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I have two sets of inputs, A (10 values) and B (20 values), and for each point (A,B) I have a measurement to make a (10x20) table of measurements C. Is there a way to use a Kalman Filter to improve these measurements if I have no physical rule to go from the inputs A and B to the value of C?

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Is there a way to use a Kalman Filter to improve these measurements if I have no physical rule...

No.

Kalman filters add value by using a model of a process to refine an estimate of the states of that process.

If you don't have a model, and you don't have enough data to develop a model, then you can't get there from here.

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