Sandra Verhagen

New Global Navigation Satellite System Ambiguity Resolution Method Compared to Existing Approaches

Integer carrier phase ambiguity resolution is the process of resolving unknown cycle ambiguities of doubledifferenced carrier phase data as integers, and it is a prerequisite for rapid and high-precision global navigation satellite system positioning and navigation. Besides integer estimation, integer ambiguity resolution also involves validation of the integer estimates. In this contribution a new ambiguity resolution method is presented, based on the class of integer aperture estimators, which for the first time reveals an overall approach to the combined problem of integer estimation and validation. Furthermore, it is shown how the different discrimination tests that are currently in use in practice can be cast into the framework of the new approach.

The ratio test for future GNSS ambiguity resolution

The performance of the popular ambiguity ratio test is analyzed. Based on experimental and simulated data, it is demonstrated that the current usage of the ratio test with fixed critical value is not sustainable in light of the enhanced variability that future global navigation satellite system (GNSS) ambiguity resolution will bring. As its replacement, the model-driven ratio test with fixed failure rate is proposed. The characteristics of this fixed-failure rate ratio test are described, and a performance analysis is given. The relation between its critical value and various GNSS model parameters is also studied. Finally, a procedure is presented for the creation of fixed failure rate look-up tables for the critical values of the ratio test.

Ps-LAMBDA: Ambiguity success rate evaluation software for interferometric applications

Integer ambiguity resolution is the process of estimating the unknown ambiguities of carrier-phase observables as integers. It applies to a wide range of interferometric applications of which Global Navigation Satellite System (GNSS) precise positioning is a prominent example. GNSS precise positioning can be accomplished anytime and anywhere on Earth, provided that the integer ambiguities of the very precise carrier-phase observables are successfully resolved. As wrongly resolved ambiguities may result in unacceptably large position errors, it is crucial that one is able to evaluate the probability of correct integer ambiguity estimation. This ambiguity success rate depends on the underlying mathematical model as well as on the integer estimation method used. In this contribution, we present the Matlab toolbox Ps-LAMBDA for the evaluation of the ambiguity success rates. It allows users to evaluate all available success rate bounds and approximations for different integer estimators. An assessment of the sharpness of the bounds and approximations is given as well. Furthermore, it is shown how the toolbox can be used to assess the integer ambiguity resolution performance for design and research purposes, so as to study for instance the impact of using different GNSS systems and/or different measurement scenarios.

Robustness of GNSS integer ambiguity resolution in the presence of atmospheric biases

Both the underlying model strength and biases are two crucial factors for successful integer GNSS ambiguity resolution (AR) in real applications. In some cases, the biases can be adequately parameterized and an unbiased model can be formulated. However, such parameterization will, as trade-off, reduce the model strength as compared to the model in which the biases are ignored. The AR performance with the biased model may therefore be better than with the unbiased model, if the biases are sufficiently small. This would allow for faster AR using the biased model, after which the unbiased model can be used to estimate the remaining unknown parameters. We assess the bias-affected AR performance in the presence of tropospheric and ionospheric biases and compare it with the unbiased case. As a result, the maximum allowable biases are identified for different situations where CORS, static and kinematic baseline models are considered with different model settings. Depending on the size of the maximum allowable bias, a user may decide to use the biased model for AR or to use the unbiased model both for AR and estimating the other unknown parameters.

Performance improvement with low-cost multi-GNSS receivers

In the next five to ten years, the evolution of Global Navigation Satellite Systems (GNSSs) will have a revolutionary impact on the positioning performance. More GNSSs will become available with improved signal characteristics. At the same time, enhancement of receiver technology and algorithms is ongoing. In light of these developments, it is investigated whether high-precision relative positioning with single-frequency receivers will become feasible, and, if so, under which circumstances. We submit that this would open the door to a wide range of applications for instance in the field of mobile Location Based Services for which users do not have professional receivers at their disposal. The closed form expression of the single-frequency Ambiguity Dilution of Precision (ADOP) gives a clear insight into how and to what extent the various factors of the underlying single-frequency model contribute to the overall ambiguity resolution performance. Furthermore, numerical studies indicate that for benign dynamics single-frequency RTK becomes feasible for baselines up to about 10–15 km if GPS+Galileo is used. In this contribution we will present analytical and numerical results. Ambiguity resolution performance as function of number of epochs, receiver noise and baseline length will be analyzed, and compared for ideal circumstances as well as for situations with bad satellite visibility and/or multipath. Furthermore, different next generation GNSS configurations will be considered. Based on the results, it is predicted that for rapid, short baseline cm-level positioning, low-cost single-frequency receivers will become very competitive in comparison to their more expensive dual-frequency cousins.

Precise Point Positioning Using GPS and Compass Observations

The Compass Navigation Satellite system, which currently provides more than 12 satellites with three carrier signals, already satisfies the requirement of stand-alone positioning in the Asia–Pacific regional area. First an initial introduction and performance assessment of dual-frequency un-differenced precise point positioning (PPP) for GPS and Compass is presented, the results of which indicate that centimeter-level positioning accuracy of Compass-PPP is comparable to that of GPS-PPP. Then the combined GPS + Compass dual-frequency PPP model is introduced, followed by a numerical performance analysis and comparison with single GNSS-PPP. The results show that the combined GPS + Compass PPP can shorten the convergence time, but not necessarily improve positioning results by much if the satellites of the single GNSS system already have a good receiver-satellite geometry.

A new ambiguity acceptance test threshold determination method with controllable failure rate

The ambiguity acceptance test is an important quality control procedure in high precision GNSS data processing. Although the ambiguity acceptance test methods have been extensively investigated, its threshold determine method is still not well understood. Currently, the threshold is determined with the empirical approach or the fixed failure rate (FF-) approach. The empirical approach is simple but lacking in theoretical basis, while the FF-approach is theoretical rigorous but computationally demanding. Hence, the key of the threshold determination problem is how to efficiently determine the threshold in a reasonable way. In this study, a new threshold determination method named threshold function method is proposed to reduce the complexity of the FF-approach. The threshold function method simplifies the FF-approach by a modeling procedure and an approximation procedure. The modeling procedure uses a rational function model to describe the relationship between the FF-difference test threshold and the integer least-squares (ILS) success rate. The approximation procedure replaces the ILS success rate with the easy-to-calculate integer bootstrapping (IB) success rate. Corresponding modeling error and approximation error are analysed with simulation data to avoid nuisance biases and unrealistic stochastic model impact. The results indicate the proposed method can greatly simplify the FF-approach without introducing significant modeling error. The threshold function method makes the fixed failure rate threshold determination method feasible for real-time applications.

Multiplatform Instantaneous GNSS Ambiguity Resolution for Triple- and Quadruple-Antenna Configurations with Constraints

Traditionally the relative positioning and attitude determination problem are treated as independent. In this contribution we will investigate the possibilities of using multiantenna (i.e., triple and quadruple) data, not only for attitude determination but also for relative positioning. The methods developed are rigorous and have the additional advantage that they improve ambiguity resolution on the unconstrained baseline(s) and the overall success rate of ambiguity resolution between a number of antennas.

Recursive Detection, Identification and Adaptation of Model Errors for Reliable High-Precision GNSS Positioning and Attitude Determination

High precision applications of Global Navigation Satellite Systems (i.e., GPS, GLONASS and GALILEO) are based on resolution of the carrier phase ambiguities. Only if these ambiguities can be reliably resolved, secure position and/or attitude information can be guaranteed. Hence it is very important that the GNSS data are cleaned for possible model errors, such as outliers and/or slips. This paper describes a rigorous procedure for the real-time statistical testing and quality control of both GNSS observations and the integer phase ambiguities. The performance of the procedure will be demonstrated using kinematic GPS data.

The future of single-frequency integer ambiguity resolution

The coming decade will bring a proliferation of Global Navigation Satellite Systems (GNSSs) that are likely to enable a much wider range of demanding applications compared to the current GPS-only situation. One such important area of application is single-frequency real-time kinematic (RTK) positioning. Presently, however, such systems lack real-time performance. In this contribution we analyze the ambiguity resolution performance of the single-frequency RTK model for different next generation GNSS configurations and positioning scenarios. For this purpose, a closed form expression of the single-frequency Ambiguity Dilution of Precision (ADOP) is derived. This form gives a clear insight into how and to what extent the various factors of the underlying model contribute to the overall performance. Analytical and simulation results will be presented for different measurement scenarios. The results indicate that low-cost, single-frequency Galileo+GPS RTK will become a serious competitor to its more expensive dual-frequency cousin.