1. Satellite positioning GPS principles

2. GPS NAVSTAR Next compatible systems: GLONASS, Galileo
Global Positioning System
NAVigation Satellite Timing And Ranging Global Positioning System
Next compatible systems: GLONASS, Galileo
It is a passive system which determines position of receiver with use of data transmitted from satellites.

3. Intersection of two circles – plane problem
Input: centers of circles and radii (equivalent to satellite position and distance).
We are able to solve coordinates x,y of intersection (receiver position) from a set of two equations:
[xS2, yS2]
[xS1, yS1] r2 r1
[x,y]

4. Intersection of three spheres – spatial problem
Our measured position on the Earth surface has coordinates (x,y,z)
We know coordinates of three sphere centers (satellite positions) and radii of them (distances from our position to satellites) – DKi=ri=radius in picture
Intersection of three spheres is our position. Coordinates x,y,z are enumerated from set of three equations
(x,y,z) x y z
(x1 ,y1 ,z1 )
(x2 ,y2 ,z2 )
(x3 ,y3 ,z3 )
Dk1
Dk3

5. Determination of distance
GPS satellite transmitter sends position and time. GPS receiver detects time of signal reception.
Let us assume absolute synchronization of clock both on satellite and receiver.
Then we can enumerate the distance to satellite knowing the speed of signal propagation which is equal to speed of light: c= ,0 m/s
In fact it is impracticable to synchronize the receiver with time accuracy 10-9s (resulting space accuracy about 0,3 m)

6. Calculation for unsynchronized receiver clock
Receiver clock is inaccurate, its time is shifted in unknown value of Δt. It results in geometrical terms to hyperbola (in 2D) instead of desired intersection point (constant difference of radii).
For all enumerated distances the same correction of distance ri must be added: Δr1= Δr2 = Δri = Δr = Δt .c
Next unknown variable Δr is to be solved together with unknown coordinates [x,y,z].

7. Set of equations for spatial solution
Set of four equations for four unknown variables must be used.
It results to desired coordinates [x,y,z] radius (distance) correction Δr.
Using set of four equations means necessity to receive data from four satellites at the same time.
More satellites may be used for higher precision.

8. Orbital trajectories
Satellites are in distance of approximately km upon Earth surface. Circulation tine is 11 hodin 58 minut. Satellite velocity is km/h. 24 satellites in function provide permanent visibility of at least four satellites from any point on the Earth.

9. Accuracy of the system
Code measurement – C/A code – theoretically about 3 m
Code measurement – P code (10 × higher frequency) – theoretically about 0,3 m
Phase measurement (oscillation frequency L1 = 1575,42 MHz, L2 = 1227,60 MHz) theoretical accuracy about 0,02 m. (For this method uninterrupted intact signal receive is essential). This method is used in geodesy.

10. Permanent stations providing corrections
Network of permanent GPS stations (např. CZEPOS) provides corrections to eliminate refraction of signal in atmosphere layers
Nearest permanent station TUBO – see: at B = 49° 12' 21" N    L = 16° 35' 34" E

11. Methods to spread corrections
SBAS – Satellite Based Augmentation System – EGNOS satellites
Terrestrial radio broadcast
Internet data distribution – – connection possible via GPS module integrated in GPS apparatus