- #1
goodspeeler
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DISCLAIMER: i may very well have exactly zero idea what I'm talking about. please feel free to berate me if i am way off base...
so i know the doppler effect is normally used to determine an unknown radial velocity, but I'm assuming that if i know the velocity of the source, i can use the frequency shift to determine the angle of the velocity vector relative to the receiver.
What I'm wondering about is the accuracy of this determination. I have heard that the standard formula for EM doppler effect is only an approximation. Does one of those assumptions require that you are parallel with the velocity vector?
Consider the following setup:
*-------->v
source moving at a known speed |v| in a known direction (angle = 0)
if [tex]\theta[/tex] is the angle between the source velocity and the source->receiver direction, can I determine this angle by simply saying the following:
and then say that
rearranging and plugging back in for [tex]v_{rad}[/tex] i get:
so that's the setup. What I'm wondering is
hopefully the setup and my questions are relatively clear. just hoping for some input with some experience working with these sorts of things.
thanks in advance.
-gs
so i know the doppler effect is normally used to determine an unknown radial velocity, but I'm assuming that if i know the velocity of the source, i can use the frequency shift to determine the angle of the velocity vector relative to the receiver.
What I'm wondering about is the accuracy of this determination. I have heard that the standard formula for EM doppler effect is only an approximation. Does one of those assumptions require that you are parallel with the velocity vector?
Consider the following setup:
* receiver (arbitrary position)
*-------->v
source moving at a known speed |v| in a known direction (angle = 0)
if [tex]\theta[/tex] is the angle between the source velocity and the source->receiver direction, can I determine this angle by simply saying the following:
[tex]|v|cos(\theta) = v_{rad}[/tex] (where [tex]v_{rad}[/tex] is the source velocity's component toward the receiver)
and then say that
[tex]f_{shift} = \frac{f_{orig}*v_{rad}}{c}[/tex] (where [tex]f_{orig}[/tex] is the original EM frequency)
rearranging and plugging back in for [tex]v_{rad}[/tex] i get:
[tex]\theta = cos^{-1}\left(\frac{f_{shift}*c}{f_{orig}*|v|}\right)[/tex]
so that's the setup. What I'm wondering is
- does the doppler effect work this way, or have i violated too many of its assumptions?
- if it works, how accurate can my angle determination be? put differently, to what precision can one measure a frequency shift? from some quick calculations with plausible [tex]|v|[/tex] and [tex]f_{orig}[/tex] values, it seemed like determining frequency to within 1-3 Hz would suffice, but i have zero idea how accurate such measurements can be. I would like to use the RF range (say, 100Mhz - 100GHz). is there some other way to get 1-3Hz accuracy in this range other than an FFT sampling at ~1THz?
hopefully the setup and my questions are relatively clear. just hoping for some input with some experience working with these sorts of things.
thanks in advance.
-gs