非线性滤波在通信与导航中的应用研究
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摘要
现实物理世界中的多数系统本质上是非线性的,对其进行线性化近似是一种有效的处理方法,其中以卡尔曼滤波为经典代表的线性滤波方法在过去几十年里取得了丰硕的成果。但是,随着计算能力的提高、数学方法的丰富以及对精度的进一步要求,对非线性系统直接进行研究的需求日趋增多,非线性滤波就是在这样的背景下逐渐发展起来的。
伴随着控制与计算机技术的飞速发展,非线性滤波已在通信与信号处理、航空航天、导航定位、计算机视觉甚至金融分析等众多领域得到了越来越广泛的应用。本文针对具有代表性的两种非线性滤波算法：无迹卡尔曼滤波(UKF)和粒子滤波(PF)展开研究,并将这两种算法应用于OFDM系统载波频偏估计、捷联惯导系统初始对准与故障诊断中。本文主要研究内容及贡献包括：
1)针对非线性动态系统滤波的基本问题,在递归贝叶斯估计理论下深入研究了三类重要的非线性滤波方法扩展卡尔曼滤波(EKF)、无迹卡尔曼滤波和粒子滤波。
着重讨论了无迹卡尔曼滤波算法,包括UT变换、采样策略在内的核心原理、算法步骤；粒子滤波的序贯重要性采样、重采样等关键技术的原理及粒子退化和匮乏等问题；综合比较了各方法的适用条件、优点和不足。
2)针对OFDM系统的载波频偏问题,提出一种基于自适应UKF的频偏值估计算法。
OFDM系统的载波频偏是一个非线性问题,传统的滤波算法如EKF通过泰勒展开对频偏的观测方程进行近似。本文将其建模为非线性、高斯的动态状态空问模型,提出将UKF用于该模型下的频偏估计问题,并与EKF进行了性能对比。结果表明UKF在提高估计精度的同时,在稳定性、收敛性上都优于EKF。给出了基于最大后验概率准则的Sage-husa噪声估计器及其指数衰减记忆改进型,并与标准UKF结合得到了一种自适应UKF算法。进一步,本文提出了基于该自适应UKF算法的OFDM载波频偏估计方法,提高了UKF在噪声统计特性未知或时变时的鲁棒性,在初始方差设置与实际值存在偏差时,该方法的滤波估值依然准确。
3)研究了基于Stirling公式的中心差分卡尔曼滤波(CDKF),并基于加权统计线性回归的理论给出了统一UKF与CDKF算法的Sigma-point卡尔曼滤波器框架。进而,本文将Sigma-point卡尔曼滤波器用于满足一阶自回归过程的时变频偏的估计,实验结果表明在时变情况下,Sigma-point卡尔曼滤波器仍能获得较好的估值结果。从降低计算复杂度的角度出发,进一步研究了平方根形式的Sigma-point卡尔曼滤波器,仿真示例表明其在保证精度的同时能降低一定的计算量。最后探讨了UKF与并行计算的融合,给出了一种并行UKF算法框架。
4)针对捷联惯导系统初始对准与故障诊断问题,提出了一种抗差无迹粒子滤波算法。
标准粒子滤波常选择先验转移概率密度作为重要性采样函数,而这忽略了观测信息,不利于解决粒子退化的问题。本文研究了基于UKF的无迹粒子滤波(UPF),其由UKF得到更为准确的统计特性从而提高了粒子滤波算法的精度。本文将UPF用于本质上为非线性的初始对准问题,获得了比EKF、UKF、PF更好的估计性能。继而,针对初始对准中的故障诊断问题,本文提出了一种抗差UPF算法。当没有故障时,滤波得到的残差应满足零均值高斯白噪声的分布,基于此,该抗差UPF算法先由UPF得到残差方差阵,进而由χ2分布准则判断是否存在如野值等故障。当检测出故障后,引入了权重函数以自适应调整卡尔曼增益因子,从而在滤波过程中对野值进行抑制。该方法是一种无需辨识具体故障原因的系统级故障检测、抑制方法。
Most systems are naturally nonlinear in the real physical world and the linear approximation is a powerful method to solve nonlinear problems. The Kalman filter is a classic representative of linear filtering methods and has achieved fruitful results in the past few decades. While as computing power increases, mathematical means enrich and accuracy requires further improvement, the demanding on handling the nonlinear systems directly is urgent and necessary.
With the rapid development of computer and control technology, non-linear filtering technique has been widely applied to various fields as signal processing, wireless communication, aerospace, navigation and positioning, computer vision and even financial analysis, etc. This dissertation directs mainly at the researches on the two representative non-linear filtering algorithms:Unscented Kalman filter and particle filter, and their application in carrier frequency offset estimation of OFDM system as well as initial alignment and fault diagnose of Strapdown inertial navigation system. The main contents of the paper are:
Firstly, under the unified framework of recursive Bayesian estimation theory, this paper gives in-depth investigation of three classes of non-linear filtering methods as extended Kalman filter, unscented Kalman filter and particle filter. In particular, this dissertation presents in detail the principle of algorithm frame of unscented Kalman filter, the unscented transformation and the sampling strategies, meanwhile the basic structure of particle filter including the sequential importance sampling and resampling together with other key points are also described. The overall comparison of advantages, disadvantages and application conditions of each method is also addressed.
Secondly, an adaptive UKF algorithm is proposed to solve the CFO estimation in OFDM system. The study analyzed the carrier frequency offset estimation of OFDM systems, when the frequency offset is large, it will produce inter-carrier interference resulting the performance degradation. To solve this problem, the CFO is modeled as dynamic state space model and UKF is used for the offset estimation. Comparing to other convention methods as SC, MLEE, EKF, UKF enhances the filtering accuracy with better stability and convergence. Further, it derives an adaptive UKF with exponential decay of memory Sage-husa noise estimator based on the maximum posterior probability criteria, which helps to improve the robustness of UKF in unknown or time varying noise conditions.
Thirdly, the Stirling formula is described and the central difference Kalman filter (CDKF) is formulated. Based on the weighted statistical linear regression theory, the UKF and CDKF filters are classified into Sigma-point Kalman filter. To reduce the computational complexity, the square root form of Sigma-point Kalman filter is derived and verified, and a brief discuss with a parallel computing framework of UKF is given.
Fourthly, this paper addresses an unscented particle filter (UPF) to solve initial alignment problem and presents a adaptive-robust UPF algorithm for fault diagnosis. UPF is obtained by combing UKF into PF algorithm framework, in which UKF is used to acquire more accurate statistical characteristics and help to overcome the drawback in standard PF. UPF is adopted in SINS initial alignment problem and shows better valuation results. When there is no abnormal exists, the residual should meet the white Gaussian noise distribution and the trace conforms Chi-square distribution criteria. Based on this, the algorithm first obtains the residual variance matrix by UPF and then makes a judgment by examining the trace. When a fault is detected, the algorithm further introduces a weighting function to adaptively adjust the Kalman gain factor and suppress the outliers. This method can't identify the specific cause of malfunction, but still it is a good choice of system-level fault detection and suppression.
伴随着控制与计算机技术的飞速发展,非线性滤波已在通信与信号处理、航空航天、导航定位、计算机视觉甚至金融分析等众多领域得到了越来越广泛的应用。本文针对具有代表性的两种非线性滤波算法：无迹卡尔曼滤波(UKF)和粒子滤波(PF)展开研究,并将这两种算法应用于OFDM系统载波频偏估计、捷联惯导系统初始对准与故障诊断中。本文主要研究内容及贡献包括：
1)针对非线性动态系统滤波的基本问题,在递归贝叶斯估计理论下深入研究了三类重要的非线性滤波方法扩展卡尔曼滤波(EKF)、无迹卡尔曼滤波和粒子滤波。
着重讨论了无迹卡尔曼滤波算法,包括UT变换、采样策略在内的核心原理、算法步骤；粒子滤波的序贯重要性采样、重采样等关键技术的原理及粒子退化和匮乏等问题；综合比较了各方法的适用条件、优点和不足。
2)针对OFDM系统的载波频偏问题,提出一种基于自适应UKF的频偏值估计算法。
OFDM系统的载波频偏是一个非线性问题,传统的滤波算法如EKF通过泰勒展开对频偏的观测方程进行近似。本文将其建模为非线性、高斯的动态状态空问模型,提出将UKF用于该模型下的频偏估计问题,并与EKF进行了性能对比。结果表明UKF在提高估计精度的同时,在稳定性、收敛性上都优于EKF。给出了基于最大后验概率准则的Sage-husa噪声估计器及其指数衰减记忆改进型,并与标准UKF结合得到了一种自适应UKF算法。进一步,本文提出了基于该自适应UKF算法的OFDM载波频偏估计方法,提高了UKF在噪声统计特性未知或时变时的鲁棒性,在初始方差设置与实际值存在偏差时,该方法的滤波估值依然准确。
3)研究了基于Stirling公式的中心差分卡尔曼滤波(CDKF),并基于加权统计线性回归的理论给出了统一UKF与CDKF算法的Sigma-point卡尔曼滤波器框架。进而,本文将Sigma-point卡尔曼滤波器用于满足一阶自回归过程的时变频偏的估计,实验结果表明在时变情况下,Sigma-point卡尔曼滤波器仍能获得较好的估值结果。从降低计算复杂度的角度出发,进一步研究了平方根形式的Sigma-point卡尔曼滤波器,仿真示例表明其在保证精度的同时能降低一定的计算量。最后探讨了UKF与并行计算的融合,给出了一种并行UKF算法框架。
4)针对捷联惯导系统初始对准与故障诊断问题,提出了一种抗差无迹粒子滤波算法。
标准粒子滤波常选择先验转移概率密度作为重要性采样函数,而这忽略了观测信息,不利于解决粒子退化的问题。本文研究了基于UKF的无迹粒子滤波(UPF),其由UKF得到更为准确的统计特性从而提高了粒子滤波算法的精度。本文将UPF用于本质上为非线性的初始对准问题,获得了比EKF、UKF、PF更好的估计性能。继而,针对初始对准中的故障诊断问题,本文提出了一种抗差UPF算法。当没有故障时,滤波得到的残差应满足零均值高斯白噪声的分布,基于此,该抗差UPF算法先由UPF得到残差方差阵,进而由χ2分布准则判断是否存在如野值等故障。当检测出故障后,引入了权重函数以自适应调整卡尔曼增益因子,从而在滤波过程中对野值进行抑制。该方法是一种无需辨识具体故障原因的系统级故障检测、抑制方法。
Most systems are naturally nonlinear in the real physical world and the linear approximation is a powerful method to solve nonlinear problems. The Kalman filter is a classic representative of linear filtering methods and has achieved fruitful results in the past few decades. While as computing power increases, mathematical means enrich and accuracy requires further improvement, the demanding on handling the nonlinear systems directly is urgent and necessary.
With the rapid development of computer and control technology, non-linear filtering technique has been widely applied to various fields as signal processing, wireless communication, aerospace, navigation and positioning, computer vision and even financial analysis, etc. This dissertation directs mainly at the researches on the two representative non-linear filtering algorithms:Unscented Kalman filter and particle filter, and their application in carrier frequency offset estimation of OFDM system as well as initial alignment and fault diagnose of Strapdown inertial navigation system. The main contents of the paper are:
Firstly, under the unified framework of recursive Bayesian estimation theory, this paper gives in-depth investigation of three classes of non-linear filtering methods as extended Kalman filter, unscented Kalman filter and particle filter. In particular, this dissertation presents in detail the principle of algorithm frame of unscented Kalman filter, the unscented transformation and the sampling strategies, meanwhile the basic structure of particle filter including the sequential importance sampling and resampling together with other key points are also described. The overall comparison of advantages, disadvantages and application conditions of each method is also addressed.
Secondly, an adaptive UKF algorithm is proposed to solve the CFO estimation in OFDM system. The study analyzed the carrier frequency offset estimation of OFDM systems, when the frequency offset is large, it will produce inter-carrier interference resulting the performance degradation. To solve this problem, the CFO is modeled as dynamic state space model and UKF is used for the offset estimation. Comparing to other convention methods as SC, MLEE, EKF, UKF enhances the filtering accuracy with better stability and convergence. Further, it derives an adaptive UKF with exponential decay of memory Sage-husa noise estimator based on the maximum posterior probability criteria, which helps to improve the robustness of UKF in unknown or time varying noise conditions.
Thirdly, the Stirling formula is described and the central difference Kalman filter (CDKF) is formulated. Based on the weighted statistical linear regression theory, the UKF and CDKF filters are classified into Sigma-point Kalman filter. To reduce the computational complexity, the square root form of Sigma-point Kalman filter is derived and verified, and a brief discuss with a parallel computing framework of UKF is given.
Fourthly, this paper addresses an unscented particle filter (UPF) to solve initial alignment problem and presents a adaptive-robust UPF algorithm for fault diagnosis. UPF is obtained by combing UKF into PF algorithm framework, in which UKF is used to acquire more accurate statistical characteristics and help to overcome the drawback in standard PF. UPF is adopted in SINS initial alignment problem and shows better valuation results. When there is no abnormal exists, the residual should meet the white Gaussian noise distribution and the trace conforms Chi-square distribution criteria. Based on this, the algorithm first obtains the residual variance matrix by UPF and then makes a judgment by examining the trace. When a fault is detected, the algorithm further introduces a weighting function to adaptively adjust the Kalman gain factor and suppress the outliers. This method can't identify the specific cause of malfunction, but still it is a good choice of system-level fault detection and suppression.
引文
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