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Smoothing a signal or data set approximates the data to reveal patterns and exclude noise, fine-scale structure and rapid changing phenomina.
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Continuous time double exponential filtering in state space form?
I think I figured it out, dumb mistake in writing the system in continuous time.
$\dot{l} = r_1(u - l)$
$\dot{s} = r_2(\dot{l} - s)$
$\ \ = r_2(r_1(u - l) + r_1 s - s)$
$\ \ = r_2(r_1(u - l) + ( …
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Continuous time double exponential filtering in state space form?
Typically, this model is expressed as a pair of discrete, recursive equations as such in @denis' post here)
Double exponential smoothing
a.k.a. … Holt-Winters smoothing
tracks level and trend of a time series in coupled IIRs:
$\qquad$ In: $Y_t$, t = 0 1 2 ... …