不完全量测下光电跟踪系统估计性能研究及其滤波器实现
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摘要
光电跟踪系统是火控系统研制过程中的关键探测设备之一,其对目标的快速捕获与精密跟踪取决于对目标运动参数的精确估计。在实际跟踪过程中,由于可能存在的浮云等障碍物遮挡、雾气等外部气象条件干扰、激光等探测设备探测能力受限、探测设备故障以及高噪声工作环境等因素,使得光电跟踪系统的探测概率总是小于1,即存在不完全量测现象。通常,对光电跟踪系统的估计性能分析是在对漏测点的外推补点基础上,应用完全量测的思路进行的。近年来,不完全量测下的估计理论在国际上获得重视,取得了一些有价值的成果,并初步形成了基本的理论体系。本文基于工程设计及设备实现的需求,借鉴不完全量测的思路,从理论分析和实际应用两个方面,深入研究了光电跟踪系统在不完全量测条件下的估计性能,并针对跟踪系统估计性能随着探测概率下降而显著降低的现象,从充分挖掘高采样率下的冗余测角信息、引入附加角速率量测信息以及分布式光电探测设备组网融合等几个方面进行了系统建模与滤波器设计,有效地提高了光电跟踪系统的估计性能。本文的主要研究成果包括：
(1)研究了不完全量测下光电跟踪系统估计误差的统计特性。首先,提出了一种基于后验置信度的残差检测算法。其主要思想是在传统残差检测方法的基础上首先增加一个检测门限,对处于两个门限之间的残差,利用模糊隶属度函数方法进行模糊化,得到残差的似然概率,进而结合跟踪系统的先验探测信息,计算出探测数据的后验置信概率,并根据计算结果,对跟踪系统的探测情况进行判定,从而提高了滤波器残差检测的正确率。然后,基于后验置信度残差检测算法,设计了不完全量测下的去偏转换量测Kalman目标跟踪滤波器(UCMKF)与基于线性最小无偏估计(BLUE)准则的目标跟踪滤波器。最后,在统计意义下给出了跟踪系统的Cramer-Rao下界(CRLB),并且在给定探测概率下,给出了一组期望的估计误差协方差上下界的计算方法。
(2)研究了光电跟踪系统的临界探测概率。证明了跟踪系统临界探测概率的存在性,并且给出了临界探测概率的一组上下界,其上界被描述成一个非线性矩阵不等式(NMI)的最优解,其下界仅与跟踪系统状态转移矩阵的特征值有关。进一步利用摄动线性化方法给出了求解临界探测概率上界的一种迭代线性矩阵不等式(ILMI)算法,为光电跟踪系统探测概率的设计提供了理论依据。
(3)针对由激光测距机与精密测角设备组成的光电跟踪系统,在不完全量测下,设计了基于后验置信度残差检测的联邦目标跟踪滤波器。首先,依据物理结构将传统光电跟踪系统的位置探测通道分解为测距与测角两个独立的探测通道,给出了独立双通道的CRLB数学模型,并且对两个探测通道的量测数据分别进行基于后验置信度残差检测的目标状态估计。然后,将估计结果送至融合中心进行信息融合。最后,利用融合结果,并根据探测通道数据可信的后验概率,对探测通道的子滤波器进行信息分配。Monte-Carlo仿真以及试验场实测数据表明,在不完全量测下,所提滤波器在不增加系统硬件成本的前提下,通过攫取高采样率下的测角信息,跟踪性能较之传统光电跟踪系统的跟踪性能有了显著改善,并且滤波器估计误差均方差(RMSE)可逼近跟踪系统统计意义下的CRLB。
(4)提出了一种将俯仰和偏航两个方向的角速度量测引入传统光电跟踪系统的设计思想,并且针对这类新型的光电跟踪系统,设计了基于后验置信度融合的目标跟踪滤波器。首先建立了跟踪系统的量测模型,利用嵌套条件方法,推导了转换量测误差前两阶矩的一致性估计；然后针对位置探测通道与角速度探测通道的四种数据探测情形设计了四个子滤波器,并根据探测通道的探测情况计算出各子滤波器的后验置信度,进而对各子滤波器的输出按后验置信度进行加权融合,得到了跟踪滤波器的全局输出；最后给出了这类新型光电跟踪系统统计意义下的CRLB。Monte-Carlo仿真表明：在不完全量测下,相比传统光电跟踪系统,附加角速度量测的光电跟踪系统的跟踪性能有了显著提高,并且滤波器RMSE可逼近跟踪系统统计意义下的CRLB。
(5)针对具有有色观测噪声的分布式光电跟踪系统,设计了一种分布式融合滤波器。其原理是依据等效观测噪声与状态噪声的相关性,将目标运动状态分解为不相关的两部分,进行非扩维Kalman滤波以及分布式状态融合,融合算法等价于集中式Kalman融合。同时,进一步针对带反馈结构的具有有色观测噪声的分布式光电跟踪系统,分析了反馈结构对跟踪系统的影响,设计了修正的分布式融合滤波器。理论分析和Monte-Carlo仿真表明：所提分布式融合滤波器的估计性能较之任何局部跟踪系统的估计性能有了显著提升,并且计算量满足实时处理的要求。
Optic-electric tracking systems are indispensable detection equipments in development of fire control systems. Fast acquiring targets and accuracy tracking targets depend on accuracy estimation of target motion parameters. However, during practical tracking processes, detection probability of optic-electric systems is always less than one, due to shading of obstacles (drifting clouds, etc), interference of weather conditions (fog, etc), limited detectability of detection equipments (laser, etc), faults of detection equipments and noises working environment, etc. Generally, estimation performance of optic-electric tracking systems with intermittent observations is analyzed using extrapolating technology with thoughts of complete observations. Recently, international scholars pay more attention to estimation theory with intermittent observations and obtain some valuable results, and basic theoretical system is established. Considering that estimation performance of optic-electric tracking systems degenerates significantly when there is a drop of detection probability with intermittent observations, based on requirements of engineering design and equipment development, using estimation theory of intermittent observations, thorough research on estimation performance and performance enhancement technology of optical-electric tracking systems with intermittent observations is conducted from fully exploiting angle redundant information, introducing angle velocity information and distributed networking of optic-electric tracking systems. Theoretical analysis and simulation research show that these technologies can effectively improve estimation performance of optical-electric tracking systems. The major research results are summed up as follows:
(1) A residual test algorithm based on posterior confidence is presented. The new algorithm firstly adds a test threshold based on traditional residual test algorithm, and then the residuals between the two thresholds can be fuzzed by means of fuzzy membership function and the likelihood probability of residuals can be obtained, and combined with the prior detection information, the posterior confidence of detection data can be calculated. Therefore the detection situation of tracking system can be determined based on the calculated posterior confidence. Then, with intermittent observations, an unbiased converted measurement Kalman filtering (UCMKF) and a target tracking filtering of linear least unbiased estimation (BLUE) are designed based on the proposed residual test algorithm. The Cramer-Rao low bounds (CRLB) of tracking system is also presented under the statistic significance, and an upper and lower bound of average of estimation error covariance can be conveniently calculated with given detection probability.
(2) The existence of critical detection probability of optic-electric tracking system is proved, and an upper and lower bound of critical detection probability is presented. The upper bound is described as the optimal solution of a nonlinear matrix inequality (NMI), and the lower bound is only related to eigenvalues of system state transition matrices. An iterative linear matrix inequality (ILMI) algorithm for solving the upper bound of critical detection probability is proposed by means of perturbation linearization. That provides theoretical basis for design of detection probability of optic-electric tracking system.
(3) For optic-electric tracking system composed of laser range finder and precision angle measurement equipment with intermittent observations, a federated filter is designed based on the posterior confidence residual test algorithm. Firstly, the position detection channel of traditional optic-electric tracking systems is decomposed into two independent detection channels according to physical structure, and the CRLB model of the independent detection channels is presented. Then, target motion states are respectively estimated by use of the detection data of the two channels, and a global state estimate can be obtained by fusing the two state estimates. Finally, the information sharing of the federated filter is done according to the global state estimate and the posterior confidence of detection channels. Monte-Carlo simulation and measured data show that the proposed tracking filter can obviously improve estimation performance of tradition optic-electric tracking systems by mining redundant angle measurements without increasing any hardware cost, and the root mean square of estimate error (RMSE) of the proposed tracking filter is closed to the average CRLB of tracking systems.
(4) A design idea, which is introducing angle velocity measurements of elevation and azimuth into traditional optic-electric tracking systems, is proposed, and a target tracking filter based on posterior confidence weighted fusion is designed with intermittent observations. Firstly, a measurement model for the new type of optic-electric tracking systems is built, and then using the nested conditioning method, the consistent estimate of the first two moments of converted measurement errors is derived. Secondly, for the four different detection cases of position and velocity detection channels, four sub-filters are designed respectively whose posterior confidences are calculated based on the detection cases of the channels, and then the output of the tracking filter is obtained by means of weighting the outputs of sub-filters with the corresponding posterior confidences. Finally, the statistic average of CRLB for tracking systems is presented. Monte-Carlo simulation results show that, with intermittent observations, the performance of optic-electric tracking systems with angle velocity measurements can be significantly improved as compared with that of traditional systems. Moreover, the RMSE of the designed tracking filter is closed to the average CRLB of tracking systems.
(5) A distributed Kalman fusion algorithm is proposed for distributed optic-electric tracking systems with colored measurement noises. The principle of the algorithm is that system states are divided into two uncorrelated parts and then the two parts are sequentially treated by non-augmented state Kalman filtering and distributed state fusion. It is proved that the distributed state fusion is equivalent to centralized Kalman fusion. Furthermore, the influence on distributed tracking systems of feedback structure is analyzed, and a modified distributed Kalman fusion algorithm is given for distributed tracking systems with colored measurement noises and feedback. Theory analysis and Monte-Carlo simulation show that the estimation performance of the proposed distributed fusion filter can be obviously improved as compared with that of local tracking filters, and it can be conveniently applied in the situation of real-time processing.
(1)研究了不完全量测下光电跟踪系统估计误差的统计特性。首先,提出了一种基于后验置信度的残差检测算法。其主要思想是在传统残差检测方法的基础上首先增加一个检测门限,对处于两个门限之间的残差,利用模糊隶属度函数方法进行模糊化,得到残差的似然概率,进而结合跟踪系统的先验探测信息,计算出探测数据的后验置信概率,并根据计算结果,对跟踪系统的探测情况进行判定,从而提高了滤波器残差检测的正确率。然后,基于后验置信度残差检测算法,设计了不完全量测下的去偏转换量测Kalman目标跟踪滤波器(UCMKF)与基于线性最小无偏估计(BLUE)准则的目标跟踪滤波器。最后,在统计意义下给出了跟踪系统的Cramer-Rao下界(CRLB),并且在给定探测概率下,给出了一组期望的估计误差协方差上下界的计算方法。
(2)研究了光电跟踪系统的临界探测概率。证明了跟踪系统临界探测概率的存在性,并且给出了临界探测概率的一组上下界,其上界被描述成一个非线性矩阵不等式(NMI)的最优解,其下界仅与跟踪系统状态转移矩阵的特征值有关。进一步利用摄动线性化方法给出了求解临界探测概率上界的一种迭代线性矩阵不等式(ILMI)算法,为光电跟踪系统探测概率的设计提供了理论依据。
(3)针对由激光测距机与精密测角设备组成的光电跟踪系统,在不完全量测下,设计了基于后验置信度残差检测的联邦目标跟踪滤波器。首先,依据物理结构将传统光电跟踪系统的位置探测通道分解为测距与测角两个独立的探测通道,给出了独立双通道的CRLB数学模型,并且对两个探测通道的量测数据分别进行基于后验置信度残差检测的目标状态估计。然后,将估计结果送至融合中心进行信息融合。最后,利用融合结果,并根据探测通道数据可信的后验概率,对探测通道的子滤波器进行信息分配。Monte-Carlo仿真以及试验场实测数据表明,在不完全量测下,所提滤波器在不增加系统硬件成本的前提下,通过攫取高采样率下的测角信息,跟踪性能较之传统光电跟踪系统的跟踪性能有了显著改善,并且滤波器估计误差均方差(RMSE)可逼近跟踪系统统计意义下的CRLB。
(4)提出了一种将俯仰和偏航两个方向的角速度量测引入传统光电跟踪系统的设计思想,并且针对这类新型的光电跟踪系统,设计了基于后验置信度融合的目标跟踪滤波器。首先建立了跟踪系统的量测模型,利用嵌套条件方法,推导了转换量测误差前两阶矩的一致性估计；然后针对位置探测通道与角速度探测通道的四种数据探测情形设计了四个子滤波器,并根据探测通道的探测情况计算出各子滤波器的后验置信度,进而对各子滤波器的输出按后验置信度进行加权融合,得到了跟踪滤波器的全局输出；最后给出了这类新型光电跟踪系统统计意义下的CRLB。Monte-Carlo仿真表明：在不完全量测下,相比传统光电跟踪系统,附加角速度量测的光电跟踪系统的跟踪性能有了显著提高,并且滤波器RMSE可逼近跟踪系统统计意义下的CRLB。
(5)针对具有有色观测噪声的分布式光电跟踪系统,设计了一种分布式融合滤波器。其原理是依据等效观测噪声与状态噪声的相关性,将目标运动状态分解为不相关的两部分,进行非扩维Kalman滤波以及分布式状态融合,融合算法等价于集中式Kalman融合。同时,进一步针对带反馈结构的具有有色观测噪声的分布式光电跟踪系统,分析了反馈结构对跟踪系统的影响,设计了修正的分布式融合滤波器。理论分析和Monte-Carlo仿真表明：所提分布式融合滤波器的估计性能较之任何局部跟踪系统的估计性能有了显著提升,并且计算量满足实时处理的要求。
Optic-electric tracking systems are indispensable detection equipments in development of fire control systems. Fast acquiring targets and accuracy tracking targets depend on accuracy estimation of target motion parameters. However, during practical tracking processes, detection probability of optic-electric systems is always less than one, due to shading of obstacles (drifting clouds, etc), interference of weather conditions (fog, etc), limited detectability of detection equipments (laser, etc), faults of detection equipments and noises working environment, etc. Generally, estimation performance of optic-electric tracking systems with intermittent observations is analyzed using extrapolating technology with thoughts of complete observations. Recently, international scholars pay more attention to estimation theory with intermittent observations and obtain some valuable results, and basic theoretical system is established. Considering that estimation performance of optic-electric tracking systems degenerates significantly when there is a drop of detection probability with intermittent observations, based on requirements of engineering design and equipment development, using estimation theory of intermittent observations, thorough research on estimation performance and performance enhancement technology of optical-electric tracking systems with intermittent observations is conducted from fully exploiting angle redundant information, introducing angle velocity information and distributed networking of optic-electric tracking systems. Theoretical analysis and simulation research show that these technologies can effectively improve estimation performance of optical-electric tracking systems. The major research results are summed up as follows:
(1) A residual test algorithm based on posterior confidence is presented. The new algorithm firstly adds a test threshold based on traditional residual test algorithm, and then the residuals between the two thresholds can be fuzzed by means of fuzzy membership function and the likelihood probability of residuals can be obtained, and combined with the prior detection information, the posterior confidence of detection data can be calculated. Therefore the detection situation of tracking system can be determined based on the calculated posterior confidence. Then, with intermittent observations, an unbiased converted measurement Kalman filtering (UCMKF) and a target tracking filtering of linear least unbiased estimation (BLUE) are designed based on the proposed residual test algorithm. The Cramer-Rao low bounds (CRLB) of tracking system is also presented under the statistic significance, and an upper and lower bound of average of estimation error covariance can be conveniently calculated with given detection probability.
(2) The existence of critical detection probability of optic-electric tracking system is proved, and an upper and lower bound of critical detection probability is presented. The upper bound is described as the optimal solution of a nonlinear matrix inequality (NMI), and the lower bound is only related to eigenvalues of system state transition matrices. An iterative linear matrix inequality (ILMI) algorithm for solving the upper bound of critical detection probability is proposed by means of perturbation linearization. That provides theoretical basis for design of detection probability of optic-electric tracking system.
(3) For optic-electric tracking system composed of laser range finder and precision angle measurement equipment with intermittent observations, a federated filter is designed based on the posterior confidence residual test algorithm. Firstly, the position detection channel of traditional optic-electric tracking systems is decomposed into two independent detection channels according to physical structure, and the CRLB model of the independent detection channels is presented. Then, target motion states are respectively estimated by use of the detection data of the two channels, and a global state estimate can be obtained by fusing the two state estimates. Finally, the information sharing of the federated filter is done according to the global state estimate and the posterior confidence of detection channels. Monte-Carlo simulation and measured data show that the proposed tracking filter can obviously improve estimation performance of tradition optic-electric tracking systems by mining redundant angle measurements without increasing any hardware cost, and the root mean square of estimate error (RMSE) of the proposed tracking filter is closed to the average CRLB of tracking systems.
(4) A design idea, which is introducing angle velocity measurements of elevation and azimuth into traditional optic-electric tracking systems, is proposed, and a target tracking filter based on posterior confidence weighted fusion is designed with intermittent observations. Firstly, a measurement model for the new type of optic-electric tracking systems is built, and then using the nested conditioning method, the consistent estimate of the first two moments of converted measurement errors is derived. Secondly, for the four different detection cases of position and velocity detection channels, four sub-filters are designed respectively whose posterior confidences are calculated based on the detection cases of the channels, and then the output of the tracking filter is obtained by means of weighting the outputs of sub-filters with the corresponding posterior confidences. Finally, the statistic average of CRLB for tracking systems is presented. Monte-Carlo simulation results show that, with intermittent observations, the performance of optic-electric tracking systems with angle velocity measurements can be significantly improved as compared with that of traditional systems. Moreover, the RMSE of the designed tracking filter is closed to the average CRLB of tracking systems.
(5) A distributed Kalman fusion algorithm is proposed for distributed optic-electric tracking systems with colored measurement noises. The principle of the algorithm is that system states are divided into two uncorrelated parts and then the two parts are sequentially treated by non-augmented state Kalman filtering and distributed state fusion. It is proved that the distributed state fusion is equivalent to centralized Kalman fusion. Furthermore, the influence on distributed tracking systems of feedback structure is analyzed, and a modified distributed Kalman fusion algorithm is given for distributed tracking systems with colored measurement noises and feedback. Theory analysis and Monte-Carlo simulation show that the estimation performance of the proposed distributed fusion filter can be obviously improved as compared with that of local tracking filters, and it can be conveniently applied in the situation of real-time processing.
引文
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