Ambiguous spacecraft relative orbits based on linear dynamics and elliptic chief orbit are studied for the purpose of sequential relative orbit estimation with range-only measurements. Using a geometric solution of the Tschauner-Hempel equation, mirror ambiguous orbits, which conserve the shape and size of the true relative orbit, are proven to exist. However, deformed ambiguous orbits, which distort the shape and size of the true relative orbit are shown to vanish due to the non-zero chief orbit eccentricity although they persist in Kalman filtering simulations. This persistent phenomenon is explained through a perturbation analysis using variation of the geometric ambiguous states. Furthermore, it is shown that the inclusion of chief orbit eccentricity and nonlinearities in the filter model can help resist the tendency of an extended Kalman filter to converge to the ambiguous orbits.
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