Regarding accuracy - I was advised here to look at N, E, U values in the solution section of the RTKNAVI monitor - I will try.
So there can be a false fix, right? Ehm, this complicates the situation even further… I most likely observed it when a fix in static measurement appeared in multiple locations serveral 10cms apart (probably multiples of wavelength?) from each other during one session. Can a false fix be detected somehow other than by checking whether it “holds” for some time (before the receiver returns to float as you say) - do you have an experience with how fast the receiver can detect it? It would be better for me to be able to detect is from the data itself somehow and not need to rely on the receiver (=RTKLIB) returning to float…