| Résumé : |
(Auteur) The DGPS technique can considerably improve the accuracy of stand-alone GPS positioning, since biases inherent in the latter technique are greatly reduced or even eliminated. But the improvement depends on the distance between the user and the reference station (spatial correlation), the latency of differential corrections (temporal correlation), and the quality of differential corrections. Therefore, how to correctly generate differential corrections is one of the keys to the DGPS positioning technique. Currently, there already exist several algorithms for the generation of differential corrections, for instance, the algorithm based on carrier filtered code observations and the algorithm based on code observations and sequential differences of carrier observations.
This research derives a new algorithm for generating differential corrections along with a recursive quality control procedure, which has some distinct features. First, it directly uses code and carrier observations in the measurement model of a Kalman filter, so that the measurements 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 of 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 corrections when dual or single frequency data are used. Third, the algorithm can be easily integrated with a recursive quality control procedure, so that the quality of the estimated states can be guaranteed with certain probability. Fourth, in addition to the 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 Trirable 4000 SST receivers, this research also investigates the relationship between satellite elevation and the accuracy of code observations. Since this investigation uses code predicted residuals, which are dominated by code observation noises, the estimation of code observation accuracy is not affected by systematic errors caused by, for example, multipath and instrumental delays in code observations. It turns out that the deterioration of GPS code accuracy with decreasing elevation is very obvious at low elevation. When satellite elevation increases, the accuracy becomes more and more stable. The change of the code accuracy with satellite elevation can quite well be modelled by an exponential function of the form y=ao+a1.exp{-x/xo}, where y (the RMS error), ao and a1 have units of metres, and x (elevation) and xo are in degrees. For different types of receivers and different types of code observables, the parameters ao, a1 and xo may be different.
It is shown that by using code and carrier data with a sampling interval of one second, the dynamic behaviour of SA clock errors and that of ionospheric delays can well be modelled by quadratic and linear functions, respectively. The modelling accuracy is at least within a few millimetres.
Biases in code measurements are found and they may behave linearly and periodically with time. By using the same receiver, code biases related to different observation conditions have different behaviours and those related to the same satellite but observed in different frequencies (i.e. L1 and L2) may also not be the same.
Model testing experiments with simulated errors show that cycle slips as small as one cycle can be indeed successfully detected and identified in real time. The recursive quality control procedure allows for detection and identification of single as well as multiple model errors. But there exists a problem that the mean of the test statistic is always smaller than its expectation. It has been shown that this problem still remains after the relationship between satellite elevation and the accuracy of code observations is taken into account.
Based on the differential corrections generated by the new algorithm, it is shown that with increasing differential-correction latencies, the accuracy of differential-correction prediction decreases quadratically when SA clock errors are present and linearly when SA clock errors are absent. For latencies up to 5, 10 and 15 seconds, the accuracies are usually within 0.05, 0.2 and 0.5 in, respectively. Using differential-correction acceleration in differential-correction prediction can improve or worsen the accuracy when SA clock errors are present or absent, respectively. But the deteriorated accuracies related to satellites without SA clock errors are still better than the improved ones related to satellites with SA clock errors. For latencies within 15 seconds, the accuracy of differential-correction prediction can usually be reduced to below 0.2 metres if differential-correction accelerations are used. |
A recursive procedure for computation and quality control of GPS differential corrections (1995)
