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

Douik, Ahmed; Liu, Xing; Ballal, Tarig; Al-Naffouri, Tareq Y.; Hassibi, Babak

doi:10.1109/tsp.2019.2959226

Cited by 10 publications

(4 citation statements)

References 30 publications

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“…As the solution set of the attitude matrix is a manifold, we formulate GNSS attitude determination as an optimization over Riemannian manifolds. An earlier study of manifold geometries has demonstrated the ability to develop efficient Riemannian algorithms with the capacity of offering accurate attitude estimations using the given carrier-phase ambiguities [36]. We demonstrate that Riemannian manifold optimization can also be utilized in the ambiguity resolution process to significantly improve the float solution.…”

Section: Introductionmentioning

confidence: 87%

Instantaneous GNSS Ambiguity Resolution and Attitude Determination via Riemannian Manifold Optimization

Liu¹,

Ballal²,

Ahmed³

et al. 2022

Preprint

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We present an ambiguity resolution method for Global Navigation Satellite System (GNSS)-based attitude determination. A GNSS attitude model with nonlinear constraints is used to rigorously incorporate a priori information. Given the characteristics of the employed nonlinear constraints, we formulate GNSS attitude determination as an optimization problem on a manifold. Then, Riemannian manifold optimization algorithms are utilized to aid ambiguity resolution based on a proposed decomposition of the objective function. The application of manifold geometry enables high-quality float solutions that are critical to reinforcing search-based integer ambiguity resolution in terms of efficiency, availability, and reliability. The proposed approach is characterized by a low computational complexity and a high probability of resolving the ambiguities correctly. The performance of the proposed ambiguity resolution method is tested through a series of simulations and real experiments. Comparisons with the principal benchmarks indicate the superiority of the proposed method as reflected by the high ambiguity resolution success rates.

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Section: Introductionmentioning

confidence: 87%

Instantaneous GNSS Ambiguity Resolution and Attitude Determination via Riemannian Manifold Optimization

Liu¹,

Ballal²,

Ahmed³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…2: Solve ( 22) to obtain RRM using the Riemannian algorithms. 3: Compute NRM using (23). 4: Initialize χ = χ 0 > 0 and k = 0.…”

Section: Integer Search Strategymentioning

confidence: 99%

Instantaneous GNSS Ambiguity Resolution and Attitude Determination via Riemannian Manifold Optimization

Liu

Ballal

Ahmed

et al. 2023

IEEE Trans. Aerosp. Electron. Syst.

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We consider the problem of Global Navigation Satellite System (GNSS)-based attitude determination. A GNSS attitude model with nonlinear orthonormality constraints is used to rigorously incorporate the a-priori knowledge of the receiver geometry. Given the characteristics of the employed nonlinear constraints, we formulate GNSS attitude determination as an optimization problem on a Riemannian manifold. We design a Riemannian algorithm to deliver the constrained float attitude matrix solution. Subsequently, the constrained float solution, combined with a proposed decomposition of the objective function, is utilized to enhance the efficiency of the integer ambiguity search. Both simulation and experimental evidences demonstrate the superiority of the proposed method. The results reveal that the proposed method can maintain the high probability of resolving the integer ambiguities correctly while enjoying the low computational complexity compared with the state-of-the-art techniques.

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“…M is a differentiable manifold, and the tangent space 35 of points scriptTboldxM is a linear space that can approximate the manifold M at each point x∈M. The tangent space is a limited dimensional linear space.…”

Section: Related Workmentioning

confidence: 99%

“…M is a differentiable manifold, and the tangent space 35 of points T x M is a linear space that can approximate the manifold M at each point x ∈ M. The tangent space is a limited dimensional linear space. From a geometric point of view, the manifold pattern can be estimated as an Euclidean space on a tiny local neighborhood, and the optimization direction of the model on the manifold, i.e., the Euclidean gradient mapping on the tangent space.…”

Section: Manifold Optimization: Definitions and Notationmentioning

confidence: 99%

Parameter-free nonlinear partial least squares regression model for image classification

Chen,

Wang,

Tao

et al. 2023

J. Electron. Imag.

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Partial least squares regression (PLSR) is a linear regression model suitable for handling data with high dimensions and small samples. However, a large amount of nonlinear structure data exists in real life, and PLSR may be not good at handling this type of data. Motivated by this, we propose a parameter-free, nonlinear PLSR model called estimating optimal transformations PLSR. First, we use the EOT model to transform a nonlinear data structure into a linear data structure without additional parameters by maximizing the correlation between data samples. In addition, the traditional PLSR model often uses a greedy algorithm, leading to suboptimal solutions. To obtain more accurate numerical solutions, we propose using manifold optimization for the PLSR model. Compared to the other existing PLSR models, our proposed model achieves lower classification error rates on several different types of datasets. The experimental results further confirm the importance of our proposed nonlinear data transformation and manifold optimization for feature extraction with nonlinear structure data.

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

Cited by 10 publications

References 30 publications

Instantaneous GNSS Ambiguity Resolution and Attitude Determination via Riemannian Manifold Optimization

Instantaneous GNSS Ambiguity Resolution and Attitude Determination via Riemannian Manifold Optimization

Instantaneous GNSS Ambiguity Resolution and Attitude Determination via Riemannian Manifold Optimization

Parameter-free nonlinear partial least squares regression model for image classification

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