Estimation of time-varying time delay and parameters of a class of jump Markov nonlinear stochastic systems

It is a challenging problem to estimate time-varying time delay and parameters, especially for systems subject to disturbances with unknown statistics in measurements. The desirable filter should be sensitive to unmodeled dynamics caused by random changes in time delay and parameters, and also be robust to disturbances. Recently, we proposed a finite-horizon robust Kalman filter (RKF) through designing and simultaneously minimizing the upper bounds of unknown covariances of prediction errors, filtering residuals and estimation errors. Unfortunately, unmodeled dynamics and disturbances must be hypothesized to be zero-mean white noises in the RKF. To cope with more general unmodeled dynamics and/or disturbances, a class of jump Markov stochastic systems (JMSS) subject to unmodeled dynamics and disturbances is considered in this article so that a priori system information, such as the value range of unknown and/or randomly changing parameters, can be introduced. Through combining the RKF with the interacting multiple model (IMM) estimation technique, a RKF/IMM algorithm is proposed for such JMSS. Then it is applied to estimate time-varying time delay and parameters of a continuous stirred tank reactor (CSTR) with sensors subject to Gaussian disturbances with unknown means and/or covariances. The RKF/IMM algorithm is compared with the extended Kalman filter (EKF), the strong tracking filter (STF) and the RKF through computer simulations. The results show that, in the case that measurement disturbances are zero-mean noise with unknown covariances, the RKF/IMM and RKF achieve almost the same accurate estimates, which are superior to those of the STF and EKF; in the case that such disturbances have unknown covariances and time-varying means, only the RKF/IMM remains the ability to estimate time-varying time delay and parameters. Furthermore the RKF/IMM has unique ability to identify the disturbance mean no matter whether it is constant or time-varying. Moreover, the RKF/IMM algorithm is shown having strong robustness against the a priori filter parameters, this may be attractive in practical applications.