论文标题
使用功率力矩通过密度参数化的非高斯贝叶斯过滤
Non-Gaussian Bayesian Filtering by Density Parametrization Using Power Moments
论文作者
论文摘要
非高斯贝叶斯过滤是随机过滤的核心问题。问题的困难在于参数化状态估计值。但是，现有方法无法很好地对待它。我们建议使用功率力矩获得参数化。与现有的参数估计方法不同，我们提出的算法不需要有关估计状态的先验知识，例如模式的数量和可行的功能类别。此外，提出的算法在过滤过程中不需要存储大量参数作为现有的非参数贝叶斯过滤器，例如粒子过滤器。所提出的参数化的参数也可以通过矩形优化方案确定，并具有矩约束，该方案被证明存在并具有唯一。提供了存在和有限的密度估计的所有功率力矩的必要条件。分析了灯尾或重尾的密度估计值的功率力矩误差。提出了一步预测的密度估计的误差上限。给出了该状态不同类型的密度功能的仿真结果，包括重尾密度，以验证所提出的算法。
Non-Gaussian Bayesian filtering is a core problem in stochastic filtering. The difficulty of the problem lies in parameterizing the state estimates. However the existing methods are not able to treat it well. We propose to use power moments to obtain a parameterization. Unlike the existing parametric estimation methods, our proposed algorithm does not require prior knowledge about the state to be estimated, e.g. the number of modes and the feasible classes of function. Moreover, the proposed algorithm is not required to store massive parameters during filtering as the existing nonparametric Bayesian filters, e.g. the particle filter. The parameters of the proposed parametrization can also be determined by a convex optimization scheme with moments constraints, to which the solution is proved to exist and be unique. A necessary and sufficient condition for all the power moments of the density estimate to exist and be finite is provided. The errors of power moments are analyzed for the density estimate being either light-tailed or heavy-tailed. Error upper bounds of the density estimate for the one-step prediction are proposed. Simulation results on different types of density functions of the state are given, including the heavy-tailed densities, to validate the proposed algorithm.
