Maximum likelihood identification algorithm for the state space model with q-Exponential Distributions

In this project, we will develop a system identification algorithm for the state space model subject to observation noise generated by q-Exponential (Tasllis) distribution. By using the Maximum Likelihood Estimation (MLE) and Expectation Maximization (EM) algorithm, we will identify the unknown parameters. with discrepant observations. Further, for the E-step in the EM algorithm we shall develop the Kalman filter and smoother for the q-Exponential state space model. Moreover, we will derive the Fisher information matrix and also present sufficient conditions to have consistent and asymptotically normally distributed estimators. A Monte Carlo simulation result will be used to show the efficiency of the proposed algorithms, the behaviour of the estimator in the sense of decreasing bias, and symmetric distribution when the sample size increases.