Frequency estimation from proper sets of correlations

• Published in: IEEE transactions on signal processing Vol. 50; no. 4; pp. 791 - 802
• Main Authors: Volker, B., Handel, P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2002; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Asymptotic properties; Autocorrelation; Automotive components; Background noise; Complement; Computation; Computational complexity; Computational modeling; Computer simulation; Correlation; Detection, estimation, filtering, equalization, prediction; Estimators; Exact sciences and technology; Frequency estimation; Geophysical measurements; Geophysical signal processing; Information, signal and communications theory; low complexity; optimization; Phase estimation; phase unwrapping; Radar applications; Radar signal processing; Signal and communications theory; Signal, noise; single-frequency; Strategy; Telecommunications and information theory; threshold; Performance evaluation; Parameter estimation; Phase unwrapping; Simulation; Signal estimation; Frequency estimation; Computational complexity; Correlation method; Periodogram; Prony method
• ISSN: 1053-587X; 1941-0476; 1941-0476
• DOI: 10.1109/78.992122

As a complement to the periodogram, low-complexity frequency estimators are of interest. One such estimator is based on Prony's method and rely on phase information of the auto correlations. Without prior knowledge of the frequency (e.g., a given frequency interval), the frequency cannot be unambiguously estimated from a single correlation only. We introduce a new method of phase unwrapping using an arbitrary number (more than one) of correlations. From this arbitrary set of correlations, we propose a weighted average estimator. We derive the asymptotic performance and show how the correlation lags should be properly chosen. From a design aspect, there is often a restriction of using a fixed number of computations. In addition, we therefore propose a strategy to find a proper set of correlation lags subject to a given computational complexity. Finally, simulation results that lend support to the theoretical findings are included.