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

Brack, Andreas

doi:10.31237/osf.io/bv6pj

Cited by 9 publications

(8 citation statements)

References 97 publications

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“…Defining the mapping S(⋅) ∶ ℝ n → ℤ |J| , the index set J can assume any of the 2 n − 1 possible non-empty realizations that follow from either including each of the n elements of the parameter vector a or not. Such an estimator can be fully described by the regions S z ⊂ ℝ n , ∀z ∈ ℤ |J| , which denotes the point set that is mapped to the same integer z via S(⋅) (Brack 2019) Then, by considering the integer constraint of ambiguity, the float solution is fixed as the integer solution, which is achieved through many-to-one mapping. The partial integer estimator corresponding to these regions can be explicitly written as: This is of importance when formulating the constraints that have to be imposed on the construction of the regions S z .…”

Section: Partial Ambiguity Resolutionmentioning

confidence: 99%

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Adaptive Kalman filter based on integer ambiguity validation in moving base RTK

et al. 2022

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In high-precision dynamic positioning, it is necessary to ensure the positioning accuracy and reliability of the navigation system, especially for safety–critical applications, such as intelligent vehicle navigation. In the face of a complex observation environment, when the global navigation satellite system (GNSS) uses carrier phase observations for high-precision relative positioning, ambiguity resolution will be affected, and it is difficult to estimate all ambiguities. In addition, when the GNSS signal quality and measurement noise level are difficult to predict in an environment with many occlusions, the received satellite observations are prone to very large errors, resulting in apparent deviations in the positioning solution. However, traditional positioning algorithms assume that the measurement noise is constant, which is unrealistic. This will cause incorrect ambiguity resolution, lead to meter-level positioning errors, reduce the reliability of the system, and increase the integrity risk of the system. We proposed an innovative adaptive Kalman filter based on integer ambiguity validation (IAVAKF) to improve the efficiency of ambiguity resolution (AR) and positioning accuracy. The partial ambiguity resolution (PAR) method is applied to solve the integer ambiguities. Then, the accuracy of the fixed ambiguity is verified by the ambiguity success rate. Taking the ambiguity success rate as a dynamic adjustment factor, the measurement noise matrix and variance–covariance matrix of the state estimation is adaptively adjusted at each time interval in the Kalman filter to provide a smoothing effect for filtering. The optimal Kalman filter gain matrix is obtained to improve positioning accuracy and reliability. As a result, the static and dynamic vehicle experiments show that the positioning accuracy of the proposed IAVAKF is improved by 26% compared with the KF. Through the IAVAKF, a more realistic PL can be obtained and applied to evaluate the integrity of the navigation system in the position domain. It can reduce the false alarm rate by 2.45% and 1.85% in the horizontal and vertical directions, respectively.

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Section: Partial Ambiguity Resolutionmentioning

confidence: 99%

“…In other words, the probability of correct ambiguity estimation, i.e., ambiguity success rate P s , is equal to the probability that â resides in the pull-in region P a with a being the true but unknown ambiguity vector (Brack 2019):…”

Section: Integer Ambiguity Verification In the Probability Domainmentioning

confidence: 99%

Adaptive Kalman filter based on integer ambiguity validation in moving base RTK

et al. 2022

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“…Although data-and model-driven schemes are widely used, they only take into account the ambiguities derived from the real-valued parameters estimation and the information brought by the covariance matrix of the ambiguities. While the requirement of a minimal precision for the fixed solution has been discussed in the context of PAR [18] (Ch. 4), its consideration as subset selection criteria has not yet been proposed.…”

Section: Precision-driven Par Schemementioning

confidence: 99%

“…Answering this question leads to the different selection heuristics, such as signalto-noise ratio [11,12], Ambiguity Dilution of Precision (ADOP) [13], or minimum bias [14]. Alternatively, the framework of Generalized Integer Aperture (GIA), introduced by Brack in his series of work [15][16][17][18], extends the concepts from Integer Aperture to PAR to jointly perform real-to-integer mapping and subset selection.…”

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confidence: 99%

Precision-Aided Partial Ambiguity Resolution Scheme for Instantaneous RTK Positioning

et al. 2021

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The use of carrier phase data is the main driver for high-precision Global Navigation Satellite Systems (GNSS) positioning solutions, such as Real-Time Kinematic (RTK). However, carrier phase observations are ambiguous by an unknown number of cycles, and their use in RTK relies on the process of mapping real-valued ambiguities to integer ones, so-called Integer Ambiguity Resolution (IAR). The main goal of IAR is to enhance the position solution by virtue of its correlation with the estimated integer ambiguities. With the deployment of new GNSS constellations and frequencies, a large number of observations is available. While this is generally positive, positioning in medium and long baselines is challenging due to the atmospheric residuals. In this context, the process of solving the complete set of ambiguities, so-called Full Ambiguity Resolution (FAR), is limiting and may lead to a decreased availability of precise positioning. Alternatively, Partial Ambiguity Resolution (PAR) relaxes the condition of estimating the complete vector of ambiguities and, instead, finds a subset of them to maximize the availability. This article reviews the state-of-the-art PAR schemes, addresses the analytical performance of a PAR estimator following a generalization of the Cramér–Rao Bound (CRB) for the RTK problem, and introduces Precision-Driven PAR (PD-PAR). The latter constitutes a new PAR scheme which employs the formal precision of the (potentially fixed) positioning solution as selection criteria for the subset of ambiguities to fix. Numerical simulations are used to showcase the performance of conventional FAR and FAR approaches, and the proposed PD-PAR against the generalized CRB associated with PAR problems. Real-data experimental analysis for a medium baseline complements the synthetic scenario. The results demonstrate that (i) the generalization for the RTK CRB constitutes a valid lower bound to assess the asymptotic behavior of PAR estimators, and (ii) the proposed PD-PAR technique outperforms existing FAR and PAR solutions as a non-recursive estimator for medium and long baselines.

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

Cited by 9 publications

References 97 publications

Adaptive Kalman filter based on integer ambiguity validation in moving base RTK

Adaptive Kalman filter based on integer ambiguity validation in moving base RTK

Precision-Aided Partial Ambiguity Resolution Scheme for Instantaneous RTK Positioning

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

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