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The unification of two measuring devices. (English. Russian original) Zbl 0614.60040

Sov. J. Comput. Syst. Sci. 24, No. 4, 88-93 (1986); translation from Izv. Akad. Nauk SSSR, Tekh. Kibern. 1986, No. 1, 139-145 (1986).
The problem of estimating Markov Gaussian random processes by two specific independent observations, one of which does not contain additive white noise, is solved. Two methods, optimal and modified, for combining (unifying) the observations are examined and qualitatively compared.
Recurrent expressions for the a posteriori probability densities of the estimated processes in discrete time are obtained for the two methods. Recurrent algorithms for estimating the a posteriori probability densities by a normal distribution law (Gaussian approximation) are also obtained.

MSC:

60G35 Signal detection and filtering (aspects of stochastic processes)
60G15 Gaussian processes
60J27 Continuous-time Markov processes on discrete state spaces