Document Type : Research Paper
Authors
Abstract
In this paper a practical method for tropospheric effects on GPS derived coordinates in absolute mode is presented. GPS observations at the permanent GPS stations can be used as source of information for the modeling. The developed model is a time-dependent model and as such differs from usual tropospheric models, which are based on atmospheric parameters, i.e. temperature, pressure and humidity. Tropospheric effect on the GPS signals are a source of error, which cannot be eliminated via dual frequency observations. In the other words troposphere is a non-dispersivences environment and therefore, unlike the ionospheric refraction, the effect of tropospheric on the absolute positions cannot be eliminated based on dual frequency observations. What we are presenting in this paper is an operational method for reduction of tropospheric refraction error of the GPS signals, based on continues GPS observations at the permanent GPS stations. The algorithmic procedure of the developed method begins with the processing of the GPS observations at the permanent GPS station according to following procedure: (1) Processing the GPS observations based on dual carrier phase technique (to remove/reduce the effect of ionospheric error and to obtain more precise coordinates based on carrier phase observations with resolived ambiguity). (2) Application of broadcast ephemeris to remove/minimize the satellite position errors. (3) Application of precise satellite clock correction to remove/minimize satellite clock errors. In this way the major sources of GPS errors are removed/minimized and the computed coordinates of the permanent GPS station are mainly affected by the tropospheric refraction. Since, the permanent GPS stations can provide us with long-term continual GPS observation, having available the precise coordinates of the permanent GPS station via precise differential GPS positioning, we are able to develop a time series of the difference between the precise coordinate of the station and the coordinates obtained based on aforementioned procedure. Next, we can subject the resulted time series, which reflects the tropospheric error in combination of random errors, to a FFT process to decompose the time series into a constant and harmonic parts. The constant and the harmonics parts can consequently be fed into a least squares adjustment as the initial value to compute the least square estimates of the constant and time dependent part of the tropospheric corrections in terms of sine and cosine base functions. In this way a tropospheric model can be developed, which is a function of time. Using the whole observations within the year 2000 of the permanent GPS station of National Cartographic Center (NCC) of Iran, located in Tehran/Iran a tropospheric model was developed according to the explained procedure. The computed model was subjected to validity test at the permanent GPS station and also at various locations with different distances to the permanent GPS station. The results can be summarized as follows:
1. Tropospheric error can be detected and modeled according the prescribed procedure due to its time repetition property.
2. The developed model can correct the tropospheric error up to 99% at the time interval used for the modeling (modeling station), and up to 98% for the observations made at the modeling station 2 years after.
3. The developed model is very much local dependent and for that reason for a station located at 1m distance to the modeling station can only remove 52% of the tropospheric error, however it still can remove 52% of the tropospheric error for the locations at 26, 28, 31, and 32 km distance from the modeling station.
Finally, we can conclude that the developed model can be very useful for real-time applications such as navigation and also implementation in the DGPS correction.
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