Noise distribution plays an essential role in state estimation using Kalman filter. However, statistical characteristics of the noise are often unknown in most practical applications. A second order mutual difference (SOMD) algorithm has been proposed to generate an estimation of the measurement noise covariance matrix R by calculating the autocorrelation of SOMD of redundant measurements, and thus it can avoid coupling with the state estimation error; however, the algorithm cannot be applied directly for a majority of practical systems due to the requirement of redundant measurements. In this paper, the SOMD algorithm is expanded to the system with single measurement by constructing a pseudo measurement. A non-zero estimation bias detection algorithm is presented to address the inconsistency between the mathematical model and the real. A modified robust adaptive Kalman filter (RAKF) is also developed to tackle this inconsistency and improve filtering accuracy by activating adaptive operation properly. The efficacy of the approach is demonstrated via a target tracking problem. Simulation results indicate that the proposed algorithm can reflect the noise properties accurately and outperform several reference algorithms in precision and robustness. (C) 2018 Elsevier Ltd. All rights reserved.