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.     

按对角阵加权自校正信息融合Kalman预报器及其收敛性分析

对于带未知噪声统计的多传感器系统,应用现代时间序列分析方法,基于滑动平均(MA)新息模型的在线辨识和相关函数矩阵方程的解,得到了噪声方差估值器,且在按对角阵加权线性最小方差最优信息融合准则下,提出了自校正信息融合Kalman预报器.它实现了状态分量的自校正解耦融合Kalman预报器.基于动态误差系统,提出了自校正融合器的一种新的收敛性分析方法.提出了按实现收敛新概念,它比以概率1收敛弱.严格证明了：假如MA新息模型参数估计是一致的,则自校正融合Kalman预报器将按实现或按概率1收敛到最优融合Kalman预报器,因而它具有渐近最优性.它可减小计算负担,且便于实时应用. 一个3传感器跟踪系统的仿真例子证明了其有效性.     

自校正对角阵加权信息融合Kalman预报器

For the multisensor systems with unknown noise statistics, using the modern time series analysis method, based on on-line identification of the moving average (MA) innovation models, and based on the solution of the matrix equations for correlation function, estimators of the noise variances are obtained, and under the linear minimum variance optimal information fusion criterion weighted by diagonal matrices, a self-tuning information fusion Kalman predictor is presented, which realizes the self-tuning decoupled fusion Kalman predictors for the state components. Based on the dynamic error system, a new convergence analysis method is presented for self-tuning fuser. A new concept of convergence in a realization is presented, which is weaker than the convergence with probability one. It is strictly proved that if the parameter estimation of the MA innovation models is consistent, then the self-tuning fusion Kalman predictor will converge to the optimal fusion Kalman predictor in a realization, or with probability one, so that it has asymptotic optimality. It can reduce the computational burden, and is suitable for real time applications. A simulation example for a target tracking system shows its effectiveness.     

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.     

含未知参数的自校正融合Kalman滤波器及其收敛性

对于带未知模型参数和噪声方差的多传感器系统,基于分量按标量加权最优融合准则,提出了自校正解耦融合Kalman滤波器,并应用动态误差系统分析(Dynamic error system analysis,DESA)方法证明了它的收敛性.作为在信号处理中的应用,对带有色和白色观测噪声的多传感器多维自回归(Autoregressive,AR)信号,分别提出了AR信号模型参数估计的多维和多重偏差补偿递推最小二乘(Bias compensated recursive least-squares,BCRLS)算法,证明了两种算法的等价性,并且用DESA方法证明了它们的收敛性.在此基础上提出了AR信号的自校正融合Kalman滤波器,它具有渐近最优性.仿真例子说明了其有效性.     

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.     

不确定多传感器系统鲁棒观测融合Kalman 预报器

对于带不确定模型参数和噪声方差的线性离散时不变多传感器系统, 用虚拟噪声补偿不确定参数, 系统转化为仅带噪声方差不确定性的多传感器系统. 用加权最小二乘法和极大极小鲁棒估计准则, 基于带噪声方差保守上界的最坏情形保守系统, 提出一种鲁棒加权观测融合稳态Kalman 预报器, 并应用Lyapunov 方程方法证明了它的鲁棒性, 同时给出了与鲁棒局部和集中式融合Kalman 预报器的精度比较. 最后通过一个仿真例子说明了如何搜索参数扰动的鲁棒域, 并验证了所提出的理论结果的正确性和有效性.

     

带未知有色观测噪声的自校正融合Kalman滤波器

对于带未知有色观测噪声的多传感器线性离散定常随机系统, 未知模型参数和噪声方差的一致的融合估值器用递推增广最小二乘法(RELS)和求解相关函数方程得到. 将这些估值器代入到最优解耦融合Kalman滤波器中, 得出了自校正解耦融合Kalman滤波器, 并用动态方差误差系统分析(DVESA)和动态误差分析(DESA)方法证明了它收敛于最优解耦融合Kalman滤波器, 因而具有渐近最优性. 一个带3传感器跟踪系统的仿真例子说明了其有效 性.     

Robust fusion time‐varying Kalman estimators for multisensor networked systems with mixed uncertainties

This paper addresses the problem of designing robust fusion time‐varying Kalman estimators for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, missing measurements, packet dropouts, and uncertain‐variance linearly correlated measurement and process white noises. By the augmented approach, the original system is converted into a stochastic parameter system with uncertain noise variances. Furthermore, applying the fictitious noise approach, the original system is converted into one with constant parameters and uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case system with the conservative upper bounds of the noise variances, the five robust fusion time‐varying Kalman estimators (predictor, filter, and smoother) are presented by using a unified design approach that the robust filter and smoother are designed based on the robust Kalman predictor, which include three robust weighted state fusion estimators with matrix weights, diagonal matrix weights, and scalar weights, a modified robust covariance intersection fusion estimator, and robust centralized fusion estimator. Their robustness is proved by using a combination method, which consists of Lyapunov equation approach, augmented noise approach, and decomposition approach of nonnegative definite matrix, 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. A simulation example is shown with application to the continuous stirred tank reactor system to show the effectiveness and correctness of the proposed results.     

广义系统信息融合稳态与自校正满阶Kalman滤波器

基于线性最小方差标量加权融合算法和射影理论,对带多个传感器和带相关噪声的广义系统,提出了分布式标量加权融合稳态满阶Kalman滤波器.推得了任两个传感器子系统之间的稳态满阶滤波误差互协方差阵,其解可任选初值离线迭代计算.所提出的稳态融合滤波器避免了每时刻计算协方差阵和融合权重,减小了在线计算负担.当系统含有未知模型参数时,基于递推增广最小二乘算法和标量加权融合算法,提出了一种两段融合自校正状态滤波器.其中第1段融合获得未知参数的融合估计;第2段融合获得分布式自校正融合状态滤波器.与局部估计和加权平均融合估计相比,所提出的标量加权融合参数估计和自校正状态估计都具有更高的精度.仿真研究验证了其有效性.     

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.     

带多层融合结构的广义系统 Kalman 融合器

对带多传感器的线性离散随机广义系统, 用奇异值分解将其化为两个降阶耦合子系统, 应用现代时间序列分析方法, 基于自回归滑动平均 (Autoregressive moving average, ARMA) 新息模型和白噪声估计理论, 提出了带三层融合结构的分布式稳态 Kalman 融合器, 它由两个加权融合器和两个复合融合器组成. 第一层给出子系统状态融合器, 实现了每个子系统分量解耦融合; 第二层给出变换后状态融合器, 实现了两个子系统的解耦融合; 第三层给出原始状态融合器, 它可统一处理状态融合滤波、平滑和预报问题. 为计算最优加权阵, 给出了计算局部估计误差互协方差阵公式, 证明了它的精度比每个局部估值器精度高. Monte Carlo 的仿真实例说明了其有效性.     

带有色观测噪声的广义系统Kalman滤波器

对于带自回归滑动平均(ARMA)有色观测噪声的多传感器为广义离散随机线性系统,应用奇异值分解,将其变换为等价的两个降阶多传感器子系统,提出了广义系统多传感器信息融合状态滤波问题。为了提高精度,采用Kalman滤波方法,在线性最小方差按块对角阵最优加权融合准则下,给出了按矩阵加权解耦的分布式Kalman滤波器,可减少计算负担和改善局部滤波精度。为了计算最优加权,提出了局部滤波误差协方差阵的计算公式。一个Monte Carlo仿真例子说明了方法的有效性。     

随机奇异系统分布式最优融合降阶卡尔曼滤波器

Based on the optimal fusion algorithm weighted by matrices in the linear minimum variance (LMV) sense, a distributed full-order optimal fusion Kalman filter (DFFKF) is given for discrete-time stochastic singular systems with multiple sensors, which involves the inverse of a high-dimension matrix to compute matrix weights. To reduce the computational burden, a distributed reduced-order fusion Kalman filter (DRFKF) is presented, which involves in parallel the inverses of two relatively low-dimension matrices to compute matrix weights. A simulation example shows the effectiveness.     

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.     

Robust centralized and integrated covariance intersection fusion Kalman estimators for networked mixed‐uncertain systems

For networked mixed uncertain time‐varying systems with uncertain noise variances, random one‐step measurement delay, state‐dependent and noise‐dependent multiplicative noises, and linearly dependent additive white noises, the robust local, centralized, and distributed fusion estimation problems are addressed. Three new approaches are presented, which include a new augmented state approach with fictitious white noises, an extended Lyapunov equation approach with two Lyapunov equations, and a universal integrated covariance intersection (ICI) fusion approach of integrating the minimax robust local Kalman estimators and their conservative cross‐covariances. They constitute a new important methodology of solving robust fusion estimation problems. Applying them, the local, centralized, and distributed ICI fusion time‐varying and steady‐state robust Kalman estimators (predictor, filter, and smoother) are presented in the sense that for all admissible uncertainties, their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds. Their robustness, convergence, and accuracy relations are proved. Specially, the proposed ICI fusers improve the robust accuracies of the original covariance intersection fusers, and overcome their drawbacks, such that the local estimators and their conservative variances are assumed to be known, and the conservative cross‐variances are ignored. A simulation example with application to a vehicle suspension system shows the effectiveness of the proposed approaches and results.     

Self-tuning weighted measurement fusion Kalman filter and its convergence

For multisensor systems, when the model parameters and the noise variances are unknown, the consistent fused estimators of the model parameters and noise variances are obtained, based on the system identification algorithm, correlation method and least squares fusion criterion. Substituting these consistent estimators into the optimal weighted measurement fusion Kalman filter, a self-tuning weighted measurement fusion Kalman filter is presented. Using the dynamic error system analysis (DESA) method, the convergence of the self-tuning weighted measurement fusion Kalman filter is proved, i.e., the self-tuning Kalman filter converges to the corresponding optimal Kalman filter in a realization. Therefore, the self-tuning weighted measurement fusion Kalman filter has asymptotic global optimality. One simulation example for a 4-sensor target tracking system verifies its effectiveness.     

Self-tuning measurement fusion Kalman predictors and their convergence analysis

For multisensor systems with unknown parameters and noise variances, three self-tuning measurement fusion Kalman predictors based on the information matrix equation are presented by substituting the online estimators of unknown parameters and noise variances into the optimal measurement fusion steady-state Kalman predictors. By the dynamic variance error system analysis method, the convergence of the self-tuning information matrix equation is proved. Further, it is proved by the dynamic error system analysis method that the proposed self-tuning measurement fusion Kalman predictors converge to the optimal measurement fusion steady-state Kalman predictors in a realisation, so they have asymptotical global optimality. Compared with the centralised measurement fusion Kalman predictors based on the Riccati equation, they can significantly reduce the computational burden. A simulation example applied to signal processing shows their effectiveness.     

多传感器组合的移动车载数据采集系统研究

多传感器数据融合作为一门新兴前沿技术,已广泛应用于许多研究领域。三维信息快速采集是真实建模与三维虚拟现实的关键。提出了一种基于多传感器融合的车载移动式三维数据快速采集系统,集成了激光扫描仪、线/面阵CCD相机及GPS与IMU等多种传感器,以完成城市路面街道和建(构)筑物的三维数据自动采集。重点探讨了定位定姿方案设计及其实现,将GPS和IMU数据通过卡尔曼(Kalm an)滤波进行融合,可推测出整个系统及各传感器的位置和最佳姿态估计,以快速获取城市目标的地理坐标和三维建模信息,重建城市路面街道的三维真实场景。