In this paper, the problem of finding an optimal polynomial state estimate for the class of stochastic Linear models with a multiplicative state noise term is studied. For such models, a technique of state augmentation is used, leading to the definition of a general polynomial filter, The theory is developed for time-varying systems with nonstationary and non-Gaussian noises. Moreover, the steady-state polynomial filter for stationary systems is also studied, Numerical simulations show the high performances of the proposed method with respect to the classical Linear filtering techniques.