1. Hyperbolic Navigation

2. Hyperbolic navigation
A class of navigational system based on the difference in timing between the reception of two signals, without reference to a common clock.
Timing reveals the difference in distance from receiver to the two stations.
plotting all potential locations for measured delay produce a series of hyperbolic lines in a chart
Taking two measurements and finding their intersection reveals receiver’s location
Any other form of navigational information can be used to eliminate ambiguity and determine a fix.

3. Hyperbolic navigation
earliest known use was during World War I as acoustic location system for locating enemy artillery
Based on radio techniques:
GEE by Royal Air Force for use by RAF Bomber Command
Decca Navigator System in 1944 by the Royal Navy
LORAN by the US Navy for long- range navigation at sea

4. Hyperbolic navigation
Timing-based navigation
baseline T R
“secondary”
300km, exactly 1ms apart at light speed T
“master”
Two ground-based radio stations
Both equipped with identical transmitter
One of the station is equipped with a radio receiver, called “secondary”
When the receiver hears the signal from the other station referred to as the “master”
The master can broadcast any series of pulses, with the secondary hearing these and generating the same series after 1ms delay.

5. Hyperbolic navigation
Absolute vs. Differential timing
Time it took to reach the receiver- basis of modern electronics
1930s: crystal oscillator- drifts 1 to 2 seconds in a month
1960s: commercial atomic clocks
Difference between two signals
1935 and 1938: Chain Home by UK – radar didplay s based on oscilloscopes, producing a “blip” when return signal sent into the scope display
The signals from secondary arrive they would cause a blip on the display in the same fashion as a target on a radar, and the exact delay between the master and secondary can be easily determined.

6. Hyperbolic navigation
If the receiver is located on the midpoint of the baseline the two signals will be received at exactly the same time, so delay between them will be zero.
Receiver cannot determine exact location, only that it lies perpendicular to the baseline
By plotting a chart, producing a measured delay they form a hyperbolic curve centred on the baseline
The operator can determine which of these lines they lie on by measuring the delay and looking at the charts
Consists of nothing more than a conventional radio receiver hooked to an oscilloscope

7. Gee System

8. GEE System Development
October 2937, R. J. Dippy : system that would measure difference in time arrival
1938, Dr R. V. Jones: suggested use of pulse transmitters but without success
1940, R. J. Dippy : for a master station with three slave for navigation
December 1942, R. J. Dippy : awarded the British Patent for his invention
Trinity – the three transmitter used to ascertain position
“Goon” – mask of the name GEE
“grid” – the meaning of GEE, the electronic grid latitude and longitude derived from the combination of three signals received by the aircraft

9. GEE System Signal Characteristics
transmission of short (6 microseconds) pulses at frequencies around 30Mhz(later extended up to 80Mhz)
Slaves operate on the same frequency as their master
On baseline extension behind the slaves the difference would be zero and the pulses would overlap.
Sample of the GEE lattice

10. GEE System Signal Characteristics
master (A) always appeared at the start of both traces of a twin trace presentation. The B slave after the master on the top trace, the C slave after the master on the lower trace, and the D slave appeared on both traces but was a double pulse. The correct A pulse for starting the time base was selected by arranging the A transmitter to transmit twice as fast as the others but making every other pulse a double one. The final appearance of the time base was as in the figure.

11. A GEE Mk II rceiver/indicator with cabling
GEE System
GEE Equipment
A GEE Mk II rceiver/indicator with cabling

12. Gee station components
GEE System
GEE Equipment
Gee station components

13. Gee set installation in a Lancaster bomber mockup
GEE System
GEE Equipment
Gee set installation in a Lancaster bomber mockup

14. Close up of Gee Indictor
GEE System
GEE Equipment
Close up of Gee Indictor

15. GEE System
GEE CHAINS
Become the standard in the US eight Air Force as well as in RAF
Radiated power output around 330kW and operated in four frequency bands between 20 and 85 MHz. Approximately limited to 150 miles at ground level and 450 miles for high flying aircraft
1954 – a new receiver was designed
1970- the last GEE chain being taken out of service
GEE coverage in UK in August 1948