Optimum choice of moving sensor trajectories for distributed-parameter system identification

Rafajłowicz, Ewaryst

doi:10.1080/00207178608933550

Cited by 78 publications

(25 citation statements)

References 9 publications

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“…In the seminal article by Rafajłowicz (1986), the D-optimality criterion is considered and an optimal time-dependent measure is sought, rather than the trajectories themselves. On the other hand, in the works by 2000a;2000b) as well as Uciński and Korbicz (2001), apart from generalizations, some computational algorithms are developed based on the FIM.…”

Section: Problem Formulation In Terms Ofmentioning

confidence: 99%

“…A logical approach is to choose a measure related to the expected accuracy of the parameter estimates to be obtained from the data collected (note that the design is to be performed off-line, before taking any measurements). Such a measure is usually based on the concept of the Fisher Information Matrix (FIM), (Sun, 1994;Rafajłowicz, 1986), which is widely used in optimum experimental design theory for lumped systems (Walter and Pronzato, 1997;Fedorov and Hackl, 1997;Atkinson et al, 2007). When the time horizon is large, the nonlinearity of the model with respect to its parameters is mild and the measurement errors are independently distributed and have small magnitudes, the inverse of the FIM constitutes a good approximation of the covariance matrix for the estimate of θ (Walter and Pronzato, 1997;Fedorov and Hackl, 1997;Atkinson et al, 2007).…”

Section: Source Identification Proceduresmentioning

confidence: 99%

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Sensor network design for the estimation of spatially distributed processes

Uciński¹,

Patan²

2010

International Journal of Applied Mathematics and Computer Science

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In a typical moving contaminating source identification problem, after some type of biological or chemical contamination has occurred, there is a developing cloud of dangerous or toxic material. In order to detect and localize the contamination source, a sensor network can be used. Up to now, however, approaches aiming at guaranteeing a dense region coverage or satisfactory network connectivity have dominated this line of research and abstracted away from the mathematical description of the physical processes underlying the observed phenomena. The present work aims at bridging this gap and meeting the needs created in the context of the source identification problem. We assume that the paths of the moving sources are unknown, but they are sufficiently smooth to be approximated by combinations of given basis functions. This parametrization makes it possible to reduce the source detection and estimation problem to that of parameter identification. In order to estimate the source and medium parameters, the maximum-likelihood estimator is used. Based on a scalar measure of performance defined on the Fisher information matrix related to the unknown parameters, which is commonly used in optimum experimental design theory, the problem is formulated as an optimal control one. From a practical point of view, it is desirable to have the computations dynamic data driven, i.e., the current measurements from the mobile sensors must serve as a basis for the update of parameter estimates and these, in turn, can be used to correct the sensor movements. In the proposed research, an attempt will also be made at applying a nonlinear model-predictive-control-like approach to attack this issue.

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Section: Problem Formulation In Terms Ofmentioning

confidence: 99%

Section: Source Identification Proceduresmentioning

confidence: 99%

Sensor network design for the estimation of spatially distributed processes

Uciński¹,

Patan²

2010

International Journal of Applied Mathematics and Computer Science

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“…Using mobile sensor network nodes, we can expect the minimal value of an adopted design criterion to be lower than the one with no mobility. In the seminal article (Rafajłowicz, 1986), the D-optimality criterion defined on the Fisher Information Matrix (FIM) associated with the estimated parameters is considered and an optimal time-dependent measure is sought, rather than the trajectories themselves. In (Porat and Nehorai, 1996), a single moving concentration sensor is used to detect and localize a vapour-emitting source for a diffusion equation.…”

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confidence: 99%

Mobile Sensor Routing for Parameter Estimation of Distributed Systems Using the Parallel Tunneling Method

Zięba¹,

Uciński²

2008

International Journal of Applied Mathematics and Computer Science

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The paper deals with the problem of optimal path planning for a sensor network with mutliple mobile nodes, whose measurements are supposed to be primarily used to estimate unknown parameters of a system modelled by a partial differential equation. The adopted framework permits to consider two-or three-dimensional spatial domains and correlated observations. Since the aim is to maximize the accuracy of the estimates, a general functional defined on the relevant Fisher information matrix is used as the design criterion. Central to the approach is the parameterization of the sensor trajectories based on cubic B-splines. The resulting finite-dimensional global optimization problem is then solved using a parallel version of the tunneling algorithm. A numerical example is included to clearly demonstrate the idea presented in the paper.

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“…In his seminal article, Rafajłowicz (1986) considers the D-optimality criterion and seeks an optimal timedependent measure, rather than the trajectories themselves. On the other hand, 2000), apart from generalizations of Rafajłowicz's results, develops some computational algorithms based on the FIM.…”

mentioning

confidence: 99%

Sensor network scheduling for identification of spatially distributed processes

Uciński¹

2012

International Journal of Applied Mathematics and Computer Science

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The work treats the problem of fault detection for processes described by partial differential equations as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A simple node activation strategy is discussed for the design of a sensor network deployed in a spatial domain that is supposed to be used while detecting changes in the underlying parameters which govern the process evolution. The setting considered relates to a situation where from among a finite set of potential sensor locations only a subset of them can be selected because of the cost constraints. As a suitable performance measure, the Ds-optimality criterion defined on the Fisher information matrix for the estimated parameters is applied. The problem is then formulated as the determination of the density of gauged sites so as to maximize the adopted design criterion, subject to inequality constraints incorporating a maximum allowable sensor density in a given spatial domain. The search for the optimal solution is performed using a simplicial decomposition algorithm. The use of the proposed approach is illustrated by a numerical example involving sensor selection for a two-dimensional diffusion process.

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Optimum choice of moving sensor trajectories for distributed-parameter system identification

Cited by 78 publications

References 9 publications

Sensor network design for the estimation of spatially distributed processes

Sensor network design for the estimation of spatially distributed processes

Mobile Sensor Routing for Parameter Estimation of Distributed Systems Using the Parallel Tunneling Method

Sensor network scheduling for identification of spatially distributed processes

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