Fundamental Limits of Doppler Shift-Based, ToA-Based, and TDoA-Based Underwater Localization

Dear Editor, This paper is concerned with the underwater localization based on acoustic signals. Specifically, we will focus on the search of an underwater target that can constantly broadcast a beacon signal, such as a black box. Common measurements for localization are Doppler shift [1], time of arrival (ToA) [2]–[4], time difference of arrival (TDoA) [5], [6], angle of arrival (AoA) [7], etc. In this paper we will investigate the fundamental limits of Doppler shift-Based, ToA-Based, TDoA-based underwater localization. Note that AoA is not covered, because Doppler shift can be viewed as one type of AoA. The discussion will focus on short-baseline positioning with a mobile anchor, i.e., an autonomous underwater vehicle (AUV). Due to the large distance and the limited battery life of the AUV, the target is quite likely to lie outside the convex hull of the AUV's trajectory. In such cases, we will show that accurate localization is almost impossible by exclusively dependent on a single type of measurements. However, system performance will be significantly improved by combing Doppler shift with ToA or TDoA measurements. The reason for such improvement will be unveiled theoretically and numerically in this letter.