Adaptive Gaussian Mixture Models for Uncertainty Propagation and Stochastic Filtering

This is a novel method for accurate uncertainty propagation through a general nonlinear system. The basic idea of this approach is to approximate the state probability density function (pdf) by a weighted average of sufficient number of distinct local Gaussian density functions. In conventional methods, both the weights of the components and the number of components of a Gaussian mixture are kept constant while propagating the uncertainty through a nonlinear system and are updated only in the presence of measurement data. This strategy is valid if the underlying dynamics are close to linear. This is not the case for general nonlinear systems, and updated estimates of weights are required for accurate propagation of the state pdf. Two schemes are provided to update the weights corresponding to different components of Gaussian mixture models for accurate uncertainty propagation through both discrete-time and continuous-time nonlinear dynamical systems driven by noise. Furthermore, the number of Gaussian components is adapted during propagation using an iterative split-merge procedure which selects the mixand with the largest contribution to the uncertainty propagation error and splits it along the direction with most nonlinear dynamics.

  • G. Terejanu, P. Singla, T. Singh, and P. D. Scott, “Adaptive Gaussian Sum Filter for Nonlinear Bayesian Estimation,” Automatic Control, IEEE Transactions on, vol. 56, iss. 9, pp. 2151-2156, 2011. doi:10.1109/TAC.2011.2141550
    [BibTeX]
    @ARTICLE{TerejanuJ_TAC_2011,
    author= {Gabriel Terejanu and Puneet Singla and Tarunraj Singh and Peter D. Scott},
    journal = {{Automatic Control, IEEE Transactions on}},
    title = {{Adaptive Gaussian Sum Filter for Nonlinear Bayesian Estimation}},
    year= {2011},
    month= {Sept.},
    volume= {56},
    number= {9},
    pages= {2151-2156},
    doi= {10.1109/TAC.2011.2141550},
    ISSN= {0018-9286},
    }

  • G. Terejanu, P. Singla, T. Singh, and P. D. Scott, “Uncertainty Propagation for Nonlinear Dynamical Systems using Gaussian Mixture Models,” Journal of Guidance, Control, and Dynamics, vol. 31, iss. 6, pp. 1622-1633, 2008.
    [BibTeX]
    @ARTICLE{TerejanuJ_JGCD_2008,
    author = {Gabriel Terejanu and Puneet Singla and Tarunraj Singh and Peter D. Scott},
    title = {{Uncertainty Propagation for Nonlinear Dynamical Systems using Gaussian Mixture Models}},
    journal = {{Journal of Guidance, Control, and Dynamics}},
    year = {2008},
    month = {Nov.},
    volume = {31},
    number = {6},
    pages = {1622-1633},
    }

  • J. George, G. Terejanu, and P. Singla, “Spacecraft Attitude Estimation Using Adaptive Gaussian Sum Filter,” Journal of the Astronautical Sciences, Special Issue: Markley Symposium, vol. 57, iss. 1, pp. 31-45, 2009.
    [BibTeX]
    @ARTICLE{GeorgeJ_JAS_2009,
    author = {Jemin George and Gabriel Terejanu and Puneet Singla},
    title = {{Spacecraft Attitude Estimation Using Adaptive Gaussian Sum Filter}},
    journal = {{Journal of the Astronautical Sciences, Special Issue: Markley Symposium}},
    volume = {57},
    number = {1},
    year = {2009},
    pages = {31-45},
    }

  • G. Terejanu, P. Singla, T. Singh, and P. D. Scott, “Uncertainty Propagation for Nonlinear Dynamical Systems using Gaussian Mixture Models,” in AIAA Guidance, Navigation and Control Conference and Exhibit, Honolulu, Hawaii, 2008.
    [BibTeX]
    @CONFERENCE{TerejanuP_AIAA_2008,
    author = {Gabriel Terejanu and Puneet Singla and Tarunraj Singh and Peter D. Scott},
    title = {{Uncertainty Propagation for Nonlinear Dynamical Systems using Gaussian Mixture Models}},
    booktitle = {{AIAA Guidance, Navigation and Control Conference and Exhibit, Honolulu, Hawaii}},
    year = {2008},
    month = {August},
    note = {AIAA-2008-7472},
    }

  • G. Terejanu, P. Singla, T. Singh, and P. D. Scott, “A Novel Gaussian Sum Filter Method for Accurate Solution to Nonlinear Filtering Problem,” in 11th International Conference on Information Fusion, Cologne, Germany, 2008.
    [BibTeX]
    @CONFERENCE{TerejanuP_IF_2008,
    author = {Gabriel Terejanu and Puneet Singla and Tarunraj Singh and Peter D. Scott},
    title = {{A Novel Gaussian Sum Filter Method for Accurate Solution to Nonlinear Filtering Problem}},
    booktitle = {{11th International Conference on Information Fusion, Cologne, Germany}},
    year = {2008},
    month = {June},
    }