Recently, lattice theory has been widely used for integer ambiguity resolution in the Global Navigation Satellite System (GNSS). When using lattice theory to deal with integer ambiguity, we need to reduce the correlation between lattice bases to ensure the efficiency of the solution. Lattice reduction is divided into scale reduction and basis vector exchange. The scale reduction has no direct impact on the subsequent search efficiency, while the basis vector exchange directly impacts the search efficiency. Hence, Lenstra-Lenstra-Lovász (LLL) is applied in the ambiguity resolution to improve the efficiency. And based on Householder transformation, the HLLL improved method is also used. Moreover, to improve the calculation speed further, a Pivoting Householder LLL (PHLLL) method based on Householder orthogonal transformation and rotation sorting is proposed here. The idea of PHLLL method is as follows: First, a sort matrix is introduced into the lattice basis reduction process to sort the original matrix. Then, the sorted matrix is used for Householder transformation. After transformation, it needs to be sorted again, until the diagonal elements in the matrix meet the ascending order. In addition, when using the Householder image operator for orthogonalization, the old column norm is modified to obtain a new norm, reducing the number of column norm calculations. Compared with the LLL reduction algorithm and HLLL reduction algorithm, the experimental results show that the PHLLL algorithm has higher reduction efficiency and effectiveness. The theoretical superiority of the algorithm is proved.
Because the traditional Cholesky decomposition algorithm still has some problems such as computational complexity and scattered structure among matrices when solving the GNSS ambiguity, it is the key problem to further improve the computational efficiency of the least squares ambiguity reduction correlation process in the carrier phase integer ambiguity solution. But the traditional matrix decomposition calculation is more complex and time-consuming, to improve the efficiency of the matrix decomposition, in this paper, the decomposition process of traditional matrix elements is divided into two steps: multiplication update and column reduction of square root calculation. The column reduction step is used to perform square root calculation and column division calculation, while the update step is used for the update task of multiplication. Based on the above ideas, the existing Cholesky decomposition algorithm is improved, and a column oriented Cholesky (C-Cholesky) algorithm is proposed to further improve the efficiency of matrix decomposition, so as to shorten the calculation time of integer ambiguity reduction correlation. The results show that this method is effective and superior, and can improve the data processing efficiency by about 12.34% on average without changing the integer ambiguity accuracy of the traditional Cholesky algorithm.
Because the traditional Cholesky decomposition algorithm still has some problems such as computational complexity and scattered structure among matrices when solving the GNSS ambiguity, in order to further improve the computational efficiency of the least squares ambiguity reduction correlation process in the carrier phase integer ambiguity solution. In this paper, the decomposition process of traditional matrix elements is divided into two steps: multiplication update and column reduction of square root calculation and column division calculation. The existing Cholesky decomposition algorithm is improved, and a column oriented Cholesky (C-Cholesky) algorithm is proposed to further improve the efficiency of matrix decomposition, so as to shorten the calculation time of integer ambiguity reduction correlation. The results show that this method is effective and superior, and can improve the data processing efficiency by about 12% without changing the integer ambiguity accuracy of the traditional Cholesky algorithm.
The Moon is the closest natural satellite to mankind, with valuable resources on it, and is an important base station for mankind to enter deep space. How to establish a reasonable lunar Global Navigation Satellite System (GNSS) to provide real-time positioning, navigation, and timing (PNT) services for Moon exploration and development has become a hot topic for many international scholars. Based on the special spatial configuration characteristics of Libration point orbits (LPOs), the coverage capability of Halo orbits and Distant Retrograde Orbit (DRO) in LPOs is discussed and analyzed in detail. It is concluded that the Halo orbit with a period of 8 days has a better coverage effect on the lunar polar regions and the DRO has a more stable coverage effect on the lunar equatorial regions, and the multi-orbital lunar GNSS constellation with the optimized combination of DRO and Halo orbits is proposed by combining the advantages of both. This multi-orbital constellation can make up for the fact that a single type of orbit requires a larger number of satellites to fully cover the Moon, using a smaller number of satellites for the purpose of providing PNT services to the entire lunar surface. We designed simulation experiments to test whether the multi-orbital constellations meet the full lunar surface positioning requirements, and compare the coverage, positioning, and occultation effects of the four constellation designs that pass the test, and finally obtain a set of well-performing lunar GNSS constellations. The results indicate that the multi-orbital lunar GNSS constellation combining DRO and Halo orbits can cover 100% of the Moon surface, provides there are more than 4 visible satellites at any time on the Moon surface, which meets the navigation and positioning requirements, and the Position Dilution of Precision (PDOP) value is stable within 2.0, which can meet the demand for higher precision Moon surface navigation and positioning.
The Moon is the closest natural planet to mankind, with valuable resources on it, and is an important base station for mankind to enter deep space. How to establish a reasonable lunar Global Navigation Satellite System (GNSS) to provide real-time positioning, navigation, and timing (PNT) services for moon exploration and development has become a hot spot for many international scholars. Based on the special spatial configuration characteristics of Libration point orbits (LPOs), the coverage capability of Halo orbits and Distant Retrograde Orbit (DRO) in LPOs is discussed and analyzed in detail. It is concluded that the Halo orbit with a period of 8 days has a better coverage effect on the lunar polar regions and the DRO has a more stable coverage effect on the lunar equatorial regions, and the multi-orbital lunar GNSS constellation with the optimized combination of DRO and Halo orbits is proposed by combining the advantages of both. This multi-orbital constellation can make up for the fact that a single type of orbit requires a larger number of satellites to fully cover the Moon, using a smaller number of satellites for the purpose of providing PNT services to the entire lunar surface. The design of the multi-orbital lunar GNSS constellation meeting the requirements of real-time positioning on the whole moon surface in two sets is given in combination with simulation calculations. The simulation experiment results show that the multi-orbital lunar GNSS constellation n combining DRO and Halo orbit can cover 100% of the moon surface, and there are more than 4 visible satellites at any time on the moon surface, which meets the navigation and positioning requirements, and the PDOP value is stable within 2.0, which can meet the demand for higher precision moon surface navigation and positioning.
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