A COMBINED DETECTION ESTIMATION ALGORITHM FOR THE HARMONIC-RETRIEVAL PROBLEM

Unlike usual separated detection-estimation methods, an efficient algorithm that can estimate both the number and the parameters of multiple complex sinusoids is proposed. The combined detection-estimation operation is accomplished by the joint applications of the Maximum Likelihood (ML) estimation approach and Zhao's efficient detection criterion (EDC). The algorithm is iterative; at each iteration it needs simply to find the peak of a notch periodogram. With the aid of FFT and a concurrent Gram-Schmidt procedure using Schur's recursions, the notch periodogram can be efficiently computed without any costly matrix operation. This also facilitates a real-time implementation of the notch periodogram in terms of a highly pipelined notch processor cascaded by two FFT processors. Simulation results show that the algorithm not only has much higher detection rate than Wax's Minimum Description Length (MDL) method, but also achieves the CR bound at a lower threshold SNR than that of the Modified Forward Backward Linear Prediction (MFBLP) method proposed by Tufts and Kumaresan. Thus, our algorithm offers both good performance and high speed.