H_∞滤波理论在多传感器信息融合状态估计中的应用研究
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摘要
随着现代信号处理技术、计算机技术、网络通信技术、人工智能技术、并行计算软件和硬件技术的快速发展以及新型传感器的不断出现,多传感器信息融合将成为我国未来大量军用和民用高科技系统的重要技术手段。多传感器信息融合有着广泛的研究领域和分支,信息融合状态估计就是其中非常重要的一个。多传感器目标跟踪、多传感器信号滤波与反卷积等问题均可归结为信息融合状态估计问题。现有的多传感器信息融合状态估计方法主要是基于传统的Kalman滤波,其算法是建立在H_2估计准则基础之上,它要求准确的系统模型和确切已知外部干扰信号的统计特性,对于多传感器信息融合状态估计中系统模型存在不确定、时滞及非线性条件等情况时,Kalman融合滤波存在不足之处。而H_∞滤波理论是现代鲁棒控制理论发展的一种重要分支,是针对系统中模型不确定性和外部干扰不确定性而发展起来的一门滤波技术,将H_∞滤波思想引入多传感器信息融合状态估计中具有重要的理论意义和实际应用价值。
本论文系统地综述了多传感器信息融合状态估计技术的发展历史、研究现状和相关经典算法,深入分析了算法的优缺点,归纳现有状态融合估计方法存在的问题,介绍H_∞滤波基础理论和分析方法,总结随机连续、离散线性系统H_∞滤波器的设计方法和思路,对比Kalman滤波器与基本H_∞滤波器的实现方法,讨论了两种滤波器在实现思路上的主要异同。论文重点研究如何将H_∞滤波理论与多传感器信息融合状态估计技术进行结合,利用H_∞滤波理论及方法解决多传感器融合估计中的系统参数存在不确定、融合系统状态存在时滞、融合过程存在稳定度约束及系统描述存在非线性条件等问题,建立起将H_∞滤波理论应用于多传感器信息融合状态估计中的方法框架。
论文的主要研究成果为:
1.针对一类随机不确定多传感器信息融合系统,提出了集中式和分布式H_∞融合滤波器的设计方法。论文给出了随机不确定多传感器融合系统数学模型描述,根据离散系统有界实引理、Schur补定理及线性矩阵不等式求解技术得到了一个针对该类多传感器系统H_∞融合滤波器的存在性定理,在该定理基础上分别得到基于H_∞滤波理论和方法的集中式和分布式多传感器信息融合滤波器。结合一个不确定多传感器目标跟踪系统融合滤波器的设计实例,对比Kalman融合滤波的性能和效果,验证了所得结论的正确性和有效性。
2.针对实际融合系统中抽象出来的系统模型状态存在时滞及系统参数存在随机摄动问题,提出了一类状态依赖于噪声的时滞多传感器融合系统H_∞滤波器的设计方法。论文给出了该类型多传感器融合系统的数学模型描述,定义了系统H_∞融合滤波器设计问题的性能指标。利用Lyapunov函数法得到了一个状态依赖于噪声的时滞融合系统H_∞滤波器稳定性定理,在该定理的基础上,为满足滤波器的性能指标,结合线性矩阵不等式求解技术得到了该类融合系统的H_∞滤波器。为说明所得结论的正确性,论文结合一个状态依赖于噪声的时滞融合估计问题实例,设计了系统的H_∞融合滤波器,仿真结果表明其具有较好的状态融合估计性能。
3.针对状态依赖于噪声的多传感器信息融合系统,提出了一种具有稳定度约束条件的H_∞融合滤波器设计方法。对于系统模型中存在随机摄动的多传感器系统状态融合估计,除了关注估计精度及约束指标等性能外,还应考虑所设计的融合滤波器在保证稳定的前提下跟踪收敛的速率问题。论文在已有的H_∞融合滤波器设计框架的基础上,进一步考虑具有稳定度约束条件的融合滤波器的设计问题,给出该类系统的数学模型,利用连续系统有界实引理及系统衰减速率控制引理,得到H_∞融合滤波器的存在性定理,利用该定理给出了滤波器的设计思路和方法。实例仿真结果表明,稳定性约束达到了调整滤波器跟踪收敛速率的目的。
4.针对一类具有非线性条件约束的多传感器信息融合系统,提出了一种基于线性矩阵不等式转换和求解技术的H_∞融合滤波器设计方法。对于线性多传感器信息融合系统的状态估计,现有的理论及方法均已趋于完善,框架体系较为成熟。将线性系统融合估计的处理方法进一步推广到非线性系统中具有重要实际意义和理论研究价值。论文总结了在非线性系统状态融合估计中存在问题及现有的解决思路,结合论文中已讨论的不同类型融合系统H_∞滤波器的设计方法,利用非线性系统稳定性引理及线性矩阵不等式转换和求解技术,针对一类状态依赖于噪声的非线性多传感器系统设计融合滤波器,推导并得到该类系统的H_∞滤波器存在性定理,利用该定理可得到融合滤波器的设计步骤和方法。仿真结果表明,论文所得结论和方法是有效的。
综上所述,本论文针对多传感器信息融合状态估计中的系统参数存在不确定、融合系统状态存在时滞等问题利用H_∞滤波理论及相关技术进行研究,得到了一些在多传感器信息融合状态估计方面有针对性的定理和滤波器设计方法,是对多传感器信息融合理论的进一步补充和发展。论文最后总结了H_∞滤波理论在多传感器信息融合状态估计应用中亟待解决的一些问题和下一步的研究重点,同时对该领域的发展趋势进行了展望。
With the rapid development of modern signal processing technology, computer technology, network communication technology, artificial intelligence technology, parallel computing by software and hardware technology, and the constantly appear of new type sensor, multi-sensor information fusion will become an important technical means in military and civilian high-tech systems. Multi-sensor information fusion has extensive research fields and branches, in which information fusion state estimation is very important one. The problems such as multi-sensor target tracking, multi-sensor signal filtering and deconvolution etc are classified to information fusion state estimation. The existing multi-sensor information fusion state estimation methods are based on classical Kalman filtering, whose algorithm is on basis of H_2 estimation rules. It requires accurate system model and the exact known statistical characteristics for external disturbance signal. Kalman filtering has deficiencies when fusion system model has uncertainty, time-delay or nonlinear condition, etc. While H_∞filtering theory is an important branch of the modern robust control, it is a filtering technology developed for uncertain system model or uncertain external disturbance. Introducing the H_∞filtering ideas into multi-sensor information fusion state estimation has the important theoretical significance and practical application value.
This dissertation systematically reviews the development history, research status and relevant classical algorithms in multi-sensor information fusion state estimation technology, deeply analyzes the advantages and disadvantages of the algorithms, and sums up the existing fusion estimation problems, introduces the basic concepts and methods of H_∞filtering, sums up the H_∞filter design methods and ideas for stochastic continuous and discrete linear system, compares the realization ways between Kalman filter and H_∞filter, and discusses the main similarities and differences on the idea of two kinds filters. It mainly studies on how to combine the H_∞filtering theory with multi-sensor information fusion state estimation technology, takes full advantage of H_∞filtering theory and methods to solve the problems of system parameters having uncertainty, fusion system state having time-delay, fusion process having stability degree constraints, and system definition having nonlinear constraints, etc, and tries to build the framework of H_∞filtering theory used in multi-sensor information fusion state estimation.
The main results of this dissertation are:
1. It proposes design methods of centralized and distributed H_∞fusion filter for one class of stochastic uncertain multi-sensor fusion system. The dissertation introduces arithmetic model for stochastic uncertain multi-sensor fusion system, and obtains an existence theory for fusion filter of this kind of stochastic uncertain multi-sensor fusion system according to discrete time bounded real lemma, schur's complement and linear matrix inequities solving techniques. On basis of this theory, it gives the design methods for centralized and distributes H_∞fusion filter. By an example of uncertain multi-sensor targets tracking fusion problem, the dissertation designs the H_∞fusion filter, compares the fusing performance and results with Kalman fusion filer, and verifies the correctness and effectiveness of the achieved theory and methods.
2. It proposes design methods of H_∞fusion filter for time-delay multi-sensor fusion system with state dependent noise to solve the problem of states abstracted from actual system model which exist time-delay or stochastic perturbation that make them difficult to be fused and estimated. The dissertation derives an arithmetic model description of this kind of multi-sensor fusion system, defines the performance index for H_∞fusion filer, obtains a stability theorem of the H_∞filer by Lyapunov function method, on basis of which to satisfy the fusion filtering performance index, makes use of LMI solving technique, and obtains the H_∞fusion filer. In order to verify the results' correctness, the dissertation gives an example of state estimation for time-delay fusion system with state dependent noise, and designs the H_∞fusion filter. The simulation results show good performance of the state estimation.
3. It proposes design methods of H_∞fusion filer with stability degree constraint for multi-sensor information fusion system with state dependent noise. For fusion system model whose parameters have stochastic perturbation, besides paying attention on performances of estimation accuracy or constraint index etc, we should also consider the tracking convergence speed under the condition of guaranteeing the designed fusion filter's stable. On basis of the H_∞fusion filer design framework, the dissertation further considers the fusion filer's design problem with stability constraints, proposes the system's mathematical model, makes use of continue time system bounded real lemma and system attenuation speed control lemma, and obtains the existence theorem of the H_∞fusion filer. Finally, we achieve the fusion filter's design method on baisis of the theorem. The simulation example shows that the stability constraint is truly at its job.
4. It proposes design method of H_∞fusion filer on basis of linear matrix inequities transforming and solving technique for one class of multi-sensor information fusion system with nonlinear condition constraints. For linear multi-senor fusion system state estimation, the existing theories, methods and research frameworks have been matured. To generalize the methods of linear fusion system state estimation to nonlinear system has important practical significance and theoratical research value. Summarized the problems existed in nonlinear fusion estimation and their ideas to solve them, the dissertation combines the design methods which had been discussed for different kinds of H_∞fusion filer, makes use of nonlinear system stability lemma and linear matrix inequities transforming and solving technique, and obtains the existence theorem of the fusion filter for one class of nonlinear fusion system with state dependent noise. Base on this theorem, the dissertation further achieves the fusion filter's design methods and steps. The simulation results show the effectiveness of the obtained conclusions and methods.
In sum, the dissertation considers the problems in multi-sensor information fusion state estimation such as system parameters having uncertainty, fusion system state having time-delay, etc, and obtains some pointed theorems and fusion filter design methods which could be considered as the furthering complement and development for multi-sensor information fusion state estimation. Finally, the problems to be solved related to H_∞filtering theory applied in multi-sensor information fusion and further research topics are summarized, and the prospect of the developing tendency is analyzed as well.
本论文系统地综述了多传感器信息融合状态估计技术的发展历史、研究现状和相关经典算法,深入分析了算法的优缺点,归纳现有状态融合估计方法存在的问题,介绍H_∞滤波基础理论和分析方法,总结随机连续、离散线性系统H_∞滤波器的设计方法和思路,对比Kalman滤波器与基本H_∞滤波器的实现方法,讨论了两种滤波器在实现思路上的主要异同。论文重点研究如何将H_∞滤波理论与多传感器信息融合状态估计技术进行结合,利用H_∞滤波理论及方法解决多传感器融合估计中的系统参数存在不确定、融合系统状态存在时滞、融合过程存在稳定度约束及系统描述存在非线性条件等问题,建立起将H_∞滤波理论应用于多传感器信息融合状态估计中的方法框架。
论文的主要研究成果为:
1.针对一类随机不确定多传感器信息融合系统,提出了集中式和分布式H_∞融合滤波器的设计方法。论文给出了随机不确定多传感器融合系统数学模型描述,根据离散系统有界实引理、Schur补定理及线性矩阵不等式求解技术得到了一个针对该类多传感器系统H_∞融合滤波器的存在性定理,在该定理基础上分别得到基于H_∞滤波理论和方法的集中式和分布式多传感器信息融合滤波器。结合一个不确定多传感器目标跟踪系统融合滤波器的设计实例,对比Kalman融合滤波的性能和效果,验证了所得结论的正确性和有效性。
2.针对实际融合系统中抽象出来的系统模型状态存在时滞及系统参数存在随机摄动问题,提出了一类状态依赖于噪声的时滞多传感器融合系统H_∞滤波器的设计方法。论文给出了该类型多传感器融合系统的数学模型描述,定义了系统H_∞融合滤波器设计问题的性能指标。利用Lyapunov函数法得到了一个状态依赖于噪声的时滞融合系统H_∞滤波器稳定性定理,在该定理的基础上,为满足滤波器的性能指标,结合线性矩阵不等式求解技术得到了该类融合系统的H_∞滤波器。为说明所得结论的正确性,论文结合一个状态依赖于噪声的时滞融合估计问题实例,设计了系统的H_∞融合滤波器,仿真结果表明其具有较好的状态融合估计性能。
3.针对状态依赖于噪声的多传感器信息融合系统,提出了一种具有稳定度约束条件的H_∞融合滤波器设计方法。对于系统模型中存在随机摄动的多传感器系统状态融合估计,除了关注估计精度及约束指标等性能外,还应考虑所设计的融合滤波器在保证稳定的前提下跟踪收敛的速率问题。论文在已有的H_∞融合滤波器设计框架的基础上,进一步考虑具有稳定度约束条件的融合滤波器的设计问题,给出该类系统的数学模型,利用连续系统有界实引理及系统衰减速率控制引理,得到H_∞融合滤波器的存在性定理,利用该定理给出了滤波器的设计思路和方法。实例仿真结果表明,稳定性约束达到了调整滤波器跟踪收敛速率的目的。
4.针对一类具有非线性条件约束的多传感器信息融合系统,提出了一种基于线性矩阵不等式转换和求解技术的H_∞融合滤波器设计方法。对于线性多传感器信息融合系统的状态估计,现有的理论及方法均已趋于完善,框架体系较为成熟。将线性系统融合估计的处理方法进一步推广到非线性系统中具有重要实际意义和理论研究价值。论文总结了在非线性系统状态融合估计中存在问题及现有的解决思路,结合论文中已讨论的不同类型融合系统H_∞滤波器的设计方法,利用非线性系统稳定性引理及线性矩阵不等式转换和求解技术,针对一类状态依赖于噪声的非线性多传感器系统设计融合滤波器,推导并得到该类系统的H_∞滤波器存在性定理,利用该定理可得到融合滤波器的设计步骤和方法。仿真结果表明,论文所得结论和方法是有效的。
综上所述,本论文针对多传感器信息融合状态估计中的系统参数存在不确定、融合系统状态存在时滞等问题利用H_∞滤波理论及相关技术进行研究,得到了一些在多传感器信息融合状态估计方面有针对性的定理和滤波器设计方法,是对多传感器信息融合理论的进一步补充和发展。论文最后总结了H_∞滤波理论在多传感器信息融合状态估计应用中亟待解决的一些问题和下一步的研究重点,同时对该领域的发展趋势进行了展望。
With the rapid development of modern signal processing technology, computer technology, network communication technology, artificial intelligence technology, parallel computing by software and hardware technology, and the constantly appear of new type sensor, multi-sensor information fusion will become an important technical means in military and civilian high-tech systems. Multi-sensor information fusion has extensive research fields and branches, in which information fusion state estimation is very important one. The problems such as multi-sensor target tracking, multi-sensor signal filtering and deconvolution etc are classified to information fusion state estimation. The existing multi-sensor information fusion state estimation methods are based on classical Kalman filtering, whose algorithm is on basis of H_2 estimation rules. It requires accurate system model and the exact known statistical characteristics for external disturbance signal. Kalman filtering has deficiencies when fusion system model has uncertainty, time-delay or nonlinear condition, etc. While H_∞filtering theory is an important branch of the modern robust control, it is a filtering technology developed for uncertain system model or uncertain external disturbance. Introducing the H_∞filtering ideas into multi-sensor information fusion state estimation has the important theoretical significance and practical application value.
This dissertation systematically reviews the development history, research status and relevant classical algorithms in multi-sensor information fusion state estimation technology, deeply analyzes the advantages and disadvantages of the algorithms, and sums up the existing fusion estimation problems, introduces the basic concepts and methods of H_∞filtering, sums up the H_∞filter design methods and ideas for stochastic continuous and discrete linear system, compares the realization ways between Kalman filter and H_∞filter, and discusses the main similarities and differences on the idea of two kinds filters. It mainly studies on how to combine the H_∞filtering theory with multi-sensor information fusion state estimation technology, takes full advantage of H_∞filtering theory and methods to solve the problems of system parameters having uncertainty, fusion system state having time-delay, fusion process having stability degree constraints, and system definition having nonlinear constraints, etc, and tries to build the framework of H_∞filtering theory used in multi-sensor information fusion state estimation.
The main results of this dissertation are:
1. It proposes design methods of centralized and distributed H_∞fusion filter for one class of stochastic uncertain multi-sensor fusion system. The dissertation introduces arithmetic model for stochastic uncertain multi-sensor fusion system, and obtains an existence theory for fusion filter of this kind of stochastic uncertain multi-sensor fusion system according to discrete time bounded real lemma, schur's complement and linear matrix inequities solving techniques. On basis of this theory, it gives the design methods for centralized and distributes H_∞fusion filter. By an example of uncertain multi-sensor targets tracking fusion problem, the dissertation designs the H_∞fusion filter, compares the fusing performance and results with Kalman fusion filer, and verifies the correctness and effectiveness of the achieved theory and methods.
2. It proposes design methods of H_∞fusion filter for time-delay multi-sensor fusion system with state dependent noise to solve the problem of states abstracted from actual system model which exist time-delay or stochastic perturbation that make them difficult to be fused and estimated. The dissertation derives an arithmetic model description of this kind of multi-sensor fusion system, defines the performance index for H_∞fusion filer, obtains a stability theorem of the H_∞filer by Lyapunov function method, on basis of which to satisfy the fusion filtering performance index, makes use of LMI solving technique, and obtains the H_∞fusion filer. In order to verify the results' correctness, the dissertation gives an example of state estimation for time-delay fusion system with state dependent noise, and designs the H_∞fusion filter. The simulation results show good performance of the state estimation.
3. It proposes design methods of H_∞fusion filer with stability degree constraint for multi-sensor information fusion system with state dependent noise. For fusion system model whose parameters have stochastic perturbation, besides paying attention on performances of estimation accuracy or constraint index etc, we should also consider the tracking convergence speed under the condition of guaranteeing the designed fusion filter's stable. On basis of the H_∞fusion filer design framework, the dissertation further considers the fusion filer's design problem with stability constraints, proposes the system's mathematical model, makes use of continue time system bounded real lemma and system attenuation speed control lemma, and obtains the existence theorem of the H_∞fusion filer. Finally, we achieve the fusion filter's design method on baisis of the theorem. The simulation example shows that the stability constraint is truly at its job.
4. It proposes design method of H_∞fusion filer on basis of linear matrix inequities transforming and solving technique for one class of multi-sensor information fusion system with nonlinear condition constraints. For linear multi-senor fusion system state estimation, the existing theories, methods and research frameworks have been matured. To generalize the methods of linear fusion system state estimation to nonlinear system has important practical significance and theoratical research value. Summarized the problems existed in nonlinear fusion estimation and their ideas to solve them, the dissertation combines the design methods which had been discussed for different kinds of H_∞fusion filer, makes use of nonlinear system stability lemma and linear matrix inequities transforming and solving technique, and obtains the existence theorem of the fusion filter for one class of nonlinear fusion system with state dependent noise. Base on this theorem, the dissertation further achieves the fusion filter's design methods and steps. The simulation results show the effectiveness of the obtained conclusions and methods.
In sum, the dissertation considers the problems in multi-sensor information fusion state estimation such as system parameters having uncertainty, fusion system state having time-delay, etc, and obtains some pointed theorems and fusion filter design methods which could be considered as the furthering complement and development for multi-sensor information fusion state estimation. Finally, the problems to be solved related to H_∞filtering theory applied in multi-sensor information fusion and further research topics are summarized, and the prospect of the developing tendency is analyzed as well.
引文
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