Particle Filter for Underwater Terrain Navigation

In an earlier contribution we proposed a particle filter for underwater (UW) navigation, and applied it to an experimental trajectory. Here we focus on performance improvements and analysis. First, the Cramér Rao lower bound (CRLB) along the experimental trajectory is computed, which is only slightly lower than the particle filter estimate after initial transients. Simple rule of thumbs for how performance depends on the map and sensor quality are derived. Second, a more realistic five state model is proposed, and Rao-Blackwellization is applied to decrease computational complexity. Monte-Carlo simulations on the map demonstrate a performance comparable to the CRLB. 1. THE NAVIGATION SYSTEM In [2], we applied the particle filter on the following model for an underwater (UW) vessel. Model I. Position model where xt ∈ R is the horizontal position state vector. xt+1 = xt + ut + wt, (1a) yt = h(xt) + et. (1b) Here yt is the measured depth, ut is the INS corrections and wt the process noise due to drift. We assumed that the velocity vector ut is measured or that, for instance, rudder angle and propeller speed can be converted to a velocity vector. We will here re-visit the Cramér-Rao lower bound (CRLB) calculations in [2], and apply it to an experimental trajectory and map from [2, 9]. A more realistic model, often used in aircraft traffic control, is based on the co-ordinated turn assumption (CT). Model II. CT-model with Cartesian position (x, y), orientation (φ) and yaw rate (ω) and velocity (v) as state variables