Particle filters flexibly represent multiple posterior modes nonparametrically, via a collection of weighted samples, but have classically been applied to tracking problems with known dynamics and observation likelihoods. Such generative models may be inaccurate or unavailable for high-dimensional observations like images. We instead leverage training data to discriminatively learn particle-based representations of uncertainty in latent object states, conditioned on arbitrary observations via deep neural network encoders. While prior discriminative particle filters have used heuristic relaxations of discrete particle resampling, or biased learning by truncating gradients at resampling steps, we achieve unbiased and low-variance gradient estimates by representing posteriors as continuous mixture densities. Our theory and experiments expose dramatic failures of existing reparameterization-based estimators for mixture gradients, an issue we address via an importance-sampling gradient estimator. Unlike standard recurrent neural networks, our mixture density particle filter represents multimodal uncertainty in continuous latent states, improving accuracy and robustness. On a range of challenging tracking and robot localization problems, our approach achieves dramatic improvements in accuracy, while also showing much greater stability across multiple training runs.

翻译：粒子滤波器通过加权样本集合以非参数方式灵活表示多个后验模态，但经典上被应用于已知动力学和观测似然的跟踪问题。这类生成模型对于图像等高维观测可能不准确或不可用。我们转而利用训练数据，通过深度神经网络编码器以判别方式学习基于粒子的潜在目标状态不确定性表示，该表示以任意观测为条件。虽然先前的判别性粒子滤波器使用了离散粒子重采样的启发式松弛，或通过在重采样步骤截断梯度来引入有偏学习，但我们通过将后验表示为连续混合密度实现了无偏且低方差的梯度估计。我们的理论与实验揭示了现有基于重参数化的混合梯度估计器存在的严重缺陷，并通过重要性采样梯度估计器解决了该问题。与标准递归神经网络不同，我们的混合密度粒子滤波器表示连续潜在状态中的多模态不确定性，从而提高了准确性和鲁棒性。在具有挑战性的跟踪和机器人定位问题中，我们的方法在准确性上实现了显著提升，同时在多次训练运行中展现出更高的稳定性。