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An Optimal Scanning Sensor Activation Policy for Parameter Estimation of Distributed Systems

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Model Based Parameter Estimation

Part of the book series: Contributions in Mathematical and Computational Sciences ((CMCS,volume 4))

Abstract

A technique is proposed to solve an optimal node activation problem in sensor networks whose measurements are supposed to be used to estimate unknown parameters of the underlying process model in the form of a partial differential equation. Given a partition of the observation horizon into a finite number of consecutive intervals, the problem is set up to select nodes which will be active over each interval while the others will remain dormant such that the log-determinant of the resulting Fisher information matrix associated with the estimated parameters is maximized. The search for the optimal solution is performed using the branch-and-bound method in which an extremely simple and efficient technique is employed to produce an upper bound to the maximum objective function. Its idea consists in solving a relaxed problem through the application of a simplicial decomposition algorithm in which the restricted master problem is solved using a multiplicative algorithm for D-optimal design. The performance evaluation of the technique is additionally presented by means of simulations.

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References

  1. Amouroux, M., Babary, J.P.: Sensor and control location problems. In: M.G. Singh (ed.) Systems & Control Encyclopedia. Theory, Technology, Applications, vol. 6, pp. 4238–4245. Pergamon Press, Oxford (1988)

    Google Scholar 

  2. Armstrong, M.: Basic Linear Geostatistics. Springer-Verlag, Berlin (1998)

    Book  MATH  Google Scholar 

  3. Atkinson, A.C., Donev, A.N., Tobias, R.D.: Optimum Experimental Designs, with SAS. Oxford University Press, Oxford (2007)

    MATH  Google Scholar 

  4. Banks, H.T., Kunisch, K.: Estimation Techniques for Distributed Parameter Systems. Systems & Control: Foundations & Applications. Birkhäuser, Boston (1989)

    Google Scholar 

  5. Banks, H.T., Smith, R.C., Wang, Y.: Smart Material Structures: Modeling, Estimation and Control. Research in Applied Mathematics. Masson, Paris (1996)

    MATH  Google Scholar 

  6. Bensoussan, A., Da Prato, G., Delfour, M.C., Mitter, S.K.: Representation and Control of Infinite Dimensional Systems, 2nd edn. Birkhäuser, Boston (2007)

    MATH  Google Scholar 

  7. Bertsekas, D.P.: Nonlinear Programming, 2nd edn. Optimization and Computation Series. Athena Scientific, Belmont, MA (1999)

    MATH  Google Scholar 

  8. Boer, E.P.J., Hendrix, E.M.T., Rasch, D.A.M.K.: Optimization of monitoring networks for estimation of the semivariance function. In: A.C. Atkinson, P. Hackl, W. Müller (eds.) mODa 6, Proc. 6th Int. Workshop on Model-Oriented Data Analysis, Puchberg/Schneeberg, Austria, 2001, pp. 21–28. Physica-Verlag, Heidelberg (2001)

    Google Scholar 

  9. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)

    MATH  Google Scholar 

  10. Cassandras, C.G., Li, W.: Sensor networks and cooperative control. European Journal of Control 11(4–5), 436–463 (2005)

    Article  MathSciNet  Google Scholar 

  11. Chong, C.Y., Kumar, S.P.: Sensor networks: Evolution, opportunities, and challenges. Proceedings of the IEEE 91(8), 1247–1256 (2003)

    Article  Google Scholar 

  12. Christofides, P.D.: Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes. Systems & Control: Foundations & Applications. Birkhäuser, Boston (2001)

    Google Scholar 

  13. Cook, D., Fedorov, V.: Constrained optimization of experimental design. Statistics 26, 129–178 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  14. Cressie, N.A.C.: Statistics for Spatial Data, revised edn. John Wiley & Sons, New York (1993)

    Google Scholar 

  15. Culler, D., Estrin, D., Srivastava, M.: Overview of sensor networks. IEEE Computer 37(8), 41–49 (2004)

    Article  Google Scholar 

  16. Curtain, R.F., Zwart, H.: An Introduction to Infinite-Dimensional Linear Systems Theory. Texts in Applied Mathematics. Springer-Verlag, New York (1995)

    Book  MATH  Google Scholar 

  17. Daescu, D.N., Navon, I.M.: Adaptive observations in the context of 4D-Var data assimilation. Meteorology and Atmospheric Physics 85, 205–226 (2004)

    Article  Google Scholar 

  18. Demetriou, M.A.: Detection and containment policy of moving source in 2D diffusion processes using sensor/actuator network. In: Proceedings of the European Control Conference 2007, Kos, Greece, July 2–5 (2006). Published on CD-ROM

    Google Scholar 

  19. Demetriou, M.A.: Power management of sensor networks for detection of a moving source in 2-D spatial domains. In: Proceedings of the 2006 American Control Conference, Minneapolis, MN, June 14–16 (2006). Published on CD-ROM

    Google Scholar 

  20. Demetriou, M.A.: Process estimation and moving source detection in 2-D diffusion processes by scheduling of sensor networks. In: Proceedings of the 2007 American Control Conference, New York City, USA, July 11–13 (2007). Published on CD-ROM

    Google Scholar 

  21. Demetriou, M.A.: Natural consensus filters for second order infinite dimensional systems. Systems & Control Letters 58(12), 826–833 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. Demetriou, M.A., Hussein, I.I.: Estimation of spatially distributed processes using mobile spatially distributed sensor network. SIAM Journal on Control and Optimization 48(1), 266–291 (2009). DOI 10. 1137/060677884

    Article  MathSciNet  MATH  Google Scholar 

  23. Fedorov, V.V.: Optimal design with bounded density: Optimization algorithms of the exchange type. Journal of Statistical Planning and Inference 22, 1–13 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  24. Fedorov, V.V., Hackl, P.: Model-Oriented Design of Experiments. Lecture Notes in Statistics. Springer-Verlag, New York (1997)

    Book  MATH  Google Scholar 

  25. Floudas, C.A.: Mixed integer nonlinear programming, MINLP. In: C.A. Floudas, P.M. Pardalos (eds.) Encyclopedia of Optimization, vol. 3, pp. 401–414. Kluwer Academic Publishers, Dordrecht, The Netherlands (2001)

    Chapter  Google Scholar 

  26. Gerdts, M.: Solving mixed-integer optimal control problems by branch&bound: A case study from automobile test-driving with gear shift. Journal of Optimization Theory and Applications 26, 1–18 (2005)

    MathSciNet  Google Scholar 

  27. Gevers, M.: Identification for control: From the early achievements to the revival of experiment design. European Journal of Control 11(4–5), 335–352 (2005)

    Article  MathSciNet  Google Scholar 

  28. Goodwin, G.C., Payne, R.L.: Dynamic System Identification. Experiment Design and Data Analysis. Mathematics in Science and Engineering. Academic Press, New York (1977)

    MATH  Google Scholar 

  29. Hearn, D.W., Lawphongpanich, S., Ventura, J.A.: Finiteness in restricted simplicial decomposition. Operations Research Letters 4(3), 125–130 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  30. Hearn, D.W., Lawphongpanich, S., Ventura, J.A.: Restricted simplicial decomposition: Computation and extensions. Mathematical Programming Study 31, 99–118 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  31. Hjalmarsson, H.: From experiment design to closed-loop control. Automatica 41, 393–438 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  32. von Hohenbalken, B.: Simplicial decomposition in nonlinear programming algorithms. Mathematical Programming 13, 49–68 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  33. Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge, UK (1986)

    Google Scholar 

  34. Hussein, I.I., Demetriou, M.A.: Estimation of distributed processes using mobile spatially distributed sensors. In: Proceedings of the 2007 American Control Conference, New York, USA, July 11–13 (2007). Published on CD-ROM

    Google Scholar 

  35. Jain, N., Agrawal, D.P.: Current trends in wireless sensor network design. International Journal of Distributed Sensor Networks 1, 101–122 (2005)

    Article  Google Scholar 

  36. Jeremić, A., Nehorai, A.: Design of chemical sensor arrays for monitoring disposal sites on the ocean floor. IEEE Transactions on Oceanic Engineering 23(4), 334–343 (1998)

    Article  Google Scholar 

  37. Jeremić, A., Nehorai, A.: Landmine detection and localization using chemical sensor array processing. IEEE Transactions on Signal Processing 48(5), 1295–1305 (2000)

    Article  Google Scholar 

  38. Kammer, D.C.: Sensor placement for on-orbit modal identification and correlation of large space structures. In: Proc. American Control Conf., San Diego, California, 23–25 May 1990, vol. 3, pp. 2984–2990 (1990)

    Google Scholar 

  39. Kammer, D.C.: Effects of noise on sensor placement for on-orbit modal identification of large space structures. Transactions of the ASME 114, 436–443 (1992)

    Google Scholar 

  40. Kincaid, R.K., Padula, S.L.: D-optimal designs for sensor and actuator locations. Computers & Operations Research 29, 701–713 (2002)

    Article  MATH  Google Scholar 

  41. Kubrusly, C.S., Malebranche, H.: Sensors and controllers location in distributed systems — A survey. Automatica 21(2), 117–128 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  42. Lam, R.L.H., Welch, W.J., Young, S.S.: Uniform coverage designs for molecule selection. Technometrics 44(2), 99–109 (2002)

    Article  MathSciNet  Google Scholar 

  43. Lange, K.: Numerical Analysis for Statisticians. Springer-Verlag, New York (1999)

    MATH  Google Scholar 

  44. Lasiecka, I., Triggiani, R.: Control Theory for Partial Differential Equations: Continuous and Approximation Theories, Encyclopedia of Mathematics and Its Applications, vol. I and II. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  45. Le, N.D., Zidek, J.V.: Statistical Analysis of Environmental Space-Time Processes. Springer-Verlag, New York (2006)

    MATH  Google Scholar 

  46. Liu, C.Q., Ding, Y., Chen, Y.: Optimal coordinate sensor placements for estimating mean and variance components of variation sources. IEE Transactions 37, 877–889 (2005)

    Article  Google Scholar 

  47. Ljung, L.: System Identification: Theory for the User, 2nd edn. Prentice Hall, Upper Saddle River, NJ (1999)

    Google Scholar 

  48. Meyer, R.K., Nachtsheim, C.J.: The coordinate-exchange algorithm for constructing exact optimal experimental designs. Technometrics 37(1), 60–69 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  49. Müller, W.G.: Collecting Spatial Data. Optimum Design of Experiments for Random Fields, 2nd revised edn. Contributions to Statistics. Physica-Verlag, Heidelberg (2001)

    Google Scholar 

  50. Munack, A.: Optimal sensor allocation for identification of unknown parameters in a bubble-column loop bioreactor. In: A.V. Balakrishnan, M. Thoma (eds.) Analysis and Optimization of Systems, Part 2, Lecture Notes in Control and Information Sciences, volume 63, pp. 415–433. Springer-Verlag, Berlin (1984)

    Google Scholar 

  51. Navon, I.M.: Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography. Dynamics of Atmospheres and Oceans 27, 55–79 (1997)

    Article  Google Scholar 

  52. Nehorai, A., Porat, B., Paldi, E.: Detection and localization of vapor-emitting sources. IEEE Transactions on Signal Processing 43(1), 243–253 (1995)

    Article  Google Scholar 

  53. Nychka, D., Piegorsch, W.W., Cox, L.H. (eds.): Case Studies in Environmental Statistics. Lecture Notes in Statistics, volume 132. Springer-Verlag, New York (1998)

    Google Scholar 

  54. Nychka, D., Saltzman, N.: Design of air-quality monitoring networks. In: D. Nychka, W.W. Piegorsch, L.H. Cox (eds.) Case Studies in Environmental Statistics, Lecture Notes in Statistics, volume 132, pp. 51–76. Springer-Verlag, New York (1998)

    Chapter  Google Scholar 

  55. Ögren, P., Fiorelli, E., Leonard, N.E.: Cooperative control of mobile sensor networks: Adaptive gradient climbing in a distributed environment. IEEE Transactions on Automatic Control 49(8), 1292–1302 (2004)

    Article  Google Scholar 

  56. Omatu, S., Seinfeld, J.H.: Distributed Parameter Systems: Theory and Applications. Oxford Mathematical Monographs. Oxford University Press, New York (1989)

    MATH  Google Scholar 

  57. Patan, M.: Optimal activation policies for continous scanning observations in parameter estimation of distributed systems. International Journal of Systems Science 37(11), 763–775 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  58. Patan, M., Patan, K.: Optimal observation strategies for model-based fault detection in distributed systems. International Journal of Control 78(18), 1497–1510 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  59. Patriksson, M.: Simplicial decomposition algorithms. In: C.A. Floudas, P.M. Pardalos (eds.) Encyclopedia of Optimization, vol. 5, pp. 205–212. Kluwer Academic Publishers, Dordrecht, The Netherlands (2001)

    Google Scholar 

  60. Pázman, A.: Foundations of Optimum Experimental Design. Mathematics and Its Applications. D. Reidel Publishing Company, Dordrecht, The Netherlands (1986)

    MATH  Google Scholar 

  61. Point, N., Vande Wouwer, A., Remy, M.: Practical issues in distributed parameter estimation: Gradient computation and optimal experiment design. Control Engineering Practice 4(11), 1553–1562 (1996)

    Article  Google Scholar 

  62. Porat, B., Nehorai, A.: Localizing vapor-emitting sources by moving sensors. IEEE Transactions on Signal Processing 44(4), 1018–1021 (1996)

    Article  Google Scholar 

  63. Pronzato, L.: Removing non-optimal support points in D-optimum design algorithms. Statistics & Probability Letters 63, 223–228 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  64. Pukelsheim, F.: Optimal Design of Experiments. Probability and Mathematical Statistics. John Wiley & Sons, New York (1993)

    MATH  Google Scholar 

  65. Quereshi, Z.H., Ng, T.S., Goodwin, G.C.: Optimum experimental design for identification of distributed parameter systems. International Journal of Control 31(1), 21–29 (1980)

    Article  MathSciNet  Google Scholar 

  66. Rafajłowicz, E.: Design of experiments for eigenvalue identification in distributed-parameter systems. International Journal of Control 34(6), 1079–1094 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  67. Rafajłowicz, E.: Optimal experiment design for identification of linear distributed-parameter systems: Frequency domain approach. IEEE Transactions on Automatic Control 28(7), 806–808 (1983)

    Article  MATH  Google Scholar 

  68. Rafajłowicz, E.: Optimum choice of moving sensor trajectories for distributed parameter system identification. International Journal of Control 43(5), 1441–1451 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  69. Reinefeld, A.: Heuristic search. In: C.A. Floudas, P.M. Pardalos (eds.) Encyclopedia of Optimization, vol. 2, pp. 409–411. Kluwer Academic Publishers, Dordrecht, The Netherlands (2001)

    Google Scholar 

  70. Russell, S.J., Norvig, P.: Artificial Intelligence: A Modern Approach, 2nd edn. Pearson Education International, Upper Saddle River, NJ (2003)

    Google Scholar 

  71. Silvey, S.D., Titterington, D.M., Torsney, B.: An algorithm for optimal designs on a finite design space. Communications in Statistics — Theory and Methods 14, 1379–1389 (1978)

    Google Scholar 

  72. Sinopoli, B., Sharp, C., Schenato, L., Schaffert, S., Sastry, S.S.: Distributed control applications within sensor networks. Proceedings of the IEEE 91(8), 1235–1246 (2003)

    Article  Google Scholar 

  73. Song, Z., Chen, Y., Sastry, C.R., Tas, N.C.: Optimal Observation for Cyber-physical Systems: A Fisher-information-matrix-based Approach. Springer-Verlag, London (2009)

    Book  MATH  Google Scholar 

  74. Sun, N.Z.: Inverse Problems in Groundwater Modeling. Theory and Applications of Transport in Porous Media. Kluwer Academic Publishers, Dordrecht, The Netherlands (1994)

    Google Scholar 

  75. Titterington, D.M.: Aspects of optimal design in dynamic systems. Technometrics 22(3), 287–299 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  76. Torsney, B.: Computing optimising distributions with applications in design, estimation and image processing. In: Y. Dodge, V.V. Fedorov, H.P. Wynn (eds.) Optimal Design and Analysis of Experiments, pp. 316–370. Elsevier, Amsterdam (1988)

    Google Scholar 

  77. Torsney, B., Mandal, S.: Construction of constrained optimal designs. In: A. Atkinson, B. Bogacka, A. Zhigljavsky (eds.) Optimum Design 2000, chap. 14, pp. 141–152. Kluwer Academic Publishers, Dordrecht, The Netherlands (2001)

    Chapter  Google Scholar 

  78. Torsney, B., Mandal, S.: Multiplicative algorithms for constructing optimizing distributions: Further developments. In: A. Di Bucchianico, H. Läuter, H.P. Wynn (eds.) mODa 7, Proc. 7th Int. Workshop on Model-Oriented Data Analysis, Heeze, The Netherlands, 2004, pp. 163–171. Physica-Verlag, Heidelberg (2004)

    Google Scholar 

  79. Uciński, D.: Measurement Optimization for Parameter Estimation in Distributed Systems. Technical University Press, Zielona Góra (1999)

    Google Scholar 

  80. Uciński, D.: Optimal sensor location for parameter estimation of distributed processes. International Journal of Control 73(13), 1235–1248 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  81. Uciński, D.: Optimal Measurement Methods for Distributed-Parameter System Identification. CRC Press, Boca Raton, FL (2005)

    MATH  Google Scholar 

  82. Uciński, D.: D-optimum sensor activity scheduling for distributed parameter systems. In: Preprints of the 15th IFAC Symposium on System Identification, Saint-Malo, France, July 6–8, (2009). Published on CD-ROM

    Google Scholar 

  83. Uciński, D., Atkinson, A.C.: Experimental design for time-dependent models with correlated observations. Studies in Nonlinear Dynamics & Econometrics 8(2) (2004). Article No. 13

    Google Scholar 

  84. Uciński, D., Bogacka, B.: T-optimum designs for discrimination between two multivariate dynamic models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 67, 3–18 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  85. Uciński, D., Bogacka, B.: A constrained optimum experimental design problem for model discrimination with a continuously varying factor. Journal of Statistical Planning and Inference 137(12), 4048–4065 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  86. Uciński, D., Chen, Y.: Time-optimal path planning of moving sensors for parameter estimation of distributed systems. In: Proc. 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville, Spain (2005). Published on CD-ROM

    Google Scholar 

  87. Uciński, D., Chen, Y.: Sensor motion planning in distributed parameter systems using Turing’s measure of conditioning. In: Proc. 45th IEEE Conference on Decision and Control, San Diego, CA (2006). Published on CD-ROM

    Google Scholar 

  88. Uciński, D., Demetriou, M.A.: An approach to the optimal scanning measurement problem using optimum experimental design. In: Proc. American Control Conference, Boston, MA (2004). Published on CD-ROM

    Google Scholar 

  89. Uciński, D., Demetriou, M.A.: Resource-constrained sensor routing for optimal observation of distributed parameter systems. In: Proc. 18th International Symposium on Mathematical Theory of Networks and Systems, Blacksburg, VA, July 28–August 1 (2008). Published on CD-ROM

    Google Scholar 

  90. Uciński, D., Korbicz, J.: Optimal sensor allocation for parameter estimation in distributed systems. Journal of Inverse and Ill-Posed Problems 9(3), 301–317 (2001)

    MathSciNet  MATH  Google Scholar 

  91. Uciński, D., Patan, M.: Optimal location of discrete scanning sensors for parameter estimation of distributed systems. In: Proc. 15th IFAC World Congress, Barcelona, Spain, 22–26 July 2002 (2002). Published on CD-ROM

    Google Scholar 

  92. Uciński, D., Patan, M.: D-optimal design of a monitoring network for parameter estimation of distributed systems. Journal of Global Optimization 39, 291–322 (2007)

    Article  MATH  Google Scholar 

  93. Uspenskii, A.B., Fedorov, V.V.: Computational Aspects of the Least-Squares Method in the Analysis and Design of Regression Experiments. Moscow University Press, Moscow (1975). (In Russian)

    Google Scholar 

  94. Vande Wouwer, A., Point, N., Porteman, S., Remy, M.: On a practical criterion for optimal sensor configuration — Application to a fixed-bed reactor. In: Proc. 14th IFAC World Congress, Beijing, China, 5–9 July, 1999, vol. I: Modeling, Identification, Signal Processing II, Adaptive Control, pp. 37–42 (1999)

    Google Scholar 

  95. Ventura, J.A., Hearn, D.W.: Restricted simplicial decomposition for convex constrained problems. Mathematical Programming 59, 71–85 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  96. Vogel, C.R.: Computational Methods for Inverse Problems. Frontiers in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia (2002)

    Book  MATH  Google Scholar 

  97. van de Wal, M., de Jager, B.: A review of methods for input/output selection. Automatica 37, 487–510 (2001)

    Article  MATH  Google Scholar 

  98. Walter, É., Pronzato, L.: Identification of Parametric Models from Experimental Data. Communications and Control Engineering. Springer-Verlag, Berlin (1997)

    MATH  Google Scholar 

  99. Zhao, F., Guibas, L.J.: Wireless Sensor Networks: An Information Processing Approach. Morgan Kaufmann Publishers, Amsterdam (2004)

    Google Scholar 

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Acknowledgements

This work was supported by the Polish Ministry of Science and Higher Education under grant No. N N519 2971 33.

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  1. Institute of Control and Computation Engineering, University of Zielona Góra, ul. Podgórna 50, 65–246, Zielona Góra, Poland

    Dariusz Uciński

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  1. Dariusz Uciński
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Editors and Affiliations

  1. Interdisciplinary Center for Scientific, Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Hans Georg Bock

  2. Institute for Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 294, Heidelberg, 69120, Germany

    Thomas Carraro

  3. Interdisciplinary Center for Scientific, Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Willi Jäger

  4. Interdisciplinary Center for, Scientific Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Stefan Körkel

  5. Institute for Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 293, Heidelberg, 69120, Germany

    Rolf Rannacher

  6. Interdisciplinary Center for Scientific, Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Johannes P. Schlöder

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Uciński, D. (2013). An Optimal Scanning Sensor Activation Policy for Parameter Estimation of Distributed Systems. In: Bock, H., Carraro, T., Jäger, W., Körkel, S., Rannacher, R., Schlöder, J. (eds) Model Based Parameter Estimation. Contributions in Mathematical and Computational Sciences, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30367-8_4

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