Multiple frequencies and AR parameters estimation from one bit quantized signal via the EM algorithm

The authors present a novel algorithm which is used to estimate the coefficients of q AR processes from a coarsely quantized signal. The input signal to the quantizer is the superposition of q AR processes and noise. In a related problem a modified version of the above algorithm is used to estimate the frequencies of coarsely quantized data obtained from q sinusoids embedded in noise. The proposed algorithm can accommodate a nonuniform m-level quantizer, as well as the special case of a one bit quantizer. The proposed estimator is based on the maximum likelihood (ML) criterion, and is realized by judiciously combining the expectation-maximization (EM) algorithm of Dempster, Laird and Rubin (1977), and the “Gaussian fit” scheme of Curry (1970). Simulations reveal that they can accurately estimate the coefficients of several AR processes, or the frequencies of several sinusoids, from one bit quantized data at low signal to noise ratios and moderate number of observations