STRATONOVICH EQUATION AND KALMAN FILTER FOR OBSERVATION DEVICES OF VARIOUS PHYSICAL NATURE
P.M. Yukhno
State Scientific Research Testing Institute for Technical Information Protection Problems of the Federal Service for Technical and Export Control, Voronezh, Russia
Keywords: Stratonovich equation, likelihood functional, Kalman filter, observation signal
Abstract
The problem of estimating the phase coordinates of an object whose motion is described by a system of differential equations is considered. The Kalman filter equations, derived from the solution of the generalized Stratonovich equation in the Gaussian approximation, are used for the estimation. The generalized Stratonovich equation allows one to consider cases where a multidimensional image of the object being observed is used as an observation signal, i.e., a scalar function of an arbitrary number of variables reflecting the specifics of the observation device. It is shown that the dataset from the multiple observation devices used is included into the generalized Stratonovich equation and the Kalman filter equations as an additive combination of the time derivatives of the likelihood functionals of each individual observation device. Moreover, each of these functionals can account for the correlation of observation noise.
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