MATLAB: How to convert UTC timestamp to unix time in MATLAB with the respect of leap seconds

convertleap secondsMATLABposixposix timeposixtimeunixunix timeunixtimeutcutc-time

I need to synchronize two sensors from UTC to unix time. The first one is an GPS which yields an NMEA GPGGA file, where UTC timestamp has the format "HHmmss.SSS". As an example "042803.00" is "4:28:03" AM and zero milliseconds.

The second sensor yields an unix time without leap seconds.

Is there an MATLAB function which I can use? I'm especially interested in an solution which respects leap seconds? My first approach is to convert the unix time into utc:

sensor=datetime(unix_timestamp,'ConvertFrom','posixtime')

Unfortunately the argument posixtime does not support leap seconds. Then I take the utc timestamp from the NMEA file:

gps=datetime(utc_timestamp,'InputFormat','HHmmss.SSS','TimeZone','UTC')

Now since i don't have any day, year, month in my NMEA protocoll, I take it from the unix_timestamp

gps.Day=sensor.Day
gps.Month=sensor.Month
gps.Year=sensor.Year

Any Idea how to do it better? What is the risk if i take the year,month,day from the unix timestamp without leap seconds?

Now I want to transfer the gps time into unix time with:

unix_time_gps=posixtime(gps)

This does not work since posixtime does not respect leap seconds.

How do I achieve this?

Thank you

Best Answer

A couple things, apologies if you already know all this:

1) POSIX time does not have leap seconds. As Jan says, unix systems variously either just ignore that 86401st second, or smear it over the entire day. That's why 'ConvertFrom','posixtime' doesn't support leap seconds -- POSIX time doesn't. And strictly speaking, POSIX time is not a "timestamp" in the sense of hh:mm:ss, it's a count of seconds. "Doesn't support leap seconds "means that the count does not increment during a leap second.

2) UTC, i.e. the "real-world" UTC, does observe leap seconds. The 'UTC' timezone that datetime in MATLAB supports is more like POSIX time in that it ignores the existence of leap seconds, because most people would be unhappy to find their calculations puzzlingly off by, say, 2 seconds when going from noon to noon. 'UTCLeapSeconds' is for those who need the exact thing.

3) GPS time also does not observe leap seconds, but in a different way than POSIX time doesn't. It is also a count of elapsed time, but the count DOES increment during a leap second, and therefore GPS time drifts from UTC by 1 second each time a leap second occurs in UTC. So, you should be really careful that the thing you are calling "GPS time" and "UTC timestamp" is in fact what you think it is. I don't even know what a NMEA GPGGA file is, so you're the expert here.

It looks like your unix_timestamp is a number, and your utc_timestamp is text in the format "HHmmss.SSS". In some sense it does not matter if you use

datetime(utc_timestamp,'InputFormat','HHmmss.SSS','TimeZone','UTC')

datetime(utc_timestamp,'InputFormat','HHmmss.SSS','TimeZone','UTCLeapSeconds')

because that timestamp is absolute, not relative (once you get the right date for it, and assuming you can synchronize the two data streams), and datetime is happy to convert either ''UTC' or 'UTCLeapSeconds' times into the correct POSIX time. If your data are never at 23:59:60.xxx on 30-Jun or 31-Dec, everything is fine, both of those lines work, and datetime automatically compensates for leap seconds when converting from 'UTCLeapSeconds' to POSIX time. If your data do happen to land during an actual leap second, the first line above will error, the second will work, but again datetime compensates -- calling posixtime will give you the value that the POSIX time for that leap second would be -- the 0th second of the next day.

So what is it that "does not work since posixtime does not respect leap seconds"?

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MATLAB: Get GPS time to calulate time since referencje epoch

Marta, that depends on what you mean by "GPS time".

MATLAB doesn't yet have direct support for GPS time, but if all you want is elapsed time since the GPS origin, it's pretty simple, although not obvious:

>> t = datetime('now','TimeZone','UTC')
t = 
  datetime
   24-Nov-2020 16:25:14
>> GPS0 = datetime(1980,1,6,0,0,0,'TimeZone','UTCLeapSeconds')
GPS0 = 
  datetime
   1980-01-06T00:00:00.000Z
>> tLS = t; tLS.TimeZone = 'UTCLeapSeconds'
tLS = 
  datetime
   2020-11-24T16:25:14.119Z
>> deltaT = tLS - GPS0; deltaT.Format = 's'
deltaT = 
  duration
   1290270332.11899 sec

Why this works is a bit confusing, but bear with me. The GPS timeline doesn't observe leap seconds, so it drifts from the real-world UTC timeline as the years go by (currently 18s apart). But 6-Jan-1980 is where the two time lines are sync'ed up, and elapsed time is the same on both timelines. So you can subtract 6-Jan-1980 from the current time and get the correct elapsed time in either time line.

The trick is that in MATLAB, you have to do this using datetime's 'UTCLeapSeconds' "time zone". Why is that? Hardly anyone wants leap seconds to randomly creep into their date/time calculations, so MATLAB leaves them out by default (that's exactly how POSIX time works, and NTP too). That's true of calculations using unzoned datetimes, as well as datetimes with time zones, including 'UTC'. If you care about leap seconds, you opt in by using 'UTCLeapSeconds'. And to get the right elapsed time in this calculation, you have to account for leap seconds, not just ignore them.

It sounds like that elapsed time is what you are looking for. GPS time is often expressed in various ways (e.g. http://leapsecond.com/java/gpsclock.htm). It's straight-forward to get to the week/second representation:

>> weeks = floor(seconds(deltaT)/(7*86400))
weeks =
        2133
>> secs = rem(deltaT,seconds(7*86400))
secs = 
  duration
   231932.118987061 sec

If you want a human-readable timestamp, it's also easy, but also not obvious. Just add your elapsed time to 6-Jan-1980 unzoned.

>> datetime(1980,1,6) + deltaT
ans = 
  datetime
   24-Nov-2020 16:25:32

18s ahead, because GPS counted the 18 leap seconds since 1980 as regular non-leap seconds. But remember, to calculate elapsed time, you need to do it using 'UTCLeapSeconds'.

MATLAB: Datenum: how many seconds in a day

With regards to the datenum and related functions, MATLAB days are exactly 24h (86400s) always. There is accounting for leap days in calendar date conversions, but NO accounting for leap seconds. There is also no accounting for time zones. So it is up to the user to use the functions properly as MATLAB gives you no help here. That is, you can use the datenum family of functions to work with local times or UTC based times or TT based times, but you need to know what you are doing and make any adjustments (time zone, leap seconds, etc) yourself to get the correct result.

To quote the doc, the "now" function "... returns the current date and time as a serial date number." Since this is obtained from your computer's clock, and since your computer likely updates its clock from a UTC based server with time zone correction, what you get with the "now" function is a local time zone corrected UTC based time. UTC based times have leap seconds applied to them, so it is not a continuous time scale.

If you need to convert to a continuous time scale like TT or GPS, you will need to get a 3rd party conversion function. Basically, a table look up to account for leap seconds and then a constant offset will do the job. For example, astronomical algorithms typically take a TT based time as an input (to get planet positions, etc), so if you are trying to see where a planet is at 10pm tonight you would need to convert that local UTC based time to a TT time before feeding it to the astronomical algorithm. Online programs typically do this conversion for you in the background, but if you are writing a program yourself you would need to include that conversion in your program.

I think I have a MATLAB based UTC -- TT conversion program if you need it, or you might be able to find one in the FEX (I haven't looked).

Best Answer

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