The Kalman Filter

Sharon Gannot*, Arie Yeredor

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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 speakerlocalization speaker localization is demonstrated.

Original languageEnglish
Title of host publicationSpringer Handbooks
Number of pages26
StatePublished - 2008

Publication series

NameSpringer Handbooks
ISSN (Print)2522-8692
ISSN (Electronic)2522-8706


  • Extend Kalman Filter
  • Kalman Filter
  • Mean Square Error
  • Speech Signal
  • Unscented Kalman Filter


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