An interval Kalman filter, interval EM algorithm with application to weather prediction

The Kalman filter (KF) gives the optimal estimates of the unknown state vector in time series linear stochastic state space model (SSM). If we have observed data of the state space model, we can identify the unknown parameters using system identification techniques. One way to do this is called Expectation Maximization (EM). In the system certain elements such as the coefficient matrices are not precisely known or gradually change with time. One way to take these uncertainties into account is to allow interval state space models and extend the statistical concepts to interval setting.;The traditional Kalman filter technique can not be used directly when the system parameters are not precisely known or change with time. So, it is important to introduce an interval Kalman filter(IKF) to handle the current situation. Also, the interval parameters could be identified from a given record of interval measurements.