GNSS Integer Ambiguity Estimation and Evaluation: LAMBDA and Ps-LAMBDA

Li, Bofeng; Verhagen, Sandra; Teunissen, Peter

doi:10.1007/978-3-642-37404-3_26

Cited by 19 publications

(8 citation statements)

References 19 publications

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“…ε includes the multipath, thermal noises, and modeling errors in the carrier phase measurements. When two GNSS receivers, master (M) and follower (F), are within several kilometers, the double difference formulation of the satellites k and l can be modeled as is resolved using various algorithms, such as LAMBDA [4][5][6]. The LAMBDA method does not place any constraints on x MF and uses no a priori information of x MF when searching for the integer ambiguty values.…”

Section: Integer Ambiguity Resolution With Rounding Using a Known Relmentioning

confidence: 99%

“…

is the double differenced integer ambiguity, and

includes the double difference noise and multipath. In a conventional RTK system,

is resolved using various algorithms, such as LAMBDA [ 4 , 5 , 6 ]. The LAMBDA method does not place any constraints on

and uses no a priori information of

when searching for the integer ambiguty values.…”

Section: Integer Ambiguity Resolution With Rounding Using a Known mentioning

confidence: 99%

“…An RTK system consists of reference and rover receivers with high-grade antennas and can provide centimeter-level positioning accuracy by using double difference code and carrier phase measurements. An RTK system must solve integer ambiguities in carrier phase measurements, for instance, by using Least-squares Ambiguity Decorrelation Adjustment (LAMBDA) algorithms [ 4 , 5 , 6 ] or a PREcise and Fast Method of Ambiguity Resolution (PREFMAR) method [ 7 , 8 ]. The LAMBDA method has been widely used in GNSS communities and it consists of three steps including a float solution generation, a decorrelation of double difference measurements, and an integer ambiguity search.…”

Section: Introductionmentioning

confidence: 99%

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GNSS Precise Relative Positioning Using A Priori Relative Position in a GNSS Harsh Environment

Kim

2021

Sensors

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To enable Global Navigation Satellite System (GNSS)-based precise relative positioning, real-time kinematic (RTK) systems have been widely used. However, an RTK system often suffers from a wrong integer ambiguity fix in the GNSS carrier phase measurements and may take a long initialization time over several minutes, particularly when the number of satellites in view is small. To facilitate a reliable GNSS carrier phase-based relative positioning with a small number of satellites in view, this paper introduces a novel GNSS carrier phase-based precise relative positioning method that uses a fixed baseline length as well as heading measurements in the beginning of the operation, which allows the fixing of integer ambiguities with rounding schemes in a short time. The integer rounding scheme developed in this paper is an iterative process that sequentially resolves integer ambiguities, and the sequential order of the integer ambiguity resolution is based on the required averaging epochs that vary for each satellite depending on the geometry between the baseline and the double difference line-of-sight vectors. The required averaging epochs with respect to various baseline lengths and heading measurement uncertainties were analyzed through simulations. Static and dynamic field tests with low cost GNSS receivers confirmed that the positioning accuracy of the proposed method was better than 10 cm and significantly outperformed a conventional RTK solution in a GNSS harsh environment.

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Section: Integer Ambiguity Resolution With Rounding Using a Known Relmentioning

confidence: 99%

“…

is the double differenced integer ambiguity, and

includes the double difference noise and multipath. In a conventional RTK system,

is resolved using various algorithms, such as LAMBDA [ 4 , 5 , 6 ]. The LAMBDA method does not place any constraints on

and uses no a priori information of

when searching for the integer ambiguty values.…”

Section: Integer Ambiguity Resolution With Rounding Using a Known mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

GNSS Precise Relative Positioning Using A Priori Relative Position in a GNSS Harsh Environment

Kim

2021

Sensors

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“…The best integer candidate a and second best integer candidate a can be obtained from the integer least-squares estimator. The details of the integer least-squares search procedure have been extensively discussed [2,3,9]. l R is the threshold for the ratio test and its value varies in the interval [0,1].…”

Section: The Ratio Test and Its Acceptance Regionmentioning

confidence: 99%

Ambiguity Acceptance Testing: A Comparison of the Ratio Test and Difference Test

Wang

Verhagen

Feng

2014

Lecture Notes in Electrical Engineering

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Integer ambiguity resolution is an indispensable procedure for all high precision GNSS applications. The correctness of the estimated integer ambiguities is the key to achieving highly reliable positioning, but the solution cannot be validated with classical hypothesis testing methods. The integer aperture estimation theory unifies all existing ambiguity validation tests and provides a new prospective to review existing methods, which enables us to have a better understanding on the ambiguity validation problem. This contribution analyses two simple but efficient ambiguity validation test methods, ratio test and difference test, from three aspects: acceptance region, probability basis and numerical results. The major contribution of this paper can be summarized as: (1) The ratio test acceptance region is overlap of ellipsoids while the difference test acceptance region is overlap of half-spaces. (2) The probability basis of these two popular tests is firstly analyzed. The difference test is an approximation to optimal integer aperture, while the ratio test follows an exponential relationship in probability. (3) The limitations of the two tests are firstly identified. The two tests may under-evaluate the failure risk if the model is not strong enough or the float ambiguities fall in particular region. (4) Extensive numerical results are used to compare the performance of these two tests. The simulation results show the ratio test outperforms the difference test in some models while difference test performs better in other models. Particularly in the medium baseline kinematic model, the difference tests outperforms the ratio test, the superiority is independent on frequency number, observation noise, satellite geometry, while it depends on success rate and failure rate tolerance. Smaller failure rate leads to larger performance discrepancy.

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“…The RTK system can achieve centimeter-level positioning by processing carrier phase measurements as ranging sources. The RTK process includes integer ambiguity resolution through various algorithms, such as the least-squares ambiguity decorrelation adjustment (LAMBDA) [ 4 , 5 ]. The success probability of correctly resolved integer ambiguities of LAMBDA improves as the number of GNSS constellations and measurement frequencies increases [ 6 , 7 , 8 , 9 ].…”

Section: Introductionmentioning

confidence: 99%

Global Navigation Satellite System Real-Time Kinematic Positioning Framework for Precise Operation of a Swarm of Moving Vehicles

Kim

2022

Sensors

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The global navigation satellite system (GNSS) real-time kinematic (RTK) technique is used to achieve relative positioning centimeter levels among multiple agents on the move. A typical GNSS RTK estimates the relative positions of multiple rover receivers with respect to a single-base receiver. In a fleet of rover GNSS receivers, this approach is inefficient because each rover receiver only uses GNSS measurements of its own and those sent from a single-base receiver. In this study, we propose a novel GNSS RTK framework that facilitates the precise positioning of a swarm of moving vehicles through the GNSS measurements of multiple receivers and broadcasts fixed-integer ambiguities of GNSS carrier phases. The proposed framework not only provides efficient RTK positioning but also reliable performance with a limited number of GNSS satellites in view. Our experimental flight tests with six GNSS receivers showed that the systematic procedure of the proposed framework could maintain lower than 6 cm of 3D RMS positioning errors, whereas the conventional RTK failed to resolve the correct integer ambiguities of double difference carrier phase measurements more than 13% in five out of nine total baselines.

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GNSS Integer Ambiguity Estimation and Evaluation: LAMBDA and Ps-LAMBDA

Cited by 19 publications

References 19 publications

GNSS Precise Relative Positioning Using A Priori Relative Position in a GNSS Harsh Environment

GNSS Precise Relative Positioning Using A Priori Relative Position in a GNSS Harsh Environment

Ambiguity Acceptance Testing: A Comparison of the Ratio Test and Difference Test

Global Navigation Satellite System Real-Time Kinematic Positioning Framework for Precise Operation of a Swarm of Moving Vehicles

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