Condition number for non-negative least squares

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If I want to analyze the stability of a non-negative least squares problem $||Ax-b||_2^2, x\ge0$, how can I measure the stability of the system? If it was a regular least squares problem, then I can compute the condition number of $A$, however, this doesn't extend to the non-negative LS case because of the constraint. My goal is to determine which $A$ out of different options is the best for this problem for some experiment. Thank you.