H-RINS: Hierarchical Tightly-coupled Radar-Inertial Navigation via Smoothing and Mapping

Millimeter-wave radar provides robust perception in visually degraded environments. However, radar-inertial state estimation is inherently susceptible to drift. Because radar yields only sparse, body-frame velocity measurements, it provides weak constraints on absolute orientation. Consequently, IMU biases remain poorly observable over the short time horizons typical of sliding-window filters. To address this fundamental observability challenge, we propose a tightly coupled, hierarchical radar-inertial factor graph framework. Our architecture decouples the estimation problem into a high-rate resetting graph and a persistent global graph. The resetting graph fuses IMU preintegration, radar velocities, and adaptive Zero-Velocity Updates (ZUPT) to generate the smooth, low-latency odometry required for real-time control. Concurrently, the persistent graph is a full-state factor graph maintaining the complete information of poses, velocities, and biases by fusing inertial data with keyframe-based geometric mapping and loop closures. Leveraging Incremental Smoothing and Mapping, the persistent graph can operate without explicit marginalization of variables, preserving their information while ensuring long-term bias observability. The cornerstone of our approach is a probabilistic tight-coupling mechanism: fully observable, optimized biases and their exact covariances are continuously injected from the persistent graph into the resetting graph's prior, effectively anchoring the high-rate estimator against integration drift. Extensive evaluations demonstrate our system achieves high accuracy with drift-reduced estimation at 27x real-time execution speeds. We release the implementation code and datasets upon the acceptance of the paper.