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<p>The point mass filter (PMF) is a widely used strategy for solving the state estimation problem. In this filter, a deterministic grid of point particles is used to numerically solve the Bayesian recursive relations. Since the probability density function of the state is only approximated at the grid points, the placement of the grid is crucial for the performance of the filter. A new strategy, named the Silverman mass filter (SMF), has recently been developed, in which a Gaussian sum filter (GSF) update is performed before placing a new grid. In the SMF, the grid is placed at the mean of the GSF-updated points and is oriented and expanded to match their covariance. While the SMF has been shown to improve upon the standard PMF, the grid placement in the SMF can be inefficient for highly multimodal problems. This work introduces two new techniques for grid placement in the SMF: a clustering-based approach and an optimal deterministic sampling technique. These new techniques are shown to improve grid placement in the SMF when applied to a bimodal distribution example. Furthermore, the techniques are evaluated in three sequential filtering problems, including: the univariate nonstationary growth model, the Ikeda map, and a cislunar orbit determination example, where they show improved performance over the standard SMF by providing a more consistent and accurate state estimate.</p>

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Optimal Sampling for Point Mass Filtering with Applications to Cislunar Orbit Determination

  • 期刊论文

  • 发表日期：

    2025年9月3日

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  • Felipe Giraldo-Grueso,
  • Andrey A. Popov,
  • Uwe D. Hanebeck,
  • Renato Zanetti

摘要

The point mass filter (PMF) is a widely used strategy for solving the state estimation problem. In this filter, a deterministic grid of point particles is used to numerically solve the Bayesian recursive relations. Since the probability density function of the state is only approximated at the grid points, the placement of the grid is crucial for the performance of the filter. A new strategy, named the Silverman mass filter (SMF), has recently been developed, in which a Gaussian sum filter (GSF) update is performed before placing a new grid. In the SMF, the grid is placed at the mean of the GSF-updated points and is oriented and expanded to match their covariance. While the SMF has been shown to improve upon the standard PMF, the grid placement in the SMF can be inefficient for highly multimodal problems. This work introduces two new techniques for grid placement in the SMF: a clustering-based approach and an optimal deterministic sampling technique. These new techniques are shown to improve grid placement in the SMF when applied to a bimodal distribution example. Furthermore, the techniques are evaluated in three sequential filtering problems, including: the univariate nonstationary growth model, the Ikeda map, and a cislunar orbit determination example, where they show improved performance over the standard SMF by providing a more consistent and accurate state estimate.