Bio-Inspired Magnetic Navigation Using Gradient Descent With Rao-Blackwellized Particle Filtering

Accurate post-processing navigation is essential for applications such as survey and mapping, where the full measurement history can be exploited to refine past state estimates. Fixed-interval smoothing algorithms represent the theoretically optimal solution under Gaussian assumptions. However, loosely coupled INS/GNSS systems fundamentally inherit the systematic position bias of raw GNSS measurements, leaving a persistent accuracy gap that model-based smoothers cannot resolve. To address this limitation, we propose BLENDS, which integrates Bayesian learning with deep smoothing to enhance navigation performance. BLENDS is a a data-driven post-processing framework that augments the classical two-filter smoother with a transformer-based neural network. It learns to modify the filter covariance matrices and apply an additive correction to the smoothed error-state directly within the Bayesian framework. A novel Bayesian-consistent loss jointly supervises the smoothed mean and covariance, enforcing minimum-variance estimates while maintaining statistical consistency. BLENDS is evaluated on two real-world datasets spanning a mobile robot and a quadrotor. Across all unseen test trajectories, BLENDS achieves horizontal position improvements of up to 63% over the baseline forward EKF.

Airborne Magnetic Anomaly Navigation (MagNav) provides a jamming-resistant and robust alternative to satellite navigation but requires the real-time compensation of the aircraft platform's large and dynamic magnetic interference. State-of-the-art solutions often rely on extensive offline calibration flights or pre-training, creating a logistical barrier to operational deployment. We present a fully adaptive MagNav architecture featuring a "cold-start" capability that identifies and compensates for the aircraft's magnetic signature entirely in-flight. The proposed method utilizes an extended Kalman filter with an augmented state vector that simultaneously estimates the aircraft's kinematic states as well as the coefficients of the physics-based Tolles-Lawson calibration model and the parameters of a Neural Network to model aircraft interferences. The Kalman filter update is mathematically equivalent to an online Natural Gradient descent, integrating superior convergence and data efficiency of state-of-the-art second-order optimization directly into the navigation filter. To enhance operational robustness, the neural network is constrained to a residual learning role, modeling only the nonlinearities uncorrected by the explainable physics-based calibration baseline. Validated on the MagNav Challenge dataset, our framework effectively bounds inertial drift using a magnetometer-only feature set. The results demonstrate navigation accuracy comparable to state-of-the-art models trained offline, without requiring prior calibration flights or dedicated maneuvers.

Reliable return navigation remains an important challenge in GPS-denied environments where external positioning infrastructure may be unavailable or unreliable. This paper presents ForestBack, an infrastructure-free pedestrian return navigation framework based on breadcrumb-based pedestrian dead reckoning (PDR). The system records a user's walking route as a sequence of reversible breadcrumb nodes and generates reverse-path guidance without requiring GPS, Wi-Fi, Bluetooth beacons, or pre-installed infrastructure. ForestBack integrates acceleration-based step detection, adaptive step-length estimation, magnetometer-assisted heading estimation, barometric-altitude correction, and bidirectional breadcrumb path reconstruction. The system was evaluated using an indoor obstacle-avoidance route with five checkpoints, where the user navigated around a central obstacle. A dataset of 36 walking trials and 42,474 time-series samples was used for evaluation, including IMU signals, magnetometer readings, barometric variables, turn-event labels, ground-truth trajectories, baseline PDR outputs, proposed ForestBack outputs, and power-related measurements. Experimental results show that ForestBack reduced the mean RMSE from 1.129 m to 0.965 m compared with traditional PDR, corresponding to a 15.76% improvement. The mean final-position error was reduced from 1.781 m to 1.388 m, while turn-event detection consistency reached approximately 99.90%. These results indicate that ForestBack improves trajectory reconstruction and route-preserving return guidance in obstacle-avoidance scenarios. The released dataset and analysis notebook support reproducibility and future benchmarking of infrastructure-free PDR-based return navigation systems.