滤波技术在高超声速大机动飞行器末制导中的应用
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摘要
近几十年来世界局势的发展状况，大体上可概括为“总体和平，局部战争”。作为一种新型作战方式，导弹武器得到了世界各国的普遍关注。以下一代战区弹道导弹（Theatre Ballistic Missile, TBM）为代表的攻击导弹飞行速度快，并具有大机动能力，对现有的拦截制导系统构成了巨大挑战。深入研究如何对这类飞行器进行有效末制导，有利于我军掌握未来战争的战略制高点，并进一步保障国家领土完整和人民生命安全。
几乎所有先进末制导律在设计时，都需使用目标运动信息；然而很多情况下该信息不能通过测量元件直接获取，必须从被噪声污染的信号中进行在线估计，这就需要滤波技术的支持。滤波技术一直都是信号处理领域的研究热点之一。对于一般的非线性、非高斯系统，最优滤波问题没有递推显式解。高超声速飞行器末制导问题的弹目相对运动关系数学模型，很多情况下存在本质非线性和非高斯特征，且整个末制导过程具有很高的实时性要求；因而对这类问题，有必要研究估计精度高计算量适中的非线性制导滤波器。
论文以下一代高超声速TBM飞行器的末制导为课题背景，研究了存在未知信息的离散系统的建模和滤波问题；并针对此类目标的末制导中，确定性等价定理的失效问题，给出了一种解决方案并设计了基于Matlab的改进型软件工具包进行了仿真验证。具体来讲，研究主要包括以下内容：
首先，从贝叶斯最优估计理论出发，研究了非线性和非高斯离散随机系统的高斯逼近滤波技术。在线性高斯随机系统的最优滤波器—卡尔曼滤波算法（Kalman Filter，KF）的基础上，对非线性随机函数的次优高斯逼近方法进行了讨论；根据噪声混入系统的不同类型，针对带有加性和隐含噪声的非线性随机系统，分别推导了两类扩展卡尔曼滤波算法（Extended Kalman Filter，EKF）和无迹卡尔曼滤波算法（Unscented Kalman Filter，UKF）；引入辅助函数技术重构采样点，增强了UKF算法在高维系统中实现上的数值鲁棒性；对一类存在多种工作模式的混杂系统进行了研究，根据混杂系统的贝叶斯估计理论进行推导，研究了两类多模型算法原理和实现，较好解决了这类系统的状态估计问题。
然后，研究了高超声速大机动飞行器的跟踪问题。针对此类问题在系统建模过程中通常存在的本质非线性和非高斯特征，采用成型滤波器模拟验前未知信息；并采用中央差分算法逼近非线性函数，针对带有加性和隐含噪声的非线性随机系统，分别推导了两类中央差分滤波算法（Central Difference Kalman Filter,CDKF）；在CDKF的第二步滤波计算过程中引入迭代更新步骤，推导了极大后验估计意义下的一种改进型迭代中央差分滤波算法（ICDKF）。通过高超声速大机动飞行器拦截中两个典型的非线性估计问题，验证了ICDKF算法同主流的EKF和UKF算法相比，具有更高的估计精度和更快的收敛速度并且计算量适中，因而更适于在实战环境中处理这两类跟踪问题。
接着，通过一个仿真算例，讨论了非线性滤波器按照噪声混入系统的不同方式进行分类设计的必要性；进而提出了高斯次优非线性滤波器的一种改进型结构设计方法。采用这种设计方法，按照项目要求，研究了一种能够解决部分高斯次优非线性滤波器的一致性检验难题、并便于在仿真开始前修改模型参数和替换滤波算法、在仿真结束后执行大量数据的统计处理的改进型滤波制导工具箱的设计方案。为科学评价两种滤波器的估计效果，提出了一种滤波器改进型初始估方法和一种能够从统计学角度比较两种滤波器估计效果的假设检验判别法，并基于上述滤波制导工具箱进行了仿真验证。
最后，以具有大机动能力的下一代高超声速TBM为例，研究了如何对此类飞行器进行有效拦截末制导，并给出了一种滤波制导一体化设计方案。将CDKF融入多模型算法（Multiple Model Adaptive Estimation, MMAE），提出了一种多模型/中央差分算法（MMAE/CDKF）用于解决建模过程中存在未知信息的末制导系统的目标加速度检测和估计问题；接着针对高超声速飞行器末制导问题较高的实时性要求，考虑到传统多模型滤波器过大的计算量在工控机上实现较为困难，在被拦截飞行器指令加速度为Bang-Bang类型时，引入聚合、尺寸裁剪等技术手段对MMAE/CDKF算法进行简化，提出了一种快速多模型/中央差分算法（fast MMAE/CDKF），在保障估计精度的同时降低了计算量；大量的仿真实验证实了这两种算法的有效性。为有效利用上述两种算法对于目标加速度信息和弹目视线角信息估计性能的改善，更好地解决高超声速大机动飞行器末制导中确定性等价定理的失效问题，分别采用上述两种估计算法作为制导滤波器，提出了一种基于逻辑判断的切换微分对策制导律DGL/N。这种滤波制导一体化设计方案充分考虑了制导滤波器的估计精度和拦截弹有限的机动能力对于末制导律设计的影响，取得了比传统制导律和基本微分对策制导律更好的拦截效果。
综上，论文给出了高超声速大机动飞行器末制导问题中，制导滤波器和拦截制导律的一些新型设计和评价方法，为下一代反导拦截系统的研发，奠定了一定理论基础，并给出了部分可能的设计思路。
The developing trend of the world for the past several decades can generally bedescribed as “overall peace marred by local wars”. In light of this very importantnotation, missile weapons have increasingly become the core focus as a new mean ofattack in the battlefield. Fast attack missile of the next generation such as the TBM(Theatre Ballistic Missile) can execute large maneuvering at super high speed,posing great challenges to the existing interception guidance systems; thus, anin-depth study of some key technique of terminal guidance laws for interception ofmissile weapons will be very helpful for the People’s Liberation Army to takecontrol of the strategic high ground in future wars, and of great significance for thedefense of the territorial integrity and the security of people’s lives and property.
Almost all advanced guidance laws used for interception require target motioninformation. While in many cases this information cannot be measured directly, itmust be obtained through online estimation from noise polluted measurements,which requires the support of filtering technique. Filtering technique has always beena hot issue in the domain of signal processing. For the general non-linear andnon-Gaussian systems, there are no recursive explicit solutions for optimal filtering.However, under many circumstances, many kinetic models of missile-targetengagement in terminal guidance problems of hypersonic aircraft are characterizedby non-linear and non-Gaussian in nature; for such problems, it is a more meaningfulpractice to develop suboptimal filtering methods.
Based on the background of terminal guidance of aircraft like TBM of the nextgeneration, the modeling and filtering problems of discrete systems in the presenceof unknown information are studied，and for the ineffectiveness of certaintyequivalence theorem in the interception of hypersonic speed target with largemaneuvering ability, a possible solution is given and multiple simulations are carriedout on improved software toolkit based on Matlab. Specifically, the followingdomains are included in the research:
First, the Gaussian approximation filtering technique for general non-linear andnon-Gaussian stochastic discrete system is studied based on optimal Bayesianestimation theory. After the derivation of the optimal filter for linear discrete Gaussian system–the KF (Kalman Filter), suboptimal Gaussian approximations ofnon-linear stochastic systems are derived based on the analogy of KF. According todifferent types of system noise, suboptimal non-linear filters with additive andhidden noise are derived respectively, namely the EKF (Extended Kalman Filter) andUKF (Unscented Kalman Filter) algorithms; To improve the numerical robustness ofUKF for systems with high dimension, an auxiliary function method is introducedwhich recalculated the sample points of UKF; A class of hybrid system with manyworking modes is investigated, and the principle and realization method of twoclasses of multiple model algorithms are studied based on Bayesian estimationtheories for hybrid systems. The algorithms provide a fine solution for stateestimation problems for the hybrid systems.
Then, the tracking problems for hypersonic aircraft with large maneuvering abilityare discussed. Shaping filters are introduced to imitate the unknown non-Gaussianvariables in systems characterized by non-linearity in nature. Central differencetheory is used to approximate non-linear functions, which lead to the derivation ofcentral difference Kalman Filter (CDKF for short) for non-linear stochastic systemswith additive and hidden noise, respectively. An iterative update step is introduced inthe second step of CDKF, giving an optimal filter named ICDKF under MAP(maximum a posteriori) sense. Two typical non-linear estimation problems from thedomain of terminal guidance in the interception of hypersonic speed demonstrate thatthe proposed ICDKF algorithm effectively improves the estimation accuracy,compared to the mainstream filter of EKF and UKF, thus demonstrate its superiority.
And then, the necessity of designing non-linear filters in accordance with thedifferent type of noise entering the system is confirmed through a simulationexample, and then a novel structure of the design of non-linear filters is proposed. Inorder to meet the requirements of the project, a improved filtering and guidancetoolbox using such design method is developed which provides a way to performconsistency checking for some non-linear filters based on suboptimal Gaussianapproximations, and makes it easy to modify the simulation parameters and replacefiltering and guidance algorithms at the beginning of the simulation, and processlarge amounts of statistical data after the end of the simulation. In order to givescientific compare between two non-linear Gaussian filters, according to the specialstructure of the Gaussian filter, an improved initialization method for general non-linear system and a hypothesis testing comparative method based on hypothesistesting theory are proposed, which guarantee the scientific performance comparisonof two non-linear filters.The effectiveness of the proposed methods are validatedthrough the novel filtering and guidance toolbox metioned above.
Finally, for the target to be intercepted as TBM of the next generation which hassupersonic speed and can execute large maneuvering how to effectively interceptsuch target is studied and an integration design method of filtering/guidance is given.Integrating CDKF into multiple model algorithms (Multiple Model AdaptiveEstimation, MMAE), a multiple model central difference algorithm (MMAE/CDKF)is used to deal with filtering task in the presence of unknown signal and gives targetacceleration estimation. Considering that the large computation burden of MMAE/CDKF can make it difficult for the implementation of the algorithm on anengineering computer, for target acceleration with the structure type bang-bang, thetechnique of aggregation and pruning are introduced to make simple the MMAE/CDKF algorithm. A fast multiple model central differential algorithm (fast MMAE/CDKF) is developed which retained much of the accuracy as MMAE/CDKF, whilegreatly reduced the amount of computation. Extensive simulation experimentsconfirm the effectiveness of the proposed two algorithms. In order to make better useof the improvement of estimation of acceleration and line-of-sight angel due to theemployment the two proposed algorithms, and solve better the problem of failure ofcertainty equivalence theorem in the interception of hypersonic target with largemaneuvering ability, a switching differential game guidance law named DGL/N isproposed based on basic logic reasoning. Such method takes fully into account theinfluence of the estimation accuracy of the guidance filter and the limited mobility ofthe interceptor, thus gives better homing performance compared to the conventionalguidance law for terminal interception.
In summary, several novel design and evaluation methods of terminal guidancelaws and guidance filters for the terminal guidance problems in the interception ofhypersonic speed target with large maneuvering ability are studied in this dissertation,thus lay some theoretical foundation and give some possible methods for thedevelopment of the next-generation missile interception system.
几乎所有先进末制导律在设计时，都需使用目标运动信息；然而很多情况下该信息不能通过测量元件直接获取，必须从被噪声污染的信号中进行在线估计，这就需要滤波技术的支持。滤波技术一直都是信号处理领域的研究热点之一。对于一般的非线性、非高斯系统，最优滤波问题没有递推显式解。高超声速飞行器末制导问题的弹目相对运动关系数学模型，很多情况下存在本质非线性和非高斯特征，且整个末制导过程具有很高的实时性要求；因而对这类问题，有必要研究估计精度高计算量适中的非线性制导滤波器。
论文以下一代高超声速TBM飞行器的末制导为课题背景，研究了存在未知信息的离散系统的建模和滤波问题；并针对此类目标的末制导中，确定性等价定理的失效问题，给出了一种解决方案并设计了基于Matlab的改进型软件工具包进行了仿真验证。具体来讲，研究主要包括以下内容：
首先，从贝叶斯最优估计理论出发，研究了非线性和非高斯离散随机系统的高斯逼近滤波技术。在线性高斯随机系统的最优滤波器—卡尔曼滤波算法（Kalman Filter，KF）的基础上，对非线性随机函数的次优高斯逼近方法进行了讨论；根据噪声混入系统的不同类型，针对带有加性和隐含噪声的非线性随机系统，分别推导了两类扩展卡尔曼滤波算法（Extended Kalman Filter，EKF）和无迹卡尔曼滤波算法（Unscented Kalman Filter，UKF）；引入辅助函数技术重构采样点，增强了UKF算法在高维系统中实现上的数值鲁棒性；对一类存在多种工作模式的混杂系统进行了研究，根据混杂系统的贝叶斯估计理论进行推导，研究了两类多模型算法原理和实现，较好解决了这类系统的状态估计问题。
然后，研究了高超声速大机动飞行器的跟踪问题。针对此类问题在系统建模过程中通常存在的本质非线性和非高斯特征，采用成型滤波器模拟验前未知信息；并采用中央差分算法逼近非线性函数，针对带有加性和隐含噪声的非线性随机系统，分别推导了两类中央差分滤波算法（Central Difference Kalman Filter,CDKF）；在CDKF的第二步滤波计算过程中引入迭代更新步骤，推导了极大后验估计意义下的一种改进型迭代中央差分滤波算法（ICDKF）。通过高超声速大机动飞行器拦截中两个典型的非线性估计问题，验证了ICDKF算法同主流的EKF和UKF算法相比，具有更高的估计精度和更快的收敛速度并且计算量适中，因而更适于在实战环境中处理这两类跟踪问题。
接着，通过一个仿真算例，讨论了非线性滤波器按照噪声混入系统的不同方式进行分类设计的必要性；进而提出了高斯次优非线性滤波器的一种改进型结构设计方法。采用这种设计方法，按照项目要求，研究了一种能够解决部分高斯次优非线性滤波器的一致性检验难题、并便于在仿真开始前修改模型参数和替换滤波算法、在仿真结束后执行大量数据的统计处理的改进型滤波制导工具箱的设计方案。为科学评价两种滤波器的估计效果，提出了一种滤波器改进型初始估方法和一种能够从统计学角度比较两种滤波器估计效果的假设检验判别法，并基于上述滤波制导工具箱进行了仿真验证。
最后，以具有大机动能力的下一代高超声速TBM为例，研究了如何对此类飞行器进行有效拦截末制导，并给出了一种滤波制导一体化设计方案。将CDKF融入多模型算法（Multiple Model Adaptive Estimation, MMAE），提出了一种多模型/中央差分算法（MMAE/CDKF）用于解决建模过程中存在未知信息的末制导系统的目标加速度检测和估计问题；接着针对高超声速飞行器末制导问题较高的实时性要求，考虑到传统多模型滤波器过大的计算量在工控机上实现较为困难，在被拦截飞行器指令加速度为Bang-Bang类型时，引入聚合、尺寸裁剪等技术手段对MMAE/CDKF算法进行简化，提出了一种快速多模型/中央差分算法（fast MMAE/CDKF），在保障估计精度的同时降低了计算量；大量的仿真实验证实了这两种算法的有效性。为有效利用上述两种算法对于目标加速度信息和弹目视线角信息估计性能的改善，更好地解决高超声速大机动飞行器末制导中确定性等价定理的失效问题，分别采用上述两种估计算法作为制导滤波器，提出了一种基于逻辑判断的切换微分对策制导律DGL/N。这种滤波制导一体化设计方案充分考虑了制导滤波器的估计精度和拦截弹有限的机动能力对于末制导律设计的影响，取得了比传统制导律和基本微分对策制导律更好的拦截效果。
综上，论文给出了高超声速大机动飞行器末制导问题中，制导滤波器和拦截制导律的一些新型设计和评价方法，为下一代反导拦截系统的研发，奠定了一定理论基础，并给出了部分可能的设计思路。
The developing trend of the world for the past several decades can generally bedescribed as “overall peace marred by local wars”. In light of this very importantnotation, missile weapons have increasingly become the core focus as a new mean ofattack in the battlefield. Fast attack missile of the next generation such as the TBM(Theatre Ballistic Missile) can execute large maneuvering at super high speed,posing great challenges to the existing interception guidance systems; thus, anin-depth study of some key technique of terminal guidance laws for interception ofmissile weapons will be very helpful for the People’s Liberation Army to takecontrol of the strategic high ground in future wars, and of great significance for thedefense of the territorial integrity and the security of people’s lives and property.
Almost all advanced guidance laws used for interception require target motioninformation. While in many cases this information cannot be measured directly, itmust be obtained through online estimation from noise polluted measurements,which requires the support of filtering technique. Filtering technique has always beena hot issue in the domain of signal processing. For the general non-linear andnon-Gaussian systems, there are no recursive explicit solutions for optimal filtering.However, under many circumstances, many kinetic models of missile-targetengagement in terminal guidance problems of hypersonic aircraft are characterizedby non-linear and non-Gaussian in nature; for such problems, it is a more meaningfulpractice to develop suboptimal filtering methods.
Based on the background of terminal guidance of aircraft like TBM of the nextgeneration, the modeling and filtering problems of discrete systems in the presenceof unknown information are studied，and for the ineffectiveness of certaintyequivalence theorem in the interception of hypersonic speed target with largemaneuvering ability, a possible solution is given and multiple simulations are carriedout on improved software toolkit based on Matlab. Specifically, the followingdomains are included in the research:
First, the Gaussian approximation filtering technique for general non-linear andnon-Gaussian stochastic discrete system is studied based on optimal Bayesianestimation theory. After the derivation of the optimal filter for linear discrete Gaussian system–the KF (Kalman Filter), suboptimal Gaussian approximations ofnon-linear stochastic systems are derived based on the analogy of KF. According todifferent types of system noise, suboptimal non-linear filters with additive andhidden noise are derived respectively, namely the EKF (Extended Kalman Filter) andUKF (Unscented Kalman Filter) algorithms; To improve the numerical robustness ofUKF for systems with high dimension, an auxiliary function method is introducedwhich recalculated the sample points of UKF; A class of hybrid system with manyworking modes is investigated, and the principle and realization method of twoclasses of multiple model algorithms are studied based on Bayesian estimationtheories for hybrid systems. The algorithms provide a fine solution for stateestimation problems for the hybrid systems.
Then, the tracking problems for hypersonic aircraft with large maneuvering abilityare discussed. Shaping filters are introduced to imitate the unknown non-Gaussianvariables in systems characterized by non-linearity in nature. Central differencetheory is used to approximate non-linear functions, which lead to the derivation ofcentral difference Kalman Filter (CDKF for short) for non-linear stochastic systemswith additive and hidden noise, respectively. An iterative update step is introduced inthe second step of CDKF, giving an optimal filter named ICDKF under MAP(maximum a posteriori) sense. Two typical non-linear estimation problems from thedomain of terminal guidance in the interception of hypersonic speed demonstrate thatthe proposed ICDKF algorithm effectively improves the estimation accuracy,compared to the mainstream filter of EKF and UKF, thus demonstrate its superiority.
And then, the necessity of designing non-linear filters in accordance with thedifferent type of noise entering the system is confirmed through a simulationexample, and then a novel structure of the design of non-linear filters is proposed. Inorder to meet the requirements of the project, a improved filtering and guidancetoolbox using such design method is developed which provides a way to performconsistency checking for some non-linear filters based on suboptimal Gaussianapproximations, and makes it easy to modify the simulation parameters and replacefiltering and guidance algorithms at the beginning of the simulation, and processlarge amounts of statistical data after the end of the simulation. In order to givescientific compare between two non-linear Gaussian filters, according to the specialstructure of the Gaussian filter, an improved initialization method for general non-linear system and a hypothesis testing comparative method based on hypothesistesting theory are proposed, which guarantee the scientific performance comparisonof two non-linear filters.The effectiveness of the proposed methods are validatedthrough the novel filtering and guidance toolbox metioned above.
Finally, for the target to be intercepted as TBM of the next generation which hassupersonic speed and can execute large maneuvering how to effectively interceptsuch target is studied and an integration design method of filtering/guidance is given.Integrating CDKF into multiple model algorithms (Multiple Model AdaptiveEstimation, MMAE), a multiple model central difference algorithm (MMAE/CDKF)is used to deal with filtering task in the presence of unknown signal and gives targetacceleration estimation. Considering that the large computation burden of MMAE/CDKF can make it difficult for the implementation of the algorithm on anengineering computer, for target acceleration with the structure type bang-bang, thetechnique of aggregation and pruning are introduced to make simple the MMAE/CDKF algorithm. A fast multiple model central differential algorithm (fast MMAE/CDKF) is developed which retained much of the accuracy as MMAE/CDKF, whilegreatly reduced the amount of computation. Extensive simulation experimentsconfirm the effectiveness of the proposed two algorithms. In order to make better useof the improvement of estimation of acceleration and line-of-sight angel due to theemployment the two proposed algorithms, and solve better the problem of failure ofcertainty equivalence theorem in the interception of hypersonic target with largemaneuvering ability, a switching differential game guidance law named DGL/N isproposed based on basic logic reasoning. Such method takes fully into account theinfluence of the estimation accuracy of the guidance filter and the limited mobility ofthe interceptor, thus gives better homing performance compared to the conventionalguidance law for terminal interception.
In summary, several novel design and evaluation methods of terminal guidancelaws and guidance filters for the terminal guidance problems in the interception ofhypersonic speed target with large maneuvering ability are studied in this dissertation,thus lay some theoretical foundation and give some possible methods for thedevelopment of the next-generation missile interception system.
引文
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