Nonparametric spectral analysis with missing data via the EM algorithm

Authors:
Yanwei Wang;Petre Stoica;Jian Li;Thomas L. Marzetta
Affiliations:
Department of Electrical and Computer Engineering, P.O. Box 116130, University of Florida, Gainesville, FL 32611, USA;Department of Information Technology, the Division of Systems and Control, Uppsala University, P.O. Box 337, SE-75105 Uppsala, Sweden;Department of Electrical and Computer Engineering, P.O. Box 116130, University of Florida, Gainesville, FL 32611, USA;Mathematical Sciences Research Center, Bell Laboratories, Lucent Technologies, 600 Mountain Avenue, Murray Hill, NJ 07974, USA
Venue:
Digital Signal Processing
Year:
2005

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Abstract

We consider nonparametric complex spectral estimation of data sequences with missing samples occurring in arbitrary patterns. The existing spectral estimation algorithms designed for uniformly sampled complete-data sequences perform poorly when applied to data sequences with missing samples if the missing samples are simply set to zero. Several nonparametric algorithms have recently been developed to deal with the missing-data problem. They include, for example, GAPES for gapped data and PG-APES, PG-CAPON for periodically gapped data. However, they are not really suitable for the general missing-data problem where the missing data samples occur in arbitrary patterns. In this paper, we deal with a general missing-data spectral estimation problem for which we develop two nonparametric missing-data amplitude and phase estimation (MAPES) algorithms, both of which make use of the expectation maximization (EM) algorithm. Numerical results are provided to demonstrate the effectiveness of the proposed algorithms.