Method for evaluating perturbation in algorithms for solving navigational problems

A method is proposed for investigating perturbations in linear algorithms which arise in solution of a number of problems in navigational support of space flights, such as in algorithms for processing trajectory measurements. Solution of various problems in the dynamics of space vehicle flights can be represented in the form y = F(u)r(v), where F(u) is a matrix and r(v) is a vector, dependent on the vector parameters u and v respectively. In each specific problem F(u) and r(v) have a specific sense. In a special case F and r can be dependent on the single vector u = v. The purpose of this investigation is the development of a method making it possible to evaluate perturbations delta y of the solution vector arising during perturbations of the vector parameters u and v. These perturbations can be caused either by rounding off errors or by inexact computation of the F matrix if the expression y = F(u)r(v) is a result of linearization of the expression y = theta (u, r, v) near some control point or inaccuracy in the a priori information used in computing the F matrix.