白噪声下调频信号的参数估计
THE PARAMETER ESTIMATION OF FREQUENCY WITH WHITE NORSE
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摘要: 设有随机过程XT=X（t）:0≤t≤T满足如下方程X(t)=\int_0^t \sin \theta s d s+W(t) \quad 0 \leqslant t \leqslant T,其中WT=W（t）:θ≤t≤T是标准维纳过程.本文讨论了均值信号s（θ,t）=\int_t^0 \sin \theta s d s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.Abstract: Suppose a stochastic process XT=X（t）:0≤t≤Tsatisfces following equation:X(t)=\int_0^t \sin \theta s d s+W(t) \quad 0 \leqslant t \leqslant T where WT=W（t）,t∈T is a standard Wiener process. In this paper we study the properties of the MLE of the parameter θ in signal \int \sin \theta s d s. We obtained strong consistence, asymptotical normality and a.s convergence rate of the parameter estimation in the unbounded parameter space.
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