Brief paper: Derivative-free estimation methods: New results and performance analysis

  • Authors:

  • Miroslav Šimandl;Jindřich Duník

  • Affiliations:

  • Department of Cybernetics & Research Centre Data-Algorithms-Decision Making, Faculty of Applied Sciences, University of West Bohemia, Univerzitníí 8, 306 14 Pilsen, Czech Republic;Department of Cybernetics & Research Centre Data-Algorithms-Decision Making, Faculty of Applied Sciences, University of West Bohemia, Univerzitníí 8, 306 14 Pilsen, Czech Republic

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2009

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Abstract

The derivative-free nonlinear estimation methods exploiting the Stirling's interpolation and the unscented transformation for discrete-time nonlinear stochastic systems are treated. The divided difference and unscented filters, smoothers, and predictors based on the methods are introduced in the unified framework. The new relations among the first order Stirling's interpolation, the second order Stirling's interpolation, and the unscented transformation are derived and their impact on the covariance matrices of the state estimates of the corresponding filters is analysed. The theoretical results are illustrated and used for the explanation of the unexpected behaviour of the sigma point Gaussian sum filters given as a mixture of the derivative-free filters.