-- AlexanderFedotov - 2015-03-03

Linear Least Squares

Wikipedia links

Uncorrelated measurements

Let with variances be measurements of functions with the known matrix and unknown parameters .

In linear least square method, one estimates the parameter vector by minimizing over the expression

where the weight matrix of dimension is diagonal and defined as the inverse of the diagonal covariance matrix for : i.e. .
In matrix notation (considering and as columns and respectively), one has

The estimate is the solution of the system of equations

In a general case of linear transformation , the covariance matrice for is transformed into that for via . Hence,
As by the definition of , this simplifies to

Edit | Attach | Watch | Print version | History: r14 | r4 < r3 < r2 < r1 | Backlinks | Raw View | Raw edit | More topic actions...
Topic revision: r1 - 2015-03-04 - AlexanderFedotov
    • Cern Search Icon Cern Search
    • TWiki Search Icon TWiki Search
    • Google Search Icon Google Search

    Main All webs login

This site is powered by the TWiki collaboration platform Powered by PerlCopyright & 2008-2019 by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
Ideas, requests, problems regarding TWiki? Send feedback