Journal
IEEE CONTROL SYSTEMS MAGAZINE
Volume 38, Issue 3, Pages 63-86Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/MCS.2018.2810460
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Funding
- Defense Advanced Research Projects Agency [DARPA HR0011-16-C-0016]
- Boeing Corporation [SSOW-BRT-W0714-0004]
- Air Force Research Labs [FA8651-16-1-0003]
- Air Force Office of Scientific Research [AFOSR FA9550-15-1-0385, AFOSR FA9550-18-1-0200]
- Army Research Office [ARO W911NF-17-1-0422]
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Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent compressibility enables sparse sensing. This article explores optimized sensor placement for signal reconstruction based on a tailored library of features extracted from training data. Sparse point sensors are discovered using the singular value decomposition and QR pivoting, which are two ubiquitous matrix computations that underpin modern linear dimensionality reduction. Sparse sensing on a tailored basis is contrasted with compressed sensing, a universal signal recovery method in which an unknown signal is reconstructed via a sparse representation on a universal basis. Although compressed sensing can recover a wider class of signals, we demonstrate the benefits of exploiting known patterns in data with optimized sensing. In particular, drastic reductions in the required number of sensors and improved reconstruction are observed in examples ranging from facial images to fluid vorticity fields. Principled sensor placement may be critically enabling when sensors are costly and provides faster state estimation for low-latency, high-bandwidth control.
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