correlation $c(\mu^j)$ of the matched filter with parameters $\mu^j$ is then just the scalar product given by, $$c(\mu^j) = \left\langle{\bf x},{\bf h}(\mu^j)\right\rangle.
\label{cor}$$ Given the data vector ${\bf x}$, the correlation is computed for the entire feasible range of parameters, continuously over the kinematic parameters $t_s$ and $\Phi$ and for discrete values of the dynamical parameters $\tau_0$ and $\tau_1$. The filters corresponding to the discrete values of $\tau_0$ and $\tau_1$ constitute the filter bank. The maximum of $c(\mu^j)$ is computed and compared with a preassigned threshold determined from the false alarm probability. A detection is announced if the maximum of $c(\mu^j)$ crosses the threshold. The parameters $\hat \mu^j$ for which the correlation is maximised are the MLE of the parameters of the signal. However, these will in general differ from the actual signal parameters $\check \mu^j$ due to the presence of noise. The difference $\Delta \mu^j = \check \mu^j - \hat \mu^j$ is the error made in estimating the parameters. When the signal is weak as compared to the noise (low SNR), the estimated parameters in general will differ by a large margin from the true ones, while in the limit of high SNR, the two will almost coincide. Thus 