GNSS navigation
GNSS receivers output location data that on their own does not allow navigation . Only the offsetting of several successively recorded position data allows navigation to a destination.
Applications
Satellite display (GPS)
The picture on the right shows a typical representation of the received GPS satellites on a GPS receiver. The concentric circles depict the visible firmament as a central projection. The red center is the zenith of your own location, the outer circle is the horizon, the intermediate circles are 30 ° and 60 ° elevation respectively. The snapshot shows six satellites, the receiving location is in southern Germany. The four satellites marked in green transmit position data. The signal strength of the two blue satellites with the numbers PRN-19 and PRN-11 is too weak for an evaluation at the time of the measurement. At approx. 30 ° W and an altitude of approx. 40 °, marked by the letter “E”, the western EGNOS transponder is on a geostationary satellite. Modern GPS receivers evaluate its correction signals. Garmin branded devices display the letter “D” in the signal intensity bars when considering EGNOS data. Under favorable circumstances, the spatial resolution increases to a few meters.
Devices made by Garmin do not issue the correct three-digit PRN code for DGPS satellites, but a value reduced by 87. EGNOS satellites with PRN codes 120 and 131 are assigned 33 and 44, WAAS satellites 35 and 47.
Course indicator
The course is the connecting line between the starting point ( Origin ) and the target ( Destination ). Usually the starting point is determined at the moment the destination is entered. The course pointer of a device shows the course direction. The splitting of the pointer is a measure of the course deviation ( off course ). In the picture the deviation is 231 m. The scale is determined by the small number at the top right next to the scale, here 0.25 km with maximum split. With some devices the color changes when the maximum value is exceeded.
drift
The quickest way to get closer to your goal when traveling on earth is to walk towards it. In the case of ships or aircraft that are exposed to transverse drift, the path to a curve, the homing curve , is longer .
Devices record the path ( track ) covered almost in real time and can therefore determine the deviation between the bearing and the track. Only when the angular deviation, the turn , is reduced to zero, one moves in a straight line to the target point. The vehicle's longitudinal axis ( heading ) is rotated by the lead angle from the direction of travel. The bearing display of the device then does not show along the vehicle axis, but offset by the lead angle.
accuracy
For navigation calculations with an accuracy of 1%, it is sufficient to set the earth as a sphere with a radius of R = 6,371 km. For small distances below 500 km, the difference between Orthodrome and Loxodrome is negligible.
Over the circumference of the earth, the distance Δs L is obtained directly from the length difference ΔL (in degrees) of two points (with known latitude B (in degrees)) :
- Δs L = 2 * π * R * ΔL / 360 ° * cos (B)
With a latitude difference ΔB at latitude B (in degrees) the distance between two points is: Δs B
- Δs B = 2 * π * R * ΔB / 360 °
The accuracy of today's GPS receivers is approx. 5 m. Conventional GPS devices therefore limit the input to a thousandth of a minute: gg ° mm, mmm 'or tenth of a second: gg ° mm' ss, s ". The following applies:
- 0.00001 degrees correspond to 1.1 m
- 0.001 minutes corresponds to 1.8 m
- 0.1 seconds corresponds to 3 m
Along the 60 ° latitude, these distance values are reduced to about half.
Data format
The interface of receiving units is standardized. The data is provided in the so-called NMEA format . Some wireless mice deliver this data stream directly. When the recipient processes the data further, he creates a so-called track from the raw data . It is a series of waypoints that are recorded at short intervals. One speaks of a route when the track has been reduced to a few essential waypoints. A waypoint itself is the coordinate representation of a point in space. It describes at least the location coordinates longitude and latitude, usually also the time of recording and altitude. Special waypoints are given further attributes, for example a description or a comment. Almost all proprietary standards can be converted into the open XML-based format GPS Exchange Format (GPX). The newer versions of Google Earth can also display GPX.
GPS signal
Commercial devices evaluate the L1 signal with GPS, which transmits user data at a data rate of 50 baud . A data block, frame , comprises 1500 bits, corresponding to a transmission time of 30 s. Each frame is made up of 5 subframes . Subframes 1 to 3 transmit the ephemeris and correction values of the transmitting satellite. The subframes 4 and 5 send data sets of the strongly rounded ephemeris and status information of other GPS satellites. 25 frames (12.5 min) are required for the transmission of a complete almanac of all satellites, a maximum of 32 according to the specifications of the GPS system. The almanac data provide clues for the identifier, the status, the position and the Doppler shift in order to accelerate the location after switching on the receiver ( time to (first) fix (TTF)).
The movement of the satellites causes a Doppler shift of ± 5 kHz, that of the receiver up to 1.46 Hz per 1 km / h speed. The 2 MHz wide signal from a satellite is therefore at the nominal frequency with an accuracy of ± 10 kHz. The first step in signal evaluation is the correlation of the satellite signal with the PRN codes of the individual satellites. Old receivers could only search the signal sequentially, modern ones search simultaneously with 200,000 or more correlators. Extended integration times increase the sensitivity for signal detection.
The signal strength of the GPS satellites in the open air is between –158 dBW and –160 dBW. GPS can also be received in buildings and vehicles, provided the attenuation does not exceed 30 dB (concrete wall) to 40 dB. In an underground car park reception is almost impossible. Once the satellites have been captured, tracking is possible even if the attenuation is higher. Metal-coated windows in ICE trains weaken the GPS signal by up to 30 dB, so that GPS signals can only be received near the exit doors.
Military systems, and later also Galileo and modern GPS, transmit on two to three frequencies. This improves the ionospheric correction for the signal propagation time and the data rate and thus the position accuracy. The integrity of the position data can still only be assessed with sufficient certainty using additional services.
Determinants
When receiving signals from a satellite:
- Time with an accuracy of <1 µs.
When receiving signals from three satellites:
- Position with an accuracy of <20 m
When receiving signals from four satellites:
- Height, mostly related to the WGS84 ellipsoid, with an accuracy of <30 m
- Determination of the speed of the receiver via Doppler shift (simple GPS receivers derive them from the change in position) with an accuracy of <0.05 m / s
- Accuracy from satellite geometry ( DOP )
When receiving signals from more than four satellites:
- Improvement of the position accuracy <10 m (height <20 m).
When receiving the signal from a DGPS satellite such as EGNOS :
- Improvement of the position accuracy <5 m
Derived quantities
- Speed (from position and time difference)
- Descent rate (from altitude and time difference)
- Glide ratio (ratio of horizontal and descent speed)
- Absolute height (conversion e.g. based on geoid undulation tables )
- Positions of stars, for example the time of sunrise and sunset
When entering a target point
- Heading angle
- speed made good
- Time to destination and estimated time of arrival
Restrictions
Civil receivers for GPS are subject to the COCOM limits . Introduced by CoCom , they still exist in the Wassenaar Agreement to this day. The restrictions apply from one
- Speed higher than 1000 knots (1900 km / h),
- Altitude over 60,000 feet (18,000 meters).
The receivers from some manufacturers switch off when one of the restrictions is exceeded. Other manufacturers interpret this limitation more generously and the receiver only switches off when both limitations are exceeded. This restriction is intended to prevent civilian GPS receivers from being used to control missiles or similar weapon systems.
See also
Individual evidence
- ↑ John Graham-Cumming: GAGA-1: CoCom limit for GPS , November 28, 2010 (English)