Urban localization using robust filtering at multiple linearization points

We propose a robust Bayesian filtering framework for state and multi-modal uncertainty estimation in urban settings by fusing diverse sensor measurements. Our framework addresses multi-modal uncertainty from various error sources by tracking a separate probability distribution for linearization points corresponding to dynamics, measurements, and cost functions. Multiple parallel robust Extended Kalman filters (R-EKF) leverage these linearization points to characterize the state probability distribution. Employing Rao–Blackwellization, we combine the linearization point distribution with the state distribution, resulting in a unified, efficient, and outlier-resistant Bayesian filter that captures multi-modal uncertainty. Furthermore, we introduce a gradient descent-based optimization method to refine the filter parameters using available data. Evaluating our filter on real-world data from a multi-sensor setup comprising camera, Global Navigation Satellite System (GNSS), and Attitude and Heading Reference System (AHRS) demonstrates improved performance in bounding position errors based on uncertainty, while maintaining competitive accuracy and comparable computation to existing methods. Our results suggest that our framework is a promising direction for safe and reliable localization in urban environments.