【作者】 梁军；

【导师】 彭喜元；

【作者基本信息】 哈尔滨工业大学 ， 仪器科学与技术， 2009， 博士

【摘要】 非线性系统状态估计一直受到国内外学者的广泛重视,成为一个具有重要理论和使用价值的热点研究课题。粒子滤波是近年来逐步兴起的一种适用于非线性系统状态估计的滤波方法,其在统计信号处理、经济学、生物统计学、通信、目标跟踪、故障诊断、卫星导航和声纳定位等领域均有广泛的应用前景。目前粒子滤波算法仍有大量的问题需要解决。例如,重要性概率密度函数的选取问题、粒子退化问题、粒子多样性匮乏问题、各种粒子滤波算法的收敛性问题、提高粒子滤波的精度和速度、粒子滤波算法的硬件实现、拓展粒子滤波新的应用领域等问题。为提高非线性系统状态估计的精度,本文研究了粒子滤波与状态平滑相结合的方法;为改善粒子退化问题,本文研究了粒子滤波的重采样方法;针对粒子滤波在实际工程领域应用中的问题,本文进行了基于粒子滤波的非线性系统故障检测研究和基于粒子滤波的单站被动纯角度目标跟踪研究。本文主要研究内容和成果如下:第一,本文提出基于观测路径相似性的粒子估计算法。该算法利用系统状态观测值路径和粒子状态观测值路径的相似性来修正粒子权值,使接近系统状态的粒子具有更大的权值。该算法在对当前时刻系统状态进行滤波操作的同时,对过去时刻系统状态进行平滑操作,提高了非线性系统状态估计的精度。在一个典型非线性系统状态估计问题的仿真实验中,当系统噪声和观测噪声均为高斯噪声时,该算法的均方根误差和误差方差均远优于SIR(sequential importance resampling)粒子滤波算法、辅助粒子滤波算法、正则化粒子滤波算法、高斯粒子滤波算法和混合高斯粒子滤波算法;当系统噪声和观测噪声服从重尾非高斯分布、χ2(2)、t(2)和F(2,20)时,该算法的均方根误差明显优于上述五种算法,误差方差也小于这五种算法。此外,由于没有重采样操作该算法的计算复杂度较低。仿真实验结果表明,该算法的计算速度优于SIR粒子滤波、辅助粒子滤波和正则化粒子滤波,接近高斯粒子滤波。第二,考虑到观测时间间隔较长时,平滑操作对上述基于观测路径相似性的粒子估计算法的实时性影响较大,本文提出基于观测路径相似性重采样的粒子滤波算法。该算法中不存在状态平滑操作。对一个典型非线性系统状态估计问题的仿真实验结果表明,在高斯噪声下当系统噪声方差大于观测噪声方差时,该算法的均方根误差优于SIR粒子滤波算法、辅助粒子滤波算法、正则化粒子滤波算法和高斯粒子滤波算法,且误差方差与这四种算法接近;当系统噪声方差等于或小于观测噪声方差时,该算法滤波精度与这四种算法接近。第三,针对在粒子退化严重使所有粒子权值都等于零的情况下,现有粒子滤波算法无法继续进行滤波,提出了先判断各粒子似然函数值是否全为零并根据判断结果决定后续执行步骤的改进策略。依据该改进策略对SIR粒子滤波算法、辅助粒子滤波算法、正则化粒子滤波算法、高斯粒子滤波算法和基于观测路径相似性重采样的粒子滤波算法提出了各自的改进算法,使各粒子滤波算法的鲁棒性得到提高。仿真实验结果验证了各改进算法的有效性。第四,针对非线性系统的故障检测问题,本文提出基于粒子滤波状态估计和残差平滑的非线性系统故障检测算法。该算法首先利用粒子滤波获得系统状态估计值,再采用系统状态观测值与系统状态估计值的理想观测值之差作为反映故障的残差,最后使用残差平滑值进行故障检测。仿真实验结果表明,在系统噪声方差小于观测噪声方差时,该算法的非线性系统故障检测性能优于基于粒子滤波似然函数值的故障检测算法。最后,针对目前单站被动纯角度目标跟踪问题缺乏有效的解决方法,本文将基于观测路径相似性重采样的粒子滤波算法应用于该问题。仿真实验结果表明,当观测噪声方差小于系统噪声方差时,该算法的跟踪精度优于SIR粒子滤波、辅助粒子滤波和高斯粒子滤波。更多还原

【Abstract】 The state estimation of nonlinear systems has caught the focus of many researchers, and becomes a hot research field with great theoritical value and application field. Over the last some years, particle filter which can be used to estimate the state of nonlinear systems has been developed. It has been widely applied in many fields such as statistical signal processing, economics, biostatistics, communications, target tracking, fault diagnosis, satellitic navigation, sonar orientation and so on.Nowadays, a lot of problems about particle filter algorithm have been in need of solution. These problems include the choice of importance probability density function, particle degeneracy, particle impoverishment, convergence, improving the accuracy and speed of particle filter, the hardware representation of particle filter, developing widely application field of particle filter and so on. In this paper the smoothing method is associated with particle filter to estimate accurately the state of nonlinear systems. At the same time our research is focused on the resampling of particles to improve the effect of particle degeneracy. Based on the particle filter, the fault detection of nonlinear systems and the single station passive target tracking with bearing-only measurement are researched to develop the application field of the particle filter. The main contributions of this dissertation are as follows:Firstly, a state estimation algorithm of nonlinear systems is proposed with the similarity between the observation path of particles and the observation path of system state. In this algorithm the weight of the particle is modified with the above similarity to increase the weight of the particle which is close to the system state. This proposed algorithm consists of the filtering for the current state and the smoothing for the previous state. Using the algorithm the state estimation accuracy of nonlinear systems is improved. When the system noise and observation noise are Gaussian, the RMSE and the error variance of the this proposed algorithm are better than SIR, APF, RPF, GPF, and GSPF in a typical example about the state estimation of a nonlinear system. When the system noise and observation noise are heavy-tail,χ2(2), t(2) or F(2,20), the RMSE of the this proposed algorithm is better than SIR, APF, RPF, GPF, and GSPF and the variance of the error of the this proposed algorithm is samller. Its time complexity is low without resampling. The results of the simulation demonstrate that the time complexity of the proposed algorithm is lower than SIR, APF, and APF and almost same with GPF.Secondly, the real-time performance of the proposed algorithm will be degraded due to the presence of the smoothing operation for more accurate state estimates. In this paper an improved algorithm is proposed, which has rasmpling based on the similarity between the observation paths without the smoothing operation. When the variance of the system Gaussian noise is bigger than the observation Gaussian noise, the RMSE of the this improved algorithm is better than SIR, APF, RPF, and GPF in a typical example about the state estimation of a nonlinear system and the variance of the error of the this improved algorithm is almost same with them. When the variance of the system Gaussian noise is samller than the observation Gaussian noise, the RMSE of the improved algorithm is almost same with them.Thirdly, those known particle filters will be inapplicable when all weights of used particles are zero due to the severe particle degeneracy. In this paper an idea is proposed to solve the problem. The idea is that the executive process is choiced according to all likelihood values of used particles. The reliability of SIR, APF, RPF, GPF, and the proposed algorithm in this paper is improved with the idea. The results of the simulation are presented to demonstrate the availability of all above improved algorithm.Fourthly, in this paper a fault detection approach based on SIR state estimation and smoothed residual is proposed for fault detection of nonlinear systems. In this approach the estimate value of the state of the nonlinear system is estimated firstly using SIR. Then the difference between these ideal observation of the estimate value and those observation of the state of the system is smoothed. The fault detection is done according to these smoothed difference. When the variance of the system noise is samller than the observation noise, the results of the simulation are presented to demonstrate the improved performance of the proposed algorithm over the fault detection approach based on SIR likelihood for fault detection. Finally, the particle filter with the resampling based on the similarity of observation paths is used for an example of single station passive target tracking with bearing-only measurement. The results of the simulation are presented to demonstrate the improved accuracy of the proposed algorithm over SIR, APF, and GPF.更多还原