Electromagnetic source localization in shallow waters using Bayesian matched-field inversion

Abstract

The propagation of an electromagnetic signal in a marine environment cannot be modelled as a plane wave due to the high attenuation in seawater and the interactions with the ocean boundaries. Consequently, conventional beamforming techniques are not applicable for electromagnetic source localization. In this work, the Bayesian approach to matched-field processing is used to localize an electromagnetic source and estimate the environmental parameters. In this formulation, the solution to the inverse problem is given by the a posteriori probability distribution calculated here using the Gibbs sampling method. Bayesian inversion theory provides the formalism for estimating parameters, their uncertainties and verification of the estimates convergence. Two situations were investigated for the case where the single frequency measurements represent the magnitudes of two orthogonal horizontal electric field components: (1) all environmental parameters known and (2) unknown seabed conductivity. The objective function that relates the array data to the propagation model and environment parameters was chosen for the practical situation considered.

Magnetometer Modeling and Validation for Tracking Metallic Targets

“…Consequently, (22) is linear in B 0 and C, which includes 3 + 9 = 12 parameters, and is nonlinear in the remaining 3 parameter v 0 , r CPA and t CPA , in total 15 parameters. Both t CPA and r CPA are related to the parameters in (20) in the following way: The traveled distance between t = 0 and t = t CPA is equal to the projection of −r 0 onto v 0 , see Fig. 3.…”

“…In [20] a Bayesian match-field approach has been used, which takes the attenuation of the seawater into consideration.…”

Silent Localization of Underwater Sensors Using Magnetometers

“…For target tracking in shallow waters, magnetometers are often a more useful sensor than acoustics, since sound scatters significantly in these environments [12]. Birsan has explored the use of magnetometers and the magnetic dipole of a vessel for target tracking [13,14].…”

“…Several studies of the electromagnetic characteristics of the maritime environment have stated that the permeability of the seabed differs considerably from the permeability of air or water. The environment should therefore be modeled as a horizontally stratified model with site specific permeability and layer thickness for each segment [12,15,16]. This has not been included in our simulation study but should be considered in field experiments.…”

Magnetometers for tracking metallic targets

“…Tracking and estimation were performed using an unscented Kalman filter [3] and an unscented particle filter [4]. Furthermore, several studies have been done exploring the use of underwater magnetometers for tracking of vessels [5,6,7], where [7] has used the dipole model not only for localizing the vessel, but also for estimating the positions of the sensors. In [6] a Bayesian match-field approach has been used, which takes the attenuation of the seawater into consideration.…”