Using instrumental variables method in problems of estimating current navigation parameters of GNSS satellites

The vast majority of problems of computational mathematics can be reduced to solving systems of algebraic equations with inaccurately given right-hand side. These problems include estimation of current navigation parameters GNSS satellites according to the trajectory measurements, performed on the spacecraft.

Error in the solution of such systems of equations depends on norm of immeasurable component of the right side of equations to be solved and, in equal measure, on the condition number of the system matrix.

The article discusses the possibility of improving the conditioning of the matrix system of equations to be solved for the vector of initial conditions the equations of motion of spacecraft, through the use of instrumental variables [1] in the formation of this system of equations.

A comparative analysis of the efficiency of use as instrumental variables Chebyshev orthogonal polynomials and linearly independent harmonic functions in conjunction with scaling vector of solution.