This paper presents a method for identification of parameters and delays of a linear system in the presence of noise. The estimation procedure is based on transforming the input-output data into the discrete Fourier domain. The transformed data is then solved block recursively to obtain both the system parameters and unknown delay. For systems with no delays or known delays, the equations are linear in the parameters and the standard estimation techniques can be applied. For systems with unknown delays, the resulting equations are nonlinear in the delay term. A recursive nonlinear estimation technique similar to the least-squares in the time domain has been developed. In the presence of Gaussian white noise, simulation studies indicate that the parameters converge to their true values in the mean.
Block-Recursive Identification of Parameters and Delay in the Presence of Noise
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Young, G. E., Rao, K. S. S., and Chatufale, V. R. (December 1, 1995). "Block-Recursive Identification of Parameters and Delay in the Presence of Noise." ASME. J. Dyn. Sys., Meas., Control. December 1995; 117(4): 600–607. https://doi.org/10.1115/1.2801120
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