The New Search Method in Precise GNSS Positioning

Cellmer, Sławomir; Nowel, Krzysztof; Kwaśniak, Dawid

doi:10.1109/taes.2017.2760578

Cited by 21 publications

(19 citation statements)

References 37 publications

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“…The optimization of the search procedure in the coordinate domain is a separate, currently open problem. In Cellmer et al (2018), we propose to use a grid ellipsoid instead of a grid cube and a cascade processing with a widelane combination in a first step. These solutions can significantly improve the computational efficiency.…”

Section: Discussionmentioning

confidence: 99%

Mixed integer–real least squares estimation for precise GNSS positioning using a modified ambiguity function approach

2018

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Mixed integer-real least squares (MIRLS) estimation still has two open scientific problems, i.e., the validation of results and computational efficiency for a large number of satellites. This paper presents and discusses a non-conventional approach to MIRLS estimation, which belongs to the ambiguity function method (AFM) class. Because the solution is searched for in the constant three-dimensional coordinate domain instead of the n-dimensional ambiguity domain, the computational efficiency does not depend as much on the number of satellites as it does in conventional MIRLS estimation. Simple numerical pretests have shown that the reliability and precision of results from the presented approach and the conventional MIRLS estimation are exactly the same. Hence, the presented approach, contrary to AFM, may be treated as MIRLS estimation. Furthermore, the presented approach is a few hundred times faster than AFM and may be considered in (near) real-time GNSS positioning. In light of the above, the new field of research on MIRLS estimation may be opened.

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Section: Discussionmentioning

confidence: 99%

Mixed integer–real least squares estimation for precise GNSS positioning using a modified ambiguity function approach

2018

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“…Another concern is the search efficiency of the MAFA. It was proved in Reference [22] that the optimal distance between the closest points in the search grid could be half of the wavelength. However, the point by point grid search method is still very low efficiency, considering the accuracy of prior position is usually about 1-2 m, which severely limits the application of MAFA by using the single-frequency receivers.…”

Section: Methods For Improving the Search Efficiency Of Mafamentioning

confidence: 99%

“…The search cube can be chosen as a cylinder, and structured base on the coordinate vector of the a priori position X 0 and its covariance matrix Q X 0 , where X 0 can be obtained by using some traditional method, for example, Extended Kalman Filter. The distance between different search layers can be half of the signal wavelength [22], shown in Figure 2. The new search method is called the Segmented Simulated Annealing (SSA) algorithm.…”

Section: Segmented Simulated Annealing (Ssa)mentioning

confidence: 99%

“…In Reference [21], a solution to minimize the size of the search cube in the MAFA method was presented. In Reference [22], the probabilistic aspect was taken into account, and the search region was formed with a certain confidence level. Above all, the AFM class methods indeed show their advantage over the LAMBDA method, which is immune to cycle slips, especially the MAFA method may give out the precise positioning result by using a single epoch of data even in the case of poor accuracy of approximate position.…”

Section: Introductionmentioning

confidence: 99%

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An Improved Ambiguity-Free Method for Precise GNSS Positioning with Utilizing Single Frequency Receivers

Yang

Liu

2020

Sensors

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The solution of carrier phase ambiguity is essential for precise global navigation satellite system (GNSS) positioning. Methods of searching in the coordinate domain show their advantage over the methods based on ambiguity fixing, for example, immune to cycle slips, far fewer epochs taken for obtaining the precise solution. However, there are still some drawbacks via using the Ambiguity Function Method (AFM), such as low computation efficiency and the existence of a false global optimum. The false global optimum is a situation where the Least Square (LS) criterion achieves minimum in another place than the point of the actual position, which restricts the application of this method to single-frequency receivers. The numerical search approach derived in this paper is based on the Modified Ambiguity Function Approach (MAFA). It focuses on eliminating the false optimum solution and reducing the computation load by utilizing single-frequency receivers without solving the ambiguity fixing problem. An improved segmented simulated annealing method is used to decrease the computation load while the Kernel Density Estimator (KDE) method is used to filter out the false optimum candidates. Static experiments were carried out to evaluate the performance of the new approach. It is shown that a precise result can be obtained by handling two epochs of data with z coordinate fixed to the referenced value. Meanwhile, the new approach can achieve a millimeter level of position accuracy after dealing with nineteen epochs of observations data when searching in x , y , z domain. The new approach shows its robustness even if the search region is broad, and the prior position is several meters away from the referenced value.

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“…Han and Rizos [ 11 ] improved computational efficiency of the ambiguity function algorithms for practical applications. Cellmer et al [ 12 ] proposed further improvement of the ambiguity function approach. They have developed a new method named the Modified Ambiguity Function Approach (MAFA), in which the dramatically reduced computational load characterizes the computational process.…”

Section: Introductionmentioning

confidence: 99%

Instantaneous Ambiguity Reinitialization and Fast Ambiguity Initialization for L1-L2 GPS Measurements

Bakuła¹

2020

Sensors

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This paper presents a PREcise and Fast Method of Ambiguity Reinitialization/Resolution (PREFMAR) for L1 and L2 in GPS measurements. The method determines NL1 and NL2 ambiguities based on the ambiguity functions: Ψ(NL1)NL1NL2 and Ψ(NL2)NL2NL1. These ambiguity functions have been described in detail in this work. The developed method of ambiguity initialization and reinitialization in relative positioning can use Global Positioning System (GPS) measurements from only two satellites and one measurement epoch. To resolve NL1 and NL2 ambiguities, a variance-covariance (VC) matrix of the float solution is not needed. The size of the search area in the PREFMAR method depends on code and phase accuracy as well as on the GNSS signal frequencies. Therefore, the search area is specific for every double or triple Global Navigation Satellite Systems (GNSS) data frequency. However, this part of the research only presents the ambiguity search area for L1 and L2 of GPS measurements. Additionally, a numerical example has been analyzed in detail with the use of the PREFMAR method and a float solution (NL1, NL2). Finally, the elaborated algorithms were successfully tested on real L1 and L2 GPS measurements for instantaneous ambiguity reinitialization. The PREFMAR method allows instantaneous ambiguity reinitialization if all satellites lose contact with a GNSS antenna, for short and long baselines. Therefore, the PREFMAR has a great potential for precise real-time kinematic GNSS navigation.

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The New Search Method in Precise GNSS Positioning

Cited by 21 publications

References 37 publications

Mixed integer–real least squares estimation for precise GNSS positioning using a modified ambiguity function approach

Mixed integer–real least squares estimation for precise GNSS positioning using a modified ambiguity function approach

An Improved Ambiguity-Free Method for Precise GNSS Positioning with Utilizing Single Frequency Receivers

Instantaneous Ambiguity Reinitialization and Fast Ambiguity Initialization for L1-L2 GPS Measurements

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