Kalman Filter: An Elementary Approach

  • Charles K. Chui
  • Guanrong Chen
Part of the Springer Series in Information Sciences book series (SSINF, volume 17)


This chapter is devoted to a most elementary introduction to the Kalman filtering algorithm. By assuming invertibility of certain matrices, the Kalman filtering “prediction-correction” algorithm will be derived based on the optimality criterion of least-squares unbiased estimation of the state vector with the optimal weight, using all available data information. The filtering algorithm is first obtained for a system with no deterministic (control) input. By superimposing the deterministic solution, we then arrive at the general Kalman filtering algorithm.


Kalman Filter Recursive Formula Elementary Approach Deterministic Solution Recursive Scheme 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Charles K. Chui
    • 1
  • Guanrong Chen
    • 2
  1. 1.Department of Mathematics and Department of Electrical EngineeringTexas A&M UniversityCollege StationUSA
  2. 2.Department of Electrical EngineeringUniversity of HoustonHoustonUSA

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