Rotation Matrix Method Based on Ambiguity Function for GNSS Attitude Determination

Yang, Ying; Mao, Xiaoyang; Tian, Weifeng

doi:10.3390/s16060841

Cited by 11 publications

(11 citation statements)

References 15 publications

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“…If the coordinates of the rover station are found correctly, the cosine value of the difference should be 1. The noise error is always the key factor to the success rate of AFM [ 27 ]. Considering the effect of noise and multipath, the highest AFV is close to 1.…”

Section: Algorithmmentioning

confidence: 99%

A New Method of High-Precision Positioning for an Indoor Pseudolite without Using the Known Point Initialization

Zhao

Zhang

Guo

et al. 2018

Sensors

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Due to the great influence of multipath effect, noise, clock and error on pseudorange, the carrier phase double difference equation is widely used in high-precision indoor pseudolite positioning. The initial position is determined mostly by the known point initialization (KPI) method, and then the ambiguities can be fixed with the LAMBDA method. In this paper, a new method without using the KPI to achieve high-precision indoor pseudolite positioning is proposed. The initial coordinates can be quickly obtained to meet the accuracy requirement of the indoor LAMBDA method. The detailed processes of the method follows: Aiming at the low-cost single-frequency pseudolite system, the static differential pseudolite system (DPL) method is used to obtain the low-accuracy positioning coordinates of the rover station quickly. Then, the ambiguity function method (AFM) is used to search for the coordinates in the corresponding epoch. The real coordinates obtained by AFM can meet the initial accuracy requirement of the LAMBDA method, so that the double difference carrier phase ambiguities can be correctly fixed. Following the above steps, high-precision indoor pseudolite positioning can be realized. Several experiments, including static and dynamic tests, are conducted to verify the feasibility of the new method. According to the results of the experiments, the initial coordinates with the accuracy of decimeter level through the DPL can be obtained. For the AFM part, both a one-meter search scope and two-centimeter or four-centimeter search steps are used to ensure the precision at the centimeter level and high search efficiency. After dealing with the problem of multiple peaks caused by the ambiguity cosine function, the coordinate information of the maximum ambiguity function value (AFV) is taken as the initial value of the LAMBDA, and the ambiguities can be fixed quickly. The new method provides accuracies at the centimeter level for dynamic experiments and at the millimeter level for static ones.

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Section: Algorithmmentioning

confidence: 99%

A New Method of High-Precision Positioning for an Indoor Pseudolite without Using the Known Point Initialization

Zhao

Zhang

Guo

et al. 2018

Sensors

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“…Taking a multi‐antenna GNSS system and the short‐baseline nature into account, a double‐difference (DD) observation equation can be formulated. It is an effective way to eliminate or weaken errors, such as the tropospheric and ionospheric errors, ephemeris errors, orbital errors and receiver clock errors [17]. In addition, the DD ambiguities are easy to be fixed using LS ambiguity decorrelation adjustment (LAMBDA) [18, 19].…”

Section: Introductionmentioning

confidence: 99%

GNSS attitude estimation based on adaptive Kalman filtering using phase measurement

Zhang

Chang

Chen

et al. 2020

IET Radar, Sonar & Navigation

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“…It is attractive because that the accuracy is moderate and hence satisfactory in many situations, that it can employ directly off-the-shelf antennas and receivers and hence is low-cost and fast-to-build, and that it is driftfree and hence suitable for long-term use. In recent years, it is receiving more and more attention in space/air/sea/land applications [7][8][9][10]. It can be used in both the dynamic and the static methods; however, in this contribution, the latter is the focus.…”

Section: Introductionmentioning

confidence: 99%

Analytical and Iterative Solutions to GNSS Attitude Determination Problem in Measurement Domain

Chen

Chang

et al. 2019

Mathematical Problems in Engineering

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Attitude determination using double-differenced GNSS carrier phase measurements is studied. A realistic stochastic model is employed to take the correlations among the double-differenced measurements into full consideration. Two important issues concerning iteratively solving the nonlinear least-squares attitude determination problem are treated, namely, the initial guess and the iteration scheme. An analytical and sub-optimal solution is employed to provide the initial guess. In this solution, the orthogonal and determinant constraints among the elements of the direction cosine matrix (DCM) of the attitude are firstly ignored, and hence a relaxed 3×3 matrix is estimated using the linear weighted least-squares method. Then a mathematically feasible DCM, i.e., orthogonal and with +1 determinant, is extracted from the relaxed matrix estimate, optimally in the sense of minimum Frobenius norm. This analytical initial guess estimation method can be used for all feasible cases, including some generated ones, e.g., the case with only 3 antennas and only 3 satellites, subject possibly to some necessary, yet minor modifications. In each iteration, an error attitude, whose DCM is parameterized using the Gibbs vector, is introduced to relate the previously estimated and the true DCM. By linearizing the measurement model at the zero Gibbs vector, the least-squares estimate of the Gibbs vector is obtained and then used to correct the previously estimated DCM. By repeating this process, the truly least-squares estimate of the attitude can be achieved progressively. These are in fact Gauss-Newton iterations. For the final estimate, the variance covariance matrix (VCM) of the attitude estimation error can be retained to evaluate or predict the estimation accuracy. The extraction of the widely used rollpitch-yaw angles and the VCM of their additive estimation errors from the final solution is also presented. Numerical experiments are conducted to check the performance of the developed theory. For the case with 3 2-meter long and orthogonally mounted baselines, 5 visible satellites, and 5-millimeter standard deviations of the carrier phase measurements, the root mean squared errors (RMSE) of the roll-pitch-yaw angles in the analytical solution are well below 0.5 degrees, and the estimates converge after only one iteration, with all three RMSEs below 0.2 degrees.

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Rotation Matrix Method Based on Ambiguity Function for GNSS Attitude Determination

Cited by 11 publications

References 15 publications

A New Method of High-Precision Positioning for an Indoor Pseudolite without Using the Known Point Initialization

A New Method of High-Precision Positioning for an Indoor Pseudolite without Using the Known Point Initialization

GNSS attitude estimation based on adaptive Kalman filtering using phase measurement

Analytical and Iterative Solutions to GNSS Attitude Determination Problem in Measurement Domain

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