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    $\begingroup$ Assume that $x(t) = A\sin(wt+\phi)$ and follow my instructions above. Kalman will do the "fitting" inherently. $\endgroup$ Commented Dec 1, 2016 at 18:15
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    $\begingroup$ See the image I posted. $\endgroup$ Commented Dec 1, 2016 at 18:29
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    $\begingroup$ The sampling interval. The amount of time in seconds between measurements. $\endgroup$ Commented Dec 1, 2016 at 18:34
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    $\begingroup$ Youre right it's not. This algorithm is called an extended Kalman filter (EKF) and the Jacobian matrix is used as a first order Taylor approximation. Hence the first derivative. $\endgroup$ Commented Dec 1, 2016 at 19:03
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    $\begingroup$ @AtulIngle maybe this picture will be more clear. $\endgroup$ Commented Dec 2, 2016 at 18:35