Discrete Square Root Filtering: A Survey of Current Techniques. Kaminski, P. G.; Bryson, A. E.; and Schmidt, S. F. Volume 16 .
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The conventional Kalman approach to discrete filtering involves propagation of a state estimate and an error covariance matrix from stage to stage. Alternate recursive relationships have been developed to propagate a state estimate and a square root error covariance instead. Although equivalent algebraically to the conventional approach, the square root filters exhibit improved numerical characteristics, particularly in ill-conditioned problems. In this paper, current techniques in square root filtering are surveyed and related by applying a duality association. Four efficient square root implementations are suggested, and compared with three common conventional implementations in terms of computational complexity and precision. The square root computational burden should not exceed the conventional by more than 50 percent in most practical problems. An examination of numerical conditioning predicts that the square root approach can yield twice the effective precision of the conventional filter in ill-conditioned problems. This prediction is verified in two examples. The excellent numerical characteristics and reasonable computation requirements of the square root approach make it a viable alternative to the conventional filter in many applications, particularly when computer word length is limited, or the estimation problem is badly conditioned.
@book{kaminskiDiscreteSquareRoot1971,
  title = {Discrete {{Square Root Filtering}}: {{A Survey}} of {{Current Techniques}}},
  volume = {16},
  isbn = {0018-9286 VO - 16},
  abstract = {The conventional Kalman approach to discrete filtering involves propagation of a state estimate and an error covariance matrix from stage to stage. Alternate recursive relationships have been developed to propagate a state estimate and a square root error covariance instead. Although equivalent algebraically to the conventional approach, the square root filters exhibit improved numerical characteristics, particularly in ill-conditioned problems. In this paper, current techniques in square root filtering are surveyed and related by applying a duality association. Four efficient square root implementations are suggested, and compared with three common conventional implementations in terms of computational complexity and precision. The square root computational burden should not exceed the conventional by more than 50 percent in most practical problems. An examination of numerical conditioning predicts that the square root approach can yield twice the effective precision of the conventional filter in ill-conditioned problems. This prediction is verified in two examples. The excellent numerical characteristics and reasonable computation requirements of the square root approach make it a viable alternative to the conventional filter in many applications, particularly when computer word length is limited, or the estimation problem is badly conditioned.},
  pagetotal = {727–736},
  number = {6},
  date = {1971},
  author = {Kaminski, Paul G. and Bryson, Arthur E. and Schmidt, Stanley F.},
  file = {/home/dimitri/Nextcloud/Zotero/storage/IPTEI89Z/Kaminski, Bryson, Schmidt - 1971 - Discrete Square Root Filtering A Survey of Current Techniques.pdf},
  doi = {10.1109/TAC.1971.1099816}
}
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