基于空频域信息的单站被动目标跟踪算法研究
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摘要
随着战场环境的日益复杂,传统的探测系统(如雷达、声纳等)受到越来越多的威胁,被动定位与跟踪技术以其隐蔽性强、探测距离远、适用性广等优点越来越受到人们的重视。本文就基于空频域信息的单站被动跟踪中的一些关键问题进行了研究,包括模型和可观测性、跟踪滤波算法、机动目标跟踪、跟踪误差理论下限等,并通过仿真和实测数据对算法进行了验证。
模型和可观测性分析是被动定位与跟踪技术的基础,只有在系统满足可观测的条件下才能对目标的状态进行求解。对匀速直线运动目标的可观测分析已有较多的研究,但对机动目标的可观测分析在很大程度上仍是空白。有鉴于此,论文第二章对两类常规机动(匀加速和匀转弯)的可观测性进行了较为系统的分析,得出了一些有意义的结论,这也是机动目标跟踪的理论前提。
被动目标跟踪的实质是非线性最优滤波问题,即通过非线性观测得到目标状态(包括位置、速度、加速度等)的估计,其关键是求解后验状态分布。基于后验状态分布的高斯解析近似前提,本文第三章首先总结了扩展卡尔曼滤波(EKF)框架下的跟踪算法并指出其可能存在的问题和缺陷。在此基础上,结合实际应用背景对UKF框架下的滤波算法进行了深入研究:1)鉴于被动跟踪系统可观测性弱、初始误差大的问题,提出了一种迭代型UKF算法(IUKF),能明显提高跟踪收敛速度和跟踪精度;2)针对被动目标跟踪模型的特点,提出了一种适合实时应用的简化UKF算法(SUKF),可在保证跟踪性能的条件下有效降低运算开销;3)考虑到转弯目标跟踪的实际特点,提出了一种能同时完成对参数(转弯率)和状态估计的联合估计UKF算法(JEUKF),可利用单个模型实现对转弯目标的有效跟踪。
对目标后验状态分布近似的另一条途径是Monte Carlo仿真。近年来迅速发展起来的粒子滤波技术为求解非线性问题提供了通用的框架,它通过Monte Carlo仿真产生的带权粒子来对状态分布进行逼近。论文第四章首先对粒子滤波的基本原理进行了阐述,在此基础上深入研究了粒子滤波框架下的被动目标跟踪算法,主要工作包括三个方面:1)鉴于传统粒子滤波算法直接从先验进行采样导致的效率低下问题,提出了一种基于最优采样函数近似的改进粒子滤波(IPF)算法,使滤波器的跟踪性能得以明显提高;2)针对UPF算法在实际应用中出现的数值敏感和性能恶化问题,提出了一种修正的UPF(MUPF)算法,有效减轻了粒子贫化现象,降低了跟踪误差;3)结合被动跟踪系统的实际特点,对“边缘化”粒子滤波技术进行了研究,提高了跟踪算法的费效比。在初始误差大、可观测性弱的被动跟踪应用背景下,粒子滤波技术由于其粒子散布特性,在跟踪收敛速度和稳定性方面表现出独特的优势。
在军事应用背景下,目标可能随时会出现各种机动运动。因此,研究机动目标的被动跟踪算法具有重要意义,本文第五章正是应此需求展开研究的。对机动目标的跟踪是通过自适应地改变模型或滤波参数来实现的,本章主要对模型匹配自适应、噪声方差自适应、神经网络自适应这三类算法进行了研究,在此基础上提出了带动态修正能力的神经网络跟踪算法以及神经网络与交互多模相结合的融合算法。与传统机动目标跟踪算法相比,文中提出的方法不存在检测时延,具有稳定性高、反应速度快等优点,因此在被动跟踪环境下具有更好的适应性。
在非线性跟踪条件下,最优滤波算法通常很难建立,实际应用的都是各种次优算法。克拉美-罗下限(CRLB)是不依赖于算法本身而能达到的理论误差下限,它表明了各种次优算法的优劣程度以及和最优算法的接近程度。论文第六章旨在通过对跟踪误差下限的分析和研究,为算法的性能评估提供统一的理论框架。首先,对于匀速运动目标,将其跟踪误差分析转化为参数估计的CRLB求取来处理;其次,采用航迹分段策略,解决了机动目标跟踪的误差下限计算问题;最后,通过引入后验克拉美-罗限(PCRB)概念,对存在过程噪声条件下的近匀速运动目标跟踪误差进行了有效分析。
论文最后对全文进行了总结,并对今后工作进行了展望。
Conventional detection systems, such as radar and sonar, have encountered more and more threats with the increasing complexity of circumstances in modern battlefield. Passive localization and tracking technology has been paid more and more attention because of its significant advantage in self-hiding, far-distance detection and extensive applicability. In this dissertation, some critical issues on single observer passive tracking are touched based on the observed information of spatial-frequency domain. These issues include localization model and observability conditions, tracking algorithms, maneuvering target tracking, and lower bound analysis of tracking errors, etc. Both theory and algorithms presented in the dissertation are validated using simulated data or real measurement data.
System model and observability are the basis for passive localization and tracking, and the state of the target can be estimated only when the system is observable. As for the observability analysis, much attention has been paid to motion target with constant velocity; however, analysis of observability for maneuvering target is still a blank to some extent. In view of these facts, observability analysis for two classes of conventional maneuvers (constant acceleration and constant turn rate) are investigated in Chapter II, and some meaningful conclusions are drawn too, which lays the base for maneuvering target tracking discussed in Chapter V.
Passive target tracking is in essence the problem of nonlinear optimal filtering, i.e., the aim is to estimate the state (including position, velocity, and acceleration etc) of the target based on nonlinear measurements, and the key is to obtain the distribution of desired posterior state. On the premise of Gaussian analytic approximation to posterior distribution, Chapter III begins with the discussion of filtering algorithms and their potential drawbacks under the framework of extended Kalman filtering (EKF), on which basis the tracking algorithms are fully investigated under unscented Kalman filtering (UKF) framework: 1) in view of the large initial error and weak observability of passive system, an iterated UKF is proposed to improve the convergence speed and tracking precision; 2) a simplified UKF is proposed to reduce the computional complexity of standard UKF, which makes the algorithm more suitable for real-time application; 3) considering the particularity of CT (constant turn) model, a joint estimation algorithm referred to as JEUKF is proposed to estimate the maneuvering parameter (turn rate) and target state simutaniously, making it possible to track CT target successfully with only one single model.
Another way to approximate the posterior state distribution is Monte Carlo simulation. The recently developed particle filtering technology provides a general framework for nonlinear problem, and posterior state distribution is approximated by weighted particles which are generated through Monte Carlo simulation. Chapter IV concentrates on passive tracking algorithms based on particle filtering, and the work is done from three main aspects: 1) in view of the inefficiency of general particle filter which samples the particles directly from the prior, an improved algorithm is proposed using optimal function approximation; 2) a modified unscented particle filter (MUPF) is proposed to address the numerical problem and performance deterioration found in conventional UPF; 3) considering the real characteristic of passive tracking system, the marginalized particle filtering approach is presented. Under the background of passive tracking, the initial estimate error is usually very large, and the system is subject to weak observability. In this case, the particle filtering methods exhibit obvious advantage in robustness and convergent speed because of the decentralization of particles.
In the application of military background, the target may exhibit different motions from time to time. In such case, it is of great significance to investigate the problem of maneuvering target tracking, and the work in Chapter V is just done under this requirement. Usually, track of maneuvering target is realized by adaptively adjusting the model and filter parameters. In this chapter, three tracking approaches have been discussed. These include the model matched adaptation method, the noise covariance adaptation method, and the neural network adaptation method. Following the discussion, two novel algorithms, i.e., neural network algorithm with dynamic correction ability and neural network algorithm integrated by interacting multiple model (IMM), are proposed to improve the tracking performance. Compared to conventional methods used in maneuvering target tracking, the proposed algorithms are not subject to detection delay and have the advantage of high stability, prompt response, so they have better applicability in passive tracking circumstance.
Under nonlinear condition, the optimal filtering algorithm is generally difficult to construct, so in real application all kinds of suboptimal algorithm are used instead. The well known Cramer-Rao lower bound (CRLB) gives an indication of performance limitation which is independent upon specified algorithm, and it is usually used to determine whether improved performance requirements are realistic for any suboptimal algorithm. Chapter VI is aimed at providing a unified framework for performance assessment of tracking algorithms by investigating the tracking error CRLB. Firstly, for the uniform velocity target, the tracking accuracy is evaluated by analyzing the general CRLB of parameter estimate; secondly, error lower bound calculation for maneuvering target tracking is solved by dividing the trajectory into multiple segments; lastly, by introducing the concept of posterior Cramer-Rao bound (PCRB), the tracking accuracy of near uniform velocity target is analyzed.
The dissertation concludes with a summary of the accomplished work and future research recommendations.
模型和可观测性分析是被动定位与跟踪技术的基础,只有在系统满足可观测的条件下才能对目标的状态进行求解。对匀速直线运动目标的可观测分析已有较多的研究,但对机动目标的可观测分析在很大程度上仍是空白。有鉴于此,论文第二章对两类常规机动(匀加速和匀转弯)的可观测性进行了较为系统的分析,得出了一些有意义的结论,这也是机动目标跟踪的理论前提。
被动目标跟踪的实质是非线性最优滤波问题,即通过非线性观测得到目标状态(包括位置、速度、加速度等)的估计,其关键是求解后验状态分布。基于后验状态分布的高斯解析近似前提,本文第三章首先总结了扩展卡尔曼滤波(EKF)框架下的跟踪算法并指出其可能存在的问题和缺陷。在此基础上,结合实际应用背景对UKF框架下的滤波算法进行了深入研究:1)鉴于被动跟踪系统可观测性弱、初始误差大的问题,提出了一种迭代型UKF算法(IUKF),能明显提高跟踪收敛速度和跟踪精度;2)针对被动目标跟踪模型的特点,提出了一种适合实时应用的简化UKF算法(SUKF),可在保证跟踪性能的条件下有效降低运算开销;3)考虑到转弯目标跟踪的实际特点,提出了一种能同时完成对参数(转弯率)和状态估计的联合估计UKF算法(JEUKF),可利用单个模型实现对转弯目标的有效跟踪。
对目标后验状态分布近似的另一条途径是Monte Carlo仿真。近年来迅速发展起来的粒子滤波技术为求解非线性问题提供了通用的框架,它通过Monte Carlo仿真产生的带权粒子来对状态分布进行逼近。论文第四章首先对粒子滤波的基本原理进行了阐述,在此基础上深入研究了粒子滤波框架下的被动目标跟踪算法,主要工作包括三个方面:1)鉴于传统粒子滤波算法直接从先验进行采样导致的效率低下问题,提出了一种基于最优采样函数近似的改进粒子滤波(IPF)算法,使滤波器的跟踪性能得以明显提高;2)针对UPF算法在实际应用中出现的数值敏感和性能恶化问题,提出了一种修正的UPF(MUPF)算法,有效减轻了粒子贫化现象,降低了跟踪误差;3)结合被动跟踪系统的实际特点,对“边缘化”粒子滤波技术进行了研究,提高了跟踪算法的费效比。在初始误差大、可观测性弱的被动跟踪应用背景下,粒子滤波技术由于其粒子散布特性,在跟踪收敛速度和稳定性方面表现出独特的优势。
在军事应用背景下,目标可能随时会出现各种机动运动。因此,研究机动目标的被动跟踪算法具有重要意义,本文第五章正是应此需求展开研究的。对机动目标的跟踪是通过自适应地改变模型或滤波参数来实现的,本章主要对模型匹配自适应、噪声方差自适应、神经网络自适应这三类算法进行了研究,在此基础上提出了带动态修正能力的神经网络跟踪算法以及神经网络与交互多模相结合的融合算法。与传统机动目标跟踪算法相比,文中提出的方法不存在检测时延,具有稳定性高、反应速度快等优点,因此在被动跟踪环境下具有更好的适应性。
在非线性跟踪条件下,最优滤波算法通常很难建立,实际应用的都是各种次优算法。克拉美-罗下限(CRLB)是不依赖于算法本身而能达到的理论误差下限,它表明了各种次优算法的优劣程度以及和最优算法的接近程度。论文第六章旨在通过对跟踪误差下限的分析和研究,为算法的性能评估提供统一的理论框架。首先,对于匀速运动目标,将其跟踪误差分析转化为参数估计的CRLB求取来处理;其次,采用航迹分段策略,解决了机动目标跟踪的误差下限计算问题;最后,通过引入后验克拉美-罗限(PCRB)概念,对存在过程噪声条件下的近匀速运动目标跟踪误差进行了有效分析。
论文最后对全文进行了总结,并对今后工作进行了展望。
Conventional detection systems, such as radar and sonar, have encountered more and more threats with the increasing complexity of circumstances in modern battlefield. Passive localization and tracking technology has been paid more and more attention because of its significant advantage in self-hiding, far-distance detection and extensive applicability. In this dissertation, some critical issues on single observer passive tracking are touched based on the observed information of spatial-frequency domain. These issues include localization model and observability conditions, tracking algorithms, maneuvering target tracking, and lower bound analysis of tracking errors, etc. Both theory and algorithms presented in the dissertation are validated using simulated data or real measurement data.
System model and observability are the basis for passive localization and tracking, and the state of the target can be estimated only when the system is observable. As for the observability analysis, much attention has been paid to motion target with constant velocity; however, analysis of observability for maneuvering target is still a blank to some extent. In view of these facts, observability analysis for two classes of conventional maneuvers (constant acceleration and constant turn rate) are investigated in Chapter II, and some meaningful conclusions are drawn too, which lays the base for maneuvering target tracking discussed in Chapter V.
Passive target tracking is in essence the problem of nonlinear optimal filtering, i.e., the aim is to estimate the state (including position, velocity, and acceleration etc) of the target based on nonlinear measurements, and the key is to obtain the distribution of desired posterior state. On the premise of Gaussian analytic approximation to posterior distribution, Chapter III begins with the discussion of filtering algorithms and their potential drawbacks under the framework of extended Kalman filtering (EKF), on which basis the tracking algorithms are fully investigated under unscented Kalman filtering (UKF) framework: 1) in view of the large initial error and weak observability of passive system, an iterated UKF is proposed to improve the convergence speed and tracking precision; 2) a simplified UKF is proposed to reduce the computional complexity of standard UKF, which makes the algorithm more suitable for real-time application; 3) considering the particularity of CT (constant turn) model, a joint estimation algorithm referred to as JEUKF is proposed to estimate the maneuvering parameter (turn rate) and target state simutaniously, making it possible to track CT target successfully with only one single model.
Another way to approximate the posterior state distribution is Monte Carlo simulation. The recently developed particle filtering technology provides a general framework for nonlinear problem, and posterior state distribution is approximated by weighted particles which are generated through Monte Carlo simulation. Chapter IV concentrates on passive tracking algorithms based on particle filtering, and the work is done from three main aspects: 1) in view of the inefficiency of general particle filter which samples the particles directly from the prior, an improved algorithm is proposed using optimal function approximation; 2) a modified unscented particle filter (MUPF) is proposed to address the numerical problem and performance deterioration found in conventional UPF; 3) considering the real characteristic of passive tracking system, the marginalized particle filtering approach is presented. Under the background of passive tracking, the initial estimate error is usually very large, and the system is subject to weak observability. In this case, the particle filtering methods exhibit obvious advantage in robustness and convergent speed because of the decentralization of particles.
In the application of military background, the target may exhibit different motions from time to time. In such case, it is of great significance to investigate the problem of maneuvering target tracking, and the work in Chapter V is just done under this requirement. Usually, track of maneuvering target is realized by adaptively adjusting the model and filter parameters. In this chapter, three tracking approaches have been discussed. These include the model matched adaptation method, the noise covariance adaptation method, and the neural network adaptation method. Following the discussion, two novel algorithms, i.e., neural network algorithm with dynamic correction ability and neural network algorithm integrated by interacting multiple model (IMM), are proposed to improve the tracking performance. Compared to conventional methods used in maneuvering target tracking, the proposed algorithms are not subject to detection delay and have the advantage of high stability, prompt response, so they have better applicability in passive tracking circumstance.
Under nonlinear condition, the optimal filtering algorithm is generally difficult to construct, so in real application all kinds of suboptimal algorithm are used instead. The well known Cramer-Rao lower bound (CRLB) gives an indication of performance limitation which is independent upon specified algorithm, and it is usually used to determine whether improved performance requirements are realistic for any suboptimal algorithm. Chapter VI is aimed at providing a unified framework for performance assessment of tracking algorithms by investigating the tracking error CRLB. Firstly, for the uniform velocity target, the tracking accuracy is evaluated by analyzing the general CRLB of parameter estimate; secondly, error lower bound calculation for maneuvering target tracking is solved by dividing the trajectory into multiple segments; lastly, by introducing the concept of posterior Cramer-Rao bound (PCRB), the tracking accuracy of near uniform velocity target is analyzed.
The dissertation concludes with a summary of the accomplished work and future research recommendations.
引文
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