Trailing loss stop is a good way to lock in profits
Not necessarily. This is opinionated and likely limited in scope and limited to sample. You also give no citations of the claim. However, this perspective doesn't necessarily impede the question, it would simply be better to be impartial and factual when asking the question, rather than biased. Certainly it can be distracting and I'll admit being the first line did put me off to start.
One way to calculate noise is to take the Average True Range.
Fine. And you have given a link, this is what you want to use for your calculations. No problems here.
I am looking for a parameter. What is a good parameter to use?
This is bad because, in my opinion, it shows a limited understanding of strategy testing and cross validation of models. The assertion that a set of good parameters, or a unique optimal parameter, or that a fixed parameter exists in all scenarios and all sorts of trading conditions is probably far-fetched and, furthermore, this is something specific that an answerer on Quantfinance cannot likely just read off.
My comment redirected you toward a better understanding about how to calculate these parameters for yourself and have (statistical) confidence that it would work in your scenario. This type of hyper parameter training is industry standard.
Had I written this question I would have posed it in the following way?
I am looking to use a trailing stop strategy. In particular doing Y an Z. I would like to determine the quantity X in my calculations. What is a recommended approach towards doing this that has properties such as being statistically reliable or robust. Can anyone give advice from experience or refer any paper specifically related to this precise method?
Certainly, written like this I would have expressed my comment as a full answer and others might also have bothered to contribute.