TY - GEN
T1 - Sensor placement minimizing the state estimation mean square error
T2 - 59th IEEE Conference on Decision and Control, CDC 2020
AU - Kohara, Akira
AU - Okano, Kunihisa
AU - Hirata, Kentaro
AU - Nakamura, Yukinori
N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Numbers 18K13778 and 20K14763.
Publisher Copyright:
© 2020 IEEE.
PY - 2020/12/14
Y1 - 2020/12/14
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85099882613&partnerID=8YFLogxK
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U2 - 10.1109/CDC42340.2020.9304166
DO - 10.1109/CDC42340.2020.9304166
M3 - Conference contribution
AN - SCOPUS:85099882613
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 1706
EP - 1711
BT - 2020 59th IEEE Conference on Decision and Control, CDC 2020
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 14 December 2020 through 18 December 2020
ER -