GNSS Integer Ambiguity Estimation And Validation: Theory And Methodology

Carrier-phase measurement is the important way to realize GNSS rapid and precise positioning at the present.Ambiguity resolution,including estimation and validation,is a very critical step.Ambiguity resolution is the process which recoveries the integer nature of ambiguity from float.Once it becomes integer,carrier-phase measurement can be seen as high precise range measurement with centimeter precision,then high precision positioning can be realized.In order to realize instantaneous quality control for GNSS ambiguity resolution,this contribution complements and developes two fundamental theories for ambiguity resolution: integer estimation and integer aperture estimation.New instantaneous and controllable ambiguity resolution method is proposed based on new theoretical foundation,which can realize quality control for instantaneous ambiguity resolution and decrease the conservativeness in the look-up table of ratio test.At the same time,the influence of bias in observations to ambiguity resolution is studied.It is proved that bias seperation is important in improving the success rates of ambiguity resolution.The main content of this contribution can be summarized as follows:1.Complement integer estimation theory in two perspectives: suboptimal ambiguities and quality evaluation.Review the existing integer estimation,and analyze the properties of suboptimal integer candidate for the first time.The quantitative relation between suboptimal and optimal integer candidates are summarized.Implement approximated quality evaluation to integer least-square by upper bound and lower bound approximation.The effectiveness of this approximation method is verified by Monte Carlo simulation,and the lower bound approximation is better.Review the properties of integer estimation in the presence of bias.Analyze and verify the probability evaluation methods for integer estimation in the presence of constant bias.The results showed that the probability evaluation method with bias was more suitable to evaluate the performance of integer estimation for weak GNSS models.As to strong GNSS models,the probability evaluation methods without bias can evaluate integer estimation much better.2.Develop the integer aperture estimation theory in quality evaluation.Review the existing integer aperture esitmation theory,and build the framwork for all kinds of integer aperture estimators.According to the geometry characteristics,the integer aperture estimators are classfied into linear and nonlinear.The uniform quality evaluation method is proposed for linear integer aperture estimators,which is verified by simulation experiment.The influence of biases to integer aperture estimation is studied,and probability evaluation formulas for linear integer aperture estimators are derived.The effectiveness of approximation formulas are tested by simulation.The results indicate that the probability approximation with bias is more accurate for weak GNSS models.For strong GNSS models,the approximation method regardless of bias has smaller approximation errors.3.Propose a new instantaneous and controllable ambiguity resolution method based on probability approximation.The advantages and drawbacks of fixed failure rate approach in practice are discussed.The performances of all existing integer aperture estimators are compared by fixed failure rate approach.Analyze the mechanism which leads to performance differences for integer aperture estimators.The probability relation between aperture pull-in region and integer pull-in region is derived.Bsed on these results,a new instantaneous and controllable ambiguity resolution(i CON)approach is proposed.Properties of the i CON approach,including time cost and failure rate control,are analyzed by simulation experiment.Based on i CON approach and fixed failure rate approach,the performances of integer aperture estimators are compared in many scenarios.The results show that the linear integer aperture estimators based on i CON approach behave better than the integer aperture estimator based on failure rate approach.4.Compare the performance of quality control methods in ambiguity resolution by GNSS compass experiments.Take the difference test and ratio test integer aperture estimators as example,and analyze the mechanism which leads to their performance difference.The results show that their differences are statistical.This comparing method can be generalized to other integer aperture estimators.Based on GNSS positioning and compass experiments,the integer aperture estimators which can realize instantaneous and controllable ambiguity resolution are compared and analyzed.Those results show that,when the influence of biases were trivial,such as ultra-short baseline applications,linear integer aperture estimators,especially integer aperture least-square,are better than fixed failure rate approach.At the same time,the introduction of integer aperture estimation usually leads to the loss of positioning precision.As contrast,if biases are large enough to be taken into account,the integer aperture estimation may benefit the precision of positioning.It is possible that the conservative ratio test based on look-up table may be better than those linar integer aperture estimators.Furthermore,based on the relative positioning experiments of medium and long baselines,how to tackle biases is more significant than integer aperture estimation in improving positioning precision.Though different integer aperture estimators have different positioning precision,their influences to positioning are much smaller than that of bias seperation.The baseline constraint also has influence to the quality control of ambiguity resolution.It changes the performance of some integer aperture estimators,and obviously improves the success rate of ambiguity resolution.