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Li B.,Tongji University | Shen Y.,Tongji University | Shen Y.,Key Laboratory of Advanced Surveying Engineering of SBSM
Acta Geodaetica et Cartographica Sinica | Year: 2010

The integer parameters must be primarily estimated in the GNSS and InSAR application, which essentially introduces a special mixed integer model with both real- and integer-valued parameters from mathematical point of view. Up to now, all methods for mixed integer model are based on the least squares criterion. In this paper, the parameter estimation will be investigated in mixed integer model with the P-norm distributed observation noises. First of all, we will employ the maximum likelihood estimation theory to derive the criterion for integer searching, considering the fact that only real parameters can be differentiated but not the integer parameters due to their discrete property, and further verify that least squares based integer searching criterion is just a case with normally distributed noises. Secondly, the approach and iterative procedure are given for estimating p , searching integers and solving real-valued parameters. Finally, the simulated experiments are implemented to verify the correctness of the derived formulae and proposed algorithm. Source

Pei X.,Tongji University | Pei X.,Chinese Academy of Sciences | Chen J.,Chinese Academy of Sciences | Wang J.,Tongji University | And 4 more authors.
Lecture Notes in Electrical Engineering | Year: 2012

GPS applies Code Division Multiple Access technique in signal coding, while GLONASS's signal is produced with Frequency Division Multiple Access technique. The differences in signal frequency results in inter-system hardware delay bias for GPS/GLONASS receivers. Subjecting to these hardware delays, strategies and models of GPS/GLONASS PPP based positioning needs to be modified. We derived a GPS/GLONASS combined PPP positioning models by introducing inter-system hardware delay biases. Several scenarios were simulated to test the introduced models using the observation of IGS stations. The results show that: Circled digit one Adding a couple of GLONASS satellites can improve the positioning accuracy in the environment without enough GPS satellites being tracked; Circled digit two The inter-system hardware delay bias is stable on daily base, and it could be predicted and be fixed in the GPS/GLONASS combined PPP. © 2012 Springer-Verlag. Source

Li B.,Tongji University | Li B.,Key Laboratory of Advanced Surveying Engineering of SBSM | Shen Y.,Tongji University | Shen Y.,Key Laboratory of Advanced Surveying Engineering of SBSM
Journal of Surveying Engineering | Year: 2010

Carrier phase ambiguity resolution is the key to precise positioning with a global navigation satellite system (GNSS); therefore, quite a few ambiguity resolution methods have been developed in the past two decades. In this paper, a new ambiguity searching algorithm by treating part of normal equations as constraints is developed. The process starts with the truncation of the terms with respect to the small eigenvalues from the normal equations of a least-squares estimation problem. The remaining normal equations are employed as the constraint equations for the efficient searching of integer ambiguities. In the case of short single baseline rapid GNSS positioning with double differenced phase measurements, there are only three real parameters of the position to be estimated. Therefore three terms of the normal equations should be truncated off due to the fact that there is a large difference between the last three eigenvalues of the normal matrix of the float solution and the others, and then the remaining ambiguities can be trivially solved with three independent ambiguities by means of the remaining normal equations. As a result, only three independent ambiguities are necessarily searched and the searching efficiency is dramatically enhanced. Moreover, a new indicator of minimizing the conditional number of the subsquare matrix of the remaining normal equations is introduced to select three independent ambiguities. Once the correct integer values of the selected three independent ambiguities are applied to solve the remaining ambiguities, the estimated real-valued solutions are very close to their integers, which can be applied as additional strong constraints to further improve the searching efficiency. Finally, two case studies, from real dual-frequency global positioning system (GPS) data of about 10-km baseline and random simulations, respectively, are carried out to demonstrate the efficiency of the new algorithm. The results show that the new algorithm is efficient, especially for the scenarios of high-dimensional ambiguity parameters. © 2010 ASCE. Source

Liu Z.-Q.,Tongji University | Liu Z.-Q.,Nanjing University | Wang J.-X.,Tongji University | Wang J.-X.,Key Laboratory of Advanced Surveying Engineering of SBSM | Wang H.,Tongji University
Yuhang Xuebao/Journal of Astronautics | Year: 2012

Precise velocity of the dynamic platform can be determined by single-difference (SD) of accumulated carrier-phase measurements between epochs. Based on the velocity estimated by the SD method, an approach for kinematic precise point positioning with Extended Kalman Filter is proposed. The algorithm enables correct description of highly dynamic system, and has an advantage over empirical dynamic models. In the meanwhile, precise velocity information can also be obtained. An aircraft dynamic test shows that the discrepancies between the single point-positioning solution and the relative double-difference (DD) TRACK solution are within a few centimeters. The RMS values are better than 3 cm in north and east components, and 6 cm in the up component. The accuracy of estimated velocity comes up to mm/s level. Source

Li B.,Tongji University | Shen Y.,Tongji University | Shen Y.,Key Laboratory of Advanced Surveying Engineering of SBSM | Lou L.,Tongji University | Lou L.,Key Laboratory of Advanced Surveying Engineering of SBSM
Wuhan Daxue Xuebao (Xinxi Kexue Ban)/ Geomatics and Information Science of Wuhan University | Year: 2010

We develop a new strategy for evaluating the GPS stochastic model in long baseline scenario. Firstly, we employ high frequency pass filtering of multiple differences in time domain to efficiently eliminate the systematic biases. Then, the mathematic models are proposed to assess the different aspects of GPS stochastic characteristics. Finally, the real GPS data is used to demonstrate the performance of the developed models. The findings can benefit the quality evaluation and integrity of CORS measurements and the quality control of positioning results in rover end. Source

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