Orbit Estimation: Range & Doppler Measurements for Position & Velocity

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Discussion Overview

The discussion revolves around the estimation of position and velocity of spacecraft using range and Doppler measurements. Participants explore the relationship between these measurements and their respective contributions to determining both position and velocity, considering various measurement methods and signal types.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that range measurements primarily provide position estimates, while Doppler measurements primarily provide velocity estimates, but both can offer some information about the other.
  • One participant notes that realistic measurement methods do not yield purely distance or purely velocity data, but rather have varying precision for each.
  • It is suggested that emitting a short signal allows for a more accurate distance estimate, while a long signal with a defined frequency yields a better velocity estimate.
  • Another participant argues that measuring Doppler shift from an unknown frequency signal provides only velocity information, without distance data.
  • Designer waveforms, such as spike-and-tail, linear chirp, and quadratic chirp, are mentioned as methods that can provide good estimates for both range and Doppler, with Fourier analysis being relevant to their effectiveness.

Areas of Agreement / Disagreement

Participants express differing views on the extent to which range and Doppler measurements can provide information about both position and velocity. There is no consensus on the effectiveness of specific measurement methods or the nature of the relationship between range and velocity estimates.

Contextual Notes

Participants highlight the limitations of measurement methods, including the dependence on signal types and the precision of estimates, but do not resolve these issues.

AT36
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Suppose I have to determine position and velocity of spacecraft from Range and Doppler measurements. Does range measurement only give position estimate and doppler only velocity estimate? Or range can give both position and velocity?How are they related?
 
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There is no realistic measurement method that would give only distance ("range") or only velocity, but some measurements will have a much higher precision for one of those values.
If you emit a short signal and measure the time when it comes back, you mainly get a distance estimate. You know that the frequency is still in your detector range, so you also get some speed estimate.
If you emit a long signal with a well-defined frequency and measure the reflected frequency, you mainly get a speed estimate. You know when approximately the response came back, so you also get some distance estimate.
 
Obviously if you measure Doppler shift of something emitted at a known frequency, but unknown time and intensity, then what you get is just velocity, without distance.
 
There are designer waveforms for radar that can give reasonably good estimates for both range and doppler. One of them is the spike-and-tail that comes from a laser pulse naturally. Then there's linear chirp and quadratic chirp, for which the waveform frequency changes with time across the pulse. And there's sequential pulse waveforms of various kinds (stutter). The potential for good estimations for range and radial speed are found from Fourier analysis.
 

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