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jBillou edited Estimating phases from signal.tex
about 9 years ago
Commit id: d7fe6552f73aba4137d8eff31f6876657a2f40ee
deletions | additions
diff --git a/Estimating phases from signal.tex b/Estimating phases from signal.tex
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\textrm{d}\theta_t =& \frac{2\pi}{T_1}\textrm{d}t + \sigma_{\theta}\textrm{d}W_t\\
\end{align*}
We added
to the model a multiplicative amplitude term $A_t$ that allows to explain variations in the amplitude of the signal, and is modeled as an Ornstein-Uhlenbeck process $\lambda_t$ such that $A_t = \exp(\lambda_t)$.
\begin{align*}
\textrm{d}\lambda_t =& -\gamma_{\lambda} (\lambda_t-\mu_{\lambda}) \textrm{d}t + \sigma_{\lambda}\textrm{d}W_t\\