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The troposphere is the lower part of the atmosphere extending nominally to 50 km above the surface of the planet The troposphere is composed essentially of electrically neutral particles and for L-Band signals it is nondispersive The troposphere experiences changes in temperature, pressure, and humidity associated with weather Because these same variables a ect the density of the air mass along the signal path and the index-of-refraction is a function of air mass density, tropospheric conditions a ect the measured time-of-propagation with the measured value being larger than that the geometric range Tropospheric delays

04/15/10

(866)

can be quite considerable ( 30m) for satellites at low elevations Tropospheric delay errors are consistent between the L1 and L2 signals and

04/19/10

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carrier and code signals The tropospheric delay cannot be computed from the GPS observables; therefore, tropospheric e ects are compensated via models For most users, especially in navigation application, the input parameters for the models are average or typical values for the user location Users with higher accuracy requirements can add meteorological instruments to sense the model input variables or may use di erential GPS methods The refractive index is a ected di erently by the water vapor and by the dry components (eg, nitrogen and oxygen) of the troposphere, so tropospheric models account for these wet and dry pressures separately The wet component is di cult to predict due to local variations in the water vapor content of the troposphere and accounts for approximately 10% of the tropospheric delay The dry component is relatively easier to predict and accounts for approximately 90% of the tropospheric delay Several models exist for the tropospheric wet and dry components [4, 104, 119, 122] The models contain two parts The rst part of the model is the estimate of the zenith delay The second part is a slant factor to account for the satellite elevation For example, the Chao model is dry Fdry wet Fwet T = = = = = 2276 10 5 P 1 000143 sin(E) + tan(E)+00445 470 102 sin(E) + e146 e123 o + 1705 106 o 3 T2 T 1

04/21/10

where is the tropospheric delay expressed in meters, P is the atmospheric N pressure in m2 , T is the temperature in K, eo is the partial pressure of water vapor in millibars, is the temperature lapse rate in K per meter, and E is the satellite elevation angle The partial pressure eo can be computed from T and the relative humidity In most navigation applications, tropospheric delay is not compensated by equations such as this due to the expense involved in measuring the required formula input variables Instead, simpli ed formulas have been determined which only depend on satellite elevation, receiver altitude, and satellite altitude The Magnavox and Collins algorithms are, respectively, TM T C = =

hr hs 2208 e 6900 e 6900 sin(E) hr 24225 e 74928 0026 + sin(E)

04/23/10

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