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Ab-initio Functional Decomposition of Kalman Filter: A Feasibility Analysis on Constrained Least Squares Problems

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Parallel Processing and Applied Mathematics (PPAM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12044))

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Abstract

The standard formulation of Kalman Filter (KF) becomes computationally intractable for solving large scale state space estimation problems as in ocean/weather forecasting due to matrix storage and inversion requirements. We introduce an innovative mathematical/numerical formulation of KF using Domain Decomposition (DD) approach. The proposed DD approach partitions ab-initio the whole KF computational method giving rise to local KF methods that can be solved independently. We present its feasibility analysis using the constrained least square model underlying variational Data Dssimilation problems. Results confirm that the accuracy of solutions of local KF methods are not impaired by DD approach.

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Notes

  1. 1.

    Let \(A\in \mathbb {R}^{n\times n}\), \(U\in \mathbb {R}^{n\times k}\), \(V\in \mathbb {R}^{k\times n}\), \(R\in \mathbb {R}^{k\times k}\) and \(B=A+URV\). Then, \(B^{-1}=A^{-1}-A^{-1}U(R+VA^{-1}U)^{-1}VA^{-1}\).

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Authors and Affiliations

  1. University of Naples Federico II, Naples, Italy

    Luisa D’Amore, Rosalba Cacciapuoti & Valeria Mele

Authors
  1. Luisa D’Amore
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  2. Rosalba Cacciapuoti
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  3. Valeria Mele
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Corresponding author

Correspondence to Luisa D’Amore .

Editor information

Editors and Affiliations

  1. Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Southern California, Marina del Rey, CA, USA

    Ewa Deelman

  3. University of Tennessee, Knoxville, TN, USA

    Jack Dongarra

  4. Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

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D’Amore, L., Cacciapuoti, R., Mele, V. (2020). Ab-initio Functional Decomposition of Kalman Filter: A Feasibility Analysis on Constrained Least Squares Problems. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2019. Lecture Notes in Computer Science(), vol 12044. Springer, Cham. https://doi.org/10.1007/978-3-030-43222-5_7

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  • DOI: https://doi.org/10.1007/978-3-030-43222-5_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-43221-8

  • Online ISBN: 978-3-030-43222-5

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