Joint Doppler and Direction of Arrival (DoA) Based Underwater Localization with a Mobile Anchor

For underwater localization, mobile anchors are generally preferred because they are easy to deploy and retrieve, such as the autonomous underwater vehicle (AUV). However, a big disadvantage is that we can only install small sonar arrays on AUVs due to their limited size. This leads to poor angular domain resolution. On the other hand, the mobility makes it possible for us to capture multiple snapshots of the acoustic signals when the AUV is located at different positions, and synthesize a virtual array, i.e., the Doppler effect. In this case we can equivalently obtain a large virtual uniform planar array (UPA), which gives much higher spatial resolution and positioning accuracy. Mathematically, we have not only the DoA (Direction of Arrival) measurements, but also the Doppler shift measurements for positioning. In this paper, we propose a low-complexity algorithm to jointly estimate Doppler shift and DoA. Based on these estimates, we can obtain a series of nonlinear equations concerning the target's position. To solve these equations, a two-phase localization algorithm of linear computational complexity will be presented. We also derive Cramer-Ran lower bound (CRLB) of the system as a benchmark. The theoretical analysis will be verified through extensive simulations.