Abstract
Underwater acoustic localization is a useful technique applied to any military and civilian applications. Among the range-based underwater acoustic localization methods, the time difference of arrival (TDOA) has received much attention because it is easy to implement and relatively less affected by the underwater environment. This paper proposes a TDOA-based localization algorithm for an underwater acoustic sensor network using the maximum-likelihood (ML) ratio criterion. To relax the complexity of the proposed localization complexity, we construct an auxiliary function, and use the majorization-minimization (MM) algorithm to solve it. The proposed localization algorithm proposed in this paper is called a T-MM algorithm. T-MM is applying the MM algorithm to the TDOA acoustic-localization technique. As the MM algorithm iterations are sensitive to the initial points, a gradient-based initial point algorithm is used to set the initial points of the T-MM scheme. The proposed T-MM localization scheme is evaluated based on squared position error bound (SPEB), and through calculation, we get the SPEB expression by the equivalent Fisher information matrix (EFIM). The simulation results show how the proposed T-MM algorithm has better performance and outperforms the state-of-the-art localization algorithms in terms of accuracy and computation complexity even under a high presence of underwater noise.
Highlights
Underwater acoustic sensor networks (UASNs) is a network composed of underwater sensor nodes randomly distributed in a certain observation area and uses underwater acoustic signals to communicate with each other
Using the time difference of arrival (TDOA) acoustic-localization, the proposed algorithm in this paper is capable to estimate the location of the sensors only by using the measured time difference between the signals arrived at different sensors it is not affected by power loss and Doppler shift, and it does not need accurate time synchronization
Rn indicates an n-dimensional real space; upper bold-face letters stand for matrices and lower bold-face letters stand for vectors; k ∗ k denotes the Euclidean distance norm of vectors ∗; ∇ f indicates the gradient of function f ; E[] denotes the expectation operator; superscript T denotes the transpose of a matrix; tr(∗) denotes the trace of a square matrix ∗; [∗]n×n is the upper left n × n submatrix of matrix ∗; ∗−1 denotes the inverse of the matrix ∗; rank(∗) indicates rank of matrix ∗
Summary
Underwater acoustic sensor networks (UASNs) is a network composed of underwater sensor nodes randomly distributed in a certain observation area and uses underwater acoustic signals to communicate with each other. Using the TDOA acoustic-localization, the proposed algorithm in this paper is capable to estimate the location of the sensors only by using the measured time difference between the signals arrived at different sensors it is not affected by power loss and Doppler shift, and it does not need accurate time synchronization. Due to all these features, the TDOA is more fitted for underwater acoustic-based localization. Rn indicates an n-dimensional real space; upper bold-face letters stand for matrices and lower bold-face letters stand for vectors; k ∗ k denotes the Euclidean distance norm of vectors ∗; ∇ f indicates the gradient of function f ; E[] denotes the expectation operator; superscript T denotes the transpose of a matrix (vector); tr(∗) denotes the trace of a square matrix ∗; [∗]n×n is the upper left n × n submatrix of matrix ∗; ∗−1 denotes the inverse of the matrix ∗; rank(∗) indicates rank of matrix ∗
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