High Order Nonlinear Least-Squares for Satellite Pose Estimation

This paper introduces a high-order nonlinear least-squares method for solving six-degree-of-freedom (6-DOF) navigation of satellite maneuvers. The approach involves developing first through fourth-order Taylor series models, which provide the necessary conditions that are iteratively adjusted to recover the unknown roots for reducing the errors arising from fitting models to a given set of observations. An initial guess is provided for the unknown parameters in the system, developing a correction vector using Taylor expansion, and then manipulating the necessary conditions to provide the least-squares algorithm. Computational differentiation (CD) tools generate the Taylor expansion partial derivative models. This paper presents an experimental work conducted using a 6-DOF platform to demonstrate the performance of the developed high-order nonlinear least-squares navigation method. An initial calibration of the sensing systems is performed in an operationally relevant ground-based environment. The experiments demonstrate that accelerated convergence is achieved for the second-, third-, and fourth-order expansions with various initial guess conditions.

Automated summary

This paper presents a high-order nonlinear least-squares method for solving the 6-DOF navigation problem of satellite maneuvers. The approach utilizes first through fourth-order Taylor series models and iterative adjustments to recover unknown roots and reduce fitting errors. The method involves an initial guess for the unknown parameters, Taylor expansion for developing correction vectors, and manipulation of necessary conditions for the least-squares algorithm. Experimental work on a 6-DOF platform demonstrates accelerated convergence with various initial guess conditions for second-, third-, and fourth-order expansions.