I am seeing occasional (e.g. once every several days) extra PPS pulses, which cause ts2phc to perform some extreme adjustments. Here's an example, which is with a u-blox M8T with an outside, but ground-level antenna (so less than perfect sky-view).
Nov 13 16:38:42 wensleydale ts2phc: [104209.501] nmea sentence: GPRMC,093842.00,A,1343.91052,N,10038.68416,E,0.000,,131122,,,A,V
Nov 13 16:38:43 wensleydale ts2phc: [104210.488] nmea delay: 147943835 ns
Nov 13 16:38:43 wensleydale ts2phc: [104210.488] eth0 extts index 0 at 1668332359.999999995 corr 0 src 1668332360.987633605 diff -5
Nov 13 16:38:43 wensleydale ts2phc: [104210.488] eth0 master offset -5 s2 freq +13780
Nov 13 16:38:43 wensleydale ts2phc: [104210.504] nmea sentence: GPRMC,093843.00,A,1343.91052,N,10038.68416,E,0.000,,131122,,,A,V
Nov 13 16:38:44 wensleydale ts2phc: [104211.496] nmea delay: 150866287 ns
Nov 13 16:38:44 wensleydale ts2phc: [104211.496] eth0 extts index 0 at 1668332360.999999981 corr 0 src 1668332361.992675857 diff -19
Nov 13 16:38:44 wensleydale ts2phc: [104211.496] eth0 master offset -19 s2 freq +13765
Nov 13 16:38:44 wensleydale ts2phc: [104211.504] nmea sentence: GPRMC,093844.00,A,1343.91052,N,10038.68416,E,0.000,,131122,,,A,V
Nov 13 16:38:45 wensleydale ts2phc: [104212.501] nmea sentence: GPRMC,093845.00,A,1343.91052,N,10038.68416,E,0.000,,131122,,,A,V
Nov 13 16:38:45 wensleydale ts2phc: [104212.504] nmea delay: 148658469 ns
Nov 13 16:38:45 wensleydale ts2phc: [104212.504] eth0 extts index 0 at 1668332361.999999998 corr 0 src 1668332362.2876398 diff -2
Nov 13 16:38:45 wensleydale ts2phc: [104212.504] eth0 master offset -2 s2 freq +13776
Nov 13 16:38:45 wensleydale ts2phc: [104213.008] nmea delay: 148658469 ns
This next pulse is is an extra, spurious pulse. I think 1668332362.43187178
is the PHC of the pulse. It's an extra one between the previous one, which is roughly 1668332362, and the next one, which is roughly 1668332363.
Nov 13 16:38:45 wensleydale ts2phc: [104213.008] eth0 extts index 0 at 1668332362.431871787 corr 0 src 1668332363.506861520 diff -568128213
Nov 13 16:38:45 wensleydale ts2phc: [104213.008] eth0 master offset -568128213 s2 freq -100000000
Nov 13 16:38:46 wensleydale ts2phc: [104213.505] nmea sentence: GPRMC,093846.00,A,1343.91052,N,10038.68416,E,0.000,,131122,,,A,V
Nov 13 16:38:46 wensleydale ts2phc: [104213.512] nmea delay: 152682848 ns
Nov 13 16:38:46 wensleydale ts2phc: [104213.512] eth0 extts index 0 at 1668332363.034413526 corr 0 src 1668332363.6911093 diff 34413526
Nov 13 16:38:46 wensleydale ts2phc: [104213.512] eth0 master offset 34413526 s2 freq +34427304
Nov 13 16:38:47 wensleydale ts2phc: [104214.504] nmea sentence: GPRMC,093847.00,A,1343.91052,N,10038.68416,E,0.000,,131122,,,A,V
Nov 13 16:38:47 wensleydale ts2phc: [104214.521] nmea delay: 151118484 ns
Nov 13 16:38:47 wensleydale ts2phc: [104214.521] eth0 extts index 0 at 1668332364.021504083 corr 0 src 1668332364.16857268 diff 21504083
Nov 13 16:38:47 wensleydale ts2phc: [104214.521] eth0 master offset 21504083 s2 freq +31841918
Nov 13 16:38:48 wensleydale ts2phc: [104215.502] nmea sentence: GPRMC,093848.00,A,1343.91052,N,10038.68416,E,0.000,,131122,,,A,V
Nov 13 16:38:48 wensleydale ts2phc: [104215.528] nmea delay: 149682950 ns
Nov 13 16:38:48 wensleydale ts2phc: [104215.528] eth0 extts index 0 at 1668332364.989240046 corr 0 src 1668332365.25860902 diff -10759954
Nov 13 16:38:48 wensleydale ts2phc: [104215.528] eth0 master offset -10759954 s2 freq +6029106
Nov 13 16:38:49 wensleydale ts2phc: [104216.504] nmea sentence: GPRMC,093849.00,A,1343.91052,N,10038.68416,E,0.000,,131122,,,A,V
Nov 13 16:38:49 wensleydale ts2phc: [104216.536] nmea delay: 151196759 ns
Nov 13 16:38:49 wensleydale ts2phc: [104216.536] eth0 extts index 0 at 1668332365.978683997 corr 0 src 1668332366.32350224 diff -21316003
Nov 13 16:38:49 wensleydale ts2phc: [104216.536] eth0 master offset -21316003 s2 freq -7754929
Nov 13 16:38:50 wensleydale ts2phc: [104217.504] nmea sentence: GPRMC,093850.00,A,1343.91052,N,10038.68416,E,0.000,,131122,,,A,V
Nov 13 16:38:50 wensleydale ts2phc: [104217.544] nmea delay: 151323978 ns
Nov 13 16:38:50 wensleydale ts2phc: [104217.544] eth0 extts index 0 at 1668332366.983917652 corr 0 src 1668332367.40235709 diff -16082348
Nov 13 16:38:50 wensleydale ts2phc: [104217.544] eth0 master offset -16082348 s2 freq -8916075
Nov 13 16:38:51 wensleydale ts2phc: [104218.504] nmea sentence: GPRMC,093851.00,A,1343.91052,N,10038.68416,E,0.000,,131122,,,A,V
Nov 13 16:38:51 wensleydale ts2phc: [104218.552] nmea delay: 151517308 ns
Nov 13 16:38:51 wensleydale ts2phc: [104218.552] eth0 extts index 0 at 1668332367.992624769 corr 0 src 1668332368.48024659 diff -7375231
Nov 13 16:38:51 wensleydale ts2phc: [104218.552] eth0 master offset -7375231 s2 freq -5033662
Nov 13 16:38:52 wensleydale ts2phc: [104219.502] nmea sentence: GPRMC,093852.00,A,1343.91052,N,10038.68416,E,0.000,,131122,,,A,V
Nov 13 16:38:52 wensleydale ts2phc: [104219.560] nmea delay: 148823090 ns
Nov 13 16:38:52 wensleydale ts2phc: [104219.560] eth0 extts index 0 at 1668332368.998448447 corr 0 src 1668332369.58759544 diff -1551553
Nov 13 16:38:52 wensleydale ts2phc: [104219.560] eth0 master offset -1551553 s2 freq -1422554
Nov 13 16:38:53 wensleydale ts2phc: [104220.501] nmea sentence: GPRMC,093853.00,A,1343.91052,N,10038.68416,E,0.000,,131122,,,A,V
Nov 13 16:38:53 wensleydale ts2phc: [104220.568] nmea delay: 147817069 ns
Nov 13 16:38:53 wensleydale ts2phc: [104220.568] eth0 extts index 0 at 1668332370.000636084 corr 0 src 1668332370.67735419 diff 636084
Nov 13 16:38:53 wensleydale ts2phc: [104220.568] eth0 master offset 636084 s2 freq +299618