Time delay estimation for MIMO dynamical systems – With time-frequency domain analysis

In MIMO dynamical systems, the time delay estimation (TDE) problem between each output and input is often confounded due to the dynamic interaction between the inputs and the outputs. In this paper, analyses are given in the time, frequency and time-frequency domains, from which a novel TDE method using combined continuous wavelet transform (CWT) and cross correlation is conceived. In the proposed method, a series of time delays over scales (frequencies) are calculated and an unbiased estimation is deduced from them, by calculating and handling the cross correlation between the CWT coefficients of system input and output data. The TDE method in closed loop case is also studied. Numerical examples with simulation and experimental data verify the feasibility and effectiveness of the proposed method.