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The Kalman Filter

  • Chapter
Springer Handbook of Speech Processing

Part of the book series: Springer Handbooks ((SHB))

Abstract

The Kalman filter and its variants are some of the most popular tools in statistical signal processing and estimation theory. In this chapter, we introduce the Kalman filter, providing a succinct, yet rigorous derivation thereof, which is based on the orthogonality principle. We also introduce several important variants of the Kalman filter, namely various Kalman smoothers, a Kalman predictor, a nonlinear extension (the extended Kalman filter), and adaptation to cases of temporally correlated measurement noise.

The application of the Kalman filter to two important speech processing problems, namely, speech enhancement and speaker localization is demonstrated.

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Abbreviations

ANC:

active noise cancelation

AR:

autoregressive

ARMA:

autoregressive moving-average

ASR:

automatic speech recognition

EKF:

extended Kalman filter

EM:

estimate-maximize

GCC:

generalized cross-correlation

HMM:

hidden Markov models

HOS:

higher-order statistics

II:

information index

IMM:

interacting multiple model

LPC:

linear prediction coefficients

M-step:

maximization stage

MA:

moving average

ML:

maximum-likelihood

MMSE:

minimum mean-square error

MSE:

mean-square error

NASA:

National Aeronautics and Space Administration

NN:

neural network

PARCOR:

partial correlation coefficients

SNR:

signal-to-noise ratio

TDOA:

time difference of arrival

UKF:

unscented Kalman filter

UT:

unscented transform

WLS:

weighted least-squares

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Author information

Authors and Affiliations

  1. School of Electrical Engineering, Bar-Ilan University, 52900, Ramat-Gan, Israel

    Sharon Gannot Ph.D

  2. Electrical Engineering - Systems, Tel-Aviv University, P.O. Box 39040, 69978, Tel-Aviv, Israel

    Arie Yeredor Ph.D

Authors
  1. Sharon Gannot Ph.D
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  2. Arie Yeredor Ph.D
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Corresponding authors

Correspondence to Sharon Gannot Ph.D or Arie Yeredor Ph.D .

Editor information

Editors and Affiliations

  1. INRS-EMT, University of Quebec, 800 de la Gauchetiere Ouest, H5A 1K6, Montreal, Quebec, Canada

    Jacob Benesty Dr.

  2. Avayalabs Research, 233 Mount Airy Road, 07920, Basking Ridge, NJ, USA

    M. Mohan Sondhi Ph.D.

  3. Alcatel-Lucent, Bell Laboratories, 600 Mountain Avenue, 07974, Murray Hill, NJ, USA

    Yiteng Arden Huang Dr.

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© 2008 Springer-Verlag Berlin Heidelberg

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Gannot, S., Yeredor, A. (2008). The Kalman Filter. In: Benesty, J., Sondhi, M.M., Huang, Y.A. (eds) Springer Handbook of Speech Processing. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49127-9_8

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  • DOI: https://doi.org/10.1007/978-3-540-49127-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49125-5

  • Online ISBN: 978-3-540-49127-9

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