Covariance Based Realization Algorithm for Identification of Linear Time Periodic Systems

Abstract

This paper focuses on the parameter estimation of multi-input multi-output (MIMO), linear time-periodic (LTP) systems in the time domain. Discrete-time state-space models are selected for the description of LTP systems and the Covariance Based Realization Algorithm (CoBRA), one branch of subspace methods, is used for the identification of the generalized time-lifted state-space model for an LTP system. The use of the CoBRA method for estimation is motivated by the robustness against output noise with (high-order) noise dynamics and a focus on the estimation of low rank deterministic model for the LTP system. In addition to the use of CoBRA, a novel method is proposed to compute a topologically equivalent realization for the original LTP system. The method includes two different but theoretically equivalent approaches of calculating the state matrices, which can be also used as a measure for the estimation quality. Finally, a simulation is given to illustrate the efficiency of the proposed method.