Accurate estimation of the states of a nonlinear dynamical system is crucial for their design, synthesis, and analysis. Particle filters are estimators constructed by simulating trajectories from a sampling distribution and averaging them based on their importance weight. For particle filters to be computationally tractable, it must be feasible to simulate the trajectories by drawing from the sampling distribution. Simultaneously, these trajectories need to reflect the reality of the nonlinear dynamical system so that the resulting estimators are accurate. Thus, the crux of particle filters lies in designing sampling distributions that are both easy to sample from and lead to accurate estimators. In this work, we propose to learn the sampling distributions. We put forward four methods for learning sampling distributions from observed measurements. Three of the methods are parametric methods in which we learn the mean and covariance matrix of a multivariate Gaussian distribution; each methods exploits a different aspect of the data (generic, time structure, graph structure). The fourth method is a nonparametric alternative in which we directly learn a transform of a uniform random variable. All four methods are trained in an unsupervised manner by maximizing the likelihood that the states may have produced the observed measurements. Our computational experiments demonstrate that learned sampling distributions exhibit better performance than designed, minimum-degeneracy sampling distributions.
翻译:对非线性动态系统状态的准确估计对于其设计、合成和分析至关重要。粒子过滤器是通过模拟取样分布的轨迹和根据其重要性的重量进行平均平均的测算器。粒子过滤器的测算器,是模拟其轨迹的测算器。要使粒子过滤器能够进行计算,就必须通过从抽样分布中提取数据来模拟轨迹。同时,这些轨迹需要反映非线性动态系统的现实,从而使由此得出的估计器准确无误。因此,粒子过滤器的柱状在于设计取样分布,既易于取样,又可导致精确的估测器。在这项工作中,我们提议学习取样分布的原理。我们提出了从所观察到的测量中学习抽样分布的四种方法。三种方法是分辨方法,我们从中学习多变量分布的平均值和变量矩阵;每一种方法都利用数据的不同方面(基因、时间结构、图表结构)。第四种方法是非参数性的替代方法,我们直接学习了抽样分布方法,我们通过经过培训的四度模型进行最高级的计算方法,可以直接地展示我们所观测到的可变的模型。