Linear Difference Equation and Method of Least Squares 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:



the equation is called 9.15.
Then, 



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...
The notation $ \hat{y} \left( k \mid k - 1 \right) $ usually means this is an estimated value of $ y \left( k \right) $ given all the available data up to time index $ k - 1 $.
So generally speaking, this is a prediction of one step in time of the data.

The case above also suggests linear estimation.
Namely, $ \hat{y} \left( k \right) $ is built using linear combination of all the given data.