Estimating the parameter of a linear difference equation with Least Squares












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I'm reading the book "Fault-Diagnosis Systems" by Isermann in the par. 9.2.1a.
The author explains how to estimate the parameter of a linear difference equation using Least Squares.
We start with a standard ordinary linear equation with an error term:



Img1



the equation is called 9.15.
Then,



Img2



The first thing i don't understand is the syntax used by the author. What's the meaning of the | inside $hat{y}(k|k-1)$ ?



ps: I'm sorry if what i ask is trivial, but when i have a kind of doubt like this, i don't know how to solve it if not asking it in this site...






ordinary-differential-equations







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    0












    $begingroup$


    I'm reading the book "Fault-Diagnosis Systems" by Isermann in the par. 9.2.1a.
    The author explains how to estimate the parameter of a linear difference equation using Least Squares.
    We start with a standard ordinary linear equation with an error term:



    Img1



    the equation is called 9.15.
    Then,



    Img2



    The first thing i don't understand is the syntax used by the author. What's the meaning of the | inside $hat{y}(k|k-1)$ ?



    ps: I'm sorry if what i ask is trivial, but when i have a kind of doubt like this, i don't know how to solve it if not asking it in this site...






    ordinary-differential-equations







    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      I'm reading the book "Fault-Diagnosis Systems" by Isermann in the par. 9.2.1a.
      The author explains how to estimate the parameter of a linear difference equation using Least Squares.
      We start with a standard ordinary linear equation with an error term:



      Img1



      the equation is called 9.15.
      Then,



      Img2



      The first thing i don't understand is the syntax used by the author. What's the meaning of the | inside $hat{y}(k|k-1)$ ?



      ps: I'm sorry if what i ask is trivial, but when i have a kind of doubt like this, i don't know how to solve it if not asking it in this site...






      ordinary-differential-equations







      share|cite|improve this question









      $endgroup$




      I'm reading the book "Fault-Diagnosis Systems" by Isermann in the par. 9.2.1a.
      The author explains how to estimate the parameter of a linear difference equation using Least Squares.
      We start with a standard ordinary linear equation with an error term:



      Img1



      the equation is called 9.15.
      Then,



      Img2



      The first thing i don't understand is the syntax used by the author. What's the meaning of the | inside $hat{y}(k|k-1)$ ?



      ps: I'm sorry if what i ask is trivial, but when i have a kind of doubt like this, i don't know how to solve it if not asking it in this site...






      ordinary-differential-equations




      ordinary-differential-equations






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      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 26 at 8:35









      JhdoeJhdoe

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