相关观测融合稳态Kalman滤波器及其最优性

对于带相关观测噪声和带不同观测阵的多传感器系统, 用加权最小二乘 (Weighted least squares, WLS) 法提出了两种相关观测融合稳态Kalman滤波算法. 其原理是用加权局部观测方程得到一个融合观测方程, 它伴随状态方程实现观测融合稳态Kalman滤波. 用信息滤波器证明了它们功能等价于集中式融合稳态Kalman滤波算法, 因而具有渐近全局最优性, 且可减少计算负担. 它们可应用于多通道自回归滑动平均 (Autoregressive moving average, ARMA) 信号观测融合滤波和反卷积. 两个数值仿真例子验证了它们的功能等价性.     

相关观测融合Kalman估值器及其全局最优性

对于带相关观测噪声和带不同观测阵的多传感器线性离散时变随机控制系统, 用加权最小二乘法(WLS)提出了两种加权观测融合Kalman估值器, 它们包括状态滤波、状态预报和状态平滑. 基于信息滤波器形式下的Kalman滤波器, 证明了在相同初值下, 它们在数值上恒等于相应的集中式观测融合Kalman估值器, 因而具有全局最优性. 但是它们可明显减轻计算负担. 数值仿真例子验证了它们在功能上等价于集中式观测融合Kalman估值器.     

自校正多传感器观测融合Kalman估值器及其收敛性分析

对于带未知噪声方差的多传感器系统,应用加权最小二乘(WLS)法得到了一个加权融合观测方程,且它与状态方程构成一个等价的观测融合系统.应用现代时间序列分析方法,基于观测融合系统的滑动平均(MA)新息模型参数的在线辨识,可在线估计未知噪声方差,进而提出了一种加权观测融合自校正Kalman估值器,可统一处理自校正融合滤波、预报和平滑问题,并用动态误差系统分析方法证明了它的收敛性,即若MA新息模型参数估计是一致的,则它按实现或按概率1收敛到全局最优加权观测融合Kalman估值器,因而具有渐近全局最优性.一个带3传感器跟踪系统的仿真例子说明了其有效性.     

不受约束的全局最优加权观测融合估计

利用矩阵满秩分解方法,基于加权最小二乘理论提出了一种不受各传感器观测阵是否相同、观测噪声是否相关约束限制的加权观测融合估计算法。证明了其估计结果每时刻恒同于集中式融合Kalman估计结果,因而具有全局最优性,且可明显减小计算负担,便于实时应用。通过对GPS目标跟踪系统的两种方案进行仿真说明了它的功能等价性、快速性以及最优性。     

非线性离散系统的相关观测融合时变Kalman滤波

针对带相关观测噪声和带不同观测函数的多传感器离散非线性系统,利用推广的离散Kalman滤波方法对状态系统和观测系统进行线性化处理,提出了基于岭估计的加权最小二乘(REWLS)分布式融合Kalman滤波算法.以风险函数为评价指标,利用信息滤波器比较了各种观测融合Kalman滤波算法,其中REWLS分布式融合算法精度最高.同时,分布式融合算法减少了计算负担,便于实时应用.仿真例子表明了理论分析的正确性.     

带有色观测噪声多传感器多重时滞系统分布式融合滤波器

基于新息分析方法, 对带有色观测噪声的多重时滞系统, 提出了一种带白噪声估值器的非增广的最优滤波器. 它等价于一个带相关白噪声多重时滞系统的一步预报器. 当系统带有多个传感器时, 推导了多重时滞系统的任意两个传感器子系统之间的估计误差互协方差阵. 基于线性最小方差最优加权融合估计算法, 给出了分布式加权融合最优滤波器. 分布式融合估计比基于每个传感器的局部估计具有更高的精度. 比增广的集中式最优滤波器具有更好的可靠性, 且避免了高维计算和大存储空间. 仿真例子验证了其有效性.     

加权观测融合非线性无迹卡尔曼滤波算法

针对非线性系统的无迹卡尔曼滤波器(UKF),应用加权最小二乘(WLS)法,提出了加权观测融合UKF滤波算法.证明了加权观测融合UKF滤波算法与集中式观测融合UKF滤波算法在数值上的完全等价性,因而具有全局最优性.一个带两传感器非线性系统的仿真例子说明了两种融合算法的有效性及等价性.     

带有色观测噪声系统多传感器标量加权最优信息融合稳态Kalman滤波器

基于标量加权多传感器线性最小方差最优信息融合准则,对被多传感器观测的带有色观测噪声的离散线性随机控制系统,提出了一种具有两层融合结构的标量加权信息融合稳态Kalman滤波器,它等价于相应的带相关噪声系统的最优信息融合稳态Kalman预报器.最优信息融合稳态预报器可在所有局部预报器达到稳态时,通过一次融合获得,且任两个子系统之间的稳态预报误差互协方差阵可通过任选初值迭代求得,并证明了它的收敛性.通过将它应用到带三个传感器的雷达跟踪系统验证了其有效性.     

网络化不确定系统集中式融合鲁棒稳态估值器

对于一类在状态转移阵和系统观测阵中带相同的状态依赖乘性噪声、带噪声依赖乘性噪声、一步随机观测滞后、丢包和不确定噪声方差的多传感器网络化系统,文章研究其鲁棒集中式融合稳态滤波问题.应用增广方法将系统转换为带随机参数矩阵、相同过程和观测噪声的集中式融合系统.应用去随机化方法和虚拟噪声技术,系统进一步转化为仅带不确定噪声方差的集中式融合系统.根据极大极小鲁棒估计原理,本文提出了鲁棒集中式融合稳态Kalman估值器(预报器、滤波器和平滑器),证明了所提出的集中式融合估值器的鲁棒性,给出了鲁棒局部与集中式融合估值器之间的精度关系.本文提出了应用于多传感器多通道滑动平均(MA)信号估计的一个实例,给出了相应的鲁棒局部和集中式融合信号估值器.仿真实验验证了所提出方法的有效性和正确性.     

基于Bayes估计的离散Kalman滤波相关观测融合

针对带相关观测噪声和带不同 未知观测函数的多传感器离散系统,在已有的融合算法基础上提出了基于Bayes估计的加权最小二乘(Bayes estimation weighted least squares,BYEWLS)分布式融合Kalman滤波算法。该方法充分利用未知参数的验前信息,以风险函数为评价指标,证明了BYEWLS融合算法优于WLS融合算法,针对YEWLS融合算法是有偏估计,提出了在线消除偏差的方法。分布式融合算法减少了计算负担,提高了融合精度,便于实时应用。最后通过仿真例子验证了该方 法的有效性和理论分析的正确性。     

Robust centralized and weighted measurement fusion Kalman estimators for uncertain multisensor systems with linearly correlated white noises

This paper addresses the design of robust centralized fusion (CF) and weighted measurement fusion (WMF) Kalman estimators for a class of uncertain multisensor systems with linearly correlated white noises. The uncertainties of the systems include multiplicative noises, missing measurements, and uncertain noise variances. By introducing the fictitious noises, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of uncertain noise variances, the robust CF and WMF time-varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities of their algorithms are analyzed and compared. Compared with CF algorithm, the WMF algorithm can significantly reduce the computational burden when the number of sensors is larger. A robust weighted least squares (WLS) measurement fusion filter is also presented only based on the measurement equation, and it is proved that the robust accuracy of the robust CF or WMF Kalman filter is higher than that of robust WLS filter. The corresponding robust fused steady-state estimators are also presented, and the convergence in a realization between the time-varying and steady-state robust fused estimators is proved by the dynamic error system analysis (DESA) method. A simulation example shows the effectiveness and correctness of the proposed results.     

Robust weighted fusion Kalman estimators for multisensor systems with multiplicative noises and uncertain‐covariances linearly correlated white noises

This paper addresses the design of robust weighted fusion Kalman estimators for a class of uncertain multisensor systems with linearly correlated white noises. The uncertainties of the systems include the same multiplicative noises perturbations both on the systems state and measurement output and the uncertain noise variances. The measurement noises and process noise are linearly correlated. By introducing two fictitious noises, the system under consideration is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case systems with the conservative upper bounds of the noise variances, the four robust weighted fusion time‐varying Kalman estimators are presented in a unified framework, which include three robust weighted state fusion estimators with matrix weights, diagonal matrix weights, scalar weights, and a modified robust covariance intersection fusion estimator. The robustness of the designed fusion estimators is proved by using the Lyapunov equation approach such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The accuracy relations among the robust local and fused time‐varying Kalman estimators are proved. The corresponding robust local and fused steady‐state Kalman estimators are also presented, a simulation example with application to signal processing to show the effectiveness and correctness of the proposed results. Copyright © 2016 John Wiley & Sons, Ltd.     

The sufficient condition for lossless linear transformation for distributed estimation with cross-correlated measurement noises

In most distributed fusion algorithms, the measurement noises in different sensors are often assumed to be uncorrelated, but in practical occasions the assumption may not be met and the measurement noises are often cross-correlated between sensors. So the lossless distributed fusion algorithms with the assumption of uncorrelated measurement noises usually cannot keep their lossless performance in practical applications. Therefore, in the case of cross-correlated measurement noises, the lossless compression rule for distributed estimation is proposed. We prove in theory that the sufficient condition of the lossless compression is the transformation matrix is of full column rank. Using the transformation matrix constructed by the proposed rule, the distributed fusion can achieve the performance of the centralized one. In addition, under this rule two optimal fusion algorithms are proposed and their performances are analyzed.     

两种最优观测融合方法的功能等价性

对于基于K alm an滤波的多传感器数据融合,有两种最优观测融合方法:第一种是集中式观测融合方法,它是通过增加观测向量的维数合并多传感器数据,而第二种是分布式观测融合方法,它是在线性最小方差准则下,通过加权合并多传感器数据,但观测向量维数不变.在数据融合所用的传感器带有相同观测阵的情形下,本文用K alm an证明了两种观测融合方法是完全功能等价的,即用两种方法得到的K alm an估值器(滤波器,预报器,平滑器),信号估值器和白噪声估值器分别在数值上是相等的.在这种情形下,第二种方法不仅可给出像第一种方法一样的全局最优融合估计,而且可明显减小计算负担,便于实时应用.一个数值例子说明了其正确性.     

多传感器异步线性测量系统的数据融合

由于采样速率和传送数据到融合中心的通信延迟的不同,现代工业生产过程中用于对未知的常值或缓变参数进行估计的多传感器通常是异步工作的,且受到加性测量噪声的干扰。在最小二乘估计意义下,对于测量噪声互不相关的多传感器异步线性测量系统,提出了集中式和分布式递推参数估计数据融合算法,两种算法完全等价,且都是全局最优的。数值仿真实验的结果表明,通过利用多传感器的测量数据,增大了对参数测量的数据流和数据率,传感器测量参数的估计准确度得到明显改善。     

Optimal linear estimators for systems with random measurement delays

This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with random measurement delays. A new model that describes the random delays is constructed where possible the largest delay is bounded. Based on this new model, the optimal linear estimators including filter, predictor and smoother are developed via an innovation analysis approach. The estimators are recursively computed in terms of the solutions of a Riccati difference equation and a Lyapunov difference equation. The steady-state estimators are also investigated. A sufficient condition for the convergence of the optimal linear estimators is given. A simulation example shows the effectiveness of the proposed algorithms.