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As I understand tone ranging is one of the technique used to determine satellite range from the earth station. In this case the position along the line of sight is being determined. How the position along the other 2 directions are determined ?

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As I understand tone ranging is one of the technique used to determine satellite range from the earth station. In this case the position along the line of sight is being determined. How the position along the other 2 directions are determined ?

By taking lots of readings, spread over time.

The problem with angle measurements is that even the most exquisitely precise angle measurements aren't that precise when it comes to determining position. Range rate measurements truly are exquisitely precise, as are range measurements, particularly with delta-DOR.

Precision orbit determination mandates taking multiple readings over a span of time, a lot more than the six degrees of freedom suggested by orbital elements. A number of filtering techniques have been developed over the last 50+ years to address the fact that the multitude of readings form an over-specified system.

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  • $\begingroup$ This makes a lot more sense! If a spacecraft is "temporarily between planets" and mostly under just the influence of the sun, and you've been making regular observations, it seems pretty straightforward. If it hibernated for a year and some event caused a deviation, but you could pick it up again when it woke up, how hard would it be to start from there with only range-rate? Actually, this sounds like an interesting question brewing. $\endgroup$ – uhoh May 22 '16 at 7:59
  • $\begingroup$ A good discussion of various ranging techniques used for Rosetta (and references) $\endgroup$ – uhoh May 22 '16 at 12:05
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If you got the position along the line of sight, you can measure the elevation and direction angle of the line of sight too. You have one distance and two angles and using a coordinate transformation from polar coordinates to a cartesian system you can get three distances in x, y and z direction.

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  • $\begingroup$ Soumajit - rather than post a comment saying thanks, on Stack Exchange the correct approach is to vote up, and the accept whichever answer best answers your question, using the check mark to the left. $\endgroup$ – Rory Alsop May 20 '16 at 10:15
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    $\begingroup$ I think tone ranging refers to a timing technique using a coded pulsed beams - usually radio - sometimes called a Gold code - in other words the standard radar ranging or GPS timing technique - am I right? It requires a radio transmission, and radio reception, sometimes from the same antenna but often from different ones. While you can get precision on the order of meters along the line of sign, it doesn't mean you can actually "see it". Can you elaborate how "you can measure the elevation and direction angle of the line of sight too"? $\endgroup$ – uhoh May 20 '16 at 12:41

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