粒子滤波改进算法研究与应用
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摘要
随着模型复杂性的增强和对滤波精度需求的不断提高,在有些应用中传统的非线性滤波方法已不能满足要求。粒子滤波作为一种新型的非线性滤波方法,以其处理非线性、非高斯动态系统滤波问题的优良特性受到广泛地关注。它面向更为复杂的非线性模型且无需对状态分布作任何假设,更符合实际滤波任务的要求。然而,粒子滤波在快速发展的过程中也遇到了一些有待解决的问题。因此,改进和完善粒子滤波方法具有重要的理论意义和实际的工程价值。本文结合统计学习理论的新方法,针对粒子滤波算法和应用中的问题进行了深入研究,主要的研究内容包括以下几个方面:
首先,针对非线性动态系统滤波的基本问题,在递推贝叶斯估计理论的统一框架下深入研究了三类具有代表性的非线性滤波方法:扩展卡尔曼滤波、Unscented卡尔曼滤波和粒子滤波。分析和比较了各方法的适用条件、优点和不足,并着重讨论了粒子滤波的基本原理、算法步骤、粒子退化和贫化问题、收敛性理论,为后续研究奠定了基础。
其次,研究了如何从概率密度估计角度解决粒子的退化和贫化问题。从具有不适定性的概率密度估计问题的数学描述出发,提出了支持向量机概率密度估计粒子滤波算法基本思想,采用支持向量机概率密度估计方法建立粒子后验分布模型并进行重采样,克服粒子的退化。通过线性规划方式进一步提高了算法的计算效率,并讨论了该方法的多维状态扩展问题。另外,针对弱观测噪声环境下粒子退化现象更为严重的问题,提出了一种基于支持向量机重采样的似然粒子滤波算法,该算法使用似然函数作为提议分布,融入了最新的观测信息,并且可以有效避免粒子退化,增强粒子的多样性,从而提高了状态估计精度。仿真结果验证了上述算法的可行性和有效性。
再次,从函数回归估计角度研究了解决粒子退化和贫化的问题。利用粒子滤波过程中的粒子及其权值,建立对应的回归估计模型对权值进行调整,来克服粒子的退化并增加多样性。为了避免求解二次优化问题,分别采用了平均场理论和等式约束方式对优化问题进行了改进,提出了基于平均场支持向量回归机的粒子滤波算法和基于最小二乘支持向量回归机的粒子滤波算法,通过仿真并与现有方法的比较,验证了算法的优越性。另外,还进一步研究了最小二乘支持向量回归机针对大规模数据集的处理方法。
然后,研究了提高粒子滤波实时性的方法。根据近似支持向量机分类算法的原理,将其扩展到回归估计问题中,采用直接求解法推导了近似支持向量回归机线性、非线性、大规模数据集算法,并与最小二乘支持向量回归机进行了比较。在此基础上,以估计窗实时粒子滤波算法为基本框架,提出了采用近似支持向量回归机融合估计窗内子粒子集滤波结果的实时粒子滤波改进算法,减小了计算复杂度,进一步增强了算法的实时性。通过对一个纯角度目标跟踪的仿真,验证了算法的可行性和有效性。
最后,研究了基于多模型的粒子滤波方法及其在机动目标跟踪中的应用问题。根据递推贝叶斯估计理论推导了交互多模型粒子滤波的基本算法,并给出了采用高斯近似方式的实用算法。在分析了机动目标基本运动模型的基础上,利用粒子滤波作为模型匹配滤波器,解决了非线性观测方程难以直接应用的问题。采用多普勒测量信息估计目标转弯角速率,从而对多模型进行优化和缩减,提高了算法计算效率。对一个多次转弯机动目标跟踪问题进行了仿真研究,结果验证了算法的可行性和有效性,扩展了粒子滤波在目标跟踪中的应用范围。
The traditional nonlinear filtering method can not meet the requirements of some applications because the models are more complex, and also those applications need higher filter precision. Particle filter, as a recent research focus of nonlinear filtering method, can deal with the nonlinear/non-Gaussian filtering problem effectively without assumption on the state distribution. So it is more applicable for practical filtering problem. However, there are still some problems need to be solved even though the particle filtering theory has been rapid development, so improvement on the particle filtering method have significant theoretical and practical value. This thesis utilized the new statistical learning theory to study the particle filtering algorithm and its applications. The research focused on following aspects.
Firstly, based on the unified recursive Bayesian estimation theory, three typical nonlinear filtering methods—Extend Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Particle Filter (PF) were studied. The thesis analyzed and compared the basic theory, application conditions, advantages and disadvantages of these three methods. Especially for particle filtering method, the basic principle, algorithm, particle degeneration and impoverishment, convergence theory were studied in depth as the basis of further study.
Secondly, the thesis improved the particle filtering method from the perspective of the probability density estimation to overcome the particle degeneration and impoverishment. Started with the mathematical description of ill-posed probability density estimation problem, the basic idea of a density estimation method based on Support Vector Machine (SVM) was proposed, which built the posterior density models and resampled the new particles. Then the efficiency of this estimation algorithm was improved by using linear optimization theory. And the multi-dimensional extension problem was discussed also. Furthermore, for the more severe degeneracy problem in weak measurement noise applications, an improved likelihood particle filter algorithm based on SVM resampling was proposed. This algorithm used likelihood function as proposed distribution, took account of the most recent observation information, and increased the diversity of sampled particles. So that the degeneration problem was solved effectively and the states estimation precision was improved. Simulation results demonstrated the feasibility and superiority of the proposed algorithms.
Thirdly, the thesis studied how to solve the problem of particle degeneration and impoverishment from the perspective of function regression estimation. The proposed algorithm used particles and their weights to build regression model during iteration, and adjusted weights of particles by this model to overcome the degeneration and increase the diversity of particles. In order to avoid solving quadratic optimization problem, the Mean Filed Support Vector Regression (MF-SVR) particle filter and Least Squares Support Vector Regression (LSSVR) particle filter were proposed, where the mean filed theory and equality constraint method were implemented respectively. Simulation results illustrated the superiority of the two algorithms to existing methods. In addition, the application on large scale data set algorithm of LSSVR was discussed.
Then, the thesis studied the method of improving the real-time performance of particle filter. The Proximal Support Vector Machines (PSVM), used in classification problems, was extended into this regression problem. By solving the optimization problem directly, the algorithms for linear, nonlinear, and large scale data sets applications were derived, and compared with LSSVR. According to that, an improved real-time particle filter algorithm was proposed, which was based on data fusion with Proximal Support Vector Regression (PSVR), to estimate the filtering result of particles within the estimation window. The new algorithm reduced the calculation complexity, and was more practical for real-time applications. The simulation results of bearings-only tracking problem demonstrated the feasibility and superiority of the proposed algorithm.
Finally, the thesis studied the particle filter that based on multiple models and its application on maneuvering target tracking. According to the principle of recursive Bayesian estimation theory, the basic algorithm of interacting multiple model particle filter was derived and also the practical algorithm based on Gaussian approximation method was provided. Based on the analysis of the basic motion model of maneuvering target, and using the particle filter as model matched filter, the thesis solved the problem that the nonlinear observation equation was difficult to apply directly. The proposed method used Doppler measurement method to estimate the turning angular rate, reduced the number of models, and improved the efficiency of the filter algorithm. The simulation results of a multi-turn maneuvering target tracking problem demonstrated the feasibility and superiority of the proposed algorithm, and also extended the applications of particle filter in target tracking.
首先,针对非线性动态系统滤波的基本问题,在递推贝叶斯估计理论的统一框架下深入研究了三类具有代表性的非线性滤波方法:扩展卡尔曼滤波、Unscented卡尔曼滤波和粒子滤波。分析和比较了各方法的适用条件、优点和不足,并着重讨论了粒子滤波的基本原理、算法步骤、粒子退化和贫化问题、收敛性理论,为后续研究奠定了基础。
其次,研究了如何从概率密度估计角度解决粒子的退化和贫化问题。从具有不适定性的概率密度估计问题的数学描述出发,提出了支持向量机概率密度估计粒子滤波算法基本思想,采用支持向量机概率密度估计方法建立粒子后验分布模型并进行重采样,克服粒子的退化。通过线性规划方式进一步提高了算法的计算效率,并讨论了该方法的多维状态扩展问题。另外,针对弱观测噪声环境下粒子退化现象更为严重的问题,提出了一种基于支持向量机重采样的似然粒子滤波算法,该算法使用似然函数作为提议分布,融入了最新的观测信息,并且可以有效避免粒子退化,增强粒子的多样性,从而提高了状态估计精度。仿真结果验证了上述算法的可行性和有效性。
再次,从函数回归估计角度研究了解决粒子退化和贫化的问题。利用粒子滤波过程中的粒子及其权值,建立对应的回归估计模型对权值进行调整,来克服粒子的退化并增加多样性。为了避免求解二次优化问题,分别采用了平均场理论和等式约束方式对优化问题进行了改进,提出了基于平均场支持向量回归机的粒子滤波算法和基于最小二乘支持向量回归机的粒子滤波算法,通过仿真并与现有方法的比较,验证了算法的优越性。另外,还进一步研究了最小二乘支持向量回归机针对大规模数据集的处理方法。
然后,研究了提高粒子滤波实时性的方法。根据近似支持向量机分类算法的原理,将其扩展到回归估计问题中,采用直接求解法推导了近似支持向量回归机线性、非线性、大规模数据集算法,并与最小二乘支持向量回归机进行了比较。在此基础上,以估计窗实时粒子滤波算法为基本框架,提出了采用近似支持向量回归机融合估计窗内子粒子集滤波结果的实时粒子滤波改进算法,减小了计算复杂度,进一步增强了算法的实时性。通过对一个纯角度目标跟踪的仿真,验证了算法的可行性和有效性。
最后,研究了基于多模型的粒子滤波方法及其在机动目标跟踪中的应用问题。根据递推贝叶斯估计理论推导了交互多模型粒子滤波的基本算法,并给出了采用高斯近似方式的实用算法。在分析了机动目标基本运动模型的基础上,利用粒子滤波作为模型匹配滤波器,解决了非线性观测方程难以直接应用的问题。采用多普勒测量信息估计目标转弯角速率,从而对多模型进行优化和缩减,提高了算法计算效率。对一个多次转弯机动目标跟踪问题进行了仿真研究,结果验证了算法的可行性和有效性,扩展了粒子滤波在目标跟踪中的应用范围。
The traditional nonlinear filtering method can not meet the requirements of some applications because the models are more complex, and also those applications need higher filter precision. Particle filter, as a recent research focus of nonlinear filtering method, can deal with the nonlinear/non-Gaussian filtering problem effectively without assumption on the state distribution. So it is more applicable for practical filtering problem. However, there are still some problems need to be solved even though the particle filtering theory has been rapid development, so improvement on the particle filtering method have significant theoretical and practical value. This thesis utilized the new statistical learning theory to study the particle filtering algorithm and its applications. The research focused on following aspects.
Firstly, based on the unified recursive Bayesian estimation theory, three typical nonlinear filtering methods—Extend Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Particle Filter (PF) were studied. The thesis analyzed and compared the basic theory, application conditions, advantages and disadvantages of these three methods. Especially for particle filtering method, the basic principle, algorithm, particle degeneration and impoverishment, convergence theory were studied in depth as the basis of further study.
Secondly, the thesis improved the particle filtering method from the perspective of the probability density estimation to overcome the particle degeneration and impoverishment. Started with the mathematical description of ill-posed probability density estimation problem, the basic idea of a density estimation method based on Support Vector Machine (SVM) was proposed, which built the posterior density models and resampled the new particles. Then the efficiency of this estimation algorithm was improved by using linear optimization theory. And the multi-dimensional extension problem was discussed also. Furthermore, for the more severe degeneracy problem in weak measurement noise applications, an improved likelihood particle filter algorithm based on SVM resampling was proposed. This algorithm used likelihood function as proposed distribution, took account of the most recent observation information, and increased the diversity of sampled particles. So that the degeneration problem was solved effectively and the states estimation precision was improved. Simulation results demonstrated the feasibility and superiority of the proposed algorithms.
Thirdly, the thesis studied how to solve the problem of particle degeneration and impoverishment from the perspective of function regression estimation. The proposed algorithm used particles and their weights to build regression model during iteration, and adjusted weights of particles by this model to overcome the degeneration and increase the diversity of particles. In order to avoid solving quadratic optimization problem, the Mean Filed Support Vector Regression (MF-SVR) particle filter and Least Squares Support Vector Regression (LSSVR) particle filter were proposed, where the mean filed theory and equality constraint method were implemented respectively. Simulation results illustrated the superiority of the two algorithms to existing methods. In addition, the application on large scale data set algorithm of LSSVR was discussed.
Then, the thesis studied the method of improving the real-time performance of particle filter. The Proximal Support Vector Machines (PSVM), used in classification problems, was extended into this regression problem. By solving the optimization problem directly, the algorithms for linear, nonlinear, and large scale data sets applications were derived, and compared with LSSVR. According to that, an improved real-time particle filter algorithm was proposed, which was based on data fusion with Proximal Support Vector Regression (PSVR), to estimate the filtering result of particles within the estimation window. The new algorithm reduced the calculation complexity, and was more practical for real-time applications. The simulation results of bearings-only tracking problem demonstrated the feasibility and superiority of the proposed algorithm.
Finally, the thesis studied the particle filter that based on multiple models and its application on maneuvering target tracking. According to the principle of recursive Bayesian estimation theory, the basic algorithm of interacting multiple model particle filter was derived and also the practical algorithm based on Gaussian approximation method was provided. Based on the analysis of the basic motion model of maneuvering target, and using the particle filter as model matched filter, the thesis solved the problem that the nonlinear observation equation was difficult to apply directly. The proposed method used Doppler measurement method to estimate the turning angular rate, reduced the number of models, and improved the efficiency of the filter algorithm. The simulation results of a multi-turn maneuvering target tracking problem demonstrated the feasibility and superiority of the proposed algorithm, and also extended the applications of particle filter in target tracking.
引文
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