带相关噪声的观测融合稳态Kalman滤波算法及其全局最优性

对于带相关的输入白噪声和观测白噪声及相关观测白噪声的多传感器线性离散定常随机系统,用加权最小二乘(WLS)法提出了一种加权观测融合稳态Kalman滤波算法,可处理状态、白噪声和信号融合滤波、平滑、预报问题。基于稳态信息滤波器证明了它完全功能等价于集中式观测融合稳态Kalman滤波算法,因而它具有渐近全局最优性,且可减少计算负担。一个跟踪系统仿真例子验证了它的功能等价性。     

自校正解耦融合Kalman预报器及其收敛性

对于带有未知模型参数和噪声方差的多传感器系统,通过系统辨识方法,得到模型参数和噪声方差的信息融合估计,将其代入到最优分量按标量加权融合Kalman预报器中,得到自校正信息融合Kalman预报器,实现了状态分量的解耦。通过动态误差系统分析（DESA）方法严格证明了提出的自校正Kalman预报器按一个实现收敛于最优融合Kalman预报器,因此它有渐近最优性。应用信号处理的仿真例子验证了其有效性。     

多传感器信息融合稳态最优Wiener反卷积滤波器

应用现代时间序列分析方法,基于ARMA新息模型和Lyapunov方程,提出了单通道ARMA信号的多传 感器信息融合稳态最优Wiener反卷积滤波器。它避免了Riccati方程,可用于设计含未知模型参数和含未知噪声方 差系统的自校正信息融合滤波器。一个仿真例子说明了其有效性。     

多传感器分布式融合Kalman预报器

应用现代时间序列分析方法,基于ARMA新息模型,在线性最小方差最优信息融合准则下,对于输入噪声与观测噪声相关且观测噪声相关的多传感器系统,分别提出了按矩阵加权、按标量加权和按对角阵加权的3种分布式融合稳态Kalman 预报器。其中提出了基于Lyapunov方程的局部预报估值误差方差阵和协方差阵计算公式。它们被用于计算最优加权,与单传感器情形相比,可提高估值器的精度。一个跟踪系统的仿真例子说明了其有效性,且说明了3种加权融合预报器的精度无显著差别。但标量加权融合预报器可显著减小计算负担,提供一种快速实时信息融合估计算法。     

多通道ARMA信号的三种多传感器信息融合Wiener滤波器

应用现代时间序列分析方法,基于ARMA新息模型、白噪声估值器和观测预报器,对带白色观测噪声的多通道ARMA信号,在线性最小方差最优信息融合准则下,提出了统一的和通用的按矩阵加权、按标量加权和按对角阵加权的多传感器信息融合Wiener滤波器,可统一处理滤波、平滑和预报问题．提出了计算局部估计误差方差和协方差的公式,它们被用于计算最优加权．同单传感器情形相比,可提高滤波精度．一个目标跟踪仿真例子说明了其有效性,且说明了三种加权融合滤波器的精度无显著差异,因而利用按标量加权融合滤波器以轻微的精度损失提供一种快速融合估计算法,便于实时应用．     

多传感器分布式融合白噪声反卷积滤波器

基于Kalman滤波方法和白噪声估计理论,在按矩阵加权线性最小方差最优融合准则下,提出了带ARMA有色观测噪声系统的多传感器分布式融合白噪声反卷积滤波器,其中推导出用Lyapunov方程计算最优加权的局部估计误差互协方差公式。与单传感器情形相比,可提高融合估值器精度。它可应用于石油地震勘探信号处理。一个三传感器分布式融合Bernoulli-Gauss白噪声反卷积平滑器的仿真例子说明了其有效性。     

多通道信号自校正分布式融合Kalman滤波器

对带未知参数的多传感器多通道自回归滑动平均(ARMA)信号,采用多维递推辅助变量(MRIV)方法得到自回归模型参数估值,通过Gevers-Wouters算法辨识滑动平均模型参数估值,再用相关方法得到噪声方差的估值。把所有的估值都代入到最优分布式融合信息滤波器中得到自校正分布式融合Kalman信息滤波器。该滤波器具有渐近全局最优性,一个多通道信号仿真例子验证了其有效性。     

不确定系统鲁棒协方差交叉融合稳态Kalman滤波器

针对带不确定模型参数和噪声方差的线性离散多传感器系统,基于极大极小鲁棒估值原理,该文提出一种鲁棒协方差交叉(CI)融合稳态Kalman滤波器。首先,用引入虚拟噪声补偿不确定模型参数,把模型参数和噪声方差两者不确定的多传感器系统转化为仅噪声方差不确定的系统。其次,应用Lyapunov方程证明局部鲁棒Kalman滤波器的鲁棒性,进而保证CI融合Kalman滤波的鲁棒性,且证明了CI融合器的鲁棒精度高于每个局部滤波器的鲁棒精度。最后,给出一个仿真例子来说明如何搜索不确定参数的鲁棒域,并验证所提出的鲁棒Kalman滤波器的优良性能。     

多传感器最优信息融合白噪声反卷积滤波器

基于Kalman滤波方法和白噪声估计理论,在线性最小方差按矩阵加权最优信息融合准则下,提出了带相关噪声系统多传感器信息融合白噪声反卷积滤波器.提出了各传感器滤波误差之间的协方差阵计算公式,可用于计算最优融合加权阵.同单传感器情形相比,可提高融合滤波精度.它可减少在线计算负担,便于实时应用.它可应用于石油地震勘探信号处理.一个3传感器信息融合Bernoulli-Gaussian白噪声反卷积滤波器的仿真例子说明了其有效性.     

加权融合鲁棒增量Kalman滤波器

在一定环境条件下,当系统的量测方程没有进行验证或校准时,使用该量测方程往往会产生未知的系统误差,从而导致较大的滤波误差。同样地,当系统的噪声方差不确定时,滤波的性能也将会变坏,甚至会引起滤波器发散。增量方程的引入可以有效消除系统的未知量测误差,从而带未知量测误差的欠观测系统的状态估计问题可以转换为增量系统的状态估计问题。该文考虑带未知量测误差和未知噪声方差的线性离散系统,首先提出一种基于增量方程的鲁棒增量Kalman滤波器。进而,基于线性最小方差最优融合准则,提出一种加权融合鲁棒增量Kalman滤波算法。仿真实例证明了所提算法的有效性和可行性。     

Self-tuning measurement fusion Kalman filter with correlated measurement noises

For the multisensor system with correlated measurement noises and unknown noise sta-tistics, based on the solution of the matrix equations for correlation function, the on-line estimators of the noise variances and cross-covariances is obtained. Further, a self-tuning weighted measurement fusion Kalman filter is presented, based on the Riccati equation. By the Dynamic Error System Analysis (DESA) method, it rigorously proved that the presented self-tuning weighted measurement fusion Kalman filter converges to the optimal weighted measurement fusion steady-state Kalman filter in a realization or with probability one, so that it has asymptotic global optimality. A simulation example for a target tracking system with 3-sensor shows that the presented self-tuning measurement fusion Kalman fuser converges to the optimal steady-state measurement fusion Kalman fuser.     

Self-tuning weighted measurement fusion white noise deconvolution estimator

For the multi-sensor linear discrete time-invariant stochastic systems with correlated measurement noises and unknown noise statistics,an on-line noise statistics estimator is obtained using the correlation method.Substituting it into the optimal weighted fusion steady-state white noise deconvolution estimator based on the Kalman filtering,a self-tuning weighted measurement fusion white noise deconvolution estimator is presented.By the Dynamic Error System Analysis(DESA) method,it proved that the self-tunin...     

Self-tuning distributed measurement fusion Kalman estimator for the multi-channel ARMA signal

For the multisensor multi-channel autoregressive moving average (ARMA) signal with white measurement noises and a common disturbance measurement white noise, when the model parameters and the noise variances are all unknown, a multi-stage information fusion identification method is presented, where the consistent fused estimates of the model parameters and noise variances are obtained by the multi-dimension recursive instrumental variable (RIV) algorithm, correlation method and Gevers-Wouters algorithm with a dead band. Substituting these estimates into the optimal distributed measurement fusion Kalman signal estimator, a self-tuning distributed measurement fusion Kalman signal estimator is presented. Its convergence is proved by the dynamic error system analysis (DESA) method, so that it has asymptotical global optimality. In order to reduce computational load, a fast recursive inversion algorithm for a high-dimension matrix is presented by the inversion formula of partitioned matrix. Especially, when the process and measurement noise variance matrices are all diagonal matrices, the inversion formula of a high-dimension matrix is presented, which extends the formula of the inverse of Pei-Radman matrix. Applying the proposed inversion algorithm, the computation of the fused measurement and fused noise variance is simplified and their computational burden is reduced. A simulation example shows effectiveness of the proposed method.     

数据融合技术在测量船组合导航系统中的应用

提出了利用数据融合技术来提高测量船的导航系统精度的方法.针对测量船上的惯性导航系统在长时间运行后产生误差的问题,通过测量船上的天文经纬仪观测恒星,利用卡尔曼滤波把惯性导航、天文导航等其他导航系统组成组合导航系统,并建立了数学模型.同时在卡尔曼滤波中引入模糊控制理论,来解决所建立的数学模型中量测噪声不满足零均值高斯白噪声的问题.实验结果与理论分析一致,证明利用多种数据融合方法能有效提高测量船导航系统的精度.     

SINS/视觉组合导航系统融合算法

捷联惯性导航系统(SINS)/视觉组合导航系统的融合算法主要是卡尔曼滤波,卡尔曼滤波实现最优估计的前提是系统的模型必须准确已知。对于SINS/视觉组合导航系统,获取量测信息需经图像处理、特征点提取和匹配等过程,使量测噪声统计模型不完全可知,这会导致卡尔曼滤波器的估计精度下降。因此,该文提出一种改进的自适应两级卡尔曼滤波,根据求解遗传因子的不同方法对传统自适应两级卡尔曼滤波进行改进。改进后的算法分别适用于系统噪声统计模型和量测噪声统计模型不准确可知两种情况,且二者具有统一的滤波框架。仿真结果表明,改进的自适应两级卡尔曼滤波比卡尔曼滤波精度高,有效解决了SINS/视觉组合导航系统因噪声统计模型不准确导致的精度下降问题。     

基于协方差加权的卡尔曼滤波融合跟踪算法

针对卡尔曼滤波融合跟踪对系统模型准确度和先验信息精度要求较高的问题,提出一种基于协方差加权的卡尔曼滤波融合方法,利用最小二乘准则作为误差加权的标准,使误差小的传感器加权因子大。基于此,再利用卡尔曼滤波融合,充分保留有用信息,抑制噪声干扰。在目标跟踪应用中,即使噪声统计信息未知且噪声互相关,利用该方法仍能够获得最小均方误差准则下的最优目标状态跟踪估计。     

Optimal and self-tuning deconvolution in time domain

This paper is concerned with both the optimal (minimum mean square error variance) and self-tuning deconvolution problems for discrete-time systems. When the signal model, measurement model, and noise statistics are known, a novel approach for the design of the optimal deconvolution filter, predictor, and smoother is proposed based on projection theory and innovation analysis in the time domain. The estimators are given in terms of an autoregressive moving average (ARMA) innovation model and one unilateral linear polynomial equation, where the ARMA innovation model is obtained by performing one spectral factorization. A self-tuning scheme can be incorporated when the noise statistics, the input model, and/or colored noise model are unknown. The self-tuning estimator is designed by identifying two ARMA innovation models