I have a large set of data recorded by a logging system which rotates at a fixed but unknown speed around an unknown location. The sensor has a very narrow field of view and each time the sensor “sees” an object the object records it’s location in two dimensions.

The data set therefore consists of a great many two dimensional points which sit somewhere on the circumference of an unknown number of concentric circles arranged around the location of the rotating logging system.

Is there a way to determine the location of the common centre that joins all of these concentric circles – in other words the logging system ?

The obvious way (looking at tangents drawn between two arbitrary points) fails because there’s no way of knowing if any two arbitrary points belong to the same circle or not. In other words there’s no way of separating out the different concentric rings.

With a small amount of data I suppose that an iterative solution might be possible but I’ve got 100,000 locations to work with ! And as my data often only covers an arc then it’s not possible to work out the centroid of the shape.

This is – to me at least – a real brain teaser. Could anyone point me in the right direction of a solution that could be automated once I’ve understood it …

Thanks in advance