This question has been explored in the context of global positioning systems, which need to account for general relativity. The traditional Minkowski coordinates $(t,x,y,z)$ of flat space-time do not allow for an immediate positioning in an unknown gravitational field. 

<A HREF="https://en.wikipedia.org/wiki/Albert_Tarantola">Tarantola</A> and colleagues propose a symmetric coordinate system with four times, see <A HREF="https://arxiv.org/abs/0905.3798">Gravimetry, Relativity, and the Global Navigation Satellite Systems</A> and this <A HREF="http://www.ipgp.fr/~tarantola/Files/Professional/Teaching/Seminar/Lessons/Coll/Coordinates-RG.pdf">talk.</A> If four satellite clocks – having an arbitrary space-time trajectory – broadcast their proper time – using electromagnetic signals,– then, any observer receives, at any point along his personal space-time trajectory, four times, corresponding to the four signals arriving at that space-time point. These four times, $\tau_1,\tau_2,\tau_3,\tau_4$, are, by definition, the coordinates of the space-time point.

In <a href="https://arxiv.org/abs/0905.4121">Using pulsars to define space-time coordinates</a> Coll and Tarantola propose to replace the satellite clocks by pulsars, to obtain a relativistic coordinate system valid in a domain larger than our Solar system.

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<IMG SRC="https://upload.wikimedia.org/wikipedia/commons/2/26/AlbertTarantola2006.jpg" WIDTH="400"/>     
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<sub>"What is a meter?" Albert Tarantola in front of the original meter.</sub>