gianluca

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.