Covariance, subspace, and intrinsic Crame/spl acute/r-Rao bounds

@article{Smith2005CovarianceSA,
  title={Covariance, subspace, and intrinsic Crame/spl acute/r-Rao bounds},
  author={S. T. Smith},
  journal={IEEE Transactions on Signal Processing},
  year={2005},
  volume={53},
  pages={1610-1630}
}
  • S.T. Smith
  • Published 2005
  • Mathematics, Computer Science
  • IEEE Transactions on Signal Processing
  • Crame/spl acute/r-Rao bounds on estimation accuracy are established for estimation problems on arbitrary manifolds in which no set of intrinsic coordinates exists. The frequently encountered examples of estimating either an unknown subspace or a covariance matrix are examined in detail. The set of subspaces, called the Grassmann manifold, and the set of covariance (positive-definite Hermitian) matrices have no fixed coordinate system associated with them and do not possess a vector space… CONTINUE READING
    176 Citations
    Intrinsic Cramér–Rao Bounds for Scatter and Shape Matrices Estimation in CES Distributions
    • 9
    • PDF
    On Intrinsic Cramér-Rao Bounds for Riemannian Submanifolds and Quotient Manifolds
    • Nicolas Boumal
    • Mathematics, Computer Science
    • IEEE Transactions on Signal Processing
    • 2013
    • 28
    • PDF
    Riemannian Geometry and Cramér-rao Bound for Blind Separation of Gaussian Sources
    • 1
    Intrinsic Variance Lower Bound (IVLB) for Unbiased Estimators on Riemannian Manifolds. Part I: Theory
    • 1
    • Highly Influenced
    • PDF
    Cramér-Rao bounds for synchronization of rotations
    • 59
    • PDF
    N ov 2 01 2 Cramér-Rao bounds for synchronization of rotations
    • Highly Influenced
    • PDF
    Asymptotically efficient estimators for multidimensional harmonic retrieval based on the geometry of the Stiefel manifold
    An intrinsic Cramér-Rao bound on SO(3) for (dynamic) attitude filtering
    • S. Bonnabel, A. Barrau
    • Mathematics, Computer Science
    • 2015 54th IEEE Conference on Decision and Control (CDC)
    • 2015
    • 13
    • PDF
    A Note on the Intrinsic Cramer-Rao Bound
    • 7
    • PDF

    References

    SHOWING 1-10 OF 109 REFERENCES
    Intrinsic Cramer-Rao bounds and subspace estimation accuracy
    • S. Smith
    • Mathematics
    • Proceedings of the 2000 IEEE Sensor Array and Multichannel Signal Processing Workshop. SAM 2000 (Cat. No.00EX410)
    • 2000
    • 16
    Geometry of the Cramer-Rao bound
    • 68
    Hilbert-Schmidt Lower Bounds for Estimators on Matrix Lie Groups for ATR
    • 137
    • PDF
    A Bayesian approach to geometric subspace estimation
    • A. Srivastava
    • Mathematics, Computer Science
    • IEEE Trans. Signal Process.
    • 2000
    • 67
    • PDF
    Lower bounds for parametric estimation with constraints
    • 311
    Monte Carlo extrinsic estimators of manifold-valued parameters
    • 77
    • PDF
    Subspace tracking with full rank updates
    • S.T. Smith
    • Mathematics
    • Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136)
    • 1997
    • 8
    Cramer-Rao bounds for deterministic modal analysis
    • 62
    • PDF
    Geodesic lower bound for parametric estimation with constraints
    • J. Xavier, V. Barroso
    • Mathematics
    • IEEE 5th Workshop on Signal Processing Advances in Wireless Communications, 2004.
    • 2004
    • 2
    • PDF
    Optimal subspace-based parameter estimation
    • R. Vaccaro, Y. Ding
    • Mathematics, Computer Science
    • 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing
    • 1993
    • 5