filter, and leading to a considerably lower implementation cost. Although it is suboptimal, the loss in performance is minor compared to the optimal filter. Two simulation examples demonstrate the advantages of the proposed approach. An industrial soft sensor application example is also used to demonstrate its practicality.     

一类新的固定点和固定区间KALMAN平滑器

应用现代时间序列分析方法,基于ARMA新息模型和白噪声估值器,对线性定常 离散随机系统提出了两种新的固定点Kalman平滑器和两种新的正向固定区间Kalman平滑 器.它们的优点是避免了解Riccati方程,算法简单,可在线实现.为了保证它们的最优性,给 出了最优初值估值公式.仿真例子说明了其有效性.     

简化高阶强跟踪容积卡尔曼滤波及其在组合导航中的应用

针对传统容积卡尔曼滤波(CKF)在面对系统模型失配和状态突变滤波精度下降的问题,将强跟踪滤波器(STF)和高阶容积卡尔曼滤波(HCKF)相结合,提出一种简化高阶强跟踪容积卡尔曼滤波(RHSTCKF)算法.该算法具有比传统CKF更高的滤波精度,并且利用滤波模型的特点,简化HCKF的计算步骤,同时在HCKF中引入多重渐消因子增强算法的自适应性和应对状态突变的能力.将所提算法应用到SINS/GPS组合导航系统中进行仿真实验,结果表明,RHSTCKF可以准确估计出突变状态的真实值,能够抑制滤波器状态异常的干扰,滤波性能明显优于HCKF,能够提高组合导航系统的自适应性和定位精度.     

一类新的固定点和固定区间KALMAN平滑器1)

Using the modern time series analysis method,based on the autoregressive moving average (ARMA)innovation model and white noise estimators,this paper presents two new fixed-point Kalman smoothers and two new forward fixed-interval Kalman smoothers for linear discrete time-invariant stochastic systems.Their advantages are that the solution of the Riccati equation is avoided,and that the algorithms are simple and can be implemented on line.The optimal initial estimate formulas are given in order to ensure the optimality of the proposed smoothers.A simulation example shows their usefulness.     

确定采样型强跟踪滤波飞机舵面故障诊断与隔离

为了克服扩展多模型自适应估计中扩展卡尔曼滤波的理论局限性,多重渐消因子强跟踪改进引起的滤波发散现象以及多维高斯故障概率计算量大等问题,本文将一类基于确定解析采样近似方法的非线性次优高斯滤波与多模型自适应估计相结合,提出了改进的多重渐消因子强跟踪非线性滤波快速故障诊断方法.确定采样型滤波克服了扩展卡尔曼滤波的理论局限性;推导了等效多重渐消因子计算方法,避免了非线性系统雅克比矩阵的计算,提高了故障突变时的跟踪性能;提出了基于平方根分解的改进的一步预测协方差更新方程,保证了滤波稳定性;提出了基于欧几里得范数简化的故障概率计算方法,降低了计算量.通过对比仿真验证了3种不同非线性滤波算法及其强跟踪改进算法的有效性,故障诊断方法跟踪性强、速度快、精度高,具有较好的鲁棒性和稳定性.     

Suboptimal filter for continuous‐time linear systems with unknown parameters

The filtering problem for continuous‐time linear systems with unknown parameters is considered. A new suboptimal filter is herein proposed. It is based on the optimal mean‐square linear combination of the local Kalman filters. In contrast to the optimal weights, the suboptimal weights do not depend on current observations; thus, the proposed filter can easily be implemented in real‐time. Examples demonstrate high accuracy and efficiency of the suboptimal filter. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society