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...

$\endgroup$
  • $\begingroup$ Hi: that notation denotes the prediction ( also referred to as estimate ) of $y(k)$ at time $(k-1)$. $\endgroup$ – mark leeds Jan 26 at 13:45
  • $\begingroup$ Is the conditional probability ? $\endgroup$ – Jhdoe Jan 26 at 14:15
  • $\begingroup$ Hi: No. Assume the model is estimated which means that the coefficients are estimated. Then, that notation denotes the prediction of the next value in the series at time $k$, given that one is at time $k-1$. Maybe check out a book or a discussion on arima models if this is not clear. $\endgroup$ – mark leeds Jan 27 at 4:01
  • $\begingroup$ So it's like the author is saying : "suppose we use a model to predict y. Than we get something like this" .... :S ? $\endgroup$ – Jhdoe Jan 27 at 10:23
  • $\begingroup$ yes. but y ONE step ahead. time matters a lot. $\endgroup$ – mark leeds Jan 27 at 19:09

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.