Comparing Radius of Convergence in Solving the Nonlinear Least Squares Problem for Precision Orbit Determination of Geodetic Satellites

What is it about?

This paper examines several methods for solving the nonlinear least squares problem for orbit determination. Specifically, the state update method, the treatment of the normal equations, and the matrix decomposition methods are examined to determine their effects on the radius of convergence. It was found that the Levenberg-Marquardt state update has a significantly larger radius of convergence versus the Gauss-Newton state update. There was no observed difference in the radius of convergence due to the treatment of the normal equations or the matrix decomposition method.

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Why is it important?

This paper gives guidance as to what mathematical processes affect the radius of convergence when solving the nonlinear least squares problem for orbit determination. The LM state update will greatly increase the radius of convergence. Since there were no effects observed due to the treatment of the normal equations or the matrix decomposition method, researchers may choose to implement the methods that make best use of computational resources, rather than those that theoretically increase the radius of convergence (because those effects were found to be negligible in practice).