On recursive Markov parameters estimation for MIMO systems

This work develops a recursive algorithm to estimate a given size sequence of Markov parameters for linear discrete-time systems, which is related to FIR models estimation. The discussion on FIR models in identification literature tends to be brief due to its poor prediction error for low order models, although Markov parameter sequence of shorter length can be used, e.g., as the input for data-driven MPC based on FIR models and for system identification combined with realization theory. Estimation of Markov parameters sequence of larger length can also be used in applications in which the prediction itself is not relevant, such as stability assessment or norm computations. The formulation is derived for SISO systems and then we extended it to the MIMO case. An analysis of the overall truncation and bias errors is also developed and illustrative examples are given to highlight the method’s performance. In the examples we also further illustrate the difference in estimation results for different inputs, since the input choice is affected by the identification method utilised.