Real Time Precise GPS Constellation and Clocks Estimation by Means of a Kalman Filter

D. Laurichesse, L. Cerri, J.P. Berthias, F. Mercier

Abstract: In the framework of the Real Time IGS (RTIGS) project, several analysis centers routinely perform the computation of GNSS orbits and clocks in real time. Generally, analysis centers use a Kalman filter to compute the clocks while the orbits are estimated using a least-squares filter based on past data and extrapolated over the time span of interest, as is the case for the predicted IGS Ultra-rapid orbits (IGUs). Although suboptimal by nature, the final performance being limited by the precision of the extrapolated orbits, this processing strategy provides the advantage of reducing the filter complexity. Nevertheless, it can be shown that the real time available part of the IGUs orbits is occasionally not accurate enough for narrow-lane ambiguity resolution (for GPS, the equivalent wavelength is 10.7 cm). This problem occurs relatively often on the Block IIA satellites during eclipse seasons, as the satellite behavior is particularly difficult to model in these conditions. In order to overcome this accuracy problem, we have conducted a study to implement clocks and orbits estimation in real time by means of a Kalman filter, the orbital dynamics being included in the state vector of the filter. We propose in this paper to present the details of this study and its results. The Kalman filter computation involves two steps: - The propagation of the state vector. We present the different components of the state vector and of the force models, the solar radiation pressure modeling strategy in particular. - The correction of the state vector. As the accuracy of the modeled measurement is very important in this step, we present the different correction terms used. We show that we can reduce significantly the computation burden by using special optimization techniques in the filter, which allows executing a complete Kalman cycle in less then 10 seconds, the size of such type of problems being relatively large (1500+ parameters, 1200 measurements per epoch). Another interesting aspect of estimating the clocks and orbits simultaneously is that it minimizes the external interfaces of the filter, thus reducing the occurrence of problems resulting from a lack of external data. We show that the a priori information to be given to the filter is only limited to the GPS time scale and to the earth rotation component UT1. Particular attention has been paid to integer ambiguity resolution. To do so, we have implemented a zero-difference widelane/narrowlane ambiguity resolution scheme, first presented at ION GNSS 2007, and adapted to the real-time context. It improves the overall quality of the solution and gives an ‘Integer’ property of the constellation, that is to say the capability for a user receiver to fix its own ambiguities using only the new orbits and clocks. The algorithm allows the filter to work in a floating and integer mode simultaneously, by fixing ambiguities to their integer values as soon as certain conditions are met, while keeping up to date the consistency of integer ambiguities over entire the network of stations. Finally, we present the results of the Kalman filter in term of accuracy and availability. In particular, we show what kind of results can be obtained using freely available real time measurements, like the ones used by the Real Time IGS project. Two constellation solutions are computed over 10 days of actual data, the first one with a purely floating process (ambiguities are estimated as real numbers in the filter) and the second one where ambiguities are fixed to integer values. Then, a statistical study is performed to compare these two solutions to a reference one (the IGS final orbit). In each case, a quality analysis is performed, by using several means like orbits and clocks comparison, or user range error estimations. We show that the fixed ambiguities solution outperforms the floating one in each metric and remains very close to the reference one. We also show that the user phase measurement residuals, below the centimeter, are sufficiently small to fix the zero-difference ambiguities in real-time, thus allowing a positioning on a global scale using an ‘integer PPP method’, which is a classical PPP approach with integer ambiguities characteristics. The obtained results are at the centimeter level.
Published in: Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013)
September 16 - 20, 2013
Nashville Convention Center, Nashville, Tennessee
Nashville, TN
Pages: 1155 - 1163
Cite this article: Laurichesse, D., Cerri, L., Berthias, J.P., Mercier, F., "Real Time Precise GPS Constellation and Clocks Estimation by Means of a Kalman Filter," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 1155-1163.
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