Calculate best estimate of multiple mesurements with known but varying variance

Question

When multiple experiments measure the same physical quantity and give a set of answers $s={s_1,s_2,...,s_n}$ for $n$ measurement and give an error with different variances $v={v_1,v_2,...,v_n}$. How is the final estimate of $s$ and $v$ calculated ? The error is assumed to be Gaussian distributed and to be unbiased.