Spectral estimation based on structured low rank matrix pencil

This paper proposes a new parameter estimation algorithm for damped sinusoidal signals. Parameter estimation for damped sinusoidal signals with additive white noise is a problem of signiicant interest in many signal processing applications, like analysis of NMR data and system identiication. The new algorithm estimates the signal parameters using a matrix pencil constructed from the measured data. To reduce the noise eeect, rank deecient Hankel approximation of prediction matrix is used. The performance of the new algorithm is signiicantly improved by structured low rank approximation of prediction matrix. Computer simulations show that the noise threshold of the new algorithm is signiicantly better than the existing algorithms. 1. INTRODUCTION High resolution parameter estimation for damped sinusoidal signals in the presence of additive white noise is a problem of signiicant interest in many signal processing applications, like spectral analysis , analysis of NMR data and system identiica-tion. Many approaches to high resolution parameter estimation have been proposed for pure si-nusoidal signals, including linear prediction (LP) techniques 1], signal subspace methods introduced by Pisarenko, and generalized by Schmidt 2] in his MUSIC (multiple signal classiication) algorithm and ESPRIT 3] which provides high resolution parameter estimation by means of sub-space rotational invariance techniques with complexity much less than MUSIC algorithm. The diiculty of parameter estimation for damped sinusoidal signals stems from the nonstationar-ity of this kind of signals. Kumaresan-Tufts (KT) algorithm 4] and Hua-Sarkar's matrix pencil method 7] are well known to provide better estimations for parameters of damped sinusoidal signals. These two methods can attain Cramer-Rao bound for a certain noise threshold if the damping factors are small. A new algorithm is proposed in this paper which estimates the signal parameters by using a matrix pencil constructed from noise corrupted data. To reduce the noise eeect, the low rank Hankel approximation of the prediction matrix is used 5, 6]. It can be shown that the performance of parameter estimation algorithm can be improved if the structure of the prediction matrix is preserved after low rank approximation. This structured low rank approximation of prediction matrix 5, 6] has a great eeect on the performance of the new algorithm. The performance of the new algorithm is compared with KT algorithm 4], modiied KT algorithm (MKT) 6] and Hua-Sarkar's matrix pencil method 7] through the computer simulations. Computer simulation results show that, this new algorithm has lower noise threshold than KT algorithm 4], MKT 6] and …