ИССЛЕДОВАНИЕ ОБЛАСТИ ОПРЕДЕЛЕНИЯ ПАРАМЕТРОВ БАЗИСНОЙ ФУНКЦИИ ДВУХ АРГУМЕНТОВ ПРИ ПОСТРОЕНИИ Λ-ОРТОГОНАЛЬНОЙ БАЗИСНОЙ ФУНКЦИИ

Abstract

The purpose of the research is to determine the area of setting the argument τ and its discretizationintervals when constructing an algorithm for adaptive nonlinearoptimal smoothing of multi-parameter data of trajectory measurements, which makes it possible tojointly implement the spatial and temporal redundancy of the data obtained. The research wascarried out by constructing a Λ-orthogonal basis function in order to obtain independent estimatesfor the coefficients of the smoothing polynomial. It is shown that it is advisable to solve the problemof determining the maximum likelihood estimate of the coefficient vector of the smoothingpolynomial by the method of successive approximations. When constructing a Λ-orthogonal basisfunction, the maximum likelihood estimate of the coefficient vector of the smoothing polynomial isachieved in 2-3 iterations. It follows from the research results presented in the paper that the accuracyindex Qт as a function of two arguments ( is the smallest value of the argument and Δτ isthe discretization interval of the argument τ) in a wide range of values of these arguments changesslightly, but increases sharply at . In this case, the values of these arguments should notexceed, respectively, the maximum and minimum possible numbers that can be written without lossof 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 andrespectively, are the minimum and maximum numbers that can be written into the bit grid of acomputer without loss of accuracy. In case of adverse conditions Approaching the edges of theinterval can lead to an increase in calculation errors in determining the secondary parameters ofthe position of the aircraft due to the fact that the main matrix of the system of equations becomesill-conditioned.