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Spectral Estimation by Computationally Reduced Kalman Filter

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Abstract

This paper introduces an innovative frequency estimation approach that relies on a new and innovative structure for Kalman Filter (KF) in signal processing. Kalman Filtering, because of its state estimating nature, excels other methods in real-time processing. However, the main drawback of Kalman Filtering is that it involves time-consuming matrix operations which makes it inferior to faster methods like fast Fourier transform (FFT). The most evident privilege of the new structure is that it “synthesizes” the components rather than “extracts” them as standard Kalman Filter does. This parallel synthesis of signal components reduces the computational order of the Kalman Filter dramatically.

In addition, in the proposed parallel structure, each component can be controlled separately by adjusting its own parameters. Hence, the convergence time and signal-to-noise ratio (SNR) can be improved. This capability surpasses the proposed structure to both KF and FFT. Equations needed for these adjustments are derived analytically and by simulation.

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Authors and Affiliations

  1. Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran

    Reza Kazemi, Mohammad Rasouli & Fereidoon Behnia

Authors
  1. Reza Kazemi
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  2. Mohammad Rasouli
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  3. Fereidoon Behnia
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Correspondence to Reza Kazemi.

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Kazemi, R., Rasouli, M. & Behnia, F. Spectral Estimation by Computationally Reduced Kalman Filter. Circuits Syst Signal Process 31, 2205–2220 (2012). https://doi.org/10.1007/s00034-012-9429-7

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  • DOI: https://doi.org/10.1007/s00034-012-9429-7

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