What is the covariance analog of the Paige and Saunders information filter

Michael R. Osborne; T PRVAN

What is the covariance analog of the Paige and Saunders information filter

Michael R. Osborne, T PRVAN

Research output: Contribution to journal › Article

Abstract

In this paper a square root covariance form of the Kalman filter is presented which is in many ways the covariance analog of the Paige and Saunders information filter [SIAM J. Numer. Anal., 14 (1977), pp. 180-193] and possesses many of the advantages of their algorithm. For example, it is a true square root implementation; but the distinctive feature which it shares with the Paige and Saunders algorithm is a compact, convenient, and effective square root implementation of the interpolation smoother. The algorithm is based on the Duncan and Horne generalised least squares form of the filter equations [J. Amer. Statist. Assoc., 67 (1972), pp. 816-821], but uses these in a recursive manner.

Original language	English
Pages (from-to)	1324-1331
Number of pages	8
Journal	Siam journal on scientific and statistical computing
Volume	12
Issue number	6
Publication status	Published - Nov 1991
Externally published	Yes

Keywords

KALMAN FILTER
COVARIANCE FILTER
INFORMATION FILTER
SQUARE ROOT FILTER
GENERALIZED LEAST SQUARES
SMOOTHING STEP
DISCRETE

Access to Document

http://dx.doi.org/10.1137/0912072

Cite this

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title = "What is the covariance analog of the Paige and Saunders information filter",

abstract = "In this paper a square root covariance form of the Kalman filter is presented which is in many ways the covariance analog of the Paige and Saunders information filter [SIAM J. Numer. Anal., 14 (1977), pp. 180-193] and possesses many of the advantages of their algorithm. For example, it is a true square root implementation; but the distinctive feature which it shares with the Paige and Saunders algorithm is a compact, convenient, and effective square root implementation of the interpolation smoother. The algorithm is based on the Duncan and Horne generalised least squares form of the filter equations [J. Amer. Statist. Assoc., 67 (1972), pp. 816-821], but uses these in a recursive manner.",

keywords = "KALMAN FILTER, COVARIANCE FILTER, INFORMATION FILTER, SQUARE ROOT FILTER, GENERALIZED LEAST SQUARES, SMOOTHING STEP, DISCRETE",

author = "Osborne, {Michael R.} and T PRVAN",

year = "1991",

month = "11",

language = "English",

volume = "12",

pages = "1324--1331",

journal = "Siam journal on scientific and statistical computing",

issn = "0196-5204",

publisher = "SIAM PUBLICATIONS",

number = "6",

}

TY - JOUR

T1 - What is the covariance analog of the Paige and Saunders information filter

AU - Osborne, Michael R.

AU - PRVAN, T

PY - 1991/11

Y1 - 1991/11

N2 - In this paper a square root covariance form of the Kalman filter is presented which is in many ways the covariance analog of the Paige and Saunders information filter [SIAM J. Numer. Anal., 14 (1977), pp. 180-193] and possesses many of the advantages of their algorithm. For example, it is a true square root implementation; but the distinctive feature which it shares with the Paige and Saunders algorithm is a compact, convenient, and effective square root implementation of the interpolation smoother. The algorithm is based on the Duncan and Horne generalised least squares form of the filter equations [J. Amer. Statist. Assoc., 67 (1972), pp. 816-821], but uses these in a recursive manner.

AB - In this paper a square root covariance form of the Kalman filter is presented which is in many ways the covariance analog of the Paige and Saunders information filter [SIAM J. Numer. Anal., 14 (1977), pp. 180-193] and possesses many of the advantages of their algorithm. For example, it is a true square root implementation; but the distinctive feature which it shares with the Paige and Saunders algorithm is a compact, convenient, and effective square root implementation of the interpolation smoother. The algorithm is based on the Duncan and Horne generalised least squares form of the filter equations [J. Amer. Statist. Assoc., 67 (1972), pp. 816-821], but uses these in a recursive manner.

KW - KALMAN FILTER

KW - COVARIANCE FILTER

KW - INFORMATION FILTER

KW - SQUARE ROOT FILTER

KW - GENERALIZED LEAST SQUARES

KW - SMOOTHING STEP

KW - DISCRETE

M3 - Article

VL - 12

SP - 1324

EP - 1331

JO - Siam journal on scientific and statistical computing

JF - Siam journal on scientific and statistical computing

SN - 0196-5204

IS - 6

ER -