How to train your differentiable filter

Abstract

In many robotic applications, it is crucial to maintain a belief about the state of a system, which serves as input for planning and decision making and provides feedback during task execution. Bayesian Filtering algorithms address this state estimation problem, but they require models of process dynamics and sensory observations and the respective noise characteristics of these models. Recently, multiple works have demonstrated that these models can be learned by end-to-end training through differentiable versions of recursive filtering algorithms. In this work, we investigate the advantages of differentiable filters (DFs) over both unstructured learning approaches and manually-tuned filtering algorithms, and provide practical guidance to researchers interested in applying such differentiable filters. For this, we implement DFs with four different underlying filtering algorithms and compare them in extensive experiments. Specifically, we (i) evaluate different implementation choices and training approaches, (ii) investigate how well complex models of uncertainty can be learned in DFs, (iii) evaluate the effect of end-to-end training through DFs and (iv) compare the DFs among each other and to unstructured LSTM models.

Differentiable Factor Graph Optimization for Learning Smoothers

“…This is particularly true for some of the richest, most information-dense sensing modalities, such as images, audio, or tactile feedback, as well as in interaction-rich applications that need to reason about difficult-to-model contact dynamics. These systems also tend to have more complex, heteroscedastic (variable) noise profiles [6]. For example, an object position estimate from an image might rapidly switch from being extremely precise under nominal operating conditions to completely useless under occlusion or poor lighting.…”

“…To retain the benefits of a probabilistic state estimator while circumventing the need for analytical models, a recent line of work has shown that we can treat Bayesian filters as a differentiable component of a computation graph [6][7][8][9][10]. These differentiable filters allow end-to-end estimation errors to be backpropagated directly through the structure of the estimator itself, enabling data-driven learning for system models and uncertainties that are optimized for a specific state estimation setting.…”

“…Each of these works demonstrate that the structure of a Bayesian filter can be used to improve the performance of a learned state estimator when compared to LSTM-based methods on visual robot localization tasks. In addition to EKFs and Particle filters, Kloss et al [6] analyses differentiable Unscented Kalman filters and the value of learning heteroscedastic noise models for both KITTI and a planar pushing task. Lee et al [10] explore differentiable filtering architectures for manipulation tasks involving both vision and touch.…”

“…In the first set of experiments, we study a synthetic visual tracking environment that has been used to evaluate differentiable filters [6,7]. This environment enables full control over the process noise and observation complexity of the underlying system.…”

Efficient Learning of the Parameters of Non-Linear Models using Differentiable Resampling in Particle Filters

“…In [25], they utilise conditional normalisation flows to construct flexible probability distributions for differentiable particle filters. A comparison of differentiable filters can be seen in [26]. The approach described in this paper differs from this body of previous work since we focus on ensuring resampling is differentiable without having to change how resampling operates.…”