A New Triple-frequency, Ionosphere-free Technique for Ambiguity Resolution of Long-range Baseline

Y. Xu, S. Ji, W. Chen, D. Weng, Y. Xu, W. Chen, D. Weng, S. Ji

Abstract:	One of the challenges in fixing ambiguity over long baselines quickly and reliably is how to reduce the effects of ionospheric delay. New GNSS systems (i.e. GPS modernization, Compass, and Galileo) will provide multiple navigation signals for reliable navigation services. The purpose of this study is to develop new techniques for ambiguity resolution using multiple GNSS navigation signals (i.e. L1, L2, L5 for GPS or B1, B2, B3 for BeiDou) for long-range baseline with a high success rate in very short time. To achieve this purpose, two specific problems have to be addressed, the first one is the elimination of double difference (DD) ionospheric delay and the other one is the selection of the correct optimal combinations. Commonly, there are three methods to eliminate the ionospherice delay: the first one is to ignore it in short baseline, which is not suited for long-range baseline. The second one is to eliminate it using ionosphere-free combinations, but the combination observation noise gets much larger and the converged time would be very long. The third way is to estimate it as a parameter in the long baseline. However, large numbers of unknown parameters would be involved, a long time should be taken to make both ionospherice delay and float ambiguity converged. A new algorithm to eliminate the ionospheric delays is proposed in this research which does not depend on the convergence of the ionospheric parameter. The substance of this algorithm is to estimate the ionospherice delay in ambiguity search process. Simply say, once a pair of ambiguity candidates of L1, L2 and L5 has been selected from the search space, the corresponding ionospherice delay can be gained. Both modernized GPS of the USA and BeiDou of China among new global navigation satellite systems (GNSS) operate with triple-frequency signals. Optimal combinations of Extra-widelane (EWL: ??2.93 m) and Widelane (WL: 0.75 m ???2.93 m) consist of triple-frequency signals significantly enhance the efficiency and reliability of the Ambiguity Resolution (AR) for long-range baseline. The ambiguities of them can be fixed more easily due to their large wavelength. The selection of the optimal combinations has become a hot spot, and the key of which is a larger wavelength-to-noise ratio. Generally speaking, ionospheric delay contributes most part of the noise in long-range baseline. In most researches, the prior ionospheric delay which would be incorrect is employed, at the same time the incorrect optimal combinations are introduced. The AR success rate of them (especially WL) would be very low. In this research, optimal combinations will be fixed twice considering the updated ionospheric delay which is estimated by modeled as a parameter in the very beginning and by the new algorithm mentioned above in ambiguity search process respectively. A new triple-frequency ionosphere-free technique for Ambiguity Resolution of long range baseline has been proposed in this research to solve the two problems above, and the detailed flow path is: 1) Model and estimate the ionospheric delay as a parameter, and then define the optimal combinations of EWL and WL considering the ionospheric delay. Fix the ambiguity of EWL and WL with the methods of integer rounding and LAMBDA respectively. 2) Get the ambiguity search space for L1, L2 and L5 (or B1, B2, B3 for BeiDou) by the triple-frequency, geometry-free observation equations and the functional relationships between ambiguities of L1, L2, L5 and the fixed ambiguities of EWL, WL. 3) Selected a pair of ambiguity candidates of L1, L2 and L5 from the search space, and then calculate the ionospheric delay of L1, L2 and L5 employing the geometry-free observation equations. Obviously, each pair of ambiguity candidates gains their own ionospheric delay. 4) Once the new ionospheric delay is obtained, a pair of new optimal combinations of EWL and WL can be determined. At the same time, we also can get a pair of new float ambiguity and its corresponding variance-covariance matrix, which are free form the effects of the ionospheric delay. Save the value of VtPV. 5) Repeat steps 3-5 until there is no ambiguity candidate remains. In the end, find the ambiguity candidates with the minimum and second minimum value of VtPV. Figure out the value of ratio, if it is more than 2.0, ambiguities are regarded as be fixed. 6) Repeat steps 1-6 until there is no data left. There are two kinds of experimental data in this research. The first one is simulated GPS triple-frequency observations, and the other one is BeiDou triple-frequency observations collected in Hubei Province, China. There are three baselines, and the lengths of them are 10km, 80km and 100km respectively. From all the experiments with the simulated GPS observations in this research, the conclusions can be drawn as below: 1) The AR success rate of EWL and WL considering the updated ionospheric delay in three baselines are all lager than 99.5%, significantly higher than that of incorrect optimal combinations. 2) The ambiguity of baseline (10Km) can be fixed instantaneously and the AR success rate is larger than that of the TCAR/CAR and LAMBDA method. 3) The ambiguity of baseline (80Km) can be fixed in five epochs and the values of ratios and success rates are increased considerably compared with the traditional LAMBDA method. 4) The ambiguity of baseline (100Km) can be fixed in twenty epochs. Although the conclusions above are gained depend on the experiments with simulated GPS observations, the accuracy of BeiDou phase observations have been proved the same as, even slightly better than GPS in other researchers and my study. So the anticipated results would be also as good as the conclusions above, which will be confirmed in my following work.
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:	1823 - 1832
Cite this article:	Xu, Y., Ji, S., Chen, W., Weng, D., Xu, Y., Chen, W., Weng, D., Ji, S., "A New Triple-frequency, Ionosphere-free Technique for Ambiguity Resolution of Long-range Baseline," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 1823-1832.
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