协方差交叉信息融合滤波器
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摘要
多传感信息融合Kalman滤波是信息融合和滤波理论相结合的产物，主要目的是对来自每个局部传感器的局部信息和数据进行关联、估计和融合，产生比基于每个局部信息的状态或者信号估计更准确的估计值。目前基本的信息融合方法有集中式融合Kalman滤波和分布式融合Kalman滤波。
分布式融合Kalman滤波在线性最小方差准则下主要有三种信息融合算法：按矩阵加权、按标量加权和按对角阵加权。相比于集中式融合估计方法，分布式融合估计减小计算负担，更灵活可靠。但是分布式融合估计需要计算局部估计的误差互协方差。在许多理论和实际问题中，互协方差的计算是非常复杂或者根本无法获得互协方差。如果不考虑局部变量的相关性，假设互协方差为零，可导致滤波实际误差方差阵增大，从而使滤波器发散。
本文提出的协方差交叉融合Kalman滤波算法完全避免辨识和计算系统的局部估计互协方差，可处理带未知局部估计互协方差的多传感器系统融合估计问题。CI融合给出融合估计实际误差方差阵的一个上界，这个上界与局部互协方差无关，即保证了CI融合估计的一致性和鲁棒性,并且可减小计算负担，避免了融合Kalman滤波器的发散问题。进一步给出了融合估计一致性证明。
对带不相关观测噪声、相关观测噪声和有色观测噪声的两传感器随机系统，在互协方差未知情况下，提出了两传感器CI融合Kalman估值器。
对传感器个数大于等于3的多传感器随机系统，提出了序贯CI融合Kalman估值器和批处理CI融合Kalman估值器，并给出了两种CI算法一致性证明。
将上述结果应用于信号处理过程，通过ARMA信号模型和状态空间模型之间的相互转化，把信号估计问题转化为状态估计问题，提出了两传感器多通道ARMA信号CI融合信号估值器。
对带观测滞后的两传感器随机系统，利用观测变换，直接将滞后系统转化为非时滞的标准系统，提出了两传感器时滞系统CI融合Kalman估值器。
本文证明了CI融合滤波器和局部Kalman滤波器、集中式融合、三种加权融合滤波器之间的精度关系。CI融合滤波器估计精度高于每个局部滤波器的精度，在多数情况下，小于且接近带已知局部互协方差的最优矩阵加权融合滤波器精度，按矩阵加权融合精度小于按标量加权融合精度，对角阵加权融合精度在两者中间。并进一步应用协方差椭圆直观给出了精度关系的几何解释，Monte-Carlo仿真结果证明了理论精度关系的准确性。
大量的仿真例子证明了理论结果的有效性和准确性。
Multisensor information fusion Kalman filtering is the combination of informationfusion and filtering theory, the main purpose is to correlation, estimation and fusionlocal information and data to get a more accurate fusion estimation than single sourceestimate. Now the commonly used method of information fusion filtering is centralizedfusion Kalman filtering and distributed fusion Kalman filtering.
Distributed fusion Kalman filtering based on linear minimum variance rules hasthree information fusion algorithm according to the matrix weighted, scalar weightedand diagonal matrix weighted. Compared with the centralized fuser, the distributed fusercan reduce the calculation burden and are more flexible and reliable. The distributedfusion estimation needs to calculate the cross-covariance of local estimate. However, inmany theoretical and application problems, the cross-covariance is unknown, or thecomputing of the cross-covariance is very difficult, or may not calculate thecross-covariance. If the cross-covariance is neglected, they are assumed to be zero,which can lead to the increase of the variance of the local filtering error, even thedivergence of the filtering.
In this paper, the covariance intersection fusion Kalman filtering algorithm ispresented, which can avoid identification and computing local cross-covariance and cansolve the fused filtering problems for multisensor systems with unknowncross-covariance. Covariance intersection fusion algorithm give an upper bound ofactual filtering error variances, and the upper bound is irrelevant of the unknowncross-covariance, so the consistency and robustness are ensured, and CI fusionalgorithm can reduce the computing burden and avoid the divergence of Kalmanfiltering. Further, the proof of consistency is given.
For the two-sensor stochastic system with uncorrelated observation noises, correlated observation noises and colored observation noises, and with unknowncross-covariance, the CI fusion Kalman filtering is presented.
For the multisensor stochastic system that the number of sensor is equal or greaterthan three, the sequential CI fusion Kalman filtering and batch CI fusion Kalmanfiltering are presented, and their consistency is proved.
Applying the proposed results to the signal processing, based on the transformationof the ARMA model to the state space model, the signal estimation problems cantranslate into the state estimation problems. The two-sensor multi-channel ARMA signalCI fusion filtering is presented.
For the two-sensor stochastic system with time-delayed measurements, using themeasurement transformation method, the time-delayed system with measurement delayscan be transformed into the standard system without measurement delays directly. TheCI fusion Kalman filtering for two-sensor system with time-delayed is presented.
In this paper, the accuracy relations among the CI fuser, local Kalman fusers,centralized fuser and fusers weighted by matrix,scalar or diagonal are proved. Theaccuracy of the CI fuser is higher than each local fusers and close to the accuracy of thefuser weighted by matrix, the accuracy of fuser weighted by matrix is higher than that ofthe fuser weighted by scalar and the accuracy of the fuser weighted by diagonal isbetween them. The geometric interpretations of these accuracy relations are given basedon the covariance ellipses, Monte-Carlo simulation results show the accuracy of therelations.
Many simulation examples show the effectiveness and correctness of thetheoretical results.
分布式融合Kalman滤波在线性最小方差准则下主要有三种信息融合算法：按矩阵加权、按标量加权和按对角阵加权。相比于集中式融合估计方法，分布式融合估计减小计算负担，更灵活可靠。但是分布式融合估计需要计算局部估计的误差互协方差。在许多理论和实际问题中，互协方差的计算是非常复杂或者根本无法获得互协方差。如果不考虑局部变量的相关性，假设互协方差为零，可导致滤波实际误差方差阵增大，从而使滤波器发散。
本文提出的协方差交叉融合Kalman滤波算法完全避免辨识和计算系统的局部估计互协方差，可处理带未知局部估计互协方差的多传感器系统融合估计问题。CI融合给出融合估计实际误差方差阵的一个上界，这个上界与局部互协方差无关，即保证了CI融合估计的一致性和鲁棒性,并且可减小计算负担，避免了融合Kalman滤波器的发散问题。进一步给出了融合估计一致性证明。
对带不相关观测噪声、相关观测噪声和有色观测噪声的两传感器随机系统，在互协方差未知情况下，提出了两传感器CI融合Kalman估值器。
对传感器个数大于等于3的多传感器随机系统，提出了序贯CI融合Kalman估值器和批处理CI融合Kalman估值器，并给出了两种CI算法一致性证明。
将上述结果应用于信号处理过程，通过ARMA信号模型和状态空间模型之间的相互转化，把信号估计问题转化为状态估计问题，提出了两传感器多通道ARMA信号CI融合信号估值器。
对带观测滞后的两传感器随机系统，利用观测变换，直接将滞后系统转化为非时滞的标准系统，提出了两传感器时滞系统CI融合Kalman估值器。
本文证明了CI融合滤波器和局部Kalman滤波器、集中式融合、三种加权融合滤波器之间的精度关系。CI融合滤波器估计精度高于每个局部滤波器的精度，在多数情况下，小于且接近带已知局部互协方差的最优矩阵加权融合滤波器精度，按矩阵加权融合精度小于按标量加权融合精度，对角阵加权融合精度在两者中间。并进一步应用协方差椭圆直观给出了精度关系的几何解释，Monte-Carlo仿真结果证明了理论精度关系的准确性。
大量的仿真例子证明了理论结果的有效性和准确性。
Multisensor information fusion Kalman filtering is the combination of informationfusion and filtering theory, the main purpose is to correlation, estimation and fusionlocal information and data to get a more accurate fusion estimation than single sourceestimate. Now the commonly used method of information fusion filtering is centralizedfusion Kalman filtering and distributed fusion Kalman filtering.
Distributed fusion Kalman filtering based on linear minimum variance rules hasthree information fusion algorithm according to the matrix weighted, scalar weightedand diagonal matrix weighted. Compared with the centralized fuser, the distributed fusercan reduce the calculation burden and are more flexible and reliable. The distributedfusion estimation needs to calculate the cross-covariance of local estimate. However, inmany theoretical and application problems, the cross-covariance is unknown, or thecomputing of the cross-covariance is very difficult, or may not calculate thecross-covariance. If the cross-covariance is neglected, they are assumed to be zero,which can lead to the increase of the variance of the local filtering error, even thedivergence of the filtering.
In this paper, the covariance intersection fusion Kalman filtering algorithm ispresented, which can avoid identification and computing local cross-covariance and cansolve the fused filtering problems for multisensor systems with unknowncross-covariance. Covariance intersection fusion algorithm give an upper bound ofactual filtering error variances, and the upper bound is irrelevant of the unknowncross-covariance, so the consistency and robustness are ensured, and CI fusionalgorithm can reduce the computing burden and avoid the divergence of Kalmanfiltering. Further, the proof of consistency is given.
For the two-sensor stochastic system with uncorrelated observation noises, correlated observation noises and colored observation noises, and with unknowncross-covariance, the CI fusion Kalman filtering is presented.
For the multisensor stochastic system that the number of sensor is equal or greaterthan three, the sequential CI fusion Kalman filtering and batch CI fusion Kalmanfiltering are presented, and their consistency is proved.
Applying the proposed results to the signal processing, based on the transformationof the ARMA model to the state space model, the signal estimation problems cantranslate into the state estimation problems. The two-sensor multi-channel ARMA signalCI fusion filtering is presented.
For the two-sensor stochastic system with time-delayed measurements, using themeasurement transformation method, the time-delayed system with measurement delayscan be transformed into the standard system without measurement delays directly. TheCI fusion Kalman filtering for two-sensor system with time-delayed is presented.
In this paper, the accuracy relations among the CI fuser, local Kalman fusers,centralized fuser and fusers weighted by matrix,scalar or diagonal are proved. Theaccuracy of the CI fuser is higher than each local fusers and close to the accuracy of thefuser weighted by matrix, the accuracy of fuser weighted by matrix is higher than that ofthe fuser weighted by scalar and the accuracy of the fuser weighted by diagonal isbetween them. The geometric interpretations of these accuracy relations are given basedon the covariance ellipses, Monte-Carlo simulation results show the accuracy of therelations.
Many simulation examples show the effectiveness and correctness of thetheoretical results.
引文
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