Abstract
In Global navigation satellite system (GNSS) data processing, integer ambiguity acceptance test is considered as a challenging problem. A number of ambiguity acceptance tests have been proposed from different perspective and then unified into the integer aperture estimation (IA) framework. Among all the IA estimators, the optimal integer aperture (OIA) achieves the highest success rate with the fixed failure rate tolerance. However, the OIA is of less practical appealing due to its high computation complexity. On the other hand, the popular discrimination tests employ only two integer candidates, which are the essential reason for their sub-optimality. In this study, a generalized difference test (GDT) is proposed to exploit the benefit of including three or more integer candidates to improve their performance from theoretical perspective. The simulation results indicate that the third best integer candidates contribute to more than 70% success rate improvement for integer bootstrapping success rate higher than 0.8 case. Therefore, the GDT with three integer candidates (GDT3) achieves a good trade-off between the performance and computation burden. The threshold function is also applied for rapid determination of the fixed failure rate (FF)-threshold for GDT3. The performance improvement of GDT3 is validated with real GNSS data set. The numerical results indicate that GDT3 achieves higher empirical success rate while the empirical failure rate remains comparable. In a 20 km baseline test, the success rate GDT3 increase 7% with almost the same empirical failure rate.
Highlights
In the global navigation satellite system (GNSS) data processing and Global navigation satellite system (GNSS) based remote sensing applications, integer ambiguity resolution is an important and challenging research problem.The mathematical model for carrier phase based GNSS positioning model can be expressed as [1]: E(y) = Aa + Bb, D (y) = Qyy, a ∈ Zn, b ∈ R pSensors 2018, 18, 3018; doi:10.3390/s18093018 (1)www.mdpi.com/journal/sensorsSensors 2018, 18, 3018 where a and b are the integer and real-valued parameters, respectively
An extensive comparison between different integer aperture estimators has been made and the results indicate that the ratio test and the difference test are suboptimal estimator in terms of fixed failure rate [8,10]
We show that the difference test is only a special case of the generalized difference test, which can be denoted as GDT2, the threshold of μ D and μG2 have following relationship: μ D = 2loge μG2 (27)
Summary
In the global navigation satellite system (GNSS) data processing and GNSS based remote sensing applications, integer ambiguity resolution is an important and challenging research problem. The integer estimation procedure can be described as a = I ( â), with I : Rn → Zn. Performing ambiguity acceptance test. The ambiguity acceptance test problem can be solved by either an integer aperture estimator or a hypothesis test. The integer aperture estimation for ambiguity acceptance test is based on the ambiguity residual distribution, which considers the stochastic property of the fixed integer candidate, provides a sound probability basis. There are four types of threshold determination methods in ambiguity acceptance test: the empirical method, significance test, likelihood ratio approach and the fixed failure rate approach [10]. An extensive comparison between different integer aperture estimators has been made and the results indicate that the ratio test and the difference test are suboptimal estimator in terms of fixed failure rate [8,10]. The relationship between the difference test and the OIA and the GDT is analyzed
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