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Malicious anchor node is a serious issue in underwater sensor networks. This problem gets compounded under sparse deployment scenario. To overcome this issue, the authors present a <bold>C</bold>ompressed <bold>S</bold>ensing for <bold>M</bold>alicious node <bold>C</bold>ompensation theorem (abbreviated as CS-MC Theorem) which would be applicable to underwater localization. To counter malicious node behavior, CS-MC Theorem is justified through three lemmas. For underwater acoustic propagation, a specific L<sub>1</sub>-norm minimization method is derived. It describes the condition for unique localization of target by discretizing the target search space. Malicious node is identified by inserting the anchor nodes into the discretized grid. An insertion vector concept is introduced to determine the extent of node metastasis. Derivations are performed to prove the mathematical basis of the proposed algorithm under acoustically stratified and unstratified scenarios. Numerical results establish the feasibility of CS-MC algorithm for sparse underwater acoustic sensor network.

Evaluation of Node-Metastasis in Sparse Underwater Acoustic Sensor Networks for Localization Under Acoustically Stratified Malicious Node Conditions