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Triangular covariance factorizations forAn improved computational form of the discrete Kalman filter is derived using an upper triangular factorization of the error covariance matrix. The covariance P is factored such that P = UDUT where U is unit upper triangular and D is diagonal. Recursions are developed for propagating the U-D covariance factors together with the corresponding state estimate. The resulting algorithm, referred to as the U-D filter, combines the superior numerical precision of square root filtering techniques with an efficiency comparable to that of Kalman's original formula. Moreover, this method is easily implemented and involves no more computer storage than the Kalman algorithm. These characteristics make the U-D method an attractive realtime filtering technique. A new covariance error analysis technique is obtained from an extension of the U-D filter equations. This evaluation method is flexible and efficient and may provide significantly improved numerical results. Cost comparisons show that for a large class of problems the U-D evaluation algorithm is noticeably less expensive than conventional error analysis methods.
Document ID
19770005172
Document Type
Thesis/Dissertation
Authors
Thornton, C. L. (Jet Propulsion Lab., California Inst. of Tech. Pasadena, CA, United States)
Date Acquired
September 3, 2013
Publication Date
October 15, 1976
Subject Category
SPACE COMMUNICATIONS, SPACECRAFT COMMUNICATIONS, COMMAND AND TRACKING
Report/Patent Number
JPL-TM-33-798
NASA-CR-149147
Funding Number(s)
CONTRACT_GRANT: NAS7-100
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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