Positioning can be done by means of triangulation in which triples of position-aware nodes estimate a neighbor's position with the help of distances. If a larger number of nodes exist, multiple position estimates can be averaged to yield a more precise mean position. Rather than applying equal weights to each position estimate, we propose an unequal weighting scheme which emphasizes those summands in the averaging process that are more reliable than others. We will show that significant improvements of the overall estimate can be achieved, given that additional information about the error variance of a contributing estimate is known. A major advantage of the approach is that the precision of existing positioning systems can be improved without technical modifications.