Maximum likelihood LM identification based on particle filtering for scarce measurement-data MIMO Hammerstein Box-Jenkins systems

The scarce measurement-data system means that the input or output of one system are sampled at scarce time series. Thus, the sampled data are incomplete in scarce measurement-data systems. In this paper, the parameter estimation of scarce measurement-data multiple input multiple output Hammerstein Box-Jenkins (S-MIMO-H-BJ) systems is studied. To make full use of the system data without adding unknown parameters, the particle filtering method is applied to obtain unknown states and variables in scarce measurement-data systems. Thus, the maximum likelihood Levenberg Marquardt (ML-LM) iterative method based on particle filtering (ML-LM-I-PF) is derived. To verify the superiority of the proposed algorithm, the ML-LM iterative method based on auxiliary model (ML-LM-I-AM) is also derived. Finally, using these two algorithms, unknown parameters in the S-MIMO-H-BJ numerical example and the two-tank level system are identified. Simulations prove that these two methods can all estimate S-MIMO-H-BJ models effectively, but the ML-LM-I-PF method behaves better because it has smaller calculation amount and more accurate parameter estimation.