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International Journal of Aerospace Engineering
Volume 2012 (2012), Article ID 910496, 13 pages
Research Article

Implementation of a Differential Geometric Filter for Spacecraft Formation Orbit Estimation

1MEEM Department, Michigan Technological University, Houghton, MI 49931, USA
2ECE Department, Michigan Technological University, Houghton, MI 49931, USA

Received 31 May 2011; Revised 31 August 2011; Accepted 11 October 2011

Academic Editor: Srinivas R. Vadali

Copyright © 2012 Shu Ting Goh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The differential geometric filter is implemented to estimate the absolute and relative positions of the spacecraft in a formation. The extended Kalman Filter is also implemented as a benchmark for the differential geometric estimation. Only relative positions between the spacecraft are measured. Relative positions are measured using a wireless local positioning system (WLPS) installed in all spacecraft. Two different scenarios are studied: (1) the observations include WLPS measurements only and (2) the observations include WLPS measurements in addition to measurements for the absolute position of one spacecraft made by a radar that takes measurements from the earth’s surface. Results show that the differential geometric estimation has better stability performance and a faster convergence rate compared to the extended Kalman filter.