Bayesian approach to direct pole estimation

In this work, the problem of pole identification of discrete-time single-input single-output (SISO) linear time-invariant (LTI) systems directly from input-output data is considered. The solution to this nonlinear estimation problem is derived in form of the general Bayesian estimation framework, as well as a practical approximate solution by application of statistical linearization. The derived direct pole estimation algorithm by statistical linearization is given in closed-form and regression point based, by the so-called Linear Regression Kalman Filter (LRKF). We consider both, an input-output and a state-space formulation. Two realizations of the LRKF algorithm are tested, namely the Unscented Kalman Filter (UKF) for low computational complexity and thus, for high update rates, and the Smart Sampling Kalman Filter (S2KF) for high precision with faster convergence. Both, the UKF and S2KF are compared to the Adaptive Pole Estimation (APE), a solution by recursive nonlinear least squares minimizing the prediction error gradient.