最优和自校正多传感器信息融合白噪声反卷积估值器
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摘要
随着信息时代的到来,多传感器信息融合因其能有效地提高和优化基于单传感器的估计、识别或决策(控制)性能而得到了日趋广泛的重视和应用,其应用领域遍及军事和民用领域的方方面面。作为其中的一个分支,最优和自校正信息融合滤波理论分别是针对模型参数和／或噪声统计已知和未知两种情况下的多传感器系统的状态或信号的融合估计问题研究。系统的输入白噪声信号估计问题即白噪声反卷积估计问题在石油地震勘探和通信系统有重要应用背景。
本文应用Kalman滤波方法和现代时间序列分析方法两种方法论,基于多传感器加权状态融合和加权观测融合两种融合方法,结合系统辨识方法,分别进行最优和自校正多传感器信息融合白噪声反卷积估值器的研究。主要工作包括以下四个方面：
首先,应用Kalman滤波方法,基于Riccati方程,对带不同局部模型和带相关噪声多传感器系统给出统一的加权融合最优和稳态最优白噪声反卷积估值器。为了计算最优加权,给出了计算局部估计误差互协方差的两种公式。
其次,应用现代时间序列分析方法,基于ARMA新息模型,对带不同局部模型和带相关噪声多传感器系统给出统一的稳态最优白噪声估值器。对带相同或不同局部动态模型的多传感器时滞系统,提出了的最优加权状态融合白噪声反卷积估值器。为了计算最优加权,分别给出了计算局部估计误差互协方差的公式。
再次,应用Kalman滤波方法,基于Riccati方程,对于带相同观测阵和相关观测噪声或带不同观测阵和相关观测噪声或带相同观测阵和相关噪声的多传感器时变系统,分别提出了最优加权观测融合白噪声反卷积估值器,并证明其与相应的集中式融合白噪声反卷积估值器的完全功能等价性和全局最优性。同时作为特殊情况又给出了相应的定常系统稳态最优加权观测融合白噪声反卷积估值器。
最后,应用Kalman滤波方法,基于Riccati方程,对带未知噪声统计的多传感器定常系统,应用基于相关函数方法的信息融合噪声统计的估值器,提出了自校正加权观测融合白噪声反卷积估值器。对带未知模型参数和带未知噪声统计的多传感器单通道AR和ARMA系统,应用相关函数方法、递推辅助变量算法和Gevers-Wounters算法给出了模型参数和噪声统计估值器,进而提出了自校正加权观测融合白噪声反卷积估值器。并基于动态误差系统分析方法证明了其收敛于相应的稳态加权观测融合白噪声反卷积估值器,即它们具有渐近全局最优性。
以上结论均通过仿真例子给出验证,证明了理论的有效性。
上述结果在多传感器信息融合滤波、石油地震勘探、信号处理和状态估计等领域有重要的理论和应用价值。
With the coming of information era, multisensor information fusion is being emphasized and applied widely in the world due to the effectively improved and optimized performance of estimation, identification and detection (control) based on the single sensor. The applications spread over various aspects of military and civil fields. As an embranchment, optimal and self-tuning information fusion filtering theory refers to the fusion estimation problem of state or signal for the multisensor systems with known or unknown model parameters and/or noise statistics, respectively. The input white noise estimation problem of systems or white noise deconvolution estimation problem has important applications in seismic exploration and communication systems.
Using two methodologies—Kalman filtering method and modern time series analysis method, this paper researches the optimal and self-tuning multisensor information fusion white noise deconvolution estimators based on two fusion methods, so-called multisensor weighted state fusion and weighted measurement fusion methods, combining with the system identification methods, respectively. The main work includes the following four aspects:
Firstly, based on the Riccati equation, the unified weighted fusion optimal and steady-state optimal white noise estimators are presented using Kalman filtering method for the multisensor systems with different local dynamic models and correlated noises. In order to compute the optimal weights, two formulae of computing the local estimation error cross-covariances are given.
Secondly, based on the ARMA innovation model, the unified steady-state optimal white noise estimators are presented using the modern time series analysis method for the multisensor systems with different local dynamic models and correlated noises. The optimal weighted state fusion white noise deconvolution estimators are presented for the multisensor time-delayed systems with the same or different local dynamic models. In order to compute the optimal weights, the formulae of computing the local estimation error cross-covariances are given, respectively.
Thirdly, based on the Riccati equation, the optimal weighted measurement fusion white noise deconvolution estimators are respectively presented using the Kalman filtering method for the multisensor time-varying systems with the same measurement matrices and correlated measurement noises or with different measurement and correlated measurement noises or with the same measurement matrices and correlated noises. Moreover, the completely functional equivalence and the global optimality of the fusers are proved compared with the corresponding centralized fusion white noise deconvolution estimators. As a special case, the corresponding steady-state optimal weighted measurement fusion white noise deconvolution estimators are also given for the time-invariant systems.
Finally, based on the Riccati equation, the self-tuning weighted measurement fusion white noise deconvolution estimators are presented using the Kalman filtering method for the multisensor time-invariant systems with unknown noise statistics, where the estimators of information fusion noise statistics by the correlation function method are used. For the multisensor single channel AR or ARMA systems with unknown model parameters and noise statistics, the self-tuning weighted measurement fusion white noise deconvolution estimators are presented using the estimators of model parameters and noise statistics by the correlation function method, recursive instrumental variable algorithm and Gevers-Wounters algorithm. Moreover, based on the Dynamic Error System Analysis method, it is proved that the fusers converge to the corresponding steady-state optimal weighted measurement fusion white noise deconvolution estimators, so that they have the asymptotical global optimality;
The above results are all proved by the simulation examples, which show the effectiveness of the theory.
They have important theoretical and application value in many fields including the multisensor information fusion filtering, oil seismic exploration, signal processing, and state estimation.
本文应用Kalman滤波方法和现代时间序列分析方法两种方法论,基于多传感器加权状态融合和加权观测融合两种融合方法,结合系统辨识方法,分别进行最优和自校正多传感器信息融合白噪声反卷积估值器的研究。主要工作包括以下四个方面：
首先,应用Kalman滤波方法,基于Riccati方程,对带不同局部模型和带相关噪声多传感器系统给出统一的加权融合最优和稳态最优白噪声反卷积估值器。为了计算最优加权,给出了计算局部估计误差互协方差的两种公式。
其次,应用现代时间序列分析方法,基于ARMA新息模型,对带不同局部模型和带相关噪声多传感器系统给出统一的稳态最优白噪声估值器。对带相同或不同局部动态模型的多传感器时滞系统,提出了的最优加权状态融合白噪声反卷积估值器。为了计算最优加权,分别给出了计算局部估计误差互协方差的公式。
再次,应用Kalman滤波方法,基于Riccati方程,对于带相同观测阵和相关观测噪声或带不同观测阵和相关观测噪声或带相同观测阵和相关噪声的多传感器时变系统,分别提出了最优加权观测融合白噪声反卷积估值器,并证明其与相应的集中式融合白噪声反卷积估值器的完全功能等价性和全局最优性。同时作为特殊情况又给出了相应的定常系统稳态最优加权观测融合白噪声反卷积估值器。
最后,应用Kalman滤波方法,基于Riccati方程,对带未知噪声统计的多传感器定常系统,应用基于相关函数方法的信息融合噪声统计的估值器,提出了自校正加权观测融合白噪声反卷积估值器。对带未知模型参数和带未知噪声统计的多传感器单通道AR和ARMA系统,应用相关函数方法、递推辅助变量算法和Gevers-Wounters算法给出了模型参数和噪声统计估值器,进而提出了自校正加权观测融合白噪声反卷积估值器。并基于动态误差系统分析方法证明了其收敛于相应的稳态加权观测融合白噪声反卷积估值器,即它们具有渐近全局最优性。
以上结论均通过仿真例子给出验证,证明了理论的有效性。
上述结果在多传感器信息融合滤波、石油地震勘探、信号处理和状态估计等领域有重要的理论和应用价值。
With the coming of information era, multisensor information fusion is being emphasized and applied widely in the world due to the effectively improved and optimized performance of estimation, identification and detection (control) based on the single sensor. The applications spread over various aspects of military and civil fields. As an embranchment, optimal and self-tuning information fusion filtering theory refers to the fusion estimation problem of state or signal for the multisensor systems with known or unknown model parameters and/or noise statistics, respectively. The input white noise estimation problem of systems or white noise deconvolution estimation problem has important applications in seismic exploration and communication systems.
Using two methodologies—Kalman filtering method and modern time series analysis method, this paper researches the optimal and self-tuning multisensor information fusion white noise deconvolution estimators based on two fusion methods, so-called multisensor weighted state fusion and weighted measurement fusion methods, combining with the system identification methods, respectively. The main work includes the following four aspects:
Firstly, based on the Riccati equation, the unified weighted fusion optimal and steady-state optimal white noise estimators are presented using Kalman filtering method for the multisensor systems with different local dynamic models and correlated noises. In order to compute the optimal weights, two formulae of computing the local estimation error cross-covariances are given.
Secondly, based on the ARMA innovation model, the unified steady-state optimal white noise estimators are presented using the modern time series analysis method for the multisensor systems with different local dynamic models and correlated noises. The optimal weighted state fusion white noise deconvolution estimators are presented for the multisensor time-delayed systems with the same or different local dynamic models. In order to compute the optimal weights, the formulae of computing the local estimation error cross-covariances are given, respectively.
Thirdly, based on the Riccati equation, the optimal weighted measurement fusion white noise deconvolution estimators are respectively presented using the Kalman filtering method for the multisensor time-varying systems with the same measurement matrices and correlated measurement noises or with different measurement and correlated measurement noises or with the same measurement matrices and correlated noises. Moreover, the completely functional equivalence and the global optimality of the fusers are proved compared with the corresponding centralized fusion white noise deconvolution estimators. As a special case, the corresponding steady-state optimal weighted measurement fusion white noise deconvolution estimators are also given for the time-invariant systems.
Finally, based on the Riccati equation, the self-tuning weighted measurement fusion white noise deconvolution estimators are presented using the Kalman filtering method for the multisensor time-invariant systems with unknown noise statistics, where the estimators of information fusion noise statistics by the correlation function method are used. For the multisensor single channel AR or ARMA systems with unknown model parameters and noise statistics, the self-tuning weighted measurement fusion white noise deconvolution estimators are presented using the estimators of model parameters and noise statistics by the correlation function method, recursive instrumental variable algorithm and Gevers-Wounters algorithm. Moreover, based on the Dynamic Error System Analysis method, it is proved that the fusers converge to the corresponding steady-state optimal weighted measurement fusion white noise deconvolution estimators, so that they have the asymptotical global optimality;
The above results are all proved by the simulation examples, which show the effectiveness of the theory.
They have important theoretical and application value in many fields including the multisensor information fusion filtering, oil seismic exploration, signal processing, and state estimation.
引文
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