A New Algorithm Based on Signal Parametric Models for Estimating the Spectral of Non-Gaussian Noisy Signal

In This study a new method for spectral estimation of signals in the presence of observation noise is proposed. Back ground noise has a non-Gaussian symmetric alpha stable distribution. Signal parameters are modeled by an AR process, using spectral methods. After the calculation of the produced bias in signal parameters, the bias is removed using the generalized Yule–Walker equations. In alpha stable distribution, there is no closed form formula for probability distribution function and cumulative distribution function. Also, the infiniteness of variance in this distribution, limits the performance of correlation coefficient based methods and other standard parameter estimation methods. In this paper, a new closed form formula based on covariation coefficient is proposed which removes the bias using an iterative algorithm. The simulation results show that, by using the proposed method, there is a 20 percent improvement in estimation accuracy of signal parameters in 10dB SNRs and higher ones. Moreover, the results show the estimations of the proposed method is more robust to displacement of poles compared to the classic Yule-Walker method and displays a significant improvement in comparison with the high-order Yule Walker method for AR models, whose poles are close to the boundaries of the unit circle.