In many robotic applications, it is crucial to maintain a belief about the state of 
 a system, like the location of a robot or the pose of an object.
 These state estimates serve as input for planning and decision making and 
 provide feedback during task execution. 
 Recursive Bayesian Filtering algorithms address the state estimation problem,
 but they require a model of the process dynamics and the sensory observations as well as 
 noise estimates that quantify the accuracy of these models. 
 Recently, multiple works have demonstrated that the process and sensor models can be 
 learned by end-to-end training through differentiable versions of Recursive Filtering methods.
 However, even if the predictive models are known, finding suitable noise models 
 remains challenging. Therefore, many practical applications rely on very simplistic noise 
 models. 
 Our hypothesis is that end-to-end training through differentiable Bayesian 
 Filters enables us to learn more complex heteroscedastic noise models for
 the system dynamics. We evaluate learning such models with different types of 
 filtering algorithms and on two different robotic tasks. Our experiments show that especially 
 for sampling-based filters like the Particle Filter, learning heteroscedastic noise 
 models can drastically improve the tracking performance in comparison to using 
 constant noise models.
We evaluate learning heteroscedastic noise models within different Differentiable Bayes Filters Proposes to learn heteroscedastic noise models from data by optimizing the prediction likelihood end-toend through differentiable Bayesian Filters and two different versions of the Unscented Kalman Filter Revisits Bayes filters and evaluates the benefit of training the observation and process noise models while keeping all other models fixed This paper presents a method to learn and use state and observation dependent noise in traditional Bayesian filtering algorithms. The approach consists of constructing a neural network model which takes as input the raw observation data and produces a compact representation and an associated diagonal covariance.