That paper addresses the problem of estimating the state and the unknown input in a continuous-time Linear Parameter Varying (LPV) system, in the presence of Gaussian white noises affecting both state and measurement equations. This estimation is made via the use of a Minimum Variance Unbiased Observer (as in Kalman Filtering). After recalling some useful results, the observer equations for state and unknown input estimation are established, and then an example is given in order to illustrate the talk.