Tropospheric Effects on GNSS

Transcription

1 Tropospheric Effects on GNSS The Atmosphere and its Effect on GNSS Systems 14 to 16 April 008 Santiago, Chile Dr. M. Bakry El-Arini

2 Background 1 of The troposphere contains about 80% of the atmosphere It is a few kilometers above the Earth s surface In this layer, the average temperature decreases with height (e.g., -5ºC to -7ºC/km) -100C -80C -60C -40C -0C 0C 0C Vertical temperature profile of the ICAO Standard Atmosphere Each layer is characterized by a uniform change in temperature with increasing altitude In some layers there is an increase in temperature with altitude In others it decreases with increasing altitude 146 of 301 The top or boundary of each layer is denoted by a 'pause' where the temperature profile abruptly changes Vertical temperature profile of the ICAO Standard Atmosphere in mid-latitude (Boundary heights increase toward Equator) Reference [1]

3 Background of Layers of Earth s Atmosphere 147 of 301 Reference []

4 Tropospheric Effects On GNSS Atmospheric and Rain Attenuation Tropospheric Scintillation Tropospheric Delay 148 of 301 Reference [3]

5 Atmospheric and Rain Attenuation 1 of Atmospheric attenuation is dominated by oxygen attenuation in the 1- GHz band Very small About 0.035dB at zenith About 0.38 db at 5 degrees elevation angle The effects of water vapor, rain, and nitrogen attenuation at L-band frequencies are negligible 149 of 301

6 Atmospheric and Rain Attenuation of Rain attenuation is very small at L-band and could be negligible For even dense rainfall (e.g., 10 cm/hour) is less than 0.01 db/km 150 of 301 Reference [3]

7 Tropospheric Scintillation 1 of It is caused by irregularities and turbulence in the atmospheric refractive index in the first few kilometers above the ground The propagation link through troposphere is affected by a combination of random absorption and scattering from a continuum of signal paths that cause random amplitude and phase scintillations in the received waveform Scintillation effect varies with time and is dependent upon frequency, elevation angle, and weather conditions, especially dense clouds At L-band, these effects are small except for a small fraction of time and at low elevation angles 151 of 301 Reference [3]

8 Tropospheric Scintillation of CCIR Model (see Appendix A): 10% of the time, the RMS of Tropospheric scintillation db at E = deg 0.9 db at E = 5 deg 0.3 db at E = 0 deg The model may not be accurate below 5 degrees 15 of 301 Reference [3]

9 Tropospheric Delay 1 of Signal received by GNSS satellite is refracted by the atmosphere as travels to the user on or near the Earth s surface The atmospheric refraction causes a delay, depends on Actual path of the curved ray Refractive index of the gases along that path For a homogenous (or symmetric) atmosphere around the user antenna, the delay depends only on the vertical profile of the atmosphere and the elevation angle 153 of 301 Reference [3]

10 Tropospheric Delay of 154 of 301 Excess delay = dry component (90%) + wet component (10%) Δ = Δ zd.m d (E) + Δ zw.m w (E) Δ zd = dry zenith delay caused mainly by N and O 90% of total delay About.3m Function of T & P Predictable within 1% in a few hours Δ zw = wet zenith delay Caused by water vapor 10% of total delay <= 0.80m Varies 10-0% in a few hours Less predictable m d (E) & m w (E) are mapping functions vary with elevation angle Vertical Integral of refractivity at Pago Pago, Samoa 1967, Balloon data, Reference [3])

11 155 of 301 Tropospheric Refraction vs. Pressure and Temperature Refractivity N = (n-1)10 6 is given by: P e N = + TZ TZ T Where d ( n 1) 10 6 = = Nh N w d w P d = partial pressure of dry (hydrostatic) air (millibars) e = partial pressure of water vapor (millibars) T = Temperature in degrees Kelvin = C Z d and Z w = compressibility factors correct for small departures of the moist atmosphere from an ideal gas. They are functions of P d, e & T Ideal gas: PV = RT Non-ideal gas: PV = ZRT R = Universal gas constant Reference [3]

12 Tropospheric Empirical Models 1. Saastamoinen Total Delay Model. Hopfield Two Quartic Model 3. Black and Eisner (B&E) Model 4. Altshuler and Kalaghan (A&K) Model 5. Davis, Chao, and Marini Mapping Functions 6. UNB SBAS Tropospheric Model (See RTCA MOPS 9D) 7. LAAS/GBAS Tropospheric Model (See RTCA MOPS 54A) For Models 1 to 5, see reference [3] for more details and summary in Appendix B 156 of 301 For Models 6 & 7 see references [4 and 5] and details in MITRE briefing tomorrow

13 Appendix A Tropospheric Scintillation 157 of 301

14 Tropospheric Scintillation 158 of 301 A received carrier from a satellite has Define the scintillation intensity x x p f [ ] () t = 0log10 A() t / A() t () = A t () A t fluctuations have a pdf ( σ ) CCIR : m x = 1 = 0.05 f At L1: σ has a log - m 1 x 7 /1 x ( sin E) = exp π db the mean (short term) amplitude of Probability density function (pdf) of normal statistics the form : A( t) sin( ωt + φ) () t as the log of the amplitude ratio A() t / A() t ( logσ logσ ) db 0.85 ( sin E) db x σ σ x that is a log - normal : () t (in db) = N ( 0, σ ) The rms value of σ in db is itself a random variable with a mean σ and its long term σ σ σ = σ σ σ = carrier frequency in GHz = GHz at L1 m the signal. Reference [3] x m,

15 Appendix B Tropospheric Models 159 of 301

16 Saastamoinen Standard Total Delay Model The tropospheric delay correction (Δ) in meters is given by (E 10 degrees): 155 Δ = T 0 0 ( + D) secψ 0 P e0 B tan ψ + δ R Where P 0 = partial pressure of dry (hydrostatic) air (mbars) e 0 = partial pressure of water vapor (mbars) T 0 = Temperature (K) B & δ R = correction terms are function of user height (lookup table) ψ 0 = 90 E = Zenith Angle E = Elevation angle D = cos(φ) h φ = local latitude h = station height in km 160 of 301 Reference [3]

17 Hopfield Two Quartic Model The refractivity is given as a function of height by N ( h) = N ( h) + N ( h) The tropospheric delay correction (Δ) in meters is given by Where 161 of 301 N N d w ( h) = ( h) = N 1 for h h = 1km Δ = Δ N d d d 0 w0 + Δ 1 w w h h d h h w = 5 for h h 6 d w = 43km ( h + N h ) Nd 0 d w0 w Δ d and Δ w can be calculated by integrating N d (h) and N w (h) h d and h w are the heights (km) above the surface level where N d0 and N w0 are measured Reference [3]

18 Black and Eisner (B&E) Model [3] The tropospheric delay correction (Δ) in meters is given by Δ = ( ) ( ) Δ + dz Δ wz m E Where m(e) is the mapping function which is function of elevation angle E 7 degrees m ( ) E = 1 ( ) sin E 16 of 301

19 Altshuler and Kalaghan (A&K) Model [3] The tropospheric delay correction (Δ) in meters is given by Where for elevation angle E(deg), height above sea level h (ft) 163 of 301 Δ m H F N (, ) ( ) ( ) (, ) meters E h N =, s s 4 ( E) = ( E 30) ( h) m E ( h ) ( h ) ( h, N s ) = ( h ) h ( ( N 315) ) s = h 0.944φ h s πm s = sin 1 Average global surface πm, c = cos, M = refractivity N H E E E = h s φ s h F h N [ ] ( winter), 4.5( spring), 7.5( summer),10.5( fall) = 34.8,st. dev. σ N N = s h c φλc

20 Davis, Chao, and Marini Mapping Functions Marini s Mapping function is a continued fraction (a, b, c, are constants) 1 m( E) = a sin E + b sin E + c sin E + sin E +... Chao s Mapping functions Davis mapping function is similar to Marini s except a and b are function of the surface temperature and pressure and c = of 301 m d ( E) =, m ( E) sin E tan E w = sin E Reference [3] tan E

21 References Spilker, J. J., Tropospheric Effects on GPS, Chapter 13, Volume I, Global Positioning System: Theory and Applications, Editors B. W. Parkinson and J. J. Spilker, The American Institute of Aeronautics and Astronautics, Inc., Washington, D.C., RTCA, Inc., Minimum Operational Performance Standards for Global Positioning System/Wide Area Augmentation System, DO-9D, RTCA, Inc., Washington, D.C., RTCA, Inc., Minimum Operational Performance Standards for Local Area Augmentation System, DO-45A, RTCA, Inc., Washington, D.C., of 301