Evaluation of ambiguity success rates based on multi-frequency GPS and Galileo
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The precise positioning applications have long been carried out using dual frequency carrier phase and code observables from the Global Positioning System (GPS). The carrier phase observables are very precise in comparison to the code ones, the reason phase observables play an important role in precise geodetic applications. The carrier phase observables can have precision of about 3 millimeters. However the precision of the estimated parameter of interest, say the receiver position, depends upon the correct resolution of integer ambiguities present in the carrier phase observables. Significant contributions have been made in the last couple of decades towards integer ambiguity estimation to make precise positioning applications possible, using GPS carrier phase and code data from geodetic receivers.Precise positioning applications have been successful in the past, but at the cost of time taken to correctly resolve the integer ambiguities. This delay in integer ambiguity estimation is caused due to the presence of various propagation and hardware related effects present in the observables of GPS or in that case, any other Global Navigation System. The propagation errors related to the atmosphere are significant for medium to long baseline lengths. Among the atmospheric errors, the ionosphere is found to have profound effect on the process of integer ambiguity estimation. With the aid of permanent reference networks, corrections for ionosphere could be interpolated and further transferred to the user with an aim to enhance users ambiguity resolution and fulfill the aim of an efficient and reliable precise positioning.With the advancement of Global Navigation Satellite Systems (GNSS) several of the limiting factors which degrade users ambiguity resolution are seen to be met. The relatively poor precision of the code data in comparison to the phase data, is foreseen to improve for third GPS frequency, also called as GPS L5. Also most of the frequencies on Galileo system would have improved code precision.The ionosphere which has been a major blockade in fast integer ambiguity resolution, for long baseline lengths, would also benefit in a multi-frequency, multi-GNSS scenario. Since a GNSS model, in which the ionosphere is considered unknown and estimated, gains strength with addition of a frequency. The addition of L5 on GPS and availability of up to four frequencies on Galileo system would strengthen the GNSS model which would be beneficial when ionosphere is parameterized for estimation. This study aims at understanding the above mentioned and other possible benefits of the future GPS and Galileo system.The benefits that the future GPS and Galileo can bring to precise applications can be evaluated in terms of correct resolution of integer ambiguities present in the carrier phase data and further by understanding the contribution of the ambiguity resolution towards improvement of fixed-precision of the parameters of interest. The correct resolution of ambiguities was judged by computing the probability of correct integer bootstrap along with LAMBDA decorrelation method. The decorrelation of the ambiguity Variance Covariance matrix resulted the probability of Integer Bootstrap to correspond to lower bounds for the probability of Integer Least Square. The ambiguities were considered to be successfully resolved only after a minimum of 0.999 probability could be obtained from Integer Bootstrap. While all the ambiguities collectively contributed to give 0.999 Ambiguity Success Rate (ASR) it was termed as full Ambiguity Resolution (AR). In scenarios when full AR took large number of epochs to give 0.999 ASR, only a subset of ambiguities were fixed which met the 0.999 ASR criteria. This approach is known as Partial AR (PAR). PAR solution was accepted only when the resolved subset of ambiguities could contribute to give a minimum value of fixed-precision for the parameters of interest. Since this research involves future GPS and Galileo system, GNSS observables, real or simulated were not used. Instead simulations were done based on model assumptions, that is the functional and the stochastic model.This research work focuses on understanding the benefits of multi-frequency GPS and Galileo to its core. This was done by planning multiple scenarios of GNSS frequencies, GNSS combinations, atmospheric considerations, latitudinal variations and baseline orientations. With the aid of this multiple scenario simulation, an estimate for time taken for successful AR and the fixed-precision of parameters of interest obtained after successful AR could be computed for a range of possible situations. When a multi-GNSS scenario consisting of future GPS and Galileo was considered, there have been challenges while a mathematical model for multi-GNSS was being formed. The design of the multi-GNSS mathematical model accounted for the Inter System Biases (ISB’s) which surface while different GNSS systems use the same reference satellite. While a rank defect between the ISB’s and the ionosphere was detected, it was mitigated by choosing an appropriate S-Basis. To make the simulation software robust and realistic, accounting for setting and rising satellites and change of reference satellite was implemented. With the above considerations a multi-GNSS, multi-frequency simulation software was developed in MATLAB programming language. The results have been obtained based on assumption in the functional and stochastic models. In real practice unmodelled errors have an impact on ASR and time to fix the integer ambiguities to its correct solution due to multipath , insufficient knowledge of the stochastic model, etcetera.Presented below are some of the important findings of this study.The Geometry Free model does not gain strength with the addition of satellites. Since with addition of a satellite a receiver-satellite range is added to the unknowns. Also for a combined GPS and Galileo system, the Geometry Free model does not have a coupling parameter in the unknowns, say troposphere or receiver coordinates. Hence while the mathematical model is formed, from a single system to a combined system, the model does not gain strength. Hence a multi-GNSS constellation would not help to reduce the time-to-fix integer ambiguities for a Geometry Free model.The permanent reference networks can benefit from an integrated GPS and Galileo system. The precision of the ionospheric estimates with a permanent network could reach 2cm instantaneously, almost any time of the day by using quadruple frequency (L1pE1q, L5pE5aq, L2,E5b) GPS and Galileo combined system with the aid of PAR.While the user aims at performing relative positioning using a permanent network, the benefits from a combined GPS and Galileo system are immense. For a user with low-end single frequency receiver, for short baseline lengths ( 10Km), obtaining its receiver positions with 2cm precision for north- and east-components and 6cm precision for the up-component would be possible instantaneously using a combined GPS and Galileo. While the user is equipped with ionospheric corrections from the network, all the ambiguities could be resolved in a short time with a combined GPS and Galileo quadruple frequency system (L1pE1q, L5pE5aq, L2,E5b). The findings from this simulation study shows that, while ionosphere corrections are given to the user, all the ambiguities could be successfully resolved (full AR) within 20 epochs (1 second sampling) by using quadruple frequency from an integrated GPS and Galileo system.
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