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The Intrinsic Geometry of Dynamic Observations

  • Arthur J. Krener
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 29)

Abstract

There are several ways to introduce geometry into the problem of estimating the state of nonlinear process given observations of it. We classify these as intrinsic or extrinsic. We show how the linearizability of this problem is related to the existence of an intrinsic Koszul connection on the output space and its curvature and torsion.

Keywords

Special Output Christoffel Symbol Intrinsic Geometry Dynamic Observation Observability Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Brockett, R.W. Remarks on finite dimensional nonlinear estimation. Asterique, 75–76 (1980) pp 47–55.Google Scholar
  2. [2]
    Krener, A.J. and W. Respondek, Nonlinear observers with linearizable error dynamics, to appear, SIAM J. Control and Optimization, 1985.Google Scholar
  3. [3]
    Marcus, S.I., Algebraic and geometric methods in nonlinear filtering, SIAM J. Control and Optimization 22 (1984) pp 817–844.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Spivak, M. A Comprehensive Introduction to Differential Geometry, V. II, Publish or Perish Press, Berkeley, 1979.Google Scholar

Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • Arthur J. Krener

There are no affiliations available

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