Peter J. Buist

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.

Automated lane identification using precise point positioning an affordable and accurate GPS technique

Nowadays, many vehicles are equipped with GPS navigation systems, that are accurate to approximately 10 meters. This is insufficient to determine the lane a vehicle is driving in. We introduce a new technique, Precise Point Positioning, which is able to get the accuracy of measurement down to approximately half a meter, without having to resort to expensive high-end GPS receivers. This accuracy is possible with a single measurement of position in real-time. We confirm this accuracy in a real-life test with a vehicle driving at motorway speeds. However, even when the vehicle position is known, the driving lane is not known since there are generally no maps with detailed lane information. Therefore, this paper also presents a self-learning method, using this Precise Point Positioning information, to create maps which include the position of lanes. This method is tested using an artificially created dataset, using the accuracies from the real-world test. This shows that the method can get the position of a lane at an accuracy of 20 cm. The combination of accurate information of the position of a vehicle and information about the position of the lane, can be used to give lane-specific advice for drivers, and can even be a step towards automated driving.

Integer Ambiguity Resolution with Nonlinear Geometrical Constraints

Integer ambiguity resolution is the key to obtain very accurate positioning solutions out of the GNSS observations. The Integer Least Squares (ILS) principle, a derivation of the least-squares principle applied to a linear system of equations in which some of the unknowns are subject to an integer constraint, was demonstrated to be optimal among the class of admissible integer estimators. In this contribution it is shown how to embed into the functional model a set of nonlinear geometrical constraints, which arise when considering a set of antennae mounted on a rigid platform. A method to solve for the new model is presented and tested: it is shown that the strengthened underlying model leads to an improved capacity of fixing the correct integer ambiguities.

Improving the GNSS Attitude Ambiguity Success Rate with the Multivariate Constrained LAMBDA Method

GNSS Attitude Determination is a valuable technique for the estimation of platform orientation. To achieve high accuracies on the angular estimations, the GNSS carrier phase data has to be used. These data are known to be affected by integer ambiguities, which must be correctly resolved in order to exploit the higher precision of the phase observables with respect to the GNSS code data. For a set of GNSS antennae rigidly mounted on a platform, a number of nonlinear geometrical constraints can be exploited for the purpose of strengthening the underlying observation model and subsequently improving the capacity of fixing the correct set of integer ambiguities. A multivariate constrained version of the LAMBDA method is presented and tested here.

Enhancing the Time-To-Fix for the unaided single-frequency integer ambiguity resolution in GNSS attitude determination applications

GNSS-based attitude determination is a viable technique with a large spectrum of applications. Attitude determination requires an accurate relative positioning solution, that can be provided by the very precise GNSS carrier phase observables. The phase observables are, however, biased by unknown integer ambiguities, that must be resolved in order to fully exploit their higher precision. By applying the optimal integer least-squares (ILS) principle and introducing a nontrivial modification of the popular LAMBDA method, a set of geometrical nonlinear constraints given by the known antennas placement on the platform is embedded in the ambiguity search method. The multivariate constrained LAMBDA method is described and tested: the large improvement in fixing the correct set of integer ambiguities from single-frequency, single-epoch observations is stressed, as this is the most challenging scenario for ambiguity resolution. The method is tested by processing and analyzing actual GNSS data, collected on both static and dynamic platforms. The experimental results show the enormous improvement obtained when applying the nonlinearly constrained, mixed integer GNSS attitude model, resulting in a very strong reduction in the Time-To-Fix.

Functional model for spacecraft formation flying using non-dedicated GPS/Galileo receivers

There is trend in spacecraft engineering toward distributed systems where a number of smaller spacecraft work as a larger multi-instrumented satellite. However, in order to make the small satellites work together as a single large platform, the precise relative positions and orientations of the elements of the formation have to be estimated. Global Navigation Satellite System (GNSS) receivers can be utilized to provide baseline estimates with centimeter to millimeter level accuracy. The legitimate spaceborne receivers can not be applied on smaller satellites due to various restrictions which are discussed in this paper, and therefore non-dedicated receivers are lately being used. However, to achieve precise relative positioning in situations with high dynamics and/or large receiver clock offsets, the standard functional model for GNSS-based relative positioning can not be applied. In the presented hardware-in-the-loop simulation of the Proba-3 spacecraft flying in formation, the error for the standard functional model can up to 16 centimeters. A new functional model is introduced that can correct the time-varying offset error and achieve the mm-level accuracy of GNSS even with non-dedicated GNSS receivers.

Attitude bootstrapped multi-frequency relative positioning

Normally, dual frequency observations are required for precise relative positioning, but under critical circumstances even with multi-frequency observations a reliable solution might not always be available. We have developed a method to rigorously integrate multiantenna data at individual platforms such that the attitude solution can be used to enhance relative positioning. Aim of the method is to instantaneously fix the ambiguities of the unconstrained baselines between platforms, whereas several epochs of data might be required with existing methods where not all available information is applied. We will analyze single epoch success rates as the most challenging application. The difference in performance for the methods for single epoch solutions, is a good indication of the strength of the underlying models, and therefore the results can also indicate how much a multi-epoch solution would benefit from the integrated approaches. This contribution will show that the new method improves the relative positioning performance, both single and dual frequency, of moving platforms significantly. The probability of correct instantaneous ambiguity resolution can be increased up to 37% for single frequency relative positioning. For dual frequency applications with at least three single frequency and one dual frequency antenna at each platform, an empirical success rate of more than 95% is achievable even with large code noise levels. An additional benefit of the method is an improved robustness and precision of the baseline estimation.