Attitude and Position Estimation from Vector Observations
نویسندگان
چکیده
This paper introduces three novel methods to evaluate attitude and position from vector observations using a vision-based technology camera. The first approach, called Linear Algebra Resection Approach (LARA), solves for attitude and position simultaneously and can be used in the lost-in-space case, when no approximate solution is available. The solution is shown to be the left eigenvector associated with the minimum singular value of a rectangular data matrix. The second and third approaches, called Attitude Free Approaches (AFA), recast the problem into a nonlinear system of equations in terms of the unknown position only. Two different methods are proposed to solve this nonlinear set of equations. The First AFA (FAFA) uses a leastsquare Newton-Raphson iterative procedure and is particularly suitable for the recursive case, while the Second AFA (SAFA) uses the toric resultant to eliminate two variables from the attitude-free system of nonlinear polynomial equations and a discretization of the Cauchy integral theorem to quickly isolate the solution. SAFA can be used either in the lost-in-space or in the recursive cases. Final numerical tests quantify the robustness of these methods in the case of measurements affected by noise. ∗Paper AAS 04-140 of the 14th AAS/AIAA Space Flight Mechanics Meeting, February 8–12, 2004, Maui, Hawaii †Associate Professor, Department of Aerospace Engineering, 701 H.R. Bright Building, Room 741A, Texas A&M University, 3141 TAMU, College Station, Texas 77843-3141 Tel. (979) 845-0734, FAX (979) 845-6051. AIAA and AAS Member. ‡Assistant Professor, Department of Mathematics, TAMU 3368, Texas A&M University, College Station, Texas 77843-3368. Tel. (979) 845-2083, Fax (979) 845-6028. E-mail: [email protected] . Rojas’ work was supported in part by the National Science Foundation through grant DMS-0211458. §Distinguished Professor, Director of the Center for Mechanics and Control, Department of Aerospace Engineering, H.R. Bright Building, Room 722, Tel: (979) 845-3912, Fax: (979) 845-6051. E-mail: [email protected]
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