【作者】 林静；

【导师】 林明；

【作者基本信息】 厦门大学 ， 统计学， 2018， 硕士

【摘要】 基于卡尔曼滤波线性高斯状态空间模型的参数估计为最优估计,然而在非线性/非高斯系统下,卡尔曼滤波将不再适用。近年来,滤波问题越来越复杂,对滤波的精度要求越来越高,过去的一些非线性滤波方法也越来越无法解决现实中的问题。粒子滤波是一种新的非线性滤波方法,对于系统模型特性以及噪声分布不作要求,因此在现实的滤波任务中应用广泛,特别在非线性、非高斯状态空间模型参数估计的运用上受到重视。但是,粒子滤波方法在快速发展的同时,一些问题仍有待解决,尤其是样本退化问题,使得粒子滤波的发展和应用受到限制,对非线性、非高斯状态空间模型的参数估计产生较大的偏差。因此,对粒子滤波方法进行优化和改进对于非线性、非高斯状态空间模型的参数估计和完善滤波理论、拓展其应用领域具有重要的意义。文章基于序贯重要性重采样粒子滤波算法提出分段粒子滤波,解决由于样本退化而带来的参数估计失真的问题。分段粒子滤波将观测数据划分成段,基于序贯重要性重采样粒子滤波对每段进行参数估计,最后运用荟萃分析将每段的参数估计结果汇总合并,得到最终的参数估计结果。性能仿真与分析实验结果表明,对比于序贯重要性重采样粒子滤波,分段粒子滤波有效地缓解了其退化问题,改进算法不仅在计算成本相当的情况下具有更好的估计效率,而且具有平行计算的特点,此外,能够实现实时估计,克服了蒙特卡罗马尔科夫模拟方法的缺点,并进一步完善了粒子滤波理论,拓展其应用领域。更多还原

【Abstract】 Kalman filter can estimate optimal parameter in linear Gaussian state space model,but it can’t be applied in the nonlinear/non-Gaussian state space model.In view of the complexity of the filtering and the increasing accuracy requirements,the traditional nonlinear filtering method has been difficult to meet the actual application requirements.As one of the new nonlinear filtering method,particle filtering is not limited by the system and noise distribution,which is more in line with the requirements of the actual filtering task.Therefore,it is widely concerned in the application of parameter estimation of nonlinear and non-Gaussian state space model.However,there are still some problems to be solved in the process of rapid development of particle filtering,especially the problem of particle degradation,which has influenced the development and application of particle filtering,and has a large deviation on the parameter estimation of nonlinear and non-Gaussian state space model.Therefore,the improvement of particle filtering method is of great significance to the parameter estimation in nonlinear and non-Gaussian state space model,perfecting filtering theory and expanding its application field.In order to solve the problem of parameter estimation performance degradation due to particle degradation,segmentational particle filtering based on sequential importance resampling particle filtering algorithm is present.Segmentational particle filtering divides the observation data into segments and estimates the parameters of each segment based on sequential importance resampling particle filtering.Finally,the parameter estimation of each segment are combined by using meta-analysis.Experimental results show that segmentational particle filtering effectively alleviates the particle degradation problem,having better estimation efficiency with roughly the same calculation and the characteristic of parallel calculation.And the improved algorithm has the characteristics of on-line estimation,overcoming the drawback of Markov Chain Monte Carlo.Also,segmentational particle filtering further improves the particle filtering theory and expands its application field.更多还原