MEASUREMENTS AGAINST NOISE BACKGROUND AND WITH FLUCTUATIONS

Abstract

When performing non-contact and remote measurements of various parameters, additional obstacles arise due to the influence of the intermediate medium and the measuring path between different links of the measuring system. These obstacles include:
 
 Noises arising in communication paths, intermediate media, complexes of measuring and auxiliary equipment. These noises are superimposed on the useful signal and distort it.
 Fluctuations of the general and selective energy absorption of the useful signal in the intermediate medium and measuring communication path. In all these cases, it is necessary to isolate the useful signal and restore its original true value and nature of non-stationarity.
 
 The task of filtering in its general form has not been completely solved until now. In order to obtain maximum information about the useful signal, such an operator L is selected that the function Y(τ)=L[X(τ)] slightly differs from the useful signal U(τ), where X(τ)= U(τ)+ V(τ ); V(τ) is noise (interference). To determine the values of the function Y(τ) at a certain time τ_0, all previous values of the function X(τ) from the interval -∞≤τ≤τ_0 should be used. To distinguish the functions Y(τ) and U(τ) the variance of the difference of these functions is used. The problem of Wiener filtering has been solved by various authors, in particular the Kalman-Busy filter equation for linear Gaussian systems. Optimal (suboptimal) Bayesian filters are constructed for a nonlinear stochastic system disturbed by "white" Gaussian noise with continuous time and discrete measurements that minimizes the root-mean-square error of estimation. The exact solution of this problem in the interval between the moments of measurement results is subject to the Fokker-Planck differential equation with private derivatives.
 Considered examples: measuring the temperature and pressure of the environment under investigation, distorted by various random factors in the form of "white" noise, as well as tracking the coordinates and velocities of an aircraft performing a maneuver in the horizontal plane - as test tasks in the construction of a sigma-point Kalman filter - as a multi-cube Kalman filter.