Greedy Sensor Selection

Greedy Sensor Selection: Leveraging Submodularity Based on Volume Ratio of Information Ellipsoid

Liu, Lingya (East China Normal University)
Hua, Cunqing (Shanghai Jiao Tong University)
Xu, Jing (East China Normal University)
Leus, G.J.T. (TU Delft Signal Processing Systems)
Wang, Yiyin (Shanghai Jiao Tong University)

2023

This article focuses on greedy approaches to select the most informative k sensors from N candidates to maximize the Fisher information, i.e., the determinant of the Fisher information matrix (FIM), which indicates the volume of the information ellipsoid (VIE) constructed by the FIM. However, it is a critical issue for conventional greedy approaches to quantify the Fisher information properly when the FIM of the selected subset is rank-deficient in the first (n-1) steps, where n is the problem dimension. In this work, we propose a new metric, i.e., the Fisher information intensity (FII), to quantify the Fisher information contained in the subset S with respect to that in the ground set N specifically in the subspace spanned by the vectors associated with S. Based on the FII, we propose to optimize the ratio between VIEs corresponding to S and N. This volume ratio is composed of a nonzero (i.e., the FII) and a zero part. Moreover, the volume ratio can be easily calculated based on a change of basis. A cost function is developed based on the volume ratio and proven monotone submodular. A greedy algorithm and its fast version are proposed accordingly to guarantee a near-optimal solution with a complexity of O Nkn-3 and O Nkn2, respectively. Numerical results demonstrate the superiority of the proposed algorithms under various measurement settings.

Greedy sensor selection
Fisher information intensity
change of basis
volume ratio
submodularity

http://resolver.tudelft.nl/uuid:e8b0d8a2-4c7e-42d4-9226-d33aaacbcc4e

https://doi.org/10.1109/TSP.2023.3283047

2023-12-21

1053-587X

IEEE Transactions on Signal Processing, 71, 2391-2406

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2023 Lingya Liu, Cunqing Hua, Jing Xu, G.J.T. Leus, Yiyin Wang