Sequential Best Integer-Equivariant Estimation for GNSS

Brack, Andreas; Henkel, Patrick; Günther, Christoph

doi:10.1002/navi.58

Cited by 14 publications

(4 citation statements)

References 12 publications

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“…In the previous section it is shown that the best integer equivariant estimateâ BIE and the parallel scalar approximationâ PBIE thereof can in a way be interpreted as the counterparts ofǎ ILS andǎ IR from the class of integer estimators. The logical consequence is therefore to also formulate the counterpart of integer bootstrappingǎ IB , i.e., to combine the principle of best integer equivariant estimation with a sequential processing strategy, in which the estimates of the previous elements are taken into account through the correlation between the elements ofâ (Brack et al 2013. Starting with the last entry and proceeding in reversed order, the elements ofâ SBIE are defined aŝ…”

Section: Sequential Scalar Approximationmentioning

confidence: 99%

Partial Carrier-Phase Integer Ambiguity Resolution for High Accuracy GNSS Positioning

Brack¹

2020

Preprint

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Global navigation satellite systems provide ranging based positioning and timing services. The use of the periodic carrier-phase signals is the key to fast and accurate solutions, given that the inherent ambiguities of the carrier-phase measurements are correctly resolved. The idea of partial ambiguity resolution is to resolve a subset of all ambiguities, which enables faster solutions but does not fully exploit the high precision of the carrier-phase measurements. Theory, methods, and algorithms for partial ambiguity resolution are discussed and analyzed with simulated and real data.

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Section: Sequential Scalar Approximationmentioning

confidence: 99%

Partial Carrier-Phase Integer Ambiguity Resolution for High Accuracy GNSS Positioning

Brack¹

2020

Preprint

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“…Verhagen and Teunissen [ 13 ] proved that this estimator is always optimal in terms of the MSE, while Wen et al [ 14 ] demonstrated the use of the BIE estimator for GNSS precise point positioning (PPP). In Brack et al [ 15 ] and Brack [ 16 ], a sequential BIE approach was developed. Subsequently, Teunissen [ 17 ] extended the theory of integer equivariant estimation by developing the principle of BIE estimation for the class of elliptically contoured distributions, while Odolinski and Teunissen [ 18 ] analyzed the BIE performance for low-cost, single- and dual-frequency, short- to long-baseline multi-GNSS RTK positioning, and they found that the BIE positions reveal a ‘star-like’ pattern when the ILS SRs are high.…”

Section: Introductionmentioning

confidence: 99%

Instantaneous Best Integer Equivariant Position Estimation Using Google Pixel 4 Smartphones for Single- and Dual-Frequency, Multi-GNSS Short-Baseline RTK

Yong

Harima

Rubinov³

et al. 2022

Sensors

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High-precision global navigation satellite system (GNSS) positioning and navigation can be achieved with carrier-phase ambiguity resolution when the integer least squares (ILS) success rate (SR) is high. The users typically prefer the float solution under the scenario of having a low SR, and the ILS solution when the SR is high. The best integer equivariant (BIE) estimator is an alternative solution since it minimizes the mean squared errors (MSEs); hence, it will always be superior to both its float and ILS counterparts. There has been a recent development of GNSSs consisting of the Global Positioning System (GPS), Galileo, Quasi-Zenith Satellite System (QZSS), and the BeiDou Navigation Satellite System (BDS), which has made precise positioning with Android smartphones possible. Since smartphone tracking of GNSS signals is generally of poorer quality than with geodetic grade receivers and antennas, the ILS SR is typically less than one, resulting in the BIE estimator being the preferred carrier phase ambiguity resolution option. Therefore, in this contribution, we compare, for the first time, the BIE estimator to the ILS and float contenders while using GNSS data collected by Google Pixel 4 (GP4) smartphones for short-baseline real-time kinematic (RTK) positioning. It is demonstrated that the BIE estimator will always give a better RTK positioning performance than that of the ILS and float solutions while using both single- and dual-frequency smartphone GNSS observations. Lastly, with the same smartphone data, we show that BIE will always be superior to the float and ILS solutions in terms of the MSEs, regardless of whether the SR is at high, medium, or low levels.

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“…The resulting position estimates are MSE optimal, and a closed-form expression for normally distributed data is provided in Teunissen (2003). An extension of the BIE principle for elliptically contoured distributions is presented in Teunissen (2020), and a sequential scalar approximation is proposed in Brack et al (2014). An evaluation of the BIE estimator based on simulations is given in Verhagen and Teunissen (2005), and its performance for multi-GNSS single-baseline RTK positioning is analyzed in Odolinski and Teunissen (2020).…”

Section: Introductionmentioning

confidence: 99%

Two-epoch centimeter-level PPP-RTK without external atmospheric corrections using best integer-equivariant estimation

2022

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Ambiguity resolution enabled precise point positioning (PPP-AR or PPP-RTK) without atmospheric corrections requires the user to estimate tropospheric and ionospheric delay parameters. The presence of the unconstrained ionosphere parameters impedes fast and reliable ambiguity resolution, so a time-to-first-fix of around 30 min for GPS-only solutions is generally reported, which can, to some extent, be reduced when combining multiple GNSS. In this contribution, we investigate the capabilities of almost instantaneous PPP-RTK, using only a few observation epochs at a sampling interval of 30 s, with the ionosphere-float model. The considered key elements are (a) the MSE-optimal best integer-equivariant estimator, (b) a combination of dual-frequency GPS, Galileo, BDS, and QZSS, (c) an area with good visibility of BDS and QZSS, and (d) a proper weighting of the PPP-RTK corrections. We provide a formal and simulation-based analysis of kinematic and static PPP-RTK with perfect, i.e., deterministic, clock and bias corrections as well as corrections computed from only a single reference station. The results indicate that, on average, one can expect centimeter-level positioning results with just slightly more than two epochs already with single-station corrections. This is confirmed with real four-system GNSS data, for which the availability of two-epoch centimeter-level horizontal positioning results is 99.7% during an exemplary day.

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Sequential Best Integer-Equivariant Estimation for GNSS

Cited by 14 publications

References 12 publications

Partial Carrier-Phase Integer Ambiguity Resolution for High Accuracy GNSS Positioning

Partial Carrier-Phase Integer Ambiguity Resolution for High Accuracy GNSS Positioning

Instantaneous Best Integer Equivariant Position Estimation Using Google Pixel 4 Smartphones for Single- and Dual-Frequency, Multi-GNSS Short-Baseline RTK

Two-epoch centimeter-level PPP-RTK without external atmospheric corrections using best integer-equivariant estimation

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