Kemalettin ERBATUR, Iyad HASHLAMON

An improved real-time adaptive Kalman filter with recursive noise covariance updating rules

: The Kalman filter (KF) is used extensively for state estimation. Among its requirements are the process and observation noise covariances, which are unknown or partially known in real-life applications. Uncertain and biased values of the covariances result in KF performance degradation or divergence. Unlike previous methods, we are using the idea of the recursive estimation of the KF to develop two recursive updating rules for the process and observation covariances, respectively designed based on the covariance matching principles. Each rule has a tuning parameter that enhances its flexibility for noise adaptation. The proposed adaptive Kalman filter (AKF) proves itself to have an improved performance over the conventional KF and, in the worst case, it converges to the KF. The results show that the AKF estimates are more accurate, have less noise, and are more stable against biased covariances.

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[1] Grewal MS, Andrews AP. Kalman Filtering: Theory and Practice Using MATLAB. 2nd ed. New York, NY, USA: John Wiley & Sons, 2001.
[2] Simon D. Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches. Hoboken, NJ, USA: Wiley & Sons, 2006.
[3] Maybeck PS. Stochastic Models, Estimation and Control. Vol. 3. New York, NY, USA: Academic Press, 1982.
[4] Heffes H. The effect of erroneous models on the Kalman filter response. IEEE T Automat Contr 1966; 11: 541543.
[5] Fitzgerald RJ. Divergence of the Kalman filter. IEEE T Automat Contr 1971; 16: 736747.
[6] Mohamed A, Schwarz K. Adaptive Kalman filtering for INS/GPS. J Geodesy 1999; 73: 193203.
[7] Myers K, Tapley BD. Adaptive sequential estimation with unknown noise statistics. IEEE T Automat Contr 1976; 21: 520523.
[8] Ding W, Wang J, Rizos C, Kinlyside D. Improving adaptive Kalman estimation in GPS/INS integration. J Navigation 2007; 60: 517.
[9] Shi E. An improved real-time adaptive Kalman filter for low-cost integrated GPS/INS navigation. In: IEEE 2012 International Conference on Measurement, Information and Control (MIC) 1820 May 2012; Harbin, China. New York, NY, USA: IEEE. pp. 10931098.
[10] Hide C, Moore T, Smith M. Adaptive Kalman filtering for low-cost INS/GPS. J Navigation 2003; 56: 143152.
[11] Mehra RK. On the identification of variances and adaptive Kalman filtering. IEEE T Automat Contr 1970; 15: 175184.
[12] B´elanger PR. Estimation of noise covariance matrices for a linear time-varying stochastic process. Automatica 1974; 10: 267275.
[13] Oussalah M, Schutter JD. Adaptive Kalman filter for noise identification. In: Proceedings of the International Seminar on Modal Analysis; 2001; Kissimmee, FL, USA. Leuven, Belgium: KU Leuven. pp. 12251232.
[14] Odelson BJ, Rajamani MR, Rawlings JB. A new autocovariance least-squares method for estimating noise covariances. Automatica 2006; 42: 303308.
[15] Odelson BJ, Lutz A, Rawlings JB. The autocovariance least-squares method for estimating covariances: application to model-based control of chemical reactors. IEEE T Contr Syst T 2006; 14: 532540.
[16] Raghavan H, Tangirala AK, Bhushan Gopaluni R, Shah SL. Identification of chemical processes with irregular output sampling. Control Eng Pract 2006; 14: 467480.
[17] Bavdekar VA, Deshpande AP, Patwardhan SC. Identification of process and measurement noise covariance for state and parameter estimation using extended Kalman filter. J Process Contr 2011; 21: 585601.
[18] Wang X. Vehicle health monitoring system using multiple-model adaptive estimation. MSc, University of Hawaii at Manoa, Manoa, HI, USA, 2003.
[19] Rong Li X, Youmin Z. Multiple-model estimation with variable structure part V: Likely-model set algorithm. IEEE T Aero Elec Sys 2000; 36: 448466.
[20] Karasalo M, Hu X. An optimization approach to adaptive Kalman filtering. Automatica 2011; 47: 17851793.
[21] Yang Y, Gao W. An optimal adaptive Kalman filter. J Geodesy 2006; 80: 177183.
[22] Bi¸cer C, Babacan EK, Ozbek L. Stability of the adaptive fading extended Kalman filter with the matrix forgetting ¨ factor. Turk J Electr Eng Co 2012; 20: 819833.
[23] Babacan EK, Ozbek L, Efe M. Stability of the extended Kalman filter when the states are constrained. IEEE T Automat Contr 2008; 53: 27072711.
[24] Khalil HK. Nonlinear Systems. 3rd ed. Upper Saddle River, NJ, USA: Prentice Hall, 2000.
[25] Reif K, Unbehauen R. The extended Kalman filter as an exponential observer for nonlinear systems. IEEE T Signal Proces 1999; 47: 23242328.