Sensor placement minimizing the state estimation mean square error: Performance guarantees of greedy solutions
Abstract
This paper studies selecting a subset of the system's output to minimize the state estimation mean square error (MSE). This results in the maximization problem of a set function defined on possible sensor selections subject to a cardinality constraint. We consider to solve it approximately by a greedy search. Since the MSE function is not submodular nor supermodular, the well-known performance guarantees for the greedy solutions do not hold in the present case. Thus, we use the quantities---the submodularity ratio and the curvature---to evaluate the degrees of submodularity and supermodularity of the objective function. By using the properties of the MSE function, we approximately compute these quantities and derive a performance guarantee for the greedy solutions. It is shown that the guarantee is less conservative than those in the existing results.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2020
- DOI:
- 10.48550/arXiv.2004.04355
- arXiv:
- arXiv:2004.04355
- Bibcode:
- 2020arXiv200404355K
- Keywords:
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- Electrical Engineering and Systems Science - Systems and Control;
- Mathematics - Optimization and Control