Maximum Likelihood Estimation of Multiple Damped Sinusoids by Using Newton's Iterations and Improved Initialization

Abstract

The maximum likelihood parameter estimation of multiple damped sinusoids in noise is considered in this paper. Since the damped signal decays exponentially with time and each signal has two parameters to estimate, the ML criterion is very Mcu l t to optimize. In computing the MLE, it is noted that the convergence performance of the iterative algorithm is highly sensitive to the initial point. Thus we resort to a Newton-type ML algorithm equipped with an improved initialization scheme, which comkts of a robust state-space method followed by a reibing alternating " b a t i o n (AM) procedure. Performance simutation shows that the overall ML algorithm can achieve the CR bound with a lower threshold SNR than other existing methods. lies on how to optimize the highly nonlinear and multidimensional ML Criterion [3-51. As is well known, a key to the global convergence of the ML algorithm is the determination of the initial point. In this paper, we present a two-step initialization scheme for finding a more stable initial point. The first step is a polynomialbased state space method that can resuit in stable estimates of the damping fixtors, and the second step is a rething alternating " b a t i o n (AM) methd used to find more accurate frequency estimates [4]. Once the initialization is completed, Newton-type iterations similar to that in [5] are perfiormed in the main loop to optimize the ML criterion. In the following sections, we will present the problem formulation and the overall ML algorithm. Then its superior performance, as compared to other methods, is confirmed by computer simulations.