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Does the Kalman Filter boil down to Recursive (i.e., incremental) Least Squares if the state is constant?

I expect it does but I am not sure.

Assume that all simplifying assumptions hold (i.e, models are linear, pdfs are all Gaussian etc).

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    $\begingroup$ yes that is right $\endgroup$ – Taylor Sep 10 '17 at 19:35
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The Recursive Least Squares deals with Measurement Noise.

If you set the Process Noise to zero energy noise then both are equivalent.

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