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Firstly, we will define the phase evolution of our signal as  \begin{equation}  \phi(t) \approx 2\pi \sum_{l=0} \frac{f^{(l)}}{(l+1)!}\left(t+\delta(t)-t_0\right)^{(l+1)} \frac{f^{(l)}}{(l+1)!}\left(t+\delta(t)-t_0\right)^{(l+1)},  \end{equation}  where $f^{(l)}$ are the $l^{\rm th}$ intrinsic frequency derivatives of the signal defined at the epoch $t_0$, and $\delta(t)$ is the time delay between the source inertial frame and the solar system barycentre (SSB).  If we Taylor expand $\delta(t)$ to second order we get  \begin{equation}  \delta(t) \approx \delta_k + \dot{\delta}_k t + \frac{1}{2}\ddot{\delta}_kt^2 \frac{1}{2}\ddot{\delta}_kt^2,  \end{equation} where $\delta_k = \delta(t_k)$ is the time delay at time $t_k$, $\dot{\delta}_k = {\rm d}\delta(t_k)/{\rm d}t$ and $\ddot{\delta}_k = {\rm d}^2\delta(t_k)/{\rm d}t^2$.