We present a new particle filtering algorithm for nonlinear systems in the discrete-time setting. Our algorithm is based on the Stein variational gradient descent (SVGD) framework, which is a general approach to sample from a target distribution. We merge the standard two-step paradigm in particle filtering into one step so that SVGD can be used. A distinguishing feature of the proposed algorithm is that, unlike most particle filtering methods, all the particles at any time step are equally weighted and thus no update on the weights is needed. We further extended our algorithm to allow for updating previous particles within a sliding window. This strategy may improve the reliability of the algorithm with respect to unexpected disturbance in the dynamics or outlier-measurements. The efficacy of the proposed algorithms is illustrated through several numerical examples in comparison with a standard particle filtering method.

翻译：我们为离散时间设置的非线性系统提出了一个新的粒子过滤算法。 我们的算法基于斯坦变异梯度下降框架(SVGD), 这是从目标分布中取样的一般方法。 我们将粒子过滤的标准两步范式合并为一步, 以便使用 SVGD 。 拟议算法的一个显著特征是, 与大多数粒子过滤方法不同, 所有粒子在任何阶段都同等加权, 因此不需要更新重量。 我们进一步扩展了我们的算法, 允许在滑动窗口中更新先前的粒子 。 这个策略可以提高算法在动态或外部测量中意外扰动的可靠性。 与标准的粒子过滤方法相比, 通过数字示例来说明拟议算法的有效性 。