Initialization of the Kalman filter with partially diffuse initial conditions

Ralph D. Snyder, Grant R. Saligari

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)

Abstract

The problem of computing estimates of the state vector when the Kalman filter is seeded with an arbitrarily large variance is considered. To date the response in the literature has been the development of a number of relatively complex hybrid filters, usually involving additional quantities and equations over and above the conventional filter. We show, however, that a certain square root covariance filter is capable of handling the complete range of variances (zero, positive and infinite) without modification to the filtering equations themselves and without additional computation loads. Instead of the more conventional Cholesky factorization, our filter employs an alternative matrix factorization procedure based on a unit lower triangular matrix and a diagonal matrix. This permits the use of a modified form of fast Givens transformations, central to the development of an efficient algorithm.

Original languageEnglish
Pages (from-to)409-424
Number of pages16
JournalJournal of Time Series Analysis
Volume17
Issue number4
DOIs
Publication statusPublished - 1 Jan 1996

Keywords

  • Fast Givens transformations
  • Initialization
  • Kalman filter

Cite this

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Initialization of the Kalman filter with partially diffuse initial conditions. / Snyder, Ralph D.; Saligari, Grant R.

In: Journal of Time Series Analysis, Vol. 17, No. 4, 01.01.1996, p. 409-424.

Research output: Contribution to journalArticleResearchpeer-review

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AB - The problem of computing estimates of the state vector when the Kalman filter is seeded with an arbitrarily large variance is considered. To date the response in the literature has been the development of a number of relatively complex hybrid filters, usually involving additional quantities and equations over and above the conventional filter. We show, however, that a certain square root covariance filter is capable of handling the complete range of variances (zero, positive and infinite) without modification to the filtering equations themselves and without additional computation loads. Instead of the more conventional Cholesky factorization, our filter employs an alternative matrix factorization procedure based on a unit lower triangular matrix and a diagonal matrix. This permits the use of a modified form of fast Givens transformations, central to the development of an efficient algorithm.

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