A Study on Stability of the Interacting Multiple Model Algorithm

The Interacting Multiple Model (IMM) algorithm has been used in various applications with good performance. However, to the best of our knowledge, stability conditions of the IMM algorithm have not been shown in the control literature. This technical note presents a sufficient condition for the exponential stability of the IMM algorithm for a class of Markov jump linear systems. We derive a lower bound and an upper bound for the error covariances of the IMM algorithm, and then derive the stability condition by the Lyapunov approach.

[1]  Yaakov Bar-Shalom,et al.  Design of an interacting multiple model algorithm for air traffic control tracking , 1993, IEEE Trans. Control. Syst. Technol..

[2]  Gene H. Golub,et al.  Matrix computations , 1983 .

[3]  J. Deyst.  Correction to "Conditions for asymptotic stability of the discrete minimum-variance linear estimator" , 1973 .

[4]  Thomas Kailath,et al.  Linear Systems , 1980 .

[5]  Inseok Hwang,et al.  Stability analysis of the Interacting Multiple Model algorithm , 2008, 2008 American Control Conference.

[6]  Guanrong Chen,et al.  Kalman Filtering with Real-time Applications , 1987 .

[7]  Guang-Ren Duan,et al.  Fault diagnosis and fault tolerant control for nonlinear satellite attitude control systems , 2014 .

[8]  J. Deyst,et al.  Conditions for asymptotic stability of the discrete minimum-variance linear estimator , 1968 .

[9]  Peter S. Maybeck,et al.  Characterization of Kalman filter residuals in the presence of mismodeling , 2000, IEEE Trans. Aerosp. Electron. Syst..

[10]  Olivier Aycard,et al.  Interacting multiple models based classification of moving objects , 2010, 2010 11th International Conference on Control Automation Robotics & Vision.

[11]  Inseok Hwang,et al.  Algorithm for Performance Analysis of the IMM Algorithm , 2011, IEEE Transactions on Aerospace and Electronic Systems.

[12]  Y. Bar-Shalom,et al.  The interacting multiple model algorithm for systems with Markovian switching coefficients , 1988 .

[13]  P. Olver.  Nonlinear Systems , 2013 .

[14]  V. Jilkov,et al.  Survey of maneuvering target tracking. Part V. Multiple-model methods , 2005, IEEE Transactions on Aerospace and Electronic Systems.