Formal Uncertainty and Dispersion of Single and Double Difference Models for GNSS-Based Attitude Determination

Chen, Wen; Yu, Caiyan; Dong, Danan; Cai, Meng; Zhou, Feng; Wang, Zhiren; Zhang, Lei; Zheng, Zhengqi

doi:10.3390/s17020408

Cited by 16 publications

(16 citation statements)

References 27 publications

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“…The data processing for obtaining the residual time series used in RCM was divided into two steps. In the first step, the baseline (between the two antennas) solutions are estimated with integer ambiguity resolution by single difference algorithm [18,21,22]. In the second step, the daily solutions of baseline components (average of all the single epoch solutions on a day) are substituted into single-differenced observation equations to generate residuals for each satellite and for each epoch.…”

Section: Residual Correlation Methods (Rcm)mentioning

confidence: 99%

Comparison of Three Methods for Estimating GPS Multipath Repeat Time

Wang

Dong

et al. 2018

Remote Sensing

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Abstract:Sidereal filtering is an effective method for mitigating multipath error in static GPS positioning. Using accurate estimates of multipath repeat time (MRT) in sidereal filtering can further improve the performance of the filter. There are three commonly used methods for estimating the MRT: Orbit Repeat Time Method (ORTM), Aspect Repeat Time Adjustment (ARTA), and Residual Correlation Method (RCM). This study utilizes advanced sidereal filtering (ASF) adopting the MRT estimates derived by the three methods to mitigate the multipath in observation domain, then evaluates the three methods in term of multipath reduction in both coordinate and observation domain. Normally, the differences between the MRT estimates from the three methods are less than 1.2 s on average. The three methods are basically identical in multipath reduction, with RCM being slightly better than the other two methods, whereas for a satellite affected by orbit maneuver (satellite number 13 in this study), the MRT estimated by the three methods differ by up to tens of seconds, and the RCM-and ARTA-derived MRT estimates are better than ORTM-derived ones for ASF multipath reduction. The RCM shows a slight advantage in multipath mitigation, while ORTM is the one of lowest computation and ARTA is the optimal one for real-time ASF. Thus, the best MRT estimation method for practical applications depends on which criterion overweighs the others.

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Section: Residual Correlation Methods (Rcm)mentioning

confidence: 99%

Comparison of Three Methods for Estimating GPS Multipath Repeat Time

Wang

Dong

et al. 2018

Remote Sensing

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“…The asymptotic analysis further demonstrated that using this multi-antenna GNSS receiver with a common clock, the pitch solutions of the SD algorithm were significantly superior to that of the DD algorithm. The dispersions of the pitch solutions from the SD algorithm were five times smaller than that from the DD algorithm [7]. These advantages allow using SD observables for attitude determination and research in other fields such as multipath [8] and stochastic models [9].…”

Section: Introductionmentioning

confidence: 99%

High-Accuracy Attitude Determination Using Single-Difference Observables Based on Multi-Antenna GNSS Receiver with a Common Clock

et al. 2021

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A global navigation satellite system (GNSS) receiver with multi-antenna using clock synchronization technology is a powerful piece of equipment for precise attitude determination and reducing costs. The single-difference (SD) can eliminate both the satellites and receiver clock errors with the common clock between antennas, which benefits the GNSS short-baseline attitude determination due to its lower noise, higher redundancy and stronger function model strength. However, the existence of uncalibrated phase delay (UPD) makes it difficult to obtain fixed SD attitude solutions. Therefore, the key problem for the fixed SD attitude solutions is to separate the SD UPD and fix the SD ambiguities into integers between antennas. This article introduces the one-step ambiguity substitution approach to separate the SD UPD, through which we merge the SD UPD parameter with the SD ambiguity of the reference satellite ambiguity as the new SD UPD parameter. Reconstructing the other SD ambiguities, the rank deficiency can be remedied by nature, and the new SD ambiguities can have a natural integer feature. Finally, the fixed SD baseline and attitude solutions are obtained by combining the ambiguity substitution approach with integer ambiguity resolution (IAR). To verify the effect of the ambiguity substitution approach and the advantages of the SD observables with a common clock in practical applications, we conducted static, kinematic, and vehicle experiments. In static experiments, the root mean squared errors (RMSEs) of the yaw and pitch angles obtained by the SD observables with a common clock were improved by approximately 80% and 93%, respectively, compared to double-difference (DD) observables with a common clock in multi-day attitude solutions. The kinematic results show that the dispersion of the SD-Fix in the pitch angle is two times less that of the DD-Fix, and the standard deviations (STDs) of the pitch angle for SD-Fix can reach 0.02°. Based on the feasibility, five bridges with low pitch angles in the vehicle experiment environment, which the DD observables cannot detect, were detected by the SD observables with a common clock. The attitude angles obtained by the SD observables were also consistent with the fiber optic gyroscope (FOG) inertial navigation system (INS). This research on the SD observables with a common clock provides higher accuracy.

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“…However, such approach would not solve the problem of receiver clock bias which still needs to be estimated. With common receiver clock technology, single-difference models can be used to simplify the complexity and reduce the influence of uncorrelated noise [18]- [20]. The phase double difference refers to the instantaneous difference between the phase (single) difference observations of two different satellites [21].…”

Section: Introductionmentioning

confidence: 99%

Precise 3-D GNSS Attitude Determination Based on Riemannian Manifold Optimization Algorithms

Douik

Liu

Ballal

et al. 2020

IEEE Trans. Signal Process.

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In the past few years, Global Navigation Satellite Systems (GNSS) based attitude determination has been widely used thanks to its high accuracy, low cost, and real-time performance. This paper presents a novel 3-D GNSS attitude determination method based on Riemannian optimization techniques. The paper first exploits the antenna geometry and baseline lengths to reformulate the 3-D GNSS attitude determination problem as an optimization over a non-convex set. Since the solution set is a manifold, in this manuscript we formulate the problem as an optimization over a Riemannian manifold. The study of the geometry of the manifold allows the design of efficient first and second order Riemannian algorithms to solve the 3-D GNSS attitude determination problem. Despite the non-convexity of the problem, the proposed algorithms are guaranteed to globally converge to a critical point of the optimization problem. To assess the performance of the proposed framework, numerical simulations are provided for the most challenging attitude determination cases: the unaided, singleepoch, and single-frequency scenarios. Numerical results reveal that the proposed algorithms largely outperform state-of-the-art methods for various system configurations with lower complexity than generic non-convex solvers, e.g., interior point methods.

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Formal Uncertainty and Dispersion of Single and Double Difference Models for GNSS-Based Attitude Determination

Cited by 16 publications

References 27 publications

Comparison of Three Methods for Estimating GPS Multipath Repeat Time

Comparison of Three Methods for Estimating GPS Multipath Repeat Time

High-Accuracy Attitude Determination Using Single-Difference Observables Based on Multi-Antenna GNSS Receiver with a Common Clock

Precise 3-D GNSS Attitude Determination Based on Riemannian Manifold Optimization Algorithms

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