Underwater Moving Object Localization by TOA and FOA Modeled With Isogradient Sound Speed Profile

The complicated acoustic propagation environment poses a great challenge to underwater localization. In this article, we address the underwater moving object self-localization problem in position and velocity using the hybrid time-of-arrival (TOA) and frequency-of-arrival (FOA) measurements, having the variation in the propagation speed described by the isogradient sound speed profile model. We start by extending the isogradient sound speed profile (SSP) model developed for TOA to FOA that is suitable for localization. Next, we theoretically analyze the performance loss of the traditional TOA and FOA models that assume a constant sound speed observed at a single instant, and show the necessity of considering the sound speed variations. Then, we propose a three-step method to solve this challenging problem. The first step finds a coarse estimate of the object position using TOAs only. Using the coarse object position estimate, the second step formulates a constrained weighted least squares problem based on both TOAs and FOAs in order to refine the object position estimate while simultaneously estimating the object velocity. In the third step, we employ a linear weighted least squares estimator to jointly refine both the object position and velocity estimates. To assess the performance of the proposed method, the mean square error analysis is performed and it verifies that the proposed method can attain the Cramer–Rao lower bound accuracy in the presence of small Gaussian noise. The proposed method gives the expected performance in the simulations.