基于粒子滤波的混合估计理论与应用
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摘要
随着科学技术的发展，系统规模及复杂性在不断增加，对系统性能的要求在不断提高，同时信息获取的手段也在不断增多，因而面向复杂系统、复杂环境、网络化平台的估计问题成为现代估计理论的前沿领域。本文基于粒子滤波方法，对混合系统以及复杂环境下动态估计中的若干关键问题，从理论和算法上进行了深入研究，主要工作如下：
1．在Bayes框架下，综述了基于序贯Monte Carlo仿真方法的粒子滤波原理、收敛性、研究进展及其应用，讨论了粒子方法的新发展、新动态。
2．对多模型混合系统的状态估计问题，利用模型的结构特点，结合Rao-Blackwellisation技术和Kalman滤波技术，分别提出了迭代粒子滤波器和固定区间、固定延迟粒子平滑器。算例分析结果表明，本文所提出的滤波器和平滑器是可行的，估计性能有明显改善。
3．混合估计理论上的Cramér-Rao下界(CRLB)需要穷举所有可能的模型序列，计算量随时间指数增加。本文通过使用有限个模型序列假设子集，提出了一种CRLB的近似表达式，并且基于粒子滤波器和Monte Carlo仿真方法，给出了CRLB的一种近似计算方法，算例分析表明了作者方法的可行性及有效性。
4．对具有未知转移概率的混合系统，提出了一种基于粒子滤波器的自适应Monte Carlo估计算法，利用状态空间的一组随机样本探索系统状态和模型的演化，对模型转移概率、系统状态和模型概率同时进行在线估计。对模型中的未知参数提出一种基于粒子滤波和SPSA随机逼近的自适应估计算法，实现了系统状态和参数的联合估计，仿真结果表明了算法的有效性。
5．针对低探测概率下的估计问题，为了充分利用传感器提供的一切信息，通过建立传感器检测概率模型，在Bayes框架下，将传感器是否检测到目标的检测信息也进行融合，从而得到一种增强的粒子滤波器，仿真结果表明该方法可以提高估计精度。
6．基于粒子滤波和似然比方法提出了一种检测跟踪一体化算法。直接利用传感器的原始数据，由粒子滤波器得到目标状态的后验概率分布，检测是基于滤波器的输出，利用Bayes似然比作为检测的判决准则。该方法较好地利用了先验信息和量测信息，将目标检测和跟踪过程统一为一个整体，仿真结果表
With the development of science and technology, the scale and complexity of system is increasing and the demand for system performance is increasing. At the same time, the means of obtaining information is also increasing. As a result, the estimation for complex system under the complex and network environment becomes a front area of estimation theory. In this dissertation some key techniques for dynamic estimation of hybrid system are studied in details based on Monte Carlo particle filtering. The main contributions are as follows:
1. An overview of the principle, convergence, development and application of Sequential Monte Carlo simulation based particle filtering is presented within Bayesian frameworks. The novel extensions and trends of particle filtering are also discussed.
2. The iterative particle filter, fixed interval and fixed lag particle smoother are proposed for the state estimation of multiple model hybrid system. The proposed methods make use of structure characteristic of the model and combine the technique of Rao-Blackwellisation with Kalman technique. The simulation results show that the proposed filter and smoother are feasible and effective.
3. The theoretical Cramer-Rao lower bound (CRLB) for hybrid estimation requires enumeration of all possible model sequences. The computational burden grows exponentially with time. An approximated formulation for the CRLB is proposed which makes use of a subset of model sequence hypotheses. The approximated computation of the CRLB is achieved through particle filtering and Monte Carlo simulation. The simulation shows the effectiveness and feasibility of the proposed method.
4. An adaptive Monte Carlo estimation algorithm based on particle filtering is proposed for hybrid system with unknown transition probabilities. A set of random samples from state space are utilized to explore the evolution of state and models. The transition probabilities, state and model probabilities are estimated online simultaneously. An adaptive estimation algorithm for unknown parameter in dynamic
1．在Bayes框架下，综述了基于序贯Monte Carlo仿真方法的粒子滤波原理、收敛性、研究进展及其应用，讨论了粒子方法的新发展、新动态。
2．对多模型混合系统的状态估计问题，利用模型的结构特点，结合Rao-Blackwellisation技术和Kalman滤波技术，分别提出了迭代粒子滤波器和固定区间、固定延迟粒子平滑器。算例分析结果表明，本文所提出的滤波器和平滑器是可行的，估计性能有明显改善。
3．混合估计理论上的Cramér-Rao下界(CRLB)需要穷举所有可能的模型序列，计算量随时间指数增加。本文通过使用有限个模型序列假设子集，提出了一种CRLB的近似表达式，并且基于粒子滤波器和Monte Carlo仿真方法，给出了CRLB的一种近似计算方法，算例分析表明了作者方法的可行性及有效性。
4．对具有未知转移概率的混合系统，提出了一种基于粒子滤波器的自适应Monte Carlo估计算法，利用状态空间的一组随机样本探索系统状态和模型的演化，对模型转移概率、系统状态和模型概率同时进行在线估计。对模型中的未知参数提出一种基于粒子滤波和SPSA随机逼近的自适应估计算法，实现了系统状态和参数的联合估计，仿真结果表明了算法的有效性。
5．针对低探测概率下的估计问题，为了充分利用传感器提供的一切信息，通过建立传感器检测概率模型，在Bayes框架下，将传感器是否检测到目标的检测信息也进行融合，从而得到一种增强的粒子滤波器，仿真结果表明该方法可以提高估计精度。
6．基于粒子滤波和似然比方法提出了一种检测跟踪一体化算法。直接利用传感器的原始数据，由粒子滤波器得到目标状态的后验概率分布，检测是基于滤波器的输出，利用Bayes似然比作为检测的判决准则。该方法较好地利用了先验信息和量测信息，将目标检测和跟踪过程统一为一个整体，仿真结果表
With the development of science and technology, the scale and complexity of system is increasing and the demand for system performance is increasing. At the same time, the means of obtaining information is also increasing. As a result, the estimation for complex system under the complex and network environment becomes a front area of estimation theory. In this dissertation some key techniques for dynamic estimation of hybrid system are studied in details based on Monte Carlo particle filtering. The main contributions are as follows:
1. An overview of the principle, convergence, development and application of Sequential Monte Carlo simulation based particle filtering is presented within Bayesian frameworks. The novel extensions and trends of particle filtering are also discussed.
2. The iterative particle filter, fixed interval and fixed lag particle smoother are proposed for the state estimation of multiple model hybrid system. The proposed methods make use of structure characteristic of the model and combine the technique of Rao-Blackwellisation with Kalman technique. The simulation results show that the proposed filter and smoother are feasible and effective.
3. The theoretical Cramer-Rao lower bound (CRLB) for hybrid estimation requires enumeration of all possible model sequences. The computational burden grows exponentially with time. An approximated formulation for the CRLB is proposed which makes use of a subset of model sequence hypotheses. The approximated computation of the CRLB is achieved through particle filtering and Monte Carlo simulation. The simulation shows the effectiveness and feasibility of the proposed method.
4. An adaptive Monte Carlo estimation algorithm based on particle filtering is proposed for hybrid system with unknown transition probabilities. A set of random samples from state space are utilized to explore the evolution of state and models. The transition probabilities, state and model probabilities are estimated online simultaneously. An adaptive estimation algorithm for unknown parameter in dynamic
引文
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