白噪声下调频信号的参数估计

THE PARAMETER ESTIMATION OF FREQUENCY WITH WHITE NORSE

设有随机过程X_T={X(t):0≤t≤T}满足如下方程X(t)=∫_o^t sin θ3 d3+W(t) 0≤t≤T(1)其中W_T={W(t):θ≤t≤T}是标准维纳过程.本文讨论了均值信号3(θ,t)=∫_o^t sin θ3d3中频率参数θ的ML估计问题.在无界参数空间中得到了其估计的强相容性,渐近正态性和a.s.收敛速度.

Suppose a stochastic process X_T={X(t): t∈T} satisfces following equation:where W_T={W(t), t∈T} is a standard Wiener process. In this paper we study the properties of the MLE of the parameter 9 in signal sin ∫ sin θs ds. We obtained strong consistence, asymptotical normality and a.s convergence rate of the parameter estimation in the unbounded parameter space.