Approximate conditional-mean type smoothers and interpolators

  • R. Douglas Martin
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 757)


A class of robust smoother and interpolator algorithms is introduced. The motivation for these smoothers and interpolators is a theorem concerning approximate conditional-mean smoothers for vector Markov processes in additive non-Gaussian noise. This theorem is the smoothing analog of Masreliez’s approximate non-Gaussian filter theorem (IEEE-Auto. Control, AC-20, 1975). The theorem presented here relies on the assumption that a certain conditional density is Gaussian, just as does Masreliez’s result. This assumption will rarely, if ever, be satisfied exactly. Thus a continuity theorem is also presented which lends support to the intuitive notion that the conditional density in question will be nearly Gaussian in a strong sense when the additive noise is nearly Gaussian in a comparatively weak sense. Approaches for implementing the robust smoothers and interpolators is discussed and an application to a real data set is presented.


Conditional Density Observation Noise Gaussian Assumption Residual Process Prediction Density 
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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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • R. Douglas Martin
    • 2
    • 1
  1. 1.Department of Electrical EngineeringUniversity of Washington, SeattleWashington
  2. 2.Bell LaboratoriesMurray Hill

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