Ranging in an underwater medium with multiple isogradient sound speed profile layers.
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In this paper, we analyze the problem of acoustic ranging between sensor nodes in an underwater environment.The underwater medium is assumed to be composed of multiple isogradient sound speed profile (SSP) layers where in each layer the sound speed is linearly related to the depth.Furthermore, each sensor node is able to measure its depth and can exchange this information with other nodes.
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Affiliation: Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, The Netherlands. h.mashhadiramezani@tudelft.nl
ABSTRACT
In this paper, we analyze the problem of acoustic ranging between sensor nodes in an underwater environment. The underwater medium is assumed to be composed of multiple isogradient sound speed profile (SSP) layers where in each layer the sound speed is linearly related to the depth. Furthermore, each sensor node is able to measure its depth and can exchange this information with other nodes. Under these assumptions, we first show how the problem of underwater localization can be converted to the traditional range-based terrestrial localization problem when the depth information of the nodes is known a priori. Second, we relate the pair-wise time of flight (ToF) measurements between the nodes to their positions. Next, based on this relation, we propose a novel ranging algorithm for an underwater medium. The proposed ranging algorithm considers reflections from the seabed and sea surface. We will show that even without any reflections, the transmitted signal may travel through more than one path between two given nodes. The proposed algorithm analyzes them and selects the fastest one (first arrival path) based on the measured ToF and the nodes' depth measurements. Finally, in order to evaluate the performance of the proposed algorithm we run several simulations and compare the results with other existing algorithms. No MeSH data available. Related in: MedlinePlus |
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Mentions: In order to compute the partial derivative , we modify the environment in such a way that we can compute the horizontal distance as an integral w.r.t. depth. In order to achieve this, we have to convert the horizontal distance and the ToF to monotonic functions of the depth. Therefore, a ray can not have maximum or minimum points on its trajectory w.r.t. the depth. Let us illustrate the proposed idea with an example. Assume that a ray has a maximum point on its trajectory. The ray angle is zero at this maximum point, and after that it changes sign. But, this sign change does not affect Snell’s law, as it is related to the cosine of the ray angle. As a result, we can assume that the ray travels upward instead of downward as depicted in Figure 6, but in a new environment. In this new environment the SSP of each imaginary region must be changed accordingly. For instance, Figure 6 shows that the real SSP is flipped and translated in the first and second imaginary regions, respectively. In other words, the SSPs of the imaginary regions follow the behavior of the modified ray trajectory. |
View Article: PubMed Central - PubMed
Affiliation: Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, The Netherlands. h.mashhadiramezani@tudelft.nl
No MeSH data available.