Discrete Square Root Filtering: A Survey of Current Techniques

IEEE Transactions on Automatic Control

Volumn 16, Issue 6, 1971, Pages 727-736

  Kaminski, Paul G ^a   Bryson, Arthur E ^b   Schmidt, Stanley F ^c  

^a USAF   (United States)

^b STANFORD UNIVERSITY   (United States)

^c Analttical Mechanics Associates Inc ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FILTERING AND PREDICTION; KALMAN FILTERS; NUMERICAL METHODS; SQUARE ROOT FILTERING;

AUTOMATIC CONTROL--OPTIMIZATION;

EID: 0015207267     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/TAC.1971.1099816     Document Type: Note

References (17)

1. R.E. Kalman, “A new approach to linear filtering and prediction problems.” Trans. ASME vol. 82D, PP. 35–50, 1960.
2. R.H. Battin; Astronautical Guidance. “New York: McGraw-Hill 1964. pp. 338–339.
3. R.B. Battin and G.M. Levine, “Application of Kalman filtering techniques in the Apollo program,” in Theory and Applications of Kalman. Filtering, NATO Advisory Group for Aerospace Research and Development, AGARDograph 139, Feb. 1970.
4. D.-C. Fraser, “A new technique for the optimal smoothing of data,” M.I.T. Instrumentation Lab., Rep. T-474, Jan. 1967, p. 114.
5. V.N. Fadeeva- Computational Methods of Linear Algebra. New York: Dover, 1959, PP. 81–84.
6. S.F. Schmidt, “Computational techniques in Kalman filtering in Theory and Applications of Kalman. Filtering, NATO Advisory Group for Aerospace Research and Development, AGARDograph-ograph 139 Feb. 1970.
7. A.-S. Householder, The Theory of Matrices in Numerical Analysis. Waltham, Mass.: 1964, ch. 5.
8. J.F. Bellantoni and K. W. Dodge, “A square root formulation of the Kalman-Schmidt filter,” AIAA J., voL 5, pp. 1309–1314, Julv 1967.
9. A. -Andrews, “A square root formulation of the Kalman covariance equations,” AIAA J., vol. 6, pp. 1165–1166, June 1968.
10. A. Bjorek, “Solving linear least squares problems by Gram-Schmidt orthogonalization,” BIT, vol. 7, pp. 1–21, 1967.
11. G.H. Golub, “Numerical methods for solving linear least squares problems,” Numer, Mom., vol. 7, pp. 206–216, 1965.
12. P.- Businger and G.H. Golub, “Linear least squares solution by Householder transformations,” Numer. Math. vol. 7, pp. 269–276. 1965.
13. T. Jordan, “Experiments on error growth associated with some linear least square procedures Math. Comput. vol. 20,- pp. 325–328 1966.
14. R.J. Hanson and C.L. Lawson, “Extensions and applications of the Householder algorithm for solving linear least squares problems,” Math. Comput., vol. 23, pp. 787–812, Oct. 1969.
15. H.C. Cox, “Estimation of state variables via dynamic programming in Proc. 1964 Joint Automatic Control Conf., pp. 376–381.
16. P. Dyer and S. McReynolds “Extension of square-root filtering to include process noise,” J. Optimiz. Theory Appl., vol. 3, no. 6. PP. 444–459. 1969.
17. P. G. Kaminski, “Square root filtering and smoothing for discrete processes,” Ph.D. dissertation, Dep. Aeronaut. Astro-naut., Stanford Univ., Stanford, Calif., Sept. 1971.