GPS glitch causes 200 m circles around stationary position- Has anyone seen this before?

I am working with GPS data from public transport buses in a city in the UK. The data have very characteristic circles of approx. 200 m diameter at bus stops. I suspect that these are caused by an estimated position but I do not know enough about the GPS technology to explain these patterns. Have you seen these patterns before?

The image shows GPS positions for several months. The white circle is the outbound bus stop and all points in yellow are outbound vehicles and inbound vehicles are shown in blue.

If the vehicle lost signal and estimated its position ahead I would expect a ring only in the direction of travel but I am getting one in both directions. These rings are always oriented in the direction of the route.
They also do not occur at traffic lights and pedestrian crossings, which would be explained by the fact the vehicle does not always stop in the same place as is the case at bus stops.

Just looking at the outbound direction the data looks like this, where the arrow shows the direction of travel.

For a randomly picked example the percentages of the data points in the circle are:

• ~52% in the centre
• ~32% behind the bus
• ~15% in front of the bus

Even though this example is from a city, we are talking about houses on either side of mostly 2-3 storeys. So no skyscraper-canyons that could seriously impact the signal. Unfortunately, I do not know the exact GPS unit used or even where it is placed on the vehicle. For all I know, it might be installed under the driver’s seat…

Below you can see an overview. with the stops highlighted in red and it the coordinates in white. These circles appear practically all along the journey at most of the 42 bus stops.

Any help explaining these circles would be amazing!

EDIT:
As suggested by jgm_GIS I have colour coded the points based on

(distance from prior point) / (Time elapsed).

The results are not that clear (I guess they never are…) but it appears that in some cases the ratio is indeed higher in front of the vehicle and lower behind. (See example A&B). But in other cases, the difference is marginal at best or not existent and the ratio is virtually the same before and after vehicle (Example C).

The image shows the colour coded ratio with the approximate values for either semi-circle next to it.

Can anyone explain the intuition behind this? Essentially this shows the speed between the last two points. So what is the software doing? It moves the points away from the bus if it is close to the stop but not quite there yet?