This work develops a TAN algorithm that relies on basic motion sensors and bathymetric observations obtained by low-power sonars (e.g. a single-beam sounder or a downward-facing ADCP while in bottom -tracking regime) and is sufficiently robust to deal with low resolution bathymetric maps. The state estimation process is performed by utilising the Rao-Blackwellised particle filter (RBPF). To make the navigation filter computationally feasible while using low-power processing boards with limited computational resources, the filter estimates the 2D vehicle's position and the 2D speed of the local water currents. Therefore, the proposed navigation solution can enable AUV deployments in remote deep oceans of the order of months, rather than hours or days, without the need for external support or regular surfacing.