i would like to learn how to convert sinusoidal model into state space form which has following equation

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our model consist of sum of periodic components with additive of white noise, given by following form

$y(t) = A_1\sin(\omega_1 t) + A_2\sin(\omega_2 t+) + ... + A_p\sin(\omega_p t) + z(t)$ where $z(t)$ is additive white noise and

$\omega_i=2*\pi*F_i $

i was reading special document Tracking a Sine Wave

i somehow understand step when we have single sinusoidal components, but what about when we have several ones? please help me

  • $\begingroup$ It seems you are confusing signals and systems. State space model applies to "systems", i..e things that have an input and output. Your sine+noise model is just a signal $\endgroup$ – Hilmar Jun 29 '18 at 19:28
  • $\begingroup$ so can't apply Kalman filter to this model? $\endgroup$ – dato datuashvili Jun 29 '18 at 20:27
  • $\begingroup$ hi: based on what you explained, you only have a measurement equation. There is no system equation. so, if you let $F$ be the $p \times 1$ vector of where each element is $A_i$ and you let $\theta$ be the $p \times 1$ vector where each element is $sin(w_i \times t)$, then $y_t = F^\prime \theta_t + \epsilon_t$ and that's it. Nothing is being estimated so there are no updates, atleast based on the way you explained it. $\endgroup$ – mark leeds Jun 30 '18 at 1:46
  • $\begingroup$ P.S: I just read Hilmar's answer again and I'm probably saying the same thing as him so my bad for duplication. $\endgroup$ – mark leeds Jun 30 '18 at 1:51

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