Wang Peng, Li Ge, Peng Yong, Ju Rusheng
College of Systems Engineering, National University of Defense Technology, Changsha 410073, China.
Entropy (Basel). 2018 Jul 31;20(8):569. doi: 10.3390/e20080569.
Parameter estimation is one of the key technologies for system identification. The Bayesian parameter estimation algorithms are very important for identifying stochastic systems. In this paper, a random finite set based algorithm is proposed to overcome the disadvantages of the existing Bayesian parameter estimation algorithms. It can estimate the unknown parameters of the stochastic system which consists of a varying number of constituent elements by using the measurements disturbed by false detections, missed detections and noises. The models used for parameter estimation are constructed by using random finite set. Based on the proposed system model and measurement model, the key principles and formula derivation of the proposed algorithm are detailed. Then, the implementation of the algorithm is presented by using sequential Monte Carlo based Probability Hypothesis Density (PHD) filter and simulated tempering based importance sampling. Finally, the experiments of systematic errors estimation of multiple sensors are provided to prove the main advantages of the proposed algorithm. The sensitivity analysis is carried out to further study the mechanism of the algorithm. The experimental results verify the superiority of the proposed algorithm.
参数估计是系统辨识的关键技术之一。贝叶斯参数估计算法对于随机系统的辨识非常重要。本文提出了一种基于随机有限集的算法，以克服现有贝叶斯参数估计算法的缺点。它可以利用受误检、漏检和噪声干扰的测量值来估计由数量可变的组成元素构成的随机系统的未知参数。用于参数估计的模型通过随机有限集构建。基于所提出的系统模型和测量模型，详细阐述了所提算法的关键原理和公式推导。然后，利用基于序贯蒙特卡罗的概率假设密度（PHD）滤波器和基于模拟回火的重要性采样给出了算法的实现。最后，提供了多传感器系统误差估计实验，以证明所提算法的主要优点。进行了灵敏度分析以进一步研究算法的机制。实验结果验证了所提算法的优越性。
