-- 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

or
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

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Topic revision: r1 - 2015-03-04 - AlexanderFedotov
 
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