HIGH-ORDER YULE-WALKER ESTIMATION OF THE PARAMETERS OF EXPONENTIALLY DAMPED CISOIDS IN NOISE

An approach for the estimation of the frequencies and damping factors of exponentially damped cisoids (complex sinusoids) is presented. The method may be seen as an extension of the method of backward linear pr ediction and singular value decomposition of Kumaresan and Tufts to th e second-order statistics domain. The proposed estimator is interprete d as a high-order Yule-Walker (HOYW) method using a data based covaria nce matrix. The HOYW method is analysed at high SNR where closed-form expressions for the accuracy of the estimates are derived. By Monte Ca rlo simulations the HOYW method is applied to data consisting of one a nd two damped cisoids in additive white noise. The simulation results are compared with the results using the Kumaresan and Tufts method, wi th the Cramer-Rao bound, and with the derived theoretical results. The method is not statistically efficient, but the comparison shows that the HOYW method outperforms the method of Kumaresan and Tufts in terms of accuracy versus algorithmic complexity and in terms of precision i n the cases considered. Due to the above properties the method is suit able to provide fast initial estimates for nonlinear search methods.