jBillou edited Estimating phases from signal.tex  over 9 years ago

Commit id: 1f6d50b0ffb27a073961a9e9d7c60812404834be

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Explain how we do this stuff  $\textrm{d}\theta = \omega_1 \frac{2\pi}{T_1}  \textrm{d}t + f_1(\theta) + F_1(\theta,\phi) \textrm{d}t + \sigma_1 \textrm{d} W^1_t $ $\textrm{d}\phi = \omega_2 \frac{2\pi}{T_2}  \textrm{d}t + f_2(\theta) + F_2(\theta,\phi) \textrm{d}t + \sigma_2 \textrm{d} W^2_t $ This is a reference \cite{bieler2014}. 

\begin{align*}   \textrm{d}\theta_t = \frac{2\pi}{T}\textrm{d}t &= \frac{2\pi}{T_1}\textrm{d}t  + \sigma\textrm{d}W_t \sigma\textrm{d}W_t\\  \textrm{d}\lambda_t = -\gamma_lambda (\lambda_t-\mu_\lambda) &= -\gamma_{\lambda} (\lambda_t-\mu_{\lambda})  \textrm{d}t + \sigma_{\lambda}\textrm{d}W_t \sigma_{\lambda}\textrm{d}W_t\\  \textrm{d}B_t = &=  -\gamma_B (B_t-\mu_B) \textrm{d}t + \sigma_{B} \textrm{d}W_t   \end{align} \textrm{d}W_t\\  \end{align*}