Geodesic
Almost periodic signal estimations
Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 2, pp. 249-263

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Let $\xi(t)=\theta(t)+\Delta(t)$ where $\Delta(t)$ is a stationary «noise» process, $\theta(t)$ is a «signal» of the form (4$'$) (the numbers $\lambda_k$ satisfy (5)). In the paper, an estimation problem is considered for an arbitrary bounded linear functional $\varphi(\theta)$. Asymptotical expressions are obtained for the variances of the leastsquares estimators and best unbiased ones. The main result is: Let the spectral density $f(\lambda)$ of the process $\Delta(t)$ satisfy (6), be uniformly bounded on $(-\infty,\infty)$ and continuous and positive at each point $\lambda_k$. Then the least-squares estimators are asymptotically effecient. As an example, the least-squares estimators of a periodic signal are considered. 
@article{TVP_1971_16_2_a3,
     author = {A. S. Holevo},
     title = {Almost periodic signal estimations},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {249--263},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a3/}
}
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A. S. Holevo. Almost periodic signal estimations. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 2, pp. 249-263. http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a3/