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My question is this: if, for example, I have multiple radars across an area, tracking a particular airborne object, can I use the returns from the radars to determine the geographical location of an object in three-dimensional space (its x-y-z coordinates)?

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Of course. That is, after all, the whole purpose of radar: to get the position of an object and plot it on a screen. You don't even need multiple radars, one radar is enough.

If you're just talking about primary radar (i.e. bounce a signal off of the skin of the target), then you're going to have some trouble with measuring the altitude. The distances involved mean that a large change in altitude would create a very small change in the beam angle, so altitude measurements are going to come with huge error bars. In fact, civilian radars almost never bother with vertical scanning at all, because such imprecise measurements aren't considered to be worth the extra complexity. Naturally, secondary radar (i.e. transponder interrogation) doesn't have this issue, since the transponder simply tells the radar what its altitude is.

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    $\begingroup$ "If you're just talking about primary radar, then you're going to have some trouble with measuring the altitude." -- Phased array antennas solve this problem. $\endgroup$ May 23 '21 at 10:18
  • $\begingroup$ @TimothyTruckle Not really. The problem is the fact that big changes in altitude create small changes in angle, so no matter what method you use to steer the beam (phased array, moving physical antenna, multiple receiver horns), the error is still going to be there. $\endgroup$ May 24 '21 at 23:19
  • $\begingroup$ "big changes in altitude create small changes in angle" -- Phased array antennas solve this problem too by splitting up the array into 4 sub arrays (2 by 2 matrix) and measuring the phase difference of the signal received between them. This way you can locate an aircraft within the beam horizontal as well as vertical. $\endgroup$ May 24 '21 at 23:35
  • $\begingroup$ @TimothyTruckle Yes, phased array antennas can provide superior resolution. But there is always going to be error, and the practical value of the error is always going to be greater in the vertical. Imagine the angular resolution for some radar is 0.5°. At a range of 50 miles, that's an error of 2300 feet. Horizontally, 2300 feet is nothing. At 200 knots, that's 7 seconds worth of flight time. But, vertically, 2300 feet is a huge value. In congested areas, airplanes are routinely separated by no more than 500 feet. So if you're depending on radar for vertical separation, you're out of luck. $\endgroup$ May 25 '21 at 4:49

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