Cislunar navigation is an observability problem: arc-length thresholds, Gramian conditioning, and the Doppler lever
Chakshu Baweja · arXiv: 2610.23871v1 · Summary page
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For lunar navigation, time is part of the instrument
A spacecraft navigating around the Earth and Moon cannot necessarily locate itself by borrowing the snapshot geometry used in satellite navigation near Earth. Range measurements directly constrain position, not velocity. This preprint instead follows how orbital motion transfers information about velocity into later measurements, using an observability Gramian to quantify which aspects of the spacecraft’s state can be recovered.
In the configurations studied, range-only tracking became fully observable after an arc of 2.09 h, with longer arcs improving conditioning. A separate filtering calculation became well-posed at the same arc. Adding range-rate measurements made an instantaneous solution possible. The practical implication is that navigation requirements should specify tracking duration and measurement type, rather than rely on a geometric precision score whose assumptions do not hold.
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