Integer Ambiguity Estimation for Satellite Navigation

Günther, Christoph; Henkel, Patrick

doi:10.1109/tsp.2012.2191549

Cited by 18 publications

(15 citation statements)

References 5 publications

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“…The proposed RieOpt method applies the procedure summarized in Algorithm 3. This method solves the optimization problem in (16) to refine the results obtained from the procedure given by (8)- (13), and obtain a final attitude estimate. While the LS and the proposed approach utilizes only carrier phase, the LAMBDA [10] and MC-LAMBDA [29] methods take advantage of both the carrier phase and pseudo-range.…”

Section: Simulation Setup and Resultsmentioning

confidence: 99%

“…Now, we are in a position to precisely estimate the pointing vectors using Riemannian Optimization (RieOpt method) developed in Section IV. The optimization problem in (16) is solved by the proposed RieOpt method initializingx and y with the LS solutionsx andý as computed in (12). As mentioned before, the constraints in Eq.…”

Section: -D Gnss Attitude Determination Using Riemannian Optimizamentioning

confidence: 99%

“…While motion-based methods are not designed for realtime applications, their search-based counterparts are independent of the platform's motion, making them good candidates for instantaneous attitude determination. Among the search-based methods, the LAMBDA approach [10] and its extended versions [14]- [16] received considerable attention in the literature. The main advantage of these methods is that the ambiguity resolution search is performed directly in the integer domain.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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Section: Simulation Setup and Resultsmentioning

confidence: 99%

Section: -D Gnss Attitude Determination Using Riemannian Optimizamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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 order to reach a very high precision, integer ambiguity must be correctly resolved. Ambiguity integer least square solution without constraint is given as [ 19 ]:

where

is float solution,

is variance matrix. As no prior information exists, there is any baseline related items in objective function.…”

Section: Baseline Vector Constrained Modelmentioning

confidence: 99%

GNSS Single Frequency, Single Epoch Reliable Attitude Determination Method with Baseline Vector Constraint

Gong

Zhao

Pang

et al. 2015

Sensors

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For Global Navigation Satellite System (GNSS) single frequency, single epoch attitude determination, this paper proposes a new reliable method with baseline vector constraint. First, prior knowledge of baseline length, heading, and pitch obtained from other navigation equipment or sensors are used to reconstruct objective function rigorously. Then, searching strategy is improved. It substitutes gradually Enlarged ellipsoidal search space for non-ellipsoidal search space to ensure correct ambiguity candidates are within it and make the searching process directly be carried out by least squares ambiguity decorrelation algorithm (LAMBDA) method. For all vector candidates, some ones are further eliminated by derived approximate inequality, which accelerates the searching process. Experimental results show that compared to traditional method with only baseline length constraint, this new method can utilize a priori baseline three-dimensional knowledge to fix ambiguity reliably and achieve a high success rate. Experimental tests also verify it is not very sensitive to baseline vector error and can perform robustly when angular error is not great.

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“…If the number of ambiguities n is large, a considerable amount of computational complexity resides in the iterative swap and decorrelation operations for finding the Z transformation of the LAMBDA method. For a low complexity implementation, which it is aimed at in this contribution, the functional decorrelation in or can serve as an alternative.…”

Section: Gnss Parameter Estimationmentioning

confidence: 99%