Robert Odolinski

Instantaneous BeiDou+GPS RTK positioning with high cut-off elevation angles

As the Chinese BeiDou Navigation Satellite System (BDS) has become operational in the Asia-Pacific region, it is of importance to better understand as well as demonstrate the capabilities that a combination of BeiDou with GPS brings to positioning. In this contribution, a formal and empirical analysis is given of the single-epoch RTK positioning capabilities of such a combined system. This will be done for the single- and dual-frequency case, and in comparison with the BDS- and GPS-only performances. It will be shown that with the combined system, when more satellites are available, much larger than the customary cut-off elevations can be used. This is important, as such measurement set-up will significantly increase the GNSS applicability in constrained environments, such as e.g. in urban canyons or when low-elevation multipath is present.

Combined BDS, Galileo, QZSS and GPS single-frequency RTK

Abstract We will focus on single-frequency single-baseline real-time kinematic (RTK) combining four Code Division Multiple Access (CDMA) satellite systems. We will combine observations from the Chinese BeiDou Navigation Satellite System (BDS), European Galileo, American Global Positioning System (GPS) and the Japanese Quasi-Zenith Satellite System (QZSS). To further strengthen the underlying model, attention will be given to overlapping frequencies between the systems. If one can calibrate the inter-system biases, a common pivot satellite between the respective systems can be used to parameterize double-differenced ambiguities. The LAMBDA method is used for ambiguity resolution. The instantaneous (single-epoch) single-frequency RTK performance is evaluated by a formal as well as an empirical analysis, consisting of ambiguity dilution of precision (ADOP), bootstrapped and integer least-squares success rates and positioning precisions. The time-to-correct-fix in some particular cases when instantaneous RTK is not possible will also be analyzed. To simulate conditions with obstructed satellite visibility or when low-elevation multipath is present, various elevation cut-off angles between 10 and 40° will be used. Four days of real data are collected in Perth, Western Australia. It will be shown that the four-system RTK model allows for improved integer ambiguity resolution and positioning performance over the single-, dual- or triple-systems, particularly for higher cut-off angles.

On the estimability of parameters in undifferenced, uncombined GNSS network and PPP-RTK user models by means of \mathcal {S}-system theory

The concept of integer ambiguity resolution-enabled Precise Point Positioning (PPP-RTK) relies on appropriate network information for the parameters that are common between the single-receiver user that applies and the network that provides this information. Most of the current methods for PPP-RTK are based on forming the ionosphere-free combination using dual-frequency Global Navigation Satellite System (GNSS) observations. These methods are therefore restrictive in the light of the development of new multi-frequency GNSS constellations, as well as from the point of view that the PPP-RTK user requires ionospheric corrections to obtain integer ambiguity resolution results based on short observation time spans. The method for PPP-RTK that is presented in this article does not have above limitations as it is based on the undifferenced, uncombined GNSS observation equations, thereby keeping all parameters in the model. Working with the undifferenced observation equations implies that the models are rank-deficient; not all parameters are unbiasedly estimable, but only combinations of them. By application of S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}

First combined COMPASS/BeiDou-2 and GPS positioning results in Australia. Part II: Single- and multiple-frequency single-baseline RTK positioning

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On the use of between-baseline differenced and instantaneous RTK positioning while using simultaneous GNSS measurements

\end{document}-system theory the model is made of full rank by constraining a minimum set of parameters, or S-basis. The choice of this S-basis determines the estimability and the interpretation of the parameters that are transmitted to the PPP-RTK users. As this choice is not unique, one has to be very careful when comparing network solutions in different S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}

Combined GPS, BeiDou, Galileo, and QZSS Single-Epoch, Single-Frequency RTK Performance Analysis

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