Accurate state and uncertainty estimation is imperative for mobile robots and self driving vehicles to achieve safe navigation in pedestrian rich environments. A critical component of state and uncertainty estimation for robot navigation is to perform robustly under out-of-distribution noise. Traditional methods of state estimation decouple perception and state estimation making it difficult to operate on noisy, high dimensional data. Here, we describe an approach that combines the expressiveness of deep neural networks with principled approaches to uncertainty estimation found in recursive filters. We particularly focus on techniques that provide better robustness to out-of-distribution noise and demonstrate applicability of our approach on two scenarios: a simple noisy pendulum state estimation problem and real world pedestrian localization using the nuScenes dataset. We show that our approach improves state and uncertainty estimation compared to baselines while achieving approximately 3x improvement in computational efficiency.