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-- AlexanderFedotov - 2015-03-03

# Linear Least Squares

Sections:

## 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 or In a general case of linear transformation , the covariance matrice for is transformed into that for via . Hence, With by the definition of , that simplifies to Note, that and ## Correlated measurements

Let be uncorrelated measurements as those in the previous section, and ( is an invertible matrix). Then are generally correlated and have the covariance matrix .

With and , one gets where .

Similarly, and Thus, all the formulae for the correlated measurements are similar to those for the uncorrelated , with the only complication being the replacement of a diagonal weight matrix with a non-diagonal one: Edit | Attach | Watch | Print version |  | Backlinks | Raw View | Raw edit | More topic actions...
Topic revision: r3 - 2015-03-05 - AlexanderFedotov Log In

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