Geodesic
On Sequential Estimates of Parameters
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 1, pp. 172-179

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The problem of sequential estimates arises in some applied questions. For example, when we are watching for the positions of a body at the moments of discrete time and it is required to estimate synchronously the parameters of the motion at each step of the observation. A method of sequential estimates is suggested to avoid the calculations of the roots of the equations for the parameters, at each step. This method in fact comes to the recurrent equations which are available for computing. In the case of the least squares estimates it is shown that the asymptotic behaviour of such sequential estimates (bias, efficiency) is that of the usual least squares estimates. 
@article{TVP_1967_12_1_a19,
     author = {A. S. Kholevo},
     title = {On {Sequential} {Estimates} of {Parameters}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {172--179},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {1967},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_1_a19/}
}
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A. S. Kholevo. On Sequential Estimates of Parameters. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 1, pp. 172-179. http://geodesic.mathdoc.fr/item/TVP_1967_12_1_a19/