Integer-estimable GLONASS FDMA model as applied to Kalman-filter-based short- to long-baseline RTK positioning
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ORIGINAL ARTICLE
Integer‑estimable GLONASS FDMA model as applied to Kalman‑filter‑based short‑ to long‑baseline RTK positioning Pengyu Hou1,2 · Baocheng Zhang1 · Teng Liu1 Received: 18 May 2020 / Accepted: 1 July 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Fast ambiguity resolution is a major challenge for GLONASS phase-based applications. The integer-estimable frequencydivision multiple-access (IE-FDMA) model succeeds in formulating a set of estimable GLONASS phase ambiguities and preserving the integer property, to which the classical integer ambiguity resolution, typically the least-squares ambiguity decorrelation adjustment (LAMBDA), becomes readily applicable. The initial assessment of the IE-FDMA model demonstrated instantaneous ambiguity resolution capability in case of short-baseline real-time kinematic (RTK) positioning based on ionosphere-fixed formulation, in which the data processing strategy is window (batch)-based least-squares estimation with window length ranging from one to a few epochs. Here, we extend the applicability of the IE-FDMA model to Kalman-filter-based, ionosphere-fixed, ionosphere-weighted, and ionosphere-free cases, which are, respectively, adoptable for short-, medium-, and long-baseline RTK positioning. To adapt the IE-FDMA model to the Kalman filter, we estimate, at each epoch, first the estimable ambiguities, then transform them into integer-estimable ones, and finally resolve them into correct integers. This enables the rigorous integer ambiguity resolution and, at the same time, eases the recursive construction of integer-estimable ambiguities. We analyze global positioning system (GPS) and GLONASS data of nine baselines with lengths varying from several meters to more than one hundred kilometers. The results demonstrate the feasibility of fast ambiguity resolution not only for the GLONASS phase-only short-baseline RTK positioning, but for the GPS + GLONASS medium- and long-baseline RTK positioning as well. In all cases, the fixed solution with faster (several-minutes) convergence and higher (centimeter-level) precision indicates the benefits from GLONASS ambiguity resolution as compared to the float solution. Moreover, the dual-system solution with decreased ambiguity dilution of precision (ADOP) and improved positioning precision confirms the advantages of integrating GLONASS with GPS in contrast to the GPS-only situation. Keywords GLONASS · Frequency-division multiple access (FDMA) · Integer-estimability · Integer ambiguity resolution (IAR) · Real-time kinematic (RTK)
Introduction Achieving high-precision global navigation satellite system (GNSS) positioning with a short observation time span depends on the ability of fast ambiguity resolution for the carrier phase observables (Leick et al. 2015; Teunissen 2003; Teunissen and Kleusberg 2012). Reliable ambiguity * Baocheng Zhang [email protected] 1
State Key Laboratory of Geodesy and Earth’s Dynamics, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan, China
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