D-optimal experimental design applied to a linear magnetostatic inverse problem

Bégot, Sylvie; Voisin, E.; Hiebel, P.; Artioukhine, E.; Kauffmann, J.M.

doi:10.1109/20.996273

Cited by 18 publications

(9 citation statements)

References 3 publications

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“…Thus a better estimation of the model parameters is likely to get [10]. On the other hand, the Uniformity design cannot keep the measurement point positions distributed evenly over the allowable region due to an affine transformation in equation (5) which transforms a regular region to a non-regular one, whereas the D-optimal design is insensitive to this transformation.…”

Section: Resultsmentioning

confidence: 99%

“…In our case, there are infinite candidates due to the continuous Euler angles space, so the above methods become impractical. A projected conjugate gradient algorithm was proposed in [10] to solve the D-optimal design. This method is useful in low dimensional problem but not feasible for our case, because the dimension of solutions composed by m data points is as high as 3m .…”

Section: B Computationsmentioning

confidence: 99%

See 1 more Smart Citation

D-Optimal Design Applied to Calibration of Strapdown Three-axis Magnetometer

Wu¹,

Hu²,

Wu³

et al. 2013

Proceedings of the 2nd International Conference on Computer Science and Electronics Engineering (ICCSEE 2013)

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Abstract-Strapdownthree-axis magnetometer needs calibration before it can be properly employed for navigation purposes. Many scalar calibration methods have been proposed to determine the calibration parameters. However, most calibration approaches seldom describe the influence of sampling distributions on the parameters estimation. As a result, some approaches lack robustness when measurement points are not well distributed. This paper presents the usage of D-optimal design to improve the accuracy and robustness of the solutions for magnetometer calibration problem. The basic idea is to choose the measurement point positions to build a Doptimal design, and then seek optimal solutions of the cost function of the D-optimal design problem by using the particle swarm optimization (PSO) algorithm. Numerical results which show the large improvement in the accuracy and robustness of the solutions are achieved.

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Section: Resultsmentioning

confidence: 99%

Section: B Computationsmentioning

confidence: 99%

D-Optimal Design Applied to Calibration of Strapdown Three-axis Magnetometer

Wu¹,

Hu²,

Wu³

et al. 2013

Proceedings of the 2nd International Conference on Computer Science and Electronics Engineering (ICCSEE 2013)

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show abstract

“…Joshi and Boyd (2009) studied sensor selection by means of convex optimization without a specific application in mind. Examples of electromagnetic applications include optimization of measurement setups for antenna measurements in the near-field (Nordebo and Gustafsson 2006), tracking of human tongue movements (Wang et al 2013), estimation of current densities in magnetic resonance imaging magnets (Begot et al 2002), and reconstruction of AC electric currents flowing in massive parallel conductors (Di Rienzo and Zhang 2010).…”

Section: Introductionmentioning

confidence: 99%

Convex optimization of measurement allocation for magnetic tracking systems

2016

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Magnetic tracking is a popular technique that exploits static and lowfrequency magnetic fields for positioning of quasi-stationary objects. One important system design aspect, which substantially influences the performance of the tracking system, is how to collect as much information as possible with a given number of measurements. In this work, we optimize the allocation of measurements given a large number of possible measurements of a generic magnetic tracking system that exploits time-division multiplexing. We exploit performance metrics based on the Fisher information matrix. In particular, the performance metrics measure worstcase or average performance in a measurement domain, i.e. the domain where the tracking is to be performed. An optimization problem with integer variables is formulated. By relaxing the constraint that the variables should be integer, a convex optimization problem is obtained. The two performance metrics are compared for several realistic measurement scenarios with planar transmitter constellations. The results show that the worst performance is obtained in the most distant parts of the measurement domain. Furthermore, measurement allocations optimized for worstcase performance require measurements in a larger area than measurement allocations optimized for average performance.

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“…In [14], a single moving sensor is used to localize a vapor emitting source by estimating the location of the source and minimizing its CR bound at each step. A recent example of D-optimal experiment design involves moving an EMI sensor to locate buried targets [15], and, in [16], D-optimal design is used for optimal sensor placement to solve an inverse problem.…”

Section: Introductionmentioning

confidence: 99%

Optimal Maneuvering of Seismic Sensors for Localization of Subsurface Targets

Alam

Cevher

McClellan

et al. 2007

IEEE Trans. Geosci. Remote Sensing

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Abstract-We consider the problem of detecting and locating subsurface objects by using a maneuvering array that receives scattered seismic surface waves. We demonstrate an adaptive system that moves an array of receivers according to an optimal positioning algorithm based on the theory of optimal experiments. The goal is to minimize the number of distinct measurements (array movements) needed to localize objects such as buried landmines. The adaptive localization algorithm has been tested using data collected in a laboratory facility. The performance of the algorithm is exhibited for cases with one or two targets, and in the presence of common types of clutter such as rocks in the soil. Results are also shown for a case where the propagation properties of the medium vary spatially. In these tests, the landmines were located using three or four array movements. It is envisioned that future systems could incorporate this new method into a portable mobile mine-location system.

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D-optimal experimental design applied to a linear magnetostatic inverse problem

Cited by 18 publications

References 3 publications

D-Optimal Design Applied to Calibration of Strapdown Three-axis Magnetometer

D-Optimal Design Applied to Calibration of Strapdown Three-axis Magnetometer

Convex optimization of measurement allocation for magnetic tracking systems

Optimal Maneuvering of Seismic Sensors for Localization of Subsurface Targets

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