Theoretical background of satellite navigation systems functioning

1. Lecture 4
Theoretical background of satellite
navigation systems functioning

2. The Soviet Union launched Sputnik 1 into an elliptical low Earth orbit on 4 October
1957. The success began the Space Age. The launch ushered in new political, military,
technological, and scientific developments.
The satellite travelled at about 29,000 kilometers per hour, taking 96.2 minutes to
complete each orbit. It transmitted on 20.005 and 40.002 MHz which were monitored
by amateur radio operators throughout the world.
Mass 83.6 kg
Semimajor axis 6,955.2 km
Eccentricity 0.05201
Inclination 65.1°
Apogee 939 km from surface
Perigee 215 km from surface
Orbital period 96.2 minutes
The history of satellite navigation begins from the first
artificial satellite launch

3. American physicists at APL (Applied Physics Laboratory) with the help of radio
signals from Sputnik 1 tested theory that it would be able to determine satellite orbit
by analyzing the Doppler shift of its radio signals during a single pass. Also were
suggested that if the satellite's position were known and predictable, the Doppler
shift could be used to locate a receiver on Earth.
receiver

4. DOPPLER EFFECT
The Doppler effect (or the Doppler shift) is the change in frequency or
wavelength of a wave for an observer who is moving relative to the
wave source.
Where
is the velocity of the receiver relative to transmitter

5. DOPPLER EFFECT VISUALIZATIONS

7. The first satellite navigation system, TRANSIT was first successfully tested in 1960.
The TRANSIT system satellites broadcast two UHF carrier signals (on 150 and
400 MHz) that provided satellite's six orbit elements and
orbit perturbation variables. The critical information that allowed the receiver to
compute location was a unique frequency curve caused by the Doppler effect
TRANSIT (USA)
Six satellites gave worldwide coverage every
90 minutes and provided positions that were
accurate to within 200 m

8. Tsiklon is the first Soviet satellite navigation system. It
was to use the Doppler navigation method and be
placed in 800 to 1000 km altitude orbit.
Experimental flights began in 1967. First trial showed a position error of 3 km,
which was intolerable. A large part of the problem was with inaccuracies in the
software models available for predicting the satellites ephemerides. Follow work
under this problem resulted in a 10 to 30 times improvement in the accuracy.
Gross mass: 800 kg .
First Launch: 1967.05.15.
Last Launch: 1978.07.27.
Total Number of satellites: 31 .
TSICLON SATELLITE SYSTEM (USSR)

9. TIMATION
Satellite Timation-1 was launched May 31,
1967 into a 500 nautical mile polar orbit.
The success of Transit stimulated to investigate more advanced versions of a
space-based navigation system with enhanced capabilities. Such system was
TIMATION. The concept of TIMATION was to broadcast an accurate time
reference for use as a ranging signal to receivers on the ground. The results of this
program formed the basis for the Global Positioning System (GPS).

10. Trilateration –based Satellite Navigation Systems
Doppler-based navigation systems have given way to systems based on the
principle of ‘trilateration’as they offer global coverage and have better
accuracy as compared to the Doppler-based systems.
Trilateration involves measuring distances. Let’s take a look into this with a
bit more detail.

11. Using a simple two-dimensional example, let’s imagine we have three satellites
each with a known position in space.
all that satellites do is broadcast a signal for your receiver to pick up with a
specific time and distance.

12. For example, the first satellite broadcasts a signal that eventually hits your GPS
receiver. We don’t know the angle, but we do know the distance. That’s why this
distance forms a circle equal in all directions.
This means that your GPS position could be anywhere on this circle at this
specific radius.

13. What happens when your equipment receives a second signal?
Again, this distance is equally broadcasted in all directions until it hits your
receiver. This means that the distance could be anywhere on that circle.
But this time, we have two known distances from two satellites. With two signals,
the precise position could be any of the two points where the circles intersect..

14. Because we have a third satellite, your true location can be revealed where all three
circles intersect.
Using three distances, trilateration can pinpoint a precise location. Each satellite is
at the center of a sphere and where they all intersect is the position of the receiver.

15. But the reality is in our three-dimensional world that satellites broadcast signals as a
sphere. Each satellite is at the center of a sphere.
Where all spheres intersect determines the position of the GPS receiver.

17. A satellite transmits a time signal. By measuring the difference in time from when
the signal left the satellite to when it is received the distance from the satellite to
the user can be calculated. This is the product of the time difference and the
speed of light (300,000 km/sec).

18. With one satellite, and knowing the position of that satellite, the location of the user
would be anywhere along an arc. If three satellites were used, the location of the
user would be at the intersection of the three arcs created by the satellites, as
shown. Stated mathematically, in order to solve for the three dimensional position
(with three variables: latitude, longitude and altitude), three equations (or
satellites) are needed.

19. RANGE MEASURING METHOD

21. The location of the receiver is somewhere in the area defined by
the clock bias for each satellite.

22. PSEUDORANGE MEASURING METHOD

24. modern satellite navigation system
GPS, GLONASS, Galileo have to use
configurations allow users to have a
simultaneous observation of at least 4
satellites in view worldwide, even in
case of partial shading .

25. In order to measure the time delay between satellite and receiver, the satellite sends
a repeating 1,023 bit long pseudo random sequence. Each PRN code is a noise-
like, but pre-determined, unique series of bits. Each satellite transmits a unique
PRN code, which does not correlate well with any other satellite's PRN code.

26. The receiver has the PRN code sequence for each satellite. The receiver
constructs an identical sequence and shifts it until the two sequences
match. Difference between transmit time and receive time Δt.
Pseudorange to satellite is R=Δt·c.

28. Algorithm for determination satellite positions