The consensus from ten or eleven years' worth of Forum contributions on the accuracy of gps devices when measuring distance covered 'on the ground' seems to be that in spite of both increased satellite numbers and new satellite networks, plus improved device performance, the various factors which can affect accuracy are still in place. These include geography (buildings, valleys, forests, water), straight-line versus 'wiggliness' of routes, and even where on the body the device is worn. For height gained and lost (net ascent) and point heights, there still appears to be more than ten percent variation between devices and networks.
(In the case of height of ascent, it is satellite numbers - at least four simultaneous signals needed for measurement in 3D rather than 2D - which affect accuracy: this and very much else is discussed in Greg Milner's remarkable 2016 book 'Pinpoint: how gps is changing our world'.)
I have previously suggested an average of the many devices carried on a hundred-mile event as a first large-scale comparison of body-worn ground-based gps measurements of cumulative distance and height (who else does annual hundred-mile walking events with maybe a hundred gps devices carried on each event ?). So far, there do not seem to have been many formal studies of cumulative gps accuracy. One 2014 cycle-based test* of ten devices over ten laps of a velodrome found an average distance error rate of 3.7%, with only 4 of the 10 devices being within 1% of each other.
However, the accuracy with which gps devices estimate their position on the planet's surface - surely one of humanity's finest achievements, even if originating in warfare technology - has increased significantly over the decade. Again citing Greg Milner's exhaustively comprehensive book, actual rather than claimed pinpointing *may* (repeat may!) now be down from 10 metres to 10 feet, and unless your device is off or the batteries are at below-threshold strength, it is continuously re-adjusting its location (latitude and longitude) with respect to as many as twelve satellites. (I learnt from this book that smartphones also use gps signals to orient themselves, even if not explicitly 'gps enabled'.) Unless you tell it not to (and this may be difficult to do!) your gps device is very good at tracking your continuously changing position on Planet Earth.
My very recent experience of tracking with a new Garmin (eTrex Touch 35) has so far been that it is successful over relatively short distances (10 to 15 miles) but has had problems on longer walks due to battery strength. I am addressing the battery issue by experimenting with its multitude of settings (and getting longer-lasting batteries, but that's another much-discussed issue). Cumulative distance and height totals have been unreliable even when continuously tracked, but the resulting gpx track files are remarkably accurate when uploaded to mapping software, both in showing every small deviation (by intent or error!) from the planned OS 1:25,000 route and in total distance covered.
In other words, the tracked route is very, very accurate even if my Garmin's own estimates of how far and high I went are not, regardless of where in or on my body I was carrying it and whether or not I had looked at it (it has an 'autopause' facility, which I think means - the online manual is awful, the only book on this device so far discovered is in German - that it stops tracking when I stand still.) Apart from a couple of glitches near water (the local canal's towpath, recorded as longer straight lines than the usual precise curves) its tracking capacity is remarkable. So long as remember to switch it on, that is ...
Iain
* http://www.singletracks.com/blog/gps/gps-distance-accuracy-test-smartphone-apps-vs-dedicated-gps