It is clear that we can give an estimate of the magnitude of a process based on past observation of this process.
In the expression of the innovation:
YK represents the magnitude to be estimated (see predictor) and represents the estimation.
In the same way, if we call:
the estimate of a process at instant K, starting from measurement y1, …, yK, … of process Y1, …, YK, …, we can write:
Let us write the innovation at instants 1, 2,…, K :
with : coefficients of the predictor of order K − 1
This expression can be put in the form: I = M Y
with M, invertible triangular matrix because |det M| = 1.
Thus Y = M−1 I.
As a consequence, each vector I