STUDY OF THE AREA OF DETERMINATION OF PARAMETERS OF THE BASIS FUNCTION OF TWO ARGUMENTS IN CONSTRUCTING THE Λ-ORTHOGONAL BASIS FUNCTION

Abstract

The purpose of the research is to determine the area of setting the argument τ and its discretization intervals when constructing an algorithm for adaptive nonlinear optimal smoothing of multi-parameter data of trajectory measurements, which makes it possible to jointly implement the spatial and temporal redundancy of the data obtained. The research was carried out by constructing a Λ-orthogonal basis function in order to obtain independent estimates for the coefficients of the smoothing polynomial. It is shown that it is advisable to solve the problem of determining the maximum likelihood estimate of the coefficient vector of the smoothing polynomial by the method of successive approximations. When constructing a Λ-orthogonal basis function, the maximum likelihood estimate of the coefficient vector of the smoothing polynomial is achieved in 2-3 iterations. It follows from the research results presented in the paper that the accuracy index Qт as a function of two arguments ( is the smallest value of the argument and Δτ is the discretization interval of the argument τ) in a wide range of values of these arguments changes slightly, but increases sharply at . In this case, the values of these arguments should not exceed, respectively, the maximum and minimum possible numbers that can be written without loss of accuracy in the re grid of the computer used. With a uniform discretization step of the argument τ it is advisable to choose the argument in the middle part of the interval¸where and respectively, are the minimum and maximum numbers that can be written into the bit grid of a computer without loss of accuracy. In case of adverse conditions Approaching the edges of the interval can lead to an increase in calculation errors in determining the secondary parameters of the position of the aircraft due to the fact that the main matrix of the system of equations becomes ill-conditioned.