A Sparse Sensor Placement Strategy Based on Information Entropy and Data Reconstruction for Ocean Monitoring

Sparse sensor placement strategies are applied to reconstruct a region's full-state data conditioned to a limited number of sensors; particularly, crucial to ocean monitoring systems. In maritime systems, existing sparse sensor placement methods mainly consider the reconstruction error of data or rely on specific requirements. Considering how sensors acquire essential information for monitoring systems, the utilization of entropy from information theory becomes quite interesting. In this article, we show that entropy measurements on different quantities of information are sensitive to indicate the border areas, thus requiring a balance between the number of sensors needed and the amount of information collected by them in coastal areas. Due to such, we propose: 1) a novel sparse sensor placement strategy based on entropy, where the entropy measurements in temporal dimension are utilized for sample selection, so portions of samples selected are utilized for training data, significantly improving the training efficiency without sacrificing accuracy of subsequent data reconstruction. In the proposed strategy, 2) we use orthogonal triangle decomposition from linear algebra where a low-cost sensor is employed as pivot and in terms of spatial dimension, the entropy of each location is adopted as entropy weight to reconstruct full state data. Additionally, 3) the strategy employs a greedy algorithm of weighted column pivoting for the orthogonal triangle decomposition, which is designed to suit yet effectively seek additional information and minimal reconstruction error in each iteration processing step. Experimental results using sea surface temperature (SST) data show that the proposed strategy outperforms existing methods, acquiring more information, ensuring higher efficiency, and reducing costs while minimizing reconstruction errors.