An underwater localization scheme for sparse sensing acoustic positioning in stratified and perturbed UASNs

There is a dearth of compressed-sensing localization in the domain of underwater acoustic sensor networks (UASNs). To address this limitation, this paper proposes SAP2: a Sparse-sensing Acoustic Positioning scheme for Stratified and Perturbed UASNs. Three conditions of underwater perturbation are defined, namely, Spin perturbation, Rectilinear dispersion condition, and Radially perturbed condition to model the sudden disturbances in the underwater network topology. Then, “Footprint Variation” is proposed to express the behavior of UASN node topology. Theorem 2.2.b is proposed for the exact retrieval of sparsely deployed UASN location under perturbation conditions. The derivation of a unique solution to the insertion vector in Lemma 3.1.a holds the estimated location of target, necessitating the incoherence of the sensing matrix with the basis vector. Block matrix representation of the coefficients is derived in Lemma 3.1.b. Invertibility of the block matrix is proven in Lemma 3.1.c to establish sparsity of underwater sensor networks. An example is illustrated with a realistic scenario to observe parameters such as correlation of sparse coefficients, distinctness of discretized samples and footprint variation based on perturbation. Footprint variation is found to be below 100m2 for uncorrelated discrete measurements using SAP2 technique. Through rigorous mathematical justification and realistic underwater channel scenario, it is established that compressed sensing based underwater localization is feasible for a sparse sensor network.