Stratonovich Equation and Kalman Filter for Surveillance Equipment of Different Physical Nature

The problem of estimation of the phase coordinates of the object whose motion is described by a system of differential equations is considered. For estimation, the Kalman filter equations following from the solution to the generalized Stratonovich equation in the Gaussian approximation are used. The generalized Stratonovich equation makes it possible to consider the cases when, as an observation signal, a multidimensional image of the observation object is applied; i.e., the scalar function of an arbitrary number of variables describing the specificity of the observation device. It is shown that the data array obtained from the used set of observation devices is included into the generalized Stratonovich equation and in the Kalman filter equations in the form of an additive combination of time derivatives of the likelihood functionals of each of the observation devices. Each of these functionals can consider the correlation of observation noises.