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I would like to locate the position of a stationary autonomous robot in x-y-z axis relative to a fixed starting point.

Could someone suggest sensors that would be suitable for this application?

I am hoping to move the robot in 3D space and be able to locate it's position wirelessly. The rate of position update is not important as I would like to stop the robot from moving and relay the information wirelessly.

The range I am looking for is roughly 2 KM + (the more the better) with accuracy of +/- 1 CM.

Is there any system that could do this? Thanks for your help.

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Differential GPS could be a starting point. But 1 cm will cost a bit.

The basic idea is to increase the accuracy of gps. Stationary antennas at known positions allow to measure the error in the gps signal transit times.

A robot can then receive the error from the antennas and use it to improve its gps result.

According to German wikipedia:

Die erreichbare Genauigkeit liegt je nach Qualität des Empfängers und der Korrekturdaten zwischen 0,3 m und 2,5 m für die Lage (x, y) und bei 0,2 m bis 5 m für die Höhe.

that is:

The possible accuracy depending on the quality of the receiver and the correction data lies between 0,3m and 2,5m for the position (x,y) and between 0,2m and 0,5m for the height.

On top of that, the phase shift of the carrier wave can be evaluated to increase accuracy even further:

Hochqualitative Systeme werten zusätzlich die Phasenverschiebung der Trägerwelle aus [...] und erreichen so Genauigkeiten von wenigen Millimetern (± 1 mm bis ± 10 mm pro km Abstand zur Referenzanlage).

that is:

High quality systems additionally evaluate the phase shift of the carrierwave and allow accuracy of few milimeters (from $\pm 1mm$ up to $\pm 10mm$ per $1km$ distance to the reference station)

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  • $\begingroup$ The source is here: de.wikipedia.org/wiki/Differential_Global_Positioning_System "erreichen so Genauigkeiten von wenigen Millimetern (± 1 mm bis ± 10 mm pro km Abstand zur Referenzanlage)." The claim is an error of +-1mm per km distance to the reference station. $\endgroup$ – FooTheBar Aug 24 '15 at 12:00
  • $\begingroup$ Instead of posting another "here at Stack Exchange..."-comment, could you maybe just cite your source? $\endgroup$ – FooTheBar Aug 24 '15 at 13:13
  • $\begingroup$ Thanks @BendingUnit22 that improves the answer substantially. $\endgroup$ – Mark Booth Aug 24 '15 at 13:59
  • $\begingroup$ Sorry FooBar, we appreciate your answer and the time that you have taken, but we have to think long term. Do you not agree that the answer in it's current form is substantially better than the original one-liner? If you consider a year down the line when both the English and German wikipedia pages could be significantly different to how they are today, the context provided will allow the answer to make as much sense then as now. $\endgroup$ – Mark Booth Aug 24 '15 at 14:07
  • $\begingroup$ Incidentally, I mentioned my source, the English wikipedia page. $\endgroup$ – Mark Booth Aug 24 '15 at 14:08
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Feel free to correct me, or add more if you feel the need and have experience implementing this, but I believe instead of blowing tons of money on an ultra-precise Diff. GPS you could purchase a precision altimeter and then use some form of directional transmitter/receiver(laser?) and get your x,y,z from a sensor fusion such as this. Just an outside of the box thought instead of jumping straight to a very expensive GPS.

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