cs.ROOct 16, 2026
SaveBio-Inspired Magnetic Navigation Using Gradient Descent With Rao-Blackwellized Particle Filtering
Organizations: Univ. Grenoble Alpes, CEA, Leti, 38000 Grenoble, France · Univ. Grenoble Alpes, CNRS, ISTerre, 38000 Grenoble, France
Abstract
Navigation in GPS-denied environments is commonly based on magnetic maps, which are used to correct trajectory drift and enable relocalization. However, such navigation systems suffer from a strong dependence on magnetic maps that are complex, heavy, and costly to construct. Bio-inspired magnetic navigation (BIMN) does not rely on magnetic maps, making it simpler and more frugal. In this paper, we present a gradient descent BIMN method based on the Rao-Blackwellized particle filter (RBPF) for local gradient estimation. We show that magnetic navigation can be performed without magnetic maps, as gradient descent naturally attracts the system toward the destination, resulting in a simple and memory-efficient approach.
Figures & tables
Fig. 1: Illustration of BIMN. An agent navigates toward a destination defined by target magnetic parameters (e.g., magnetic field intensity, inclination, and declination of the Earth’s magnetic field). The agent has no global magnetic map and relies only on locally measured or extracted magnetic parameters, which are compared with the target values to infer the direction of movement.
Fig. 2: In the (north, east, nadir) reference frame, the inclination ( ) is the angle between the magnetic field vector and its horizontal projection . The declination ( ) is the angle between and north.
Fig. 3: Global Mercator projection of geomagnetic inclination and declination derived from the IGRF-14 model at sea level on 1 January 2025. The experimental area is shown in gray and represented in a two-dimensional Cartesian coordinate system. The goal is to navigate from the start point ( , ), corresponding to km, to the destination ( , ), corresponding to km. The destination is chosen because it has unique magnetic parameters within the experimental area, and no map information is available to the agent; only the magnetic parameters of the destination and the currently measured magnetic parameters are known. The navigation frame is centered at the starting position, with the -axis pointing east and the -axis pointing north.
Fig. 4: The navigation paths of both methods show that the proposed method is attracted to the destination, whereas the baseline method diverges.
Fig. 5: This figure shows the estimated gradient with respect to the true gradient, along with the uncertainty region corresponding to one standard deviation. Uncertainty decreases approximately along the direction of motion. This can be seen clearly in the two abrupt changes in uncertainty, which correspond to changes in direction approximately along and then . The -axis is expressed in , and the -axis (not shown) represents time.
Fig. 6: Variation of the objective function for the two methods. The proposed method exhibits a monotonic decrease due to gradient descent, whereas the baseline method does not, particularly near the end of the trajectory where the initial gradient no longer matches the local gradient.
Fig. 7: For the RBPF method, the error between the estimated and true positions reaches a maximum of at the end of the trajectory, for a traveled distance of more than .
Fig. 8: The figure shows the evolution of the estimated gradient and the true gradient in the presence of noise and drift. The uncertainty matches the observation noise level . Toward the end, the true gradient approaches zero, making it difficult to observe given this level of noise.
Fig. 9: The figure shows the distribution of particles at different time steps. For clarity, the distribution is zoomed in by a factor of 5/3. The particles remain around the true position and form a local, weighted map of possible positions. The evolution of the distribution suggests a unimodal behavior, in which centrally located particles carry higher weights than those at the periphery, indicating that an EKF may adequately capture this evolution. We also note that no particle resampling occurred during this experiment with , which means that more than half of the particles remain effective.
Fig. 10: The figure clearly shows the attenuation of drift when using the estimated gradient for localization in the proposed method. We can see that the error sometimes increases and then decreases; for example, around 120 h, accurate relocalization is achieved (approximately 10 km). For the RBPF, drift is observed toward the end, likely due to poor gradient estimation as the system approaches the destination (see Fig. 8 ). This indicates that the proposed method provides relocalization in addition to guiding the system toward the destination. In contrast, when the commands are blindly integrated, the drift increases linearly and exceeds 500 km.
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