不完全量测的误差方差约束下的容许采样频率

本文主要研究了不完全量测的误差方差约束下的传感器所能容许的采样频率这一问题. 分析了不完全量测下的目标跟踪系统的误差方差的稳态特性, 给出了不完全量测下误差协方差阵的一些性质. 在给定探测概率下, 利用线性矩阵不等式(LMI)求解这一问题. 工程意义在于, 在满足给定滤波器的误差方差约束指标下, 可以选择采样间隔较长的传感器, 放宽对传感器的采样频率的要求, 从而降低测量装置成本. 数值算例说明了算法的有效性.     

加权融合法处理无序量测问题

针对集中式多传感器目标跟踪系统中存在的无序量测问题,基于协方差加权融合的思想,在融合估计误差协方差矩阵迹最小意义下,建立了基于最优融合的多步延迟无序量测更新算法。该算法先将无序量测配准到最新状态估计的时刻,将其与之进行协方差加权融合。为进行无序量测与各传感器量测噪声相关性的计算,引入了等效量测。通过理论分析和仿真实验说明该算法能有效处理无序量测多延迟问题,其性能接近最优且随延迟步数增加性能下降非常小,而且有与最优的数据缓存法相同的滤波精度,以及较小的额外存储量。     

基于变分贝叶斯势均衡多目标多伯努利滤波的 多扩展目标跟踪算法

由于传统多扩展目标跟踪算法在量测噪声协方差未知情况下跟踪性能急剧下降,本文提出一种基于变分贝叶斯的势均衡多目标多伯努利滤波(VB--CBMe MBer)跟踪算法,并给出了高斯混合实现.该算法在未知量测噪声协方差的情况下,将量测看成随机分布在扩展目标上的量测产生点所产生,利用变分贝叶斯方法近似地求出各量测产生点状态和量测噪声协方差的联合概率密度,并给出其递归形式以估计量测产生点,继而将得到的量测产生点状态进行聚类得到扩展目标的状态.仿真实验表明,所提算法可以自适应地跟踪未知数目、未知量测噪声协方差的多扩展目标.其跟踪精度与传统的CBMe MBer跟踪算法相比,有明显提高.     

基于梯度自适应规则的自适应UKF算法及其应用

针对量测噪声方差统计值未知的非线性UKF(Unscented Kalman Filter)滤波问题,提出了一种基于梯度自适应规则的自适应UKF算法;在标准的非线性UKF算法基础上,根据残差方差阵的估计值与真实值之差构造代价指标函数,并将该函数相对于参数变化的负梯度方向作为参数更新的方向,构建自适应调节机制;将算法应用于GPS/DR(Dead-Reckoning)组合导航系统中,仿真结果显示状态估计误差具有良好的收敛性,估计精度较噪声观测器有明显改善,表明算法对量测噪声方差阵的动态变化具有较强的适应性。     

广义系统Kalman融合器的研究

研究带自回归滑动平均(ARMA)有色观测噪声的多传感器广义离散随机线性系统,根据Kalman滤波方法和白噪声估计理论,在线性最小方差信息融合准则下,应用奇异值分解和增广状态空间模型,为了提高融合器的精度,提出了按矩阵加权降阶稳态广义Kalman融合器,可统一处理稳态滤波、平滑和预报问题,可减少计算负担和改善局部估计精度。并提出最优加权系数的局部估计误差方差和协方差阵的计算公式。用一个Monte Carlo数值仿真实例说明了所提方法的有效性。     

基于融合反馈的多传感器空间偏差配准方法

利用多传感器的目标状态融合估计和融合估计误差协方差作为反馈信息,提出了带反馈机制的多传感器空间偏差配准方法.对二阶段Kalman滤波偏差配准方法进行扩展和改进,在不同噪声条件下对目标状态融合和偏差进行估计.仿真结果表明,带反馈信息的偏差配准方法可有效改善目标的状态估计和传感器的偏差配准,Crmaer-Rao下界分析说明了该算法的有效性.     

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.     

面向无线传感器网络节点定位的自适应卡尔曼滤波算法收敛条件分析

分析了新息序列是有色噪声时白适应卡尔曼滤波算法(Adaptive Kalman Filter,AKF)的滤波效果,在范数意义下,证明了k时刻AKF算法中估计误差协方差矩阵和k时刻最优KF算法中估计误差协方差矩阵间距离与新息序 列相关性成正比.利用上述结论,证明了所有AKF算法中估计误差协方差矩阵必逐渐远离1时刻最优KF算法中估计误差协方差矩阵.总结上述结论,发现AKF算法收敛条件可描述成以下几个等价命题:1)AKF算法中估计误差协方差矩阵与1时刻最优KF算法中估计误差协方差矩阵差有极限;2)k时刻AKF算法中估计误差协方差矩阵和k时刻最优KF算法中估计误差方差矩阵间距离极限是0;3)AKF算法渐进收敛于k时刻最优KF算法;4)AKF算法中新息序列渐进收敛于白噪声序列;5)k时刻AKF算法中滤波增益矩阵与k时刻最优KF算法中滤波增益矩阵间距离极限是0.上述理论为最终解决复杂环境下无线传感器网络节点定位问题奠定了基础.     

有色量测噪声下带广义未知扰动的递推上限滤波

针对博弈对抗环境下利用快速采样雷达进行非合作目标跟踪带来的有色噪声和未知干扰共存问题, 本文提出有色量测噪声下带广义未知扰动的随机动态系统递推上限滤波. 这里, 有色量测噪声用于描述由于快速采样或持续干扰带来的噪声相关性, 广义未知扰动用于建模博弈对抗对雷达观测带来的异常影响(先验信息缺失). 针对所考虑系统, 通过参数优化实现状态估计误差协方差上限(而不是理论值)的在线递推, 提出有色噪声下上限滤波(CU-BF), 给出状态估计误差协方差最小上限的近似实现, 讨论了所提CUBF的存在性条件. 在具有时变未知扰动和有色量测噪声的目标跟踪仿真中验证了所提方法的有效性.     

基于改进卡尔曼滤波的陀螺仪误差补偿算法

针对基于卡尔曼滤波的MEMS陀螺仪误差补偿算法中量测噪声方差选取不准确的问题,提出一种基于改进卡尔曼滤波的陀螺仪误差补偿算法.卡尔曼滤波通常采用统计特性估计得到固定的量测噪声方差,无法自适应地估计不同环境下陀螺仪噪声特性.该算法将卡尔曼滤波与神经网络相融合,使用卡尔曼滤波新息矩阵作为神经网络输入,通过神经网络得到新息协方差矩阵,以此自适应地估计卡尔曼滤波量测噪声方差.将该算法应用到陀螺仪信号误差补偿中,使用Allan方差分析法对原始信号以及误差补偿后的陀螺仪信号进行分析,实验结果表明该算法能够有效地抑制陀螺仪随机误差,提高MEMS陀螺仪的精度.     

Kalman filtering with intermittent observations

Motivated by navigation and tracking applications within sensor networks, we consider the problem of performing Kalman filtering with intermittent observations. When data travel along unreliable communication channels in a large, wireless, multihop sensor network, the effect of communication delays and loss of information in the control loop cannot be neglected. We address this problem starting from the discrete Kalman filtering formulation, and modeling the arrival of the observation as a random process. We study the statistical convergence properties of the estimation error covariance, showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded state error covariance occurs. We also give upper and lower bounds on this expected state error covariance.     

Stochastic stability of the unscented Kalman filter with intermittent observations

In this paper, the stochastic stability of the discrete-time unscented Kalman filter for general nonlinear stochastic systems with intermittent observations is proposed. It is shown that the estimation error remains bounded if the system satisfies some assumptions. And the statistical convergence property of the estimation error covariance is studied, showing the existence of a critical value for the arrival rate of the observations. An upper bound on this expected state error covariance is given. A numerical example is given to illustrate the effectiveness of the techniques developed.     

能量和带宽受限下的分布式一致性融合估计器

针对网络化多传感器分布式估计中传感器能量和通信网络带宽约束问题,提出一种基于降低发送频率和数据压缩降维的分布式一致性融合估计算法.为了满足通信网络带宽要求,各传感器节点直接选取局部估计信号的部分分量进行传输;与此同时,各节点随机间歇式发送数据包到其他节点来节省能量.在给定一致性权重下,建立以一致性估计器增益为决策变量,以所有传感器节点有限时域下状态融合估计误差协方差矩阵的迹的和为代价函数的优化问题,基于Lyapunov稳定性理论给出使得融合估计误差在无噪声时渐近稳定的一致性估计器增益存在的充分条件,并通过最小化代价函数的上界得到一组次优的一致性估计器增益值.最后,通过算例仿真验证算法的有效性.     

Kalman Filtering Over Graphs: Theory and Applications

In this technical note we consider the problem of distributed discrete-time state estimation over sensor networks. Given a graph that represents the sensor communications, we derive the optimal estimation algorithm at each sensor. We further provide a closed-form expression for the steady-state error covariance matrices when the communication graph reduces to a directed tree. We then apply the developed theoretical tools to compare the performance of two sensor trees and convert a random packet-delay model to a random packet-dropping model. Examples are provided throughout the technical note to support the theory.     

Consensus based overlapping decentralized estimation with missing observations and communication faults

In this paper a new algorithm for discrete-time overlapping decentralized state estimation of large scale systems is proposed in the form of a multi-agent network based on a combination of local estimators of Kalman filtering type and a dynamic consensus strategy, assuming intermittent observations and communication faults. Under general conditions concerning the agent resources and the network topology, conditions are derived for the convergence to zero of the estimation error mean and for the mean-square estimation error boundedness. A centralized strategy based on minimization of the steady-state mean-square estimation error is proposed for selection of the consensus gains; these gains can also be adjusted by local adaptation schemes. It is also demonstrated that there exists a connection between the network complexity and efficiency of denoising, i.e., of suppression of the measurement noise influence. Several numerical examples serve to illustrate characteristic properties of the proposed algorithm and to demonstrate its applicability to real problems.     

Robust detection of intermittent multiplicative sensor fault

In this paper, the detection problem of intermittent multiplicative sensor fault is investigated for stochastic uncertain systems. A robust optimal filter is designed according to the criterion of minimum estimation error covariance. Then, based on this, a residual generator is constructed, and the quantitative effect of the fault on it is discussed in detail. After that we design the evaluation function and detection threshold to achieve intermittent fault detection. Our proposed strategy has a recursive form and only includes simple arithmetic operations, thus it is suitable for real‐time online applications. Finally, a simulation example is given to demonstrate the effectiveness of the proposed strategy.     

基于多传感器的运动姿态测量算法

在基于MEMS传感技术的运动姿态测量中, 陀螺仪信号的漂移和载体线性加速度与重力加速度的叠加是影响测量结果准确性的主要原因, 实践中一般采用静态补偿和滤波技术减小测量误差. 基于自主研发的惯性测量单元, 设计了一种新型两级扩展卡尔曼滤波器: 基于四元数的运动姿态测量模型, 首先构造自适应加速度误差协方差矩阵, 消除载体线性加速度, 再采用多传感器融合技术进行数据融合, 修正陀螺仪信号漂移产生的误差. 实验表明, 本文算法结果与业界认可的动作捕捉系统Xsens的测量结果一致, 可有效满足应用需求.     

L-DACS中的信号分离算法的研究

L波段数字航空通信系统(L-DACS)是未来20年乃至更长时间航空通信需求的航空通信系统。为了解决接收机更好地区别有用信号,通过研究固定步长EASI算法和变步长EASI(VS-EASI)算法,提出一种基于优选估计函数的EASI峭度变步长(Q-EASI)算法。该算法根据信号的分离状态与峭度方差的关系,使步长随峭度方差的变化而变化,从而使收敛速度与稳态误差之间的矛盾得以缓解,并在信号分离的不同阶段使用不同的估计函数,使稳态误差得以减小。仿真验证,新算法相对于传统算法在稳定性和收敛速度上都有较大提高。     

Suboptimal sensors location in the state estimation problem for stochastic non-linear distributed parameter systems

The present paper deals with the minimal number sensor choice and their optimal location for the estimation in non-linear stochastic distributed parameter systems described by parabolic and hyperbolic partial differential equations. The necessary condition for the optimal sensor location by using the matrix minimum principle was obtained. In turn, the computational algorithm of the sensors location was determined on the basis of the necessary condition, applying the optimal control theory. The computational efficiency of this algorithm is defined by the suboptimal filtering algorithm which does not require solving of the matrix Riccati equation for the filter error covariance. Finally, one example is given to demonstrate the effectiveness of the present approach.     

Distributed estimation based on LQG control over homogeneous sensor networks

Motivated by navigation and tracking applications within sensor networks, we consider the distributed estimation problem over wireless sensor network. We propose a consensus based Kalman filtering algorithm based on optimal Linear Quadratic Gaussian control, in which each sensor can observe the dynamical system state, process the information data individually and communicate with each other within a sensing range. We provide a sufficient condition for the convergence of the proposed algorithm, and also give an upper bound for the estimation error covariance. Further, we find an optimal consensus gain for minimizing the network estimation error. Considering the occasional sensor fault and limited sensor energy, we investigate the proposed algorithm using only a subset of sensors to observe the dynamical system. With the assistance of the simulations, we verify the effectiveness of the proposed algorithms and present some interesting examples.