Algorithm 675: Fortran subroutines for computing the square root covariance filter and square root information filter in dense or Hessenberg forms

ABSTRACT

In this paper, codes are provided for two of the most popular square root filters: the Square Root Covariance Filter and the Square Root Information Filter. We also give efficient implementations for the time invariant case based on so-called condensed forms. All routines make extensive use of BLAS routines.

REFERENCES

• 1: ANDERSON, B. D. O., AND MOORZ, J.B. Optimal Filtering. Prentice-Hall, Englewood Cliffs, N.J., 1979.
• 2: BIERMAN, G. J. Factorization Methods for Discrete Sequential Estimation. Academic Press, Orlando, Fla., 1977.
• 3: DONGARRA, J. J., BUNCH, J. R., MOLER, C. B., AND STEWART, G.W. LINPACK Users's Guide, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1979.
• 4: Jack J. Dongarra , Jeremy Du Croz , Sven Hammarling , Richard J. Hanson, An extended set of FORTRAN basic linear algebra subprograms, ACM Transactions on Mathematical Software (TOMS), v.14 n.1, p.1-17, March 1988 [doi>10.1145/42288.42291]
• 5: C. L. Lawson , R. J. Hanson , F. T. Krogh , D. R. Kincaid, Algorithm 539: Basic Linear Algebra Subprograms for Fortran Usage [F1], ACM Transactions on Mathematical Software (TOMS), v.5 n.3, p.324-325, Sept. 1979 [doi>10.1145/355841.355848]
• 6: PAIGE, C. C. Covariance matrix representation in linear filtering, in the Special Issue of Contemporary Mathematics in Linear Algebra and its Role in Systems Theory. American Mathematical Society, Providence, R.I., 1985.
• 7: VAN DOOREN, P., AND VERHAEGEN, M. On the use of unitary state-space transformations. In the Special Issue of Contemporary Mathematics in Linear Algebra and its Role in Systems Theory. American Mathematical Society, Providence, R.I., 1985.
• 8: Paul van Dooren , Michel Verhaegen, Condensed forms for efficient time-invariant Kalman filtering, SIAM Journal on Scientific and Statistical Computing, v.9 n.3, p.516-530, May 1988 [doi>10.1137/0909034]

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Algorithm design and analysis

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on matrices

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Linear systems (direct and iterative methods)

General Terms:
Algorithms, Measurement