The limits of averaging
Averaging is the first thing anyone reaches for, and it works. Watch for longer, take more measurements, and the number settles down. The question this page exists to answer is what it settles on.
What averaging can and cannot do
Averaging removes random error. It does not remove bias.
If half your measurements are 30 cm too far east and half are too far west, that averages out. If all of them are 1 m too far north, that never goes away, no matter how long you watch — because there is nothing about the measurements themselves that disagrees.
In the vocabulary this topic uses elsewhere: averaging improves precision and never improves trueness.
The same shape in three places
This is not a GNSS quirk. It is what averaging does, and it shows up wherever you average.
Position. A receiver working out where its own antenna is gets a better answer for a while, then stops getting better. NIST measured a receiver’s built-in survey converging tidily — and converging to an answer biased high, for reasons they could not explain. Their 24-hour results were far more repeatable than their 1-hour results, and no more correct. See configuring antenna position.
Time. Averaging phase measurements against a reference tightens the estimate of your offset, and does nothing at all about an uncompensated cable delay sitting in every one of those measurements identically.
Frequency. This one is the most instructive, because the limit is drawn for you. Plot Allan deviation against averaging interval and the curve falls as you average longer — and then it stops falling. The flat part is the flicker floor, and past it the curve turns and rises. The picture the frequency world has been drawing for decades is this page: a region where averaging pays, a floor where it stops paying, and a region beyond where averaging actively hurts.
Everything on this page assumes you can measure again. Where you cannot — a timestamp taken once, on an event that happened once — the improvement averaging buys is not merely bounded, it is unavailable, and scatter lands in your answer with the same weight as bias.
That case is common enough in datacenter timing to have its own page, and it is where this one’s conclusions stop applying.
The improvement is real, it is bounded, and the bound is set by whatever part of the error is systematic rather than random. When the curve flattens, you are no longer measuring your patience — you are measuring your bias.
How to find your own floor
You do not need a reference better than the thing you are measuring to discover that you have hit the floor. You need to restart.
Average for your chosen interval, record the answer, throw the state away and do it again. Fourteen times over fourteen days is plenty.
- If the answers cluster tightly, the random part is averaged out and you are looking at your floor. Averaging longer will not move it.
- If they scatter, you have not averaged enough yet and there is still improvement to buy.
Either way you have learned where you are, using only the equipment you already own. What the test cannot tell you is whether that floor sits on the right answer — for that you need something traceable to compare against.
Why the benefit stops when it does
For GNSS position specifically, the ceiling has a cause worth knowing: the satellites repeat. GPS’s orbital geometry cycles on roughly a sidereal day, so after a couple of days of watching you have largely seen the geometry you are going to see, and further averaging re-samples conditions you have already sampled. Multipath from a nearby wall does not average away, because tomorrow the satellite will be in the same place doing the same thing.
That is the practical reason the recommendation on the antenna page is “a couple of days” rather than “as long as possible.”
Sources
- Montare, Novick & Sherman (NIST, 2024), Evaluating Common-View Time Transfer Using a Low-Cost Dual-Frequency GNSS Receiver — the measured case of a survey converging on a biased answer. https://tf.nist.gov/general/pdf/3280.pdf