arXiv:2610.23097v1 Announce Type: new 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.