Use of the Kalman filter for inference in state-space models with unknown noise distributions

@article{Maryak2004UseOT,
  title={Use of the Kalman filter for inference in state-space models with unknown noise distributions},
  author={J. L. Maryak and J. Spall and Bryan D. Heydon},
  journal={IEEE Transactions on Automatic Control},
  year={2004},
  volume={49},
  pages={87-90}
}
  • J. L. Maryak, J. Spall, Bryan D. Heydon
  • Published 2004
  • Mathematics, Computer Science
  • IEEE Transactions on Automatic Control
    • The Kalman filter is frequently used for state estimation in state-space models when the standard Gaussian noise assumption does not apply. A problem arises, however, in that inference based on the incorrect Gaussian assumption can lead to misleading or erroneous conclusions about the relationship of the Kalman filter estimate to the true (unknown) state. This note shows how inequalities from probability theory associated with the probabilities of convex sets have potential for characterizing… CONTINUE READING
    View on IEEE
    doi.org
    Top 3 of 39 Citations
    Kalman-like filtering with intermittent observations and non-Gaussian noise
    S. Battilotti, F. Cacace, … B. Sinopoli2019
    Bayesian Inference for Linear Dynamic Models With Dirichlet Process Mixtures
    F. Caron, M. Davy, … P. VanheegheIEEE Transactions on Signal Processing2008
    91
    Reduced-Order Quadratic Kalman-Like Filtering of Non-Gaussian Systems
    A. Fasano, A. Germani, A. MonteriùIEEE Trans. Autom. Control.2013
    11

    Figures and Topics from this paper.

    Figures

    Explore Further: Topics Discussed in This Paper

    39 Citations
    Citation Type

    Citation Type

    Kalman-like filtering with intermittent observations and non-Gaussian noise
    Bayesian Inference for Linear Dynamic Models With Dirichlet Process Mixtures
    • 91
    • PDF
    Reduced-Order Quadratic Kalman-Like Filtering of Non-Gaussian Systems
    • 11
    Adaptive High-degree Cubature Kalman Filter with Unknown Noise Statistics ?
    • 6
    Bayesian Inference for Dynamic Models with Dirichlet Process Mixtures
    • 40
    • PDF
    A Modified Kalman Filter for Non-gaussian Measurement Noise
    • 5
    Confidence Analysis of Linear Unbiased Estimates under Uncertain Unimodal Noise Distributions
    Robust planar tracking via a virtual measurement approach
    • 9
    Worst-Case Prediction Performance Analysis of the Kalman Filter
    • 4
    • PDF
    Robust Filtering Through Coherent Lower Previsions
    • 36
    • Highly Influenced
    • PDF

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 32 REFERENCES
    Use of the Kalman filter for inference in state-space models with unknown noise distributions
    • 22
    Use of the Kalman Filterfor Inference in State-Space Models with Unknown Noise Distributions
    • 3
    The Kantorovich inequality for error analysis of the Kalman filter with unknown noise distributions
    • J. Spall
    • Mathematics, Computer Science
    • 1995
    • 31
    Evaluation of convergence rate in the central limit theorem for the Kalman filter
    • 26
    Bayesian State Estimation for Tracking and Guidance Using the Bootstrap Filter
    • 165
    Uncertainties for recursive estimators in nonlinear state-space models, with applications to epidemiology
    • 14
    Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models
    • 2,274
    A three-state Kalman tracker using position and rate measurements
    • 23
    On Gibbs sampling for state space models
    • 1,920
    A Monte Carlo Approach to Nonnormal and Nonlinear State-Space Modeling
    • 585
    • PDF