GPS-errors-1
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GPS measurements are affected by random and systematic errors that impact accuracy. Errors originate from satellites, signal propagation through the atmosphere, and receivers. Satellite errors include orbital inaccuracies and clock errors. Signals pass through the ionosphere, a dispersive layer, causing refraction dependent on frequency. Receivers have clock errors. Combining dual-frequency measurements eliminates ionospheric delay, the main source of error.
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GPS-errors-1
- 1. GNSS Surveying, GE 205 Kutubuddin ANSARI kutubuddin.ansari@ikc.edu.tr Lecture 3, March 8, 2015 GPS Error
- 2. X GPS Errors GPS measurements are both affected by several types of random errors and systematic errors which affects the accuracy of measurements
- 3. GPS Errors Originating at the satellites Originating signal propagation or atmospheric refraction Originating at the receiver
- 4. Satellites Errors 1. Ephemeris or Orbital Error •Satellite positions are a function of time •Forces acting on the GPS satellites are not perfect •Errors in the estimated satellite positions known as ephemeris errors.
- 5. Satellite Position Error Baseline Error Range Satellite Baseline Length = Thumb Rule to estimate Orbital Error
- 6. 2. Selective Availability Selective availability (SA) is a technique to deny accurate real-time autonomous positioning to unauthorized users. • δ -process is achieved by dithering the fundamental frequency of the satellite clock. • ε-error is the truncation of the orbital information in the transmitted navigation message so that the coordinates of the satellites cannot accurately be computed. • SA turned on, nominal horizontal and vertical errors could be up to 100m and 156m, respectively.
- 7. SA is on SA is off
- 8. Each GPS Block II and Block IIA satellite contains two cesium and two rubidium atomic clocks. The satellite clock error is about 8.64 to 17.28 nanoseconds per day. The corresponding range error is 2.59 m to 5.18 m GPS receivers, in contrast, use inexpensive crystal clocks. The receiver clock error is much larger than that of the GPS satellite clock. 3. Satellite and Receiver Clock Errors
- 9. B M O C •A signal that bounces of a smooth object and hits the receiver antenna. •Increases the length of time for a signal to reach the receiver. •A big position error results. •Gravel roads •Open water •Snow fields •Rock walls •Buildings Receiver Error Multipath Error
- 10. PHASE Phase is the fraction of a wave cycle which has elapsed relative to an arbitrary point
- 11. If a and φ denote the amplitude and the phase of the signal direct signal = a cosφ indirect signal =β a cos(φ+Δ φ) Where β is a damping factor a cos + a cos( + ) (1+ a cos ) a cos - ( sin ) a sin ϕ β ϕ ϕ β ϕ ϕ β ϕ ϕ ∆ ∆ ∆ Multipath Error The superposition of signals is represented by: 1+ cos cos sin sin M M M M β ϕ β ϕ β ϕ β ϕ ∆ = ∆ ∆ = ∆ Let us consider where the subscript M indicates multipath
- 12. 2 sin = 1+ +2 cos , tan 1 cos M M β ϕ β β β ϕ ϕ β ϕ ∆ ∆ ∆ = + ∆ β may vary between 0 and 1 β = 0 (no reflected signal and no multipath) βM = 1 and ΔφM =0 the resultant signal is identical to the direct signal β =1 (The strongest possible reflection ) = 2(1+cos ) =2 cos 2 sin 1 tan tan 1 cos 2 2 M M M ϕ β ϕ ϕ ϕ ϕ ϕ ϕ ϕ ∆ ∆ ∆ ∆ ∆ = = → ∆ = ∆ + ∆ The best way to eliminate multipath error is to construct the observation site with no reflecting surface and objects in its locality.
- 13. Earth’s Atmosphere Solid Structures Meta l Signal Propagation or Atmospheric Refraction Errors
- 14. 1. Ionosphere •The uppermost part of the earth’s atmosphere (50 km and 1000 km), ultraviolet and X-ray radiations coming from the sun interact with the gas molecules and atoms. •These interactions result in gas ionization, a large number of free, negatively charged, electrons and positively charged, atoms and molecules, such a region of the atmosphere where gas ionization takes place is called the ionosphere.
- 15. • The electron density within the ionospheric region is not constant, it changes with altitude. As such, the ionospheric region is divided into sub regions, or layers, according to the electron density • The altitude and thickness of those layers vary with time, as a result of the changes in the sun’s radiation and the Earth’s magnetic field. • The ionosphere is a dispersive medium, which means that it bends the GPS radio signal and changes its speed as it passes through the various ionospheric layers to reach a GPS receiver
- 16. The dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency and such type of medium is called dispersive medium Dispersive Medium In a dispersive prism, material dispersion causes different colors to refract at different angles, splitting white light into a rainbow.
- 17. Phase and Group velocity The phase velocity of a wave is the rate at which the phase of the wave propagates in space (red dot). The group velocity of a wave is the velocity with which the overall shape of the wave’s amplitudes propagates through space (green dot).
- 18. Phase and Group velocity For a single electromagnetic wave propagating in space with wavelength λ and frequency f The phase velocity: phv fλ= The group velocity: 2 gr df v d λ λ = −
- 19. Rayleigh Equation 2 1 , , ph ph ph ph ph gr ph dvdf dv df fd f d d dv dvdf df f f d d d d dv v v d λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ = + = − = − = − = − +
- 20. Refractive Index c n v = The refractive index n of a material is a dimensionless number that describes how light propagates through that medium. It is defined as: where c is the speed of light in vacuum and v is the phase velocity of light in the medium
- 21. Depends on Refractive Index (n) Modified Rayleigh Equation ph gr ph gr c c v and v n n = = 2 2 1 1 1 1 1 , 1 1 1 1 1 , 1 (1 ) 1 ph ph gr ph ph gr ph ph ph ph gr ph gr ph ph ph ph gr ph dn dnc c c n n n d n n n d dn dn n n n n n d n d dn a a n n d λ λ λ λ λ λ λ λ λ λ − − = + = + = + = + ÷ ÷ ÷ ÷ − = − ⇒ = −
- 22. Modified Rayleigh Equation ph gr ph we have c f d df f dn n n f df λ λ λ = = − ⇒ = +
- 23. Ionospheric Refraction The ionosphere extending in various layers from about 50 km to 1,000 km above earth is a dispersive medium with respect to the GPS radio signal. Following Seeber series .. Neglect higher order terms 32 2 3 1 ......ph cc n f f = + + + 2 2 2 2 3 2 1 , 2 1 ph ph gr c n f dn c c n df f f = + = − → = −
- 24. Ionosphere dispersive relative to GPS Radio Signal Ionospheric Refraction 2 2 2 2 2 2 2 gr ph gr ph 1 , 1 c = - 40.3 Ne (electron density) 40.3 40.3 1 , 1 n > n , v < v ph gr ph gr c c n n f f n Ne n Ne f f = + = − = − = +
- 25. Pseudorange = Geometric range + Range correction (Measured Range) = (Actual Range) + Error Pseudorange
- 28. Total Electron Content (TEC) TEC is an important descriptive quantity for the ionosphere of the Earth. TEC is the total number of electrons integrated between two points, along a tube of one meter squared cross section. The TEC is measured in a unit called TECU, where 1TECU=1×1016 electrons/m2
- 29. GPS Frequencies • Each satellite sends down exactly the same two radio frequencies L1 at 1575.43 MHz L2 at 1227.60 MHz •At these microwave frequencies the signal are highly directional and hence are easily blocked, as well as highly reflected by solid objects and water surfaces
- 30. For the dual frequency (L1, L2) observation, TEC in the slant direction can be calculated from the pseudo range (P) and phase observations ( ) asɸ Total Electron Content (TEC) 2 2 1 2 2 12 2 1 2 2 2 1 2 1 22 2 1 2 1 ( ) 40.3 1 ( ) 40.3 f f TEC P P f f f f TEC f f φ φ = − ÷ − = − ÷ − Here, P1 and P2 are pseudoranges and ɸ1 and ɸ2 are phases of carriers L1 and L2 respectively. For simplification: 2 19.52 ( )TEC P P= −
- 31. STEC is the total electron content calculated on the path different than local zenith. The value of TEC consists of both the STEC along a satellite receiver ray path and instrumental bias B (constant) STEC= TEC + B Slant Total Electron Content (STEC)
- 32. Vertical Total Electron Content (VTEC) The electron content calculated on the local zenith path is called Vertical Total Electron Content (VTEC) 2 E max R cosα VTEC=STEC× 1- Re+h ÷ where α is the elevation angle, RE the radius of the earth (RE=6378 km) and hmax (=350 km) is the height of the ionospheric shell above the surface of the earth
- 33. • TEC is a very complicated quantity depends on sunspot activities line of sight (includes elevation and azimuth of satellites) position of observation etc. • Determination of TEC is essential • TEC effects needs to be measured, estimated, modelled or eliminated Total Electron Content
- 34. Various time its very difficult to measure , estimate or model the value of TEC Most efficient method is to eliminate the value of TEC Its very easy to eliminate it by using two signals with different frequencies and this the main reason why the GPS signal has two carrier waves L1 and L2 It can be done by linear combination of pseudorange models so that ionospheric refraction cancels out Elimination
- 35. Start with Code Pseudorange model with ionosphere affects Elimination L1 1 L2 2 R ( ) R ( ) Iono L Iono L c f c f ρ δ ρ δ = + ∆ + ∆ = + ∆ + ∆ fL1,fL2 frequency of the two carriers Linear Combination RL1, L2=n1RL1 + n2RL2
- 36. L1,L2 1 1 2 2 L1,L2 1 2 1 1 2 2 1 1 2 2 1 1 2 2 R [ ( )] [ ( )] R ( )( ) ( ) ( ) For Elimanation ( ) ( ) 0 ( ) Assuming n =1, n ( ) Iono Iono L L Iono Iono L L Iono Iono L L Iono L Iono L n c f n c f n n c n f n f n f n f f f ρ δ ρ δ ρ δ = + ∆ + ∆ + + ∆ + ∆ = + + ∆ + ∆ + ∆ ∆ + ∆ = ∆ → = ∆ Elimination
- 37. 2 2 2 2 2 1 2 2 L1, L2 L1 L22 1 But 40.3 TEC f n R =1.R .R Iono ph L L L L f f f f ∆ =− =− ⇒ − Elimination
- 38. Ionosphere free linear combinations Code ranges This is the ionospheric free linear combination for code ranges. A similar ionospheric free linear combination for carrier phase may be derived as Carrier phases 2 L1, L2 L1 L2 1 =1. .L L f f Φ Φ − Φ 2 2 L1, L2 L1 L22 1 R =1.R .RL L f f −