Noise distribution arising in certain applications frequently deviates from the assumed gaussian model, often being characterized by heavier tails generating the outliers. Since, in the presence of outliers, the performance of a Kalman filter can be very poor, a statistical approach-named QQ-plot-is suggested to make the Kalman filter more robust. In addition, the first and the second-order moments of noise processes are estimated simultaneously with the system states, using the QQ-plot of the noise samples generated in the ’robustified’ Kalman filter algorithm. Results of simulation demonstrating the robustness of the proposed state estimators are also included.