© Brooke Clarke 2015 - 2023

    Position, Velocity, Time
        2015 Receivers
    Garmin 67i


For decades I've been interested in the relationship between time and position which is called Navigation.  This also relates to Surveying.  To determine the location of seaport cities accurately telegraph lines were run across the oceans connecting cities where one of them had an astronomically set clock allowing the longitude of the other city to be accurately determined.  The synchronization of clocks, like the Western Union clocks made by the Self Winding Clock Company was a hot topic in the late 1800s and early 1900s and the Swiss patent office saw many applications, many (most, all?) of them read by a college drop out named Einstein who used that knowledge as background to come up with the idea that time was relative but the speed of light was absolute.  Without him the GPS would not work for a couple of reasons.

Einstein's theories of time dilation and the effect of gravity on clocks both show up in the GPS system, see:
PROVING EINSTEIN RIGHT! (YouTube, Gresham College) - although if the satellite clocks were left uncorrected, but all with the same error, the system would work without any errors.


1957 Sputnik (Wiki)

The Doppler shift plot allowed the orbital parameters of the satellite to be determined.  The idea developed that if you knew the orbital parameters of the satellite then you could find out where you were which resulted in the Transit (Wiki) satellite system.

1959 Vella Hotel (Wiki) part of the Project Vella (Wiki)

Satellites to monitor compliance with the 1963 Nuclear Test Ban Treaty (Wiki). 

1959 - 1996 Transit (Wiki)

An operational Doppler (Wiki) based navigation (and surveying) system that requires a very high quality frequency standard in the receiver and also requires 10 to 16 minutes of data gathering to make the Doppler plot.  Transmits on 150 & 400 MHz.  Does not include altitude just Latitude and Longitude.  Since a precision frequency standard is part of the receiver precision time could be part of the receiver.  I don't think time transfer was part of the design.
Developed so that a submarine carrying Polaris missiles (Wiki) could get position fixes to update their inertial navigation systems (Wiki).  The gyroscopes in inertial navigation systems drift so the position accuracy drifts with time and thus periodically needs a new fix.  This was done using a chronometer and sextant prior to Transit.

YouTube - Transit: Three Decades of Helping the World Find Its Way (1996) - 1/10 nutical mile system accuracy.
Yo-yo de-spin (Wiki) was not quite good enough, so magnetic
Developed gravity gradient stabilization (Wiki)
There was no space program so many aspects were developed in parallel with the Transit specific aspects.  One of these was geodesy (Wiki) since be measuring the position of the satellite allows calculation of the gravity that's perturbing it's orbit, just as today retro-reflectors on GPS satellites allow making scientific measurements that are not part of the GPS functioning.

1967 - 1974 Timation (Wiki)

An experimental system to test ideas related to satellite navigation, not an operational system.
Five hundred mile high orbit and 12 to 16 minutes of visibility per pass.  Transmits on 150 & 400 MHz.  While the user can get by with a quartz based frequency standard the control stations used Cesium frequency standards.  48 meters CEP type of accuracy.

1967 AF Project 621B (Wiki: Francis X. Kane)

Includes the idea that four satellites are used to get not only three dimensional position but also recover time so a low cost crystal oscillator can be used in the receiver.

Nuclear Detonation Detection System

This is an upgraded version of Project Vela Hotel where the location of any nuclear detonation is to be determined by satellite.  Because the GPS satellites are in very well known positions by simply adding the X-Ray and Gamma ray sensors the location of ground or air nuclear blast could be determined. It's my understanding that by adding this function to the navigation system developed under Project 621B the GPS program received adequate funding to proceed, but without it the system would not have flown.
GPS uses the L3 frequency for NDS (Wiki)

1978 GPS (Wiki)

Development started in 1978 prototype satellites were launched.

1983 KAL007 Shot Down (Wiki)

A navigation error caused the plane to overfly the USSR during the cold war.  Ronald Reagan published details of the GPS system allowing civilians to use it, but with Selective Avaliablity turned on to degrade the accuracy compared to military users who have the needed cryptographic codes to get higher accuracy.

2000 SA Turned Off (Wiki)

During the 1990 Gulf wars SA was turned off from time to time so that civilian GPS receivers, like the Trimble Trimpack, would be more accurate.  This was the first use of GPS in planning and actual combat.  In 2000 Bill Clinton turned off Selective Availability so everyone now gets maybe 10 meter accuracy rather than the 100+ meter accuracy with SA turned on.

2023 update - current civilian accuracy is much better, see Garmin 67i for a test.


The satellites broadcast a signal.  They do not receive any signal from the receivers.  While a GPS receiver knows it's position the system as a whole has no idea where each GPS receiver is located.  Hollywood does not seem to understand this.

Modern passenger jets, like MH370 (Wiki), have GPS receivers and their position is part of the outgoing message on the transponder (Wiki).  But since the range of the transponder is line of sight if the plane is more than about 100 miles out to sea, or the transponder is turned off, there's no secondary radar receiver that's going to hear it.   Note the GPS receiver may be on and operational, but the position information is only known to the receiver, not the GPS system.

Position, Velocity, Time(PVT)

The military in interested in learning about the position, velocity and time from a GPS receiver.
Position: Most people know GPS is good for determining your position.
Velocity:  In my opinion this is a carryover from the Transit system where Doppler shift (relative velocity) was a key idea.
Time: Modern cryptographic systems require that their system clock be accurate to a fraction of a second in order to work.  So getting accurate time from GPS has always been a part of military GPS receivers.


There are a number of ways of looking at accuracy.

A standalone GPS receiver can get into the area of 1 to 4 meters accuracy in real time readings.  This accuracy can be greatly increased by using post processing (logging the raw GPS data and some days later using reference station data on the actual position of the satellites rather than the broadcast ephemeris data) to determine the actual location of a fixed receiving antenna.  This can provide sub cm accuracy.

A Real Time GPS receiver that is getting real time correction data is called Real Time Kinemetic (Wiki RTK).  There are many sources for argumentation (correction) data (AF GPS web page) such as:

Nationwide Differential GPS System (NDGPS) - These are low frequency correction stations that pretty much blanket the U.S. and many other countries, mostly near coastlines. Operated by governments and free to users.  The range of the transmitters is on the order of hundreds of miles so you use the station closest to were you are and so the quality of the corrections is better than systems tha have broader coverage.

Wide Area Augmentation System (WAAS) - The transmitters are located on stationary satellites and so the corrections are for a Wide Area and in my opinion are not as good as local differential corrections.  Only the newer GPS receivers get these free signals, but they do help get receiver accuracy into the 1 meter area.

Continuously Operating Reference Stations (CORS) - these are precision receivers of geodetic quality that record data on all the satellites and make it public for post processing GPS data to survey accuracy.  Free to users but not real time.

Global Differential GPS (GDGPS) - Only for big money users in the future.

International GNSS Service (IGS)  - Only for research organizations with money.

Commercial services - There are satellites that broadcast real time correction data that you can subscribe to.

Your own GPS reference station.  The idea is to have a geodetic quality GPS receiver send data to a VHF or UHF radio transmitter from a known location.  The GP in the field receives the correction data and uses that to improve it's accuracy.  The receivers that achieve 1 meter or less accuracy need some type of real time correction signal.

2015 Accurate Receivers

The thing that prompted me to make this was page was a list of GPS receivers with enhanced accuracy available to civilians, which at the time GPS was developed was an impossible idea. 
esri  - The Democratization of Accuracy, Sep 2015- esri is the company that makes GIS mapping software, and it's used for the maps in the DAGR GPS receiver.

Bad-Elf GNSS Surveyor
The Democratization of Accuracy
The Democratization of Accuracy

1 meter

Bad Elf GNSS Surveyor -   hand held - 1 meter accuracy 3300 (1 meter, $600 retail), 2200, Pro, Pro+ (2.5 meters)

sub meter

Trimble Navigation R1 - hand held - pocket - submeter with correction signal (RTX) $2500 retail
Spectra Precision Mobile Mapper 300 - antenna on tripod - no display - requires a smart phone $(ask)
Geneq iSXBlue - hand held, pocket - no display - requires a smart phone $2,000 to $4,000 range

Single cm

Eos Arrow 200 - pole mounted antenna & receiver, no display - requires a smart phone, 10cm with satellite corrections, 1cm requires local reference receiver, $(ask)


Septentrio Altus NR2 - combined antenna + receiver requires tripod and


Spectra Precision Mobile Mapper 300, the Geneq iSXBlue - See more at:
At the time GPS was developed there was a limit on how accurately an orbit could be described using the Two-line Element (Wiki: TLE)  The model used is based on classical physics where the location of the shape of the orbit is described as well as some terms for drag and maybe solar winds.  This approach would treat all satellites in the same orbit the same independent of the actual particulars of the satellite.  Thus each GPS satellite transmits it's location using the on board ephemeris (Wiki) data that is determined by the control ground stations.  This set of data is built into the hardware of the GPS system, satellites and receivers.

YouTube - Ian Morison - Proving Einstein right! -

A better way is to add the effects of photons bouncing off each satellite.  This perturbation can be determined and more accurate orbital parameters determined.  But this is  not part of the GPS system but rather an enhancement some scientists are using.

Trimble Navigation R1

 Garmin GPSMAP 67i

2023 Nov 23: Tried averaging for a couple of minutes over a survey nail in my driveway.  Done with Milti-GNSS Satellite System. (GPS, GALLIEO, QZSS, BEIDU, IRNSS)

N  39:11:24.94  (deg:min:sec - 1 sec = 101' so least significant digit = 1 foot)
W 123:09:51.58  (deg:min:sec - 1 sec = 80' so least significant digit ~ 10 inches)
867' elevation (sitting in chair with 67i held up).




JPL - GIPSY-OASIS - The Automatic Precise Positioning Service, of the Global Differential GPS (GDGPS) System. (on line post processing)


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