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.