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Theory of Carrier Adjusted DGPS Positioning Approach and Some Experimental Results/Xin Xiang Jin
The DGPS technigue can greatly reducc cr even eliminate biases in GPS observations and conseguently provide guite precise relative positioning accuracy. It has been, therefore. paid more and more attention in many real-time positioning applications. The performance of DGPS positioning is a function of three elements: 1) generation of differential GPS corrections at 3 known DGPS reference station, 2) transmission of the corrections to mobile stations: and 3) computation of the mobile position. This research derives a new algorithm for generating differential corrections, which has some distinct features. First, it directly uses code and carrier observations in the measurement model of a Kalman filter, so that the input measurements of the filter are not correlated in time if code-and carrier observations can be assumed to have no time correlation. This makes it possible to use a simple stochastic observation model and to use the standard algorithm cf the Kalman filter. Second, the algorithm accounts for biases like multipath errors and instrumental delays in code observations. It explicitly shows how code biases affect differential correcuons when dual or single freguency data is used. Third, the algorithm can be easily integrated with a guality control procedure, so that the guality of the estimated states can be guaranteed with a certain probability. Fourth, in addition to generation of differential corrections, it also produces the change of ionospheric delays and that of code biases with time. It can, therefore, be used to investigate properties of ionospheric delays and code biases. Finally, all state estimates including differential correction are not affected by the opposite influence of ionospheric delay on code and carrier observations. On the basis of data collected by TurboRogue SNR-8000, Trimble 4000 SSE and Trimble 4000 SST receivers, this research also investigates the rela'-onship between satellite elevation and the precision of code observations. It turns out that the deterioration of code precision With decreasing elevation is very obvious at low elevation. When satellite elevation increases, the precision becomes more and more stable. The change of the code precision with satellite elevation can guite well be modelled by an exponential function of the form y-—agta, exp(X/Xy|), where y (the RMS error), a, and a, have units of metres, and x (elevation) and x, are in degrees. For different types of receivers and different types of code observables. the parameters a,, a, and x, may be different. By using code and carrier data with a sampling interval of one second, the dynamic behaviour of SA ciock errors and that of ionospheric delays can well be modelled by guadrauc and linear functions. respectively. The modelling accuracy is within a few millimetres. An alternauve algorithm for computation of mobile positions is developed. This algorithm san be applicd ata mobile site when code and carrier observatons are available. The ag Orithny directly uses code and carrier observations, rather than carrier filiered code observatuons inputs. thercfore the stochastic model of observations can be easily specified. The algorh can be applied in the case that the dynamic behaviour of mobile positions and receiver Cloek biases can or cannot be modelled. In the former case, the algorithm provides TECUF Iv estimates of mobile positions. Whereas in the latter case, it provides instantanedus Estimate, of mobile positions. In addition, the algorithm can also be integrated with a real time gualir, Control procedure s0 as to ensure the guality of position estimates with a certain probability Since in the use of the algorithm there always exist redundant observations unless the POSition parameters are inestimable, the guality control can even be performed when only fouw Satellites are tracked. Ha By the use of data collected at a 100-km baseline, DGPS positioning experiments show tha when dual-freguency data is used in both reference and mobile stations, half-metre instantaneous positioning accuracy can be achieved. While the data used in the mobile station Is replaced by single-freguency data (Ll code and carrier), the accuracy can be still better than 7.5 decimeters. In addition, the use of an levation-dependent standard deviation for code observations can improve DGPS positioning accuracies and it is more important to use dual: freguency data at a reference station than at a mobile station. When ephemeris errors, vertical ionospheric delays, and vertical tropospheric delays are less than 10. 4.5, and 2.6 metres, respectively, using three reference stations in a 500x500 km' area can reduce the effect of ephemeris errors to one decimeter, ionospheric delays to less than two decimeters, and tropospheric delays to less than 2.5 decimeters. If a tropospheric delay model is used, the tropospheric delays can be further reduced to less than one decimeter. GPS observation eguations can be expanded into Taylor series which contain only up to firsiorder derivative guantities. Since the Taylor expansion does not contain the travel time ot 3 GPS signal, solving it does not need iterations or code observations for the determination of the transmission time of the GPS signal. As a result, ine use of the Taylor expansion can s:ve Computing time and can avoid the impact of any gross errors in code observation: on determining satelli: positions and satellite-clock biases, and COonseguently on compured observations.
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