For the linear discrete time-invariant stochastic systems with unknown variances, by introducing a left coprime decomposition, a new measurement process is obtained, which is described by the sum of two moving average(MA) process. The estimators of the noise variances Q and R are obtained by solving the matrix equations for correlation function, and based on the sampled correlation function of the new measurement process and its ergodicity, the strong consistent estimators of the noise variances Q and R are obtained. The algorithm is simple, and they are suitable for real time applications. A simulation example for a target tracking system shows their effectiveness.