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I have some noisy data (x-y coordinates) containing two distinct clusters of data. Each cluster is centred at an unknown point on the unit circle. How can I estimate these two points (green points in the diagram)?

We can assume the noise is Gaussian and noise power is equal in x and y directions.

Computational power is extremely limited, so I'm probably looking for a non-iterative approach involving as few 'complicated' operations (e.g. square roots) as possible.

We can assume the noise is Gaussian and noise power is equal in x and y directions.

Computational power is extremely limited, so I'm probably looking for a non-iterative approach involving as few 'complicated' operations (e.g. square roots) as possible.

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