不完全观测下非线性非齐次随机系统的参数估计

Parameter Estimation for Partially Observed Nonlinear Nonhomogeneous Stochastic System

本文研究不完全观测下非线性非齐次随机系统的参数估计问题.首先,通过构造扩展的Kalman滤波方程,得到系统状态的次优估计,并通过状态估计方程给出似然函数的表达式.其次,找到一个闭区间,似然函数在这个闭区间上连续且在端点处取不到最大值.最后,当样本量足够大时,运用Lepingle强大数定律和均方可积鞅强大数定律,证明了极大似然估计量的存在性和强相合性.

The parameter estimation problem for partially observed nonlinear nonhomogeneous stochastic system is concerned in this paper.Firstly,the suboptimal estimation of the state is obtained by constructing the extended Kalman filtering equation and the likelihood function is provided based on state estimation equation.Secondly,we find a closed interval on which the likelihood function is continuous and does not attain the maximum at two endpoints of this interval.Then,we prove that the maximum likelihood estimator exists in the interval when the sample size is large enough.Finally,the strong consistency of the estimator is proved by the Lepingle law of large numbers and mean square integrable martingale strong law of large numbers.