Optimum Estimation of the Moment of Emergence of a Signal in the Presence of Multiplicative High-frequency Gaussian Noise

A process $\xi_\lambda(t)$ of the form (2) is observed, where $S(t-\tau)$ is a signal of a well-known form, which depends on an unknown parameter $\tau$; $\nu(t)$ is Gaussian noise with a spectral density as in (1a). The problem is to detect a class of estimations of the parameter $\tau$, whose exactness does not vary when the process $\xi_\lambda(t)$ changes somewhat. A class of processes $\tilde{\xi}_\lambda(t)$ approximating the process $\xi_\lambda(t)$ is determined by means of relation (3). A class of estimations $\tilde\tau$, whose exactness is the same for all processes $\tilde\xi_\lambda$ approximating the process $\xi_\lambda$, is determined from (4). An optimum estimation for this class is found.