Simulation of a mobile object stochastic trajectory on the basis of the fractal Wiener process taking into account the Hurst indicator is offered. For numerical realization of this process the wavelet based decomposition is used. The peculiarities of trajectory parameters estimation by using the Kalman filter and the synthetic algorithms of nonlinear filtering are considered. An example of the object motion in a spherical system of coordinates is reviewed in the absence of its motion in the vertical plane. The state vector of the object is estimated by using nonlinear measurements of polar range and azimuth coordinates from a two-coordinate radar station.