Hello,
An overdetermined system of linear equation
y = A x + z
with y vector of known real numbers of dimension m; x vector of unknown real numbers of dimension n; z vector of Gaussian noise of dimension m and A the known coefficient matrix.
it is characterized by 3 aspects:
1)
The unknown x exhibits elements with order of magnitude difference among them.
example: x is 4 elements and I know in advance that two of them will be around 10^4 and 2 around 10^0
2)
The vector z is a noise and each of its element is a Gaussian number with zero mean and known variance.
Basically those are measurements coming from sensors of different "quality", i.e., different variance
3)
Eventually z is composed by elements with a predominant variance.
Example, 80% of the elements of z comes from the same sensor with the same variance and 20% from others
Question:
can someone please link me to a textbook where such numerical aspects are elaborated?
I'm not an expert but I guess that a simple pseudoinverse is not the "best" solution
Thanks in advance,
g.