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GENERAL GPS FAQs:
1. What is GPS ?
2. Why buy and use a GPS receiver ?
3. Who use GPS receivers ?
5. Latitudes and Longitudes (which is which?)
7. How do I convert a location's waypoint to a different map datum ?
8. What is Selective availability ?
9. What reference point is used for the waypoints of towns, cities and other large surface areas ?
10. GPS Antennae - How do they differ ?
12. How do I convert degrees from decimal degrees, degree-minutes and degree-minute-second formats?
13. How do I calculate the distance between two waypoints?
GPS is an acronym for "Global Positioning system".
The Global Positioning System (GPS) is a space-based radio navigation system, consisting of 24 satellites and ground support, that provides accurate, three-dimensional position, velocity, and time, 24 hours a day, everywhere in the world, and in all weather conditions. It was initiated in 1973 and the first GPS satellite was launched on 21 February 1978.
Currently there are two main systems in the world used for Global Positioning and navigation, that of the United State's NAVSTAR GPS and that of the Russians, called the GLONASS (GLOobal Navigation Satellite System). Due to the inherent limitations and relative inaccurate positioning obtained from the GLONASS , all commercial and most military use is based on the United State's GPS system. All references in the GPS WAYPOINT REGISTER are based on the NAVSTAR GPS system.
The GPS "Global Positioning system" consists of three main components.
1. GPS Ground control stations. (operated by the US Defense force)
The ground control component includes the master control station at Falcon Air Force Base, Colorado Springs, Colorado and monitor stations at Falcon AFB, Hawaii, Ascension Island in the Atlantic, Diego Garcia in the Indian Ocean, and Kwajalein Island in the South Pacific. The control segment uses measurements collected by the monitor stations to predict the behaviour of each satellite's orbit and atomic clocks. The prediction data is linked up to the satellites for transmission to users. The control segment also ensures that GPS satellite orbits remain within limits and that the satellite clocks do not drift too far from nominal orbits.
2. GPS satellites (The space component) The space segment includes the satellites and the Delta rockets that launch the satellites from Cape Canaveral in Florida, United States. GPS satellites orbit in circular orbits at 17,440 km altitude, each orbit lasting 12 hours. The orbits are tilted to the equator by 55° to ensure coverage in polar regions. The satellites are powered by solar cells to continually orientate themselves to point the solar panels towards the Sun and the antennas towards the Earth. Each satellite contains four atomic clocks. (Currently (Y2000) only 21 of the 24 launched satellites are operational on 6 orbital levels.)
3. GPS receivers (what you buy and use to determine your position and support your personal navigation)
When you buy a GPS, you are actually buying only the GPS receiver and get free use of the other two main components, worth billions of dollars - compliments of the Government of the United States. (If you don't have a GPS, BUY ONE NOW, before losing out on the free use of billions of dollars of technology !)
The ground stations send control signals to the GPS satellites, The GPS satellites transmit radio signals and the GPS receivers, receive these signals and use it to calculate its position.
The calculations used to determine your GPS receiver's position is based on very small time differences, from when the satellite transmitted the signal, to, when the GPS receiver received the signal. These small differences is then used to calculate the distance from the receiver to the satellite. However, when receiving only one signal, we can only calculate how far away from the satellite we are. When receiving two signals, we can determine two likely positions where we are. We need three satellite signals to determine our exact position on the earth's surface. (2D/2 Dimensional positioning). When more than three satellites are "visible" to the GPS receiver, it will also calculate the altitude of the receiver (3D/3 dimensional positioning).
Your GPS receiver requires signals from at least three satellites to determine your unique position on the earth's surface. With a fourth signal your altitude can also be determined. Receiving signals from more than four different satellites, the position of the GPS receiver can more accurately be determined. (See accuracy hereafter)
The GPS satellite constellation is designed in such a manner as to guarantee that at least 4 satellites are visible from any place on earth at any moment in time. Most of the time (+95%) however, you should have at least 6 satellites visible. Many commercial GPS receivers can receive and process signals from 8 to 12 satellite signals for increased reliability and accuracy.
GPS satellites carry atomic clocks that measure time to a high degree of accuracy. The time information is placed in the codes broadcast by the satellite so that a receiver can continuously determine the time the signal was broadcast. The signal contains data that a receiver uses to compute the locations of the satellites and to make other adjustments needed for accurate positioning. The receiver uses the time difference between the time of signal reception and the broadcast time to compute the range to the satellite. The receiver must account for propagation delays caused by the ionosphere and the troposphere. With three ranges to three satellites and knowing the location of the satellite when the signal was sent, the receiver can compute its three-dimensional position.
To compute ranges directly, however, the user must have an atomic clock synchronized to the global positioning system. By taking a measurement from an additional satellite, the receiver avoids the need for an atomic clock. The result is that the receiver uses four satellites to compute latitude, longitude, altitude, and time.
Why buy and use a GPS receiver ?
"Many people look and ask why? , I look and ask why not?" - JF Kennedy
The GPS system is doing for navigation what cell phones are doing for communication. Personal navigation instruments (GPS receivers) will become as commonplace as personal communication instruments (Cell phones) - very soon !
Why should you use a GPS receiver ?
1. No more getting lost - Get to your destination on time.
2. Have confidence when traveling - no more wondering which way, left or right, at the un-mapped fork in the road.
3. Ease of use - It is easier to use a GPS receiver than to navigate by using a map. On the GPS screen you can see where you want to go (as in a map) but also where you are (as must be guessed on a map)
4. GPS receivers are going to replace traveling maps - GPS receivers are smaller to carry, easier to handle, much more versatile and updateable.
5. Personal navigation with a GPS also means you can customize maps as you go along - plotting points of interest and marking all those wonderful places in an easy, neat and ordered manner.
6. GPS receivers (like GARMIN's GPS III+) will also provide you with traveling support information, such as your :
Estimated time of arrival (ETA) at your selected destination,
How much fuel you have left (much more accurate than your fuel gauge in the car or truck)
Your true speed (with an accuracy of +/- 0.1 km/h)
and much more....
7. Log your route as you travel to keep an accurate record of your traveling in case you need to "trace back your steps". This is true for walking distances of a few meters to routes of many hundreds of kilometers.
8. GPS maps are scaleable with scales ranging from 30 meters to many hundreds of kilometers
9. Time information on all GPS receivers are continuously adjusted from the atomic clocks used in the GPS system - the most accurate time and timing sources available today.
10. Use, for your own personal benefit, technology worth billions of dollars - for free with the compliments of the USA !
Should we go on explaining why you will be using a GPS receiver very soon ?
Who use GPS receivers ?
Although the GPS system was initially created as a means of supporting the navigational and positioning requirements of the military, it has entered our personal lives and will become a more and more indispensable aid to personal navigation.
GPS receivers are currently used by:
1. Off-road travelers in:
desert areas (eg. Namib) ,
in the bushveld,
swamp areas (eg. the Okavango),
mountainous areas (eg. Drakensberg),
ice and snow fields (eg. Antarctica)
unknown or newly visited areas.
2. All those in aviation and shipping, from pleasure trips to all commercial and military cruising, sailing and flying
3. Tourists to:
locate their own positions in unknown areas,
find the position of their destinations,
Get route from where they are to where they want to go
avoid identified "dangerous or hazardous" areas
let them enjoy the scenery instead of worrying where they are.
4. To mark and find all those special:
Fishing spots
Diving spots
Look-out points
Game-viewing spots
Adventure sport venues
etc.
5. Rescuers in search-and-rescue operations
6. BMW owners with the built-in GPS receivers now in BMW cars in South Africa (all the new 3,5 and 7 series)
7. It is expected that Daimler-Benz will soon announce their satellite navigation system in their cars as well. - so Mercedes and JEEP might be next.
8. Soon all vehicle manufacturers will follow BMW's direction with regards to satellite navigation systems.
See the press release (01 May 2000)from the Clinton Administration regarding GPS Accuracy !
The physical laws governing the theory on the GPS and navigational issues are exact and should, in the ideal world, leave us with exact navigational calculations and positioning. The GPS relies on the integration of many aspects in order to eventually calculate the exact or true position at any point in time. However - we live in an imperfect world and the GPS, as smart as it is, is also not perfect. Hence the inherent inaccuracy of GPS positioning. To understand accuracy factors when using GPS receivers for positioning, we should understand the different errors and their combined (non-linear) impact on positioning accuracy. Error analysis can be performed by a so-called "truth"-model, but again, is only as good as the "truth"-model itself. However, for general Traveling purposes, we should not be to worried about GPS errors and inaccuracies. How close to an oasis do you need to get in the desert before you actually can see it ?
For all practical purposes we can combine all error effects and rely on the following accuracies:
1. Military purposes - Accurate to 1 meter (not available for commercial or other use)
2. Civilian GPS receivers - Horizontally : between 7 and 20 meters (Have a look at our Error histogram)
- Vertically: between 60 and 100 meters
3. Civilian DGPS** receivers - Horizontally between 2 and 7 meters
- Vertically between 60 and 100 meters
** DGPS = Differential GPS (with differential beacon receiver) A differential receiver can be fitted to most
GARMIN GPS receivers, including some handhelds.
4. Civilian survey class differential instruments
(with acknowledgement to Anton Reynecke (Land Surveyor - Thanks Anton !)
Civilian survey class differential instruments gives accuracies in the order of one to two centimetre for horizontal, and three to four for vertical, depending on the distance from the base (fixed) station. The centimeter level accuracy is for anything up to the order of 20 km from the base, and degrades slightly for longer distances.
These accurate receivers were available and operative even with Selective avalability stil active since some 12 (I think) years ago.
These type of instruments are rather pricey, currently (Nov 2000) in the order of R 300 000.00 for a rover and a base station.
GPS errors can be classified according to the sources of the errors:
1. Environmental induced errors
These errors arise from inaccuracies in the modeling of the environment, Ionospheric conditions and changes in ionospheric conditions, inability to determine or predict the direction and magnitude of the gravitational vectors at any given time at a given location, inaccuracies in modeling the earth's shape etc. Ionospheric interference on GPS signals are counteracted by using dual frequencies to completely remove the impact of the ionospheric interferences in military receivers. Unfortunately, only one frequency is available for civilian GPS receivers and they have to rely on mathematical models to estimate the distortion impact of free electrons on the satellite signals. Of the inherent inaccuracy of 15 meters for civilian GPS receivers without SA, about 5-10 meters are due to the influence of ionospheric interferences, and unless that improves, we can do nothing else to increase the accuracy of one-frequency, civilian GPS receivers.
Satellite geometry or constellation, is another source of errors or inaccuracy. DOP (dilution of precision) is the term used to describe the impact of the satellite geometry on the accuracy of GPS receiver readings. On the GARMIN 3+, the DOP figure can be read directly on the main screen as an indication of the effect thereof. DOP has a number of components: horizontal, vertical, position, time and geometric. When visible satellites are in a straight line and relatively close to each other, DOP will be at its greatest. GARMIN GPS receivers calculates the different DOP figures from all visible satellites and uses the "best" positioned satellites based on the LPDOP, (lowest position DOP) A calculated DOP value of more than 6 might lead to a GPS receiver not locking onto the satellites due to the large error that might result. The best thing to do in such a case is to wait a few minutes and the try again.
Reflected satellite signals (ie. from mountains) might lead to a multi-path signal (that is more than one path of one satellite's signal) which cannot be corrected by normal civilian GPS receivers and readings based on multi-path signals will therefore not be accurate.
2. Computational errors
All our GPS components rely on digital computer systems to perform all calculations. Rounding errors, Overflow errors, limited stack space etc. all contributes little by little to the inherent accuracy capability of our GPS receivers. When performing velocity calculations, we can use State-estimation techniques, relating to the motion of the sensor (ie. acceleration), to perform measurements with the resultant impact on accuracy.
3. Alignment errors
GPS sensors should all, theoretically, be perfect aligned with their "assumed" directions. Again, differences in actual alignment and "assumed" alignments lead to small errors in the "chain of calculations" and influence the accuracy of our GPS receiver coordinate read-outs.
4. Instrumentation induced errors
From the GPS ground control stations to the GPS Satellite constellation to our GPS receivers, uses sensors to sense various variables. These sensors may sense variables that do not equal the actual physical quantity it is measuring. Impurities in sensor material, random noise sensed, sensor noise (especially at high frequencies), inaccurate zero-settings or bias, sampling rate, scale factors etc. may all influence the accurate sensing of physical sensed quantities and lead to instrument induced errors.
The above errors lead to the so-called inherent accuracy limitation on commercially available GPS receivers which is currently in the order of 15m. Again nothing to get really worried about when navigating to that oasis in the desert.
5. Human induced errors.
Very obviously but sometimes forgotten - are your map-datum on your GPS corresponding to the Map datum that was used for determining the original Waypoint ?? Large errors might result from using two different map-datums to reference the same location.
For a view on the impact on accuracy while marking waypoints on the move - look here
A map datum is a reference surface which is defined mathematically and approximates the shape of the earth in particular areas. At different areas across the world, different map datums were (and some still are) used due to the differences in the earth's general surface shape at different places. Specific map datums are more applicable to particular areas or regions than others.
A particular map datum is physically represented by a group of surface based trigonometric stations, whose positions have been accurately measured and is used to determine the reference surface (or map datum)
A map datum enables us to calculate the position of a specific location accurately and consistently. However, there are significant deviations, when a waypoint (a longitude and latitude set) located with a particular map datum, is used with a different map datum as reference. So it might appears that a specific point on the earth's surface, have different latitudes and longitudes, depending on the map datum that was used, or alternatively, one waypoint (a longitude and latitude set) may seems to point to different physical positions !
Currently there are many, many map datums in use. The Garmin III+ supports more than 100 different map datums (see our list and applicable countries) to reduce the inaccuracy caused by the deviations of different map datums. Theoretically this implies that one waypoint can locate more than 100 different places, all depending on the map datum that was used as reference.
All GPS and map users should be aware of this peculiarity and take note of the most applicable map datum to be used. If you use waypoints from any source, or use a map with longitudes and latitudes, make sure that your GPS is using the same map datum as used originally to determine the waypoint.
In South Africa, most maps use the CAPE datum (based on the modified Clarke 1880 ellipsoid), (not to be confused with the CAPE CANAVERAL map datum). So if you are working with South African maps and would like to use waypoints indicated on them, SET YOUR GPS to the "CAPE" map datum.
The World Geodetic System 1984 ellipsoid, or WGS84 in short, is the basis for the Hartebeeshoek94 datum, suitable for all GPS users. Slowly but surely, all waypoints references are moving towards this internationally accepted datum. So if you use data with this map datum, SET YOUR GPS to the "WGS84" map datum.
With the Garmin III Plus receiver, you can set the Map datum under the main menus's option : setup / Position / Map datum.
THE GPS WAYPOINTS in the GPS WAYPOINT REGISTER, are using the WGS84 map datum, unless indicated otherwise.
For another view on Map datums, click here.
For free download of software to convert from one Map datum to another, click here.
For a comprehensive (VERY GOOD) description of the WGS 84 map datum and formulas on map conversions, in South Africa look at this.
How do I convert a location's waypoint to a different map datum?
The mathematics involved in map datum conversions are quite involved and will not be discussed here. Have a look here for software capable of transforming between different map datums. However, there is quite and easy way to convert from one map datum to another - available directly on your GPS !
Say for example that you would like to convert a waypoint from the CAPE map datum to the WGS84 map datum.
1. Set your GPS map datum to "CAPE". With the Garmin III Plus receiver, you can set this under the main menus's option : setup / Position / Map datum.
Enter a waypoint such as
S 25d50.653m E028d09.282m.2. Now set your GPS map datum to "WGS84" and note the converted waypoint.
S 25d50.687m E028d09.264mThe differences in the longitude and latitudes in the above example, translates to an error of 69 meters if map datums are used incorrectly.
The GPS satellites are owned and controlled by the U.S. Department of Defense and they used to degrade the accuracy of the GPS signal available to commercial users. This is known as "Selective Availability" (commonly known as "SA").
Since 01 May 2000, SA was however dropped by the Clinton Administration and we no longer have to worry about it. See the press release. (however, it is not to say that SA may not be switched on again for whatever reason !!!)
What reference is used for the waypoints of towns, cities and other large surface areas ?
Traditionally, post-offices was used by some institutions as a reference point for cities and towns. Due to the mapping of other large surface areas like dams, lakes and pans, the currently used method is to use the calculated centroid of the area as the reference point.
GPS Antennae - How do they differ ?
For recreational and traveling purposes, standard GPS receiver antennas can be classified into two groups:
1. Upright antennas (or rather Quadrifilar helix antennas) as used in the GARMIN GPS 3+ receiver:
Rectangular in shape, mostly visible and external to the main housing of the receiver
Can detect satellites right on the horizon
Cannot normally detect satellites directly overhead
Should be held upright for best reception
2. Flat antennas (or rather Patch microstrip antennas) as used in the GARMIN 12 GPS receiver
Flat patch, usually not visible and internal to the receiver's housing
Can detect satellites directly overhead
Cannot detect satellites on the horizon
Should be held flat for best reception
External antennas linked via cable to the GPS receiver, are normally much more sensitive than internal antennas and allows for comfortable positioning within a vehicle, boat or other enclosures. Some "active" external antennas are available to actively amplify the antennas signal before sending it to the GPS receiver in order to compensate for the signal loss through the cable.
Degrees are the POPULAR method of measuring angles. Normally we do that by expressing an angle in the "degree-minute-second" format. However, degrees are not the NATURAL measure of angles. If we look at scientific calculations we realise that RADIANS are the natural means of calculating angles. RADIANS are always expressed as decimal figures and hence are easy to use in calculations. However, indicating an angle as 0.785398163 radians is not as meaningful as expressing it as 45 degrees. So, we end up between the need to calculate and the need to quickly understand. Radians calculates easily in formulas (i.e. to determine the distance between two waypoints) but degrees, minutes, seconds are more easily understood.
In the GPS WAYPOINT REGISTER, we express all co-ordinates in the decimal degree format. This is a compromise that we do to still allow easy calculations but also to be easily understood. Using decimal degrees therefore allows us to easily do calculations (12.3 degrees + 12.6 degrees = 24.9 degrees) instead of some more complicated calculations involved when working with degree-minutes or degree-minute-seconds (i.e. 12d36.55m + 12d29m49s = ??) while still being able to produce an understandable figure. (How large is and angle of 0.66519 radians ??)
The conversion between decimal degrees and radians are straight forward when using the following formulas:
degrees = radians * 180 / PI
Radians = degress * PI / 180
How do I convert degrees from decimal degrees, degree-minutes and degree-minute-second formats?
by using the following formulas in a MS Excel spreadsheet: (which you can Download)
To convert decimal degree (DD) to degrees-minute (DM) format:
DM = TRUNC(DD)&"d "&INT((B6-TRUNC(DD))*60*1000)/1000&"m"
which will yield DM=12d 7.407m when DD=12.12345
To convert decimal degree (DD) to degree-minute-second (DMS) format:
DMS = TRUNC(DD)&"d " &TRUNC((DD-TRUNC(DD))*60)&"m"
&INT(((B6-TRUNC(DD))*60-(TRUNC((DD-TRUNC(DD))*60)))*60*10)/10&"s","")
which will yield DMS = 12d 7m 24.4s when DD=12.12345
To convert degree-minute-seconds (DMS) to decimal degrees (DD) format:
DD = INT((LEFT(DMS,2)+MID(DMS,4,2)/60+MID(DMS,7,4)/3600)*100000)/100000&"d"
which will yield DD = 12.58241d when DMS = 12.34.56.7
To do these calculations, you can download the degree format conversion calculator as an MS Excel spreadsheet. (Note that it has macros which you need to enable - if your browser asks you)
How do I calculate the distance between two waypoints?
To calculate distances between two waypoints requires the use of the "great circle formula" because the earth is round (approx) and we have to take that into consideration when working with relatively large distances.
The formula is:
Distance = acos(sin(lat1)*sin(lat2)+cos(lat1)*cos(lat2)*cos(lon1-lon2))
where lat1,lon1 = latitude and longitude of waypoint1 (in radians)
and lat2,lon2 = latitude and longitude of waypoint2 (in radians)
When using decimal degrees (instead of radians as above) to perform the calculations it becomes:
Distance = ACOS(SIN(lat1/180*PI)*SIN(lat2/180*PI)+ COS(lat1/180*PI)*COS(lat2/180*PI)*COS(lon1/180*PI-lon2/180*PI))*180*60/PI)
where PI = 3.141592654.......
or you can download the Distance calculator in MS Excel format.
