Mathematical Aspects

  • Rolf Isermann
  • Marco Münchhof


In this appendix, some important fundamental notions of estimation theory shall be repeated. Also, the calculus for vectors and matrices shall very shortly be outlined. A detailed overview of the fundamental notions for estimation theory can e.g. be found in (Papoulis and Pillai, 2002; Doob, 1953; Davenport and Root, 1958; Richter, 1966; Åström, 1970; Fisher, 1922, 1950).


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  1. Åström KJ (1970) Introduction to stochastic control theory. Academic Press, New YorkzbMATHGoogle Scholar
  2. Brookes M (2005) The matrix reference manual. URL
  3. Davenport W, Root W (1958) An introduction to the theory of random signals and noise. McGraw-Hill, New YorkzbMATHGoogle Scholar
  4. Deutsch R (1965) Estimation theory. Prentice-Hall, Englewood Cliffs, NJzbMATHGoogle Scholar
  5. Doob JL (1953) Stochastic processes. Wiley, New York, NYzbMATHGoogle Scholar
  6. Fisher RA (1922) On the mathematical foundation of theoretical statistics. Philos Trans R Soc London, Ser A 222:309–368CrossRefGoogle Scholar
  7. Fisher RA (1950) Contributions to mathematical statistics. J. Wiley, New York, NYzbMATHGoogle Scholar
  8. Gauss KF (1809) Theory of the motion of the heavenly bodies moving about the sun in conic sections: Reprint 2004. Dover phoenix editions, Dover, Mineola, NYGoogle Scholar
  9. Goldberger AS (1964) Econometric theory. Wiley Publications in Applied Statistics, John Wiley and Sons LtdzbMATHGoogle Scholar
  10. Kendall MG, Stuart A (1961) The advanced theory of statistics. Volume 2. Griffin, London, UKGoogle Scholar
  11. Kendall MG, Stuart A (1977) The advanced theory of statistics: Inference and relationship (vol. 2). Charles Griffin, LondonGoogle Scholar
  12. Papoulis A, Pillai SU (2002) Probability, random variables and stochastic processes, 4th edn. McGraw Hill, BostonGoogle Scholar
  13. Richter H (1966) Wahrscheinlichkeitstheorie, 2nd edn. Spinger, BerlinzbMATHGoogle Scholar
  14. Wilks SS (1962) Mathematical statistics. Wiley, New YorkzbMATHGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Technische Universität Darmstadt, Institut für AutomatisierungstechnikDarmstadtGermany

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