The paper presents two Kalman filtering approaches for a leveling loop problem of low cost strap down inertial navigation system where the inertial unit measurements are sampled and corrupted with additive white noise. It is shown that in this case the equations of motion lead to a stochastic time-varying system with additive and multiplicative state-dependent white noise terms. The state vector of this system includes the body position vector, the body velocity vector which is the projection of the ground velocity vector onto the body axes, and the three direction cosines related to the roll and the pitch angles. It is assumed that the body velocity vector is measured using a Doppler velocity log device consisting of four antennas measuring the Doppler effect. The corresponding body position vector is measured using the received signal power at these four antennas. If these measurements are sampled and corrupted with additive white noise, the estimation of the roll and pitch angles of the platform leads to a filtering problem for a time-varying stochastic system with additive and multiplicative state-dependent noises. Two Kalman-type filtering procedures for such models of the platform are presented. Numerical simulations and discussions of implementation aspects related to the sampled measurements nature are also presented.