D-optimal sensor selection in the presence of correlated measurement noise
•A relaxation technique to sensor selection for ordinary least squares is proposed.•The problem is reduced to a sequence of convex optimum experimental design problems.•A simple technique to convert the relaxed solutions to sensor locations is exposed.•An example demonstrates that the method is high...
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| Vydané v: | Measurement : journal of the International Measurement Confederation Ročník 164; s. 107873 |
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| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier Ltd
01.11.2020
Elsevier Science Ltd |
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| ISSN: | 0263-2241, 1873-412X |
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| Abstract | •A relaxation technique to sensor selection for ordinary least squares is proposed.•The problem is reduced to a sequence of convex optimum experimental design problems.•A simple technique to convert the relaxed solutions to sensor locations is exposed.•An example demonstrates that the method is highly competitive with traditional ones.
A sensor selection technique is developed for maximizing the parameter estimation accuracy of spatiotemporal systems when the system in question is modeled by a partial differential equation and the measurement noise is correlated. Since the exact correlation structure may not be known exactly, the ordinary least squares method is supposed to be used for estimation and the determinant of the covariance matrix of the resulting estimator is the measure of estimation accuracy. To make the sensor selection computationally tractable, a relaxed formulation is considered. Owing to its nonconvexity, a majorization-minimization algorithm is employed. At each of its iterations, a convex tangent surrogate function that majorizes the original nonconvex design criterion is minimized using extremely efficient simplicial decomposition. As the resulting relaxed solution is a measure on the set of candidate measurements and not a specific subset of selected sensors, randomization and a restricted exchange algorithm are used to convert it to a nearly-optimal subset. A simulation experiment is reported to demonstrate that the proposed approach is highly competitive with the exchange algorithm which has been the only technique available so far. The generality of the proposed technique makes it suitable for other measurement selection problems for least-squares estimation subject to correlated observations. |
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| AbstractList | •A relaxation technique to sensor selection for ordinary least squares is proposed.•The problem is reduced to a sequence of convex optimum experimental design problems.•A simple technique to convert the relaxed solutions to sensor locations is exposed.•An example demonstrates that the method is highly competitive with traditional ones.
A sensor selection technique is developed for maximizing the parameter estimation accuracy of spatiotemporal systems when the system in question is modeled by a partial differential equation and the measurement noise is correlated. Since the exact correlation structure may not be known exactly, the ordinary least squares method is supposed to be used for estimation and the determinant of the covariance matrix of the resulting estimator is the measure of estimation accuracy. To make the sensor selection computationally tractable, a relaxed formulation is considered. Owing to its nonconvexity, a majorization-minimization algorithm is employed. At each of its iterations, a convex tangent surrogate function that majorizes the original nonconvex design criterion is minimized using extremely efficient simplicial decomposition. As the resulting relaxed solution is a measure on the set of candidate measurements and not a specific subset of selected sensors, randomization and a restricted exchange algorithm are used to convert it to a nearly-optimal subset. A simulation experiment is reported to demonstrate that the proposed approach is highly competitive with the exchange algorithm which has been the only technique available so far. The generality of the proposed technique makes it suitable for other measurement selection problems for least-squares estimation subject to correlated observations. A sensor selection technique is developed for maximizing the parameter estimation accuracy of spatiotemporal systems when the system in question is modeled by a partial differential equation and the measurement noise is correlated. Since the exact correlation structure may not be known exactly, the ordinary least squares method is supposed to be used for estimation and the determinant of the covariance matrix of the resulting estimator is the measure of estimation accuracy. To make the sensor selection computationally tractable, a relaxed formulation is considered. Owing to its nonconvexity, a majorization-minimization algorithm is employed. At each of its iterations, a convex tangent surrogate function that majorizes the original nonconvex design criterion is minimized using extremely efficient simplicial decomposition. As the resulting relaxed solution is a measure on the set of candidate measurements and not a specific subset of selected sensors, randomization and a restricted exchange algorithm are used to convert it to a nearly-optimal subset. A simulation experiment is reported to demonstrate that the proposed approach is highly competitive with the exchange algorithm which has been the only technique available so far. The generality of the proposed technique makes it suitable for other measurement selection problems for least-squares estimation subject to correlated observations. |
| ArticleNumber | 107873 |
| Author | Uciński, Dariusz |
| Author_xml | – sequence: 1 givenname: Dariusz surname: Uciński fullname: Uciński, Dariusz email: d.ucinski@issi.uz.zgora.pl organization: Institute of Control and Computation Engineering, University of Zielona Góra, ul. Szafrana 2, 65-516 Zielona Góra, Poland |
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| Snippet | •A relaxation technique to sensor selection for ordinary least squares is proposed.•The problem is reduced to a sequence of convex optimum experimental design... A sensor selection technique is developed for maximizing the parameter estimation accuracy of spatiotemporal systems when the system in question is modeled by... |
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| SubjectTerms | Accuracy Algorithms Computer simulation Correlated observations Correlation analysis Covariance matrix Estimating techniques Exchanging Least squares method Measurement Noise Noise measurement Optimization Ordinary least squares Parameter estimation Partial differential equations Sensor selection Sensors Studies |
| Title | D-optimal sensor selection in the presence of correlated measurement noise |
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