In this paper, a novel methodology for state estimation of stochastic dynamical systems is proposed. In this formulation, finite-term Karhunen-Loève (KL) expansion is used to approximate the process noise, resulting in a nonautonomous deterministic approximation (with parametric uncertainty) of the original stochastic nonlinear system. It is proved that the solutions of the approximate dynamical system asymptotically converge to the true solutions in a mean-square sense. The evolution of uncertainty for the KL-approximated system is predicted via the Perron-Frobenius (PF) operator. Furthermore, a nonlinear estimation algorithm, using the proposed uncertainty propagation scheme, is developed. It is found that for finite-dimensional linear and nonlinear filters, the evolving posterior densities obtained from the KLPF-based estimator are closer than those obtained from the particle filter to the true posterior densities. The methodology is then applied to estimate states of a hypersonic reentry vehicle. It is observed that the KLPF-based estimator outperformed the particle filter in terms of capturing localization of uncertainty through posterior densities and reduction of uncertainty.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Nonlinear estimation with Perron-Frobenius operator and Karhunen-Loève expansion


    Contributors:


    Publication date :

    2015-10-01


    Size :

    1272229 byte




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English



    Hypersonic State Estimation Using the Frobenius-Perron Operator

    Dutta, Parikshit / Bhattacharya, Raktim | AIAA | 2011



    Karhunen-Loeve Expansion of Non-Gaussian Random Process

    Mulani, Sameer / Kapania, Rakesh / Walters, Robert | AIAA | 2007


    Efficient Sequential Karhunen-Loeve Basis Extraction

    Levy, A. / Lindenbaum, M. / IEEE | British Library Conference Proceedings | 2001


    Onboard Density Modeling for Planetary Entry via Karhunen-Loève Expansion

    Albert, Samuel W. / Doostan, Alireza / Schaub, Hanspeter | IEEE | 2023