I'm working on a project which involves tracking air crafts in real time and I'm having a problem of estimating center of a circle given three or more points, which should be as precise as possible, and I need this to track air craft in circle maneuver. I know how to calculate the center if you have thee points on circumference (I'm using this method), but the problem is that I have points which are not exactly on circumference, and can be on either side of circumference. Because the center is used to calculate a radius of the circle, depending on the points I get (the points are measures from the radar, and that is why they are inaccurate) I can get circles of different sizes, and what is worst I can get a circle on opposite side of that of the maneuver.
You can see what I mean in images 1 and 2 in attachment. On image one I estimate a center using the method I mentioned and its almost a perfect estimate. But in the second image I'm using an extra point, which gives me a completely different result, which is unacceptable. This is just an example of maneuver, in other situation may be different...
So this is what I need:
- to estimate center of the circle given three or more points - 3 - 5 points, not more, because after the sixth point its already too late to track maneuver
- during the maneuver I can update the center and radius with new data
Things to have in mind:
- points are not on the circumference, can be on either side of it
If some one know a method for this, or have an idea please share I will be thankful
Cheers and thank you