Satellite positioning GPS principles 1 GPS NAVSTAR Global

Satellite positioning GPS principles 1

GPS NAVSTAR 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. 2

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: [x. S 2, y. S 2] [x. S 1, y. S 1] r 2 r 1 [x, y] 3

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 2 , y 2 , z 2 ) (x 1 , y 1 , z 1 ) (x 3 , y 3 , z 3 ) Dk 1 z Dk 3 (x, y, z) y x 4

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= 299 792 458, 0 m/s In fact it is impracticable to synchronize the receiver with time accuracy 10 -9 s (resulting space accuracy about 0, 3 m) 5

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 2 D) instead of desired intersection point (constant difference of radii). • For all enumerated distances the same correction of distance ri must be added: Δr 1= Δr 2 = Δri = Δr = Δt. c • Next unknown variable Δr is to be solved together with unknown coordinates [x, y, z]. 6

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. 7

Orbital trajectories • Satellites are in distance of approximately 20200 km upon Earth surface. Circulation tine is 11 hodin 58 minut. Satellite velocity is 11 300 km/h. 24 satellites in function provide permanent visibility of at least four satellites from any point on the Earth. 8

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 L 1 = 1575, 42 MHz, L 2 = 1227, 60 MHz) theoretical accuracy about 0, 02 m. (For this method uninterrupted intact signal receive is essential). This method is used in geodesy. 9

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: http: //tubo. fce. vutbr. cz/new/ at B = 49° 12' 21" N L = 16° 35' 34" E 10

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