9. Background and Related Information

This section presents some background information and other related stuff that one may find interesting or entertaining.

9.1. What is Mills-speak?
9.2. How can I convert a date to NTP format?
9.3. How can I convert an NTP Timestamp to UNIX Time?
9.4. Where can I find more Information?

9.1. What is Mills-speak?

Most people using NTP know that it has been invented by Professor David L. Mills. So they frequently address him to solve their problems. Unfortunately they mostly don't know about Mills-speak, the language used by the aforementioned person. To avoid some disappointment, I'll give a small example of Mills-speak.

Example 12. Mills-speak

Someone once had the misconception that the thing referred to as "nanokernel" were a kernel even smaller than a "microkernel". Forwarding the problem to Professor David L. Mills, the answer was:

"A nanokernel is a species of korn. Korn is grown on Jupiter as a dietary supplement by the Nanos, a prehistoric people of predominantly aquatic descent. The ancient enemy of the Nanos are the Micros, who also grow a variety of korn. Their variet is closely related to the eggplant of today, although we know the eggplant is distantly related to chickens. In Micro myuthology, chickens farm fields of eggplants that are specially grafted to korn and eventually evolve and emerge has hackers. Both Nanos and Micros prize hackers, which when planted in fields of chicken manure greatly vex the environmental authorities, since the confluence of the two peoples generally degenerate to clouds of messy, smelly swamp gas."

Another example follows.

Note: I'm not sure what question this answer refers to, but it could be referring to the fact that some black box NTP servers exist that use Linux as operating system. If you can correct me, please do!


Fancy that; when you pop the cover off the CPU chip, a little guy with pointy ears and a pitchfork snarls back at you. Like the time I popped the lid off a digital wristwatch and found a little Micky Mouse etched in the silicon.


Still another one dealing with specifications of clock errors:[1]


A little clarification. 12 PPM = 12 parts per million = 12 microseconds per second = 43 milliseconds per day = 0.602 seconds per fortnight. Most computer clocks have systematic frequency errors less than 100 PPM (see the briefings at the NTP project page), but some considerably more. These errors are due to the manufacturing tolerance and each clock oscillator is different.

Computer clocks are like a cat who never remembers where it has been, only steps ahead in more or less random directions. The cat has a general idea in which direction leads to food, just not a precise idea of how to get there. Mathematically, this represents random walk frequency noise. The important fact about this is that predictions of future cat directions get worse more rapidly as future time recedes.

The "after one year" has to do with crystal aging characteristics. The cat gets old and starts steering more to one direction than the other. Really clever clock discipline algorithms attempt to learn the particular cat aging characteristic and compensate for it. Unless you are talking about oven controlled quartz or rubidium or cesium, this is not something we do with computer cats.

This brings up the notion of specifications "after one day". Whoever said that doesn't understand cats. The cat forgets just about everything after maybe an hour. Anything said after one day applies equally after one hour as the cat wanders. The really ugly bottom line is that, considering the cat's memory, it doesn't make sense to try to discipline the feline by averaging things over much more than a thousand seconds or so. Lots and lots of professional folks who should know better don't understand this.

Most folks, including me, characterize each clock oscillator in terms of what is called Allan deviation. You can find much more detail on that at the NTP project page. The bottom line is that most computer clocks can steer to something like 1 PPM relative to its intrinsic frequency error and without outside discipline as long as nothing violent temperature-wise is happening.


9.2. How can I convert a date to NTP format?

NTP uses seconds since 1900, while UNIX uses seconds since 1970. The following routine by Tom Van Baak will convert the times accordingly:

 * Return Modified Julian Date given calendar year,
 * month (1-12), and day (1-31). See sci.astro FAQ.
 * - Valid for Gregorian dates from 17-Nov-1858.

DateToMjd (int y, int m, int d)
        367 * y
        - 7 * (y + (m + 9) / 12) / 4
        - 3 * ((y + (m - 9) / 7) / 100 + 1) / 4
        + 275 * m / 9
        + d
        + 1721028
        - 2400000;

 * Calculate number of seconds since 1-Jan-1900.
 * - Ignores UTC leap seconds.

SecondsSince1900 (int y, int m, int d)
    long Days;

    Days = DateToMjd(y, m, d) - DateToMjd(1900, 1, 1);
    return (__int64)Days * 86400;

9.3. How can I convert an NTP Timestamp to UNIX Time?

The following Perl code presented by Terje Mathisen (slightly improved by Ulrich Windl) will do the job:

# usage: perl n2u.pl timestamp
# timestamp is either decimal: [0-9]+.?[0-9]*
# or hex: (0x)?[0-9]+.?(0x)?[0-9]*

# Seconds between 1900-01-01 and 1970-01-01
my $NTP2UNIX = (70 * 365 + 17) * 86400;

my $timestamp = shift;
die "Usage perl n2u.pl timestamp (with or without decimals)\n"
    unless ($timestamp ne "");

my ($i, $f) = split(/\./, $timestamp, 2);
$f ||= 0;
if ($i =~ /^0x/) {
    $i = oct($i);
    $f = ($f =~ /^0x/) ? oct($f) / 2 ** 32 : "0.$f";
} else {
    $i = int($i);
    $f = $timestamp - $i;

my $t = $i - $NTP2UNIX;
while ($t < 0) {
    $t += 65536.0 * 65536.0;

my ($year, $mon, $day, $h, $m, $s) = (gmtime($t))[5, 4, 3, 2, 1, 0];
$s += $f;

printf("%d-%02d-%02d %02d:%02d:%06.3f\n",
       $year + 1900, $mon+1, $day, $h, $m, $s);

9.4. Where can I find more Information?

There are various sources of information about NTP. The following list is definitely not complete, but probably a good starting point:

  • Although intended for Solaris, the material mentioned in footnote [4] for Q: is a good introduction for system administrators.

  • The traditional NTP home page is located at http://www.eecis.udel.edu/~ntp. There you can find a lot of information about NTP and related topics. You will also find a collection of news articles that are indexed. That collection is also known as pseudo FAQ.

  • There is also a newer link http://www.ntp.org/ that currently is redirected to the one mentioned before. In 2005 the project page moved to http://support.ntp.org/.

  • One of the oldest sources of useful information is the newsgroup news://comp.protocols.time.ntp. That newsgroup is visited by many beginners as well as a few experts, and occasionally even the father of NTP will post a note there.

  • The page http://www.ijs.si/time/ (Time, with focus on NTP and Slovenia) contains a good summary of time synchronization using NTP as well as valuable references.[2]

  • Several technical papers by Professor David L. Mills are available at http://www.eecis.udel.edu/~mills/papers.htm.

  • Various RFCs deal with NTP. While newer RFCs obsolete older ones, it might still be interesting to read the older ones. Specifically there are PostScript versions with figures available.

    Table 4. RFCs related to NTP

    RFC NumberDateTitle or Description
    956September 1985Algorithms for synchronizing network clocks
    957September 1985Experiments in network clock synchronization
    958September 1985Network Time Protocol (NTP)
    1059July 1988Network Time Protocol (version 1) - specification and implementation
    1119September 1989Network Time Protocol (version 2) - specification and implementation
    1305March 1992Network Time Protocol (Version 3) - Specification, Implementation and Analysis
    1589March 1994A Kernel Model for Precision Timekeeping
    2030October 1996Simple Network Time Protocol (SNTP) version 4 for IPv4, IPv6 and OSI. Obsoletes [RFC 1361] and [RFC 1769])
    2783March 2000Pulse-Per-Second API for UNIX-like Operating Systems, Version 1.0
  • Never underestimate the usefulness of Internet Search Engines like Google. Take the time once to learn how to search efficiently, and benefit from that knowledge every time.

9.1. GPS

This section tries to give some information about GPS.

The Navstar Global Positioning System (GPS) had been developed in the seventies by U.S. military forces to supply position and time information all over the world. The system (to be precise: the GPS Space Segment) consists of 28 satellites (also termed Space Vehicles) orbiting the earth in six groups with four satellites in each group, roughly 20000km above the surface (12 hour orbits).[3] Each satellite has four atomic clocks (two Cesium, two Rubidium) for very high precision timing on board.[4] Currently it is controlled by the United States Air Force Space Command, Second Space Wing, Satellite Control Squadron located at the Falcon Air Force Base in Colorado. The satellites are monitored and controlled from four additional terrestial stations (Hawaii, Ascension Island, Kwajalein, and Diego Garcia).

To maintain the specified accuracy, most of the satellites require daily updates of their data, but some of them can receive and store corrections for several days. Under normal conditions the attitude error of the satellites is within 0.5, and the error on the surface is 16m. If no corrections are uploaded for 14 days, the positioning error on the surface will increase to 425m. After 180 days the error will be 10km. If a satellite operates without current correction data, it is called to be in extended operation.

The carrier used by the satellites to broadcast is 1.57542GHz, and the basic information consists of a pseudo random noise code of 1023 bits, sent within 1ms (clocked at 1.023MHz). The noise code is specific for each satellite, modulating the base carrier to produce a spread-spectrum signal. Transmission starts at the beginning of a new millisecond. This allows to set the receiver's clock modulo 1ms. The pseudo code can be used to lock the receiver within up to 10ns, depending on the noise of the signal. When using the carrier phase, the phase in the receiver could be correlated as close as 1ps.

Due to the military origin of GPS, the data is sent in a way that will not allow obvious decoding (despite of pure technical reasons). For example, one bit stream is combined with a pseudo random number sequence that spans seven days. Fortunately most of the secrets are explained today.

Basically the system works as follows:

The system offers two classes of precision:

Although derived from UTC (as presented by the U.S. Naval Observatory master clock, the UTC(USNO MC)), GPS time does not include leap seconds found in UTC, but the data stream provides the difference from UTC in seconds (See also Q: 2.2. and ftp://tycho.usno.navy.mil/pub/gps/gpstt.txt). At the time of writing the difference is 13s. While the difference between UTC and GPS time will change over time, there's a fixed offset between TAI and GPS time (19 seconds).

There is a military document describing the details of GPS, and it is very technical, but unclassified. The document is named ICD-GPS-200, and it can be found on ftp://ftp.navcen.uscg.mil/policy/icd200/icd200c.pdf (thanks to Nicolai E M Plum). The current version seems to be ftp://ftp.navcen.uscg.mil/policy/icd200/ICD200Cw1234.pdf (thanks to John Sager).

Example 13. A Glance at the GPS Sky

At the time of writing I could (virtually) see five out of nine visible satellites, the best candidates being 24, 5, 4, and 9 (From Table 5 you can see that my window is in the east, and that I have a rather nice view out there ;-). From these data GPS receiver computed my position as 49 11' 42" N, 12 16' 12" E, 260m.

Table 5. GPS Satellites

NumberElevationAzimuthDistanceDoppler Effect

Example 14. The Effects of Selective Availability

Most GPS receivers are unable to compensate for Selective Availability. As a virtually changing position causes time offsets (roughly 3ns per meter), it's interesting what the effects of SA are. For my GPS167 from Meinberg I examined the gps_position(LLA) that the clock driver showed. The following graphic shows the changing position over time, including a smoothed path.

These position changes have a comparatively small effect on time accuracy, but if one considers the computed altitude, the huge changes can accumulate to a few hundred nanoseconds. The following graph shows the varying altitude over time.

Finally, the following figure combines the three coordinates in space to give you an impression on how accurate GPS is:

9.1.1. Selective Availability revisited

On May 1st, 2000 there was an announcement about turning off Selective Availability (SA). The document titled President Clinton: Improving the Civilian Global Positioning System (GPS) quotes Bill Clinton: "The decision to discontinue Selective Availability is the latest measure in an ongoing effort to make GPS more responsive to civil and commercial users worldwide. --This increase in accuracy will allow new GPS applications to emerge and continue to enhance the lives of people around the wworld."

However the algorithm that is used for SA is not explained, and it seems SA has just been replaced by more selective availability ("New technologies demonstrated by the military enable the U.S. to degrade the GPS signal on a regional basis. GPS users worldwide would not be affected by regional, security-motivated, GPS degradations, and businesses reliant on GPS could continue to operate at peak efficiency." Pay attention to the wording "(...) could continue to operate (...)").

"Additional information about GPS and the Selective Availability decision is available online at the Interagency GPS Executive Board web site: http://www.igeb.gov"



As David Craggs (and others) pointed out, the calculation is obviously wrong: 12 PPM correspond to 43 ms per hour, and not per day. Likewise an error of 0.602 s per fortnight corresponds to a frequency error of 0.49 PPM.


The author allowed inclusion of his material into this FAQ. I really appreciate that.


Current Kepler data can be found at http://www.celestrak.com/NORAD/elements/gps-ops.txt. There is also some visualization software named WXtrack available at http://www.satsignal.net.


The very first and the latest satellites lack one Cesium clock.