Frequency domain estimation and parameter decoupling using modulating function techniques

An extended adaptive weighted least squares (EAWLS) algorithm using a modulating function technique (MFT) is developed for the identification of a continuous-time differential system with complex parameters. Using the EAWLS and the adaptive weighted least squares (AWLS/MFT) by Pearson et al., high resolution frequency estimators are devised for complex-valued and real sinusoids, respectively. A Modified EAWLS (MEAWLS) algorithm is also devised for the frequency estimation of pure complex sinusoids which gives better performance than the EAWLS. For the real sinusoidal case, resolution bands are compared for the AWLS and LS estimates. The results show that the AWLS estimator is a high resolution frequency estimator and has much wider resolution bands with respect to SNR, sample frequency, observation time interval, and the highest modulating function frequency index M. Also developed is a modified parameter decoupling algorithm for transfer function identification using AWLS/MFT. The use of a high frequency sinusoid input just above the system bandwidth is suggested in order to decouple the denominator parameters during transient operation. This makes it possible to use lower harmonic Fourier series coefficients and results in better performance than the low frequency input signal. In the second stage for the decoupling of numerator parameters, a one-step estimation is suggested using a nonharmonic input signal which improves the computational efficiency. Lastly, the identification of a modal system with initial conditions is studied and compared with an alternative approach.