In many practical situations, the measurement result z depends not only on the measured value x, but also on the parameters s describing the experiment's setting and on the values of some auxiliary quantities y; the dependence z=f(x,s,y) of z on x, s, and y is usually known. In the ideal case when we know the exact value of the auxiliary parameter y, we can solve the above equation and find the desired value x. In many real-life situations, we only know y with some uncertainty, and this uncertainty leads to additional uncertainty in x.
If we are trying to reconstruct x based on a single measurement result, then, of course, the measurement error in y leads to the corresponding measurement error in x - and, unless we perform more accurate measurements, we cannot improve x's accuracy.
In many practical situations, however, if we have several measurement results corresponding to different values of t and/or y, we can reconstruct x with a much higher accuracy - because we can combine these measurement results in such a way that the influence of y drastically decreases. As a result, we get a sub-noise measurement accuracy, the accuracy that is much better than the accuracy with which we know y.