CEEMDAN combined wavelet denoising improved the MW cycle slip detection algorithm.

In the preprocessing of high-precision navigation and positioning data, the most widely used MW combination cycle slip detection method is greatly affected by pseudorange noise. It has issues such as missing small cycle slips and failing to promptly reset the recursive averaging process after cycle slip detection failure, which leads to subsequent threshold divergence. This paper proposes an improved MW combination cycle slip detection method based on Complete Ensemble Empirical Mode Decomposition (CEEMDAN), permutation entropy, and wavelet denoising, which uses CEEMDAN to decompose the cycle slip signal into a series of intrinsic modal functions (IMFs) and then selects the IMFs that require denoising through the permutation entropy algorithm, and the wavelet denoising technique is combined to eliminate the residual noise further, so that the noise can be removed more accurately.

A hierarchical combination algorithm for real-time cycle slip detection and repair in low satellite elevation and high ionospheric activity conditions.

To enhance the accuracy and robustness of cycle slip detection and repair for triple-frequency data while minimizing the adverse effects of low satellite elevation and high ionospheric activity, a hierarchical combination algorithm for real-time cycle slip detection and repair is proposed. This algorithm begins by prioritizing the reduction of noise and ionospheric delay coefficients. It determines the optimal coefficients for the combination of observations from the BeiDou Navigation Satellite System's (BDS) Extra-Wide Lane (EWL), Wide Lane (WL), and Narrow Lane (NL).

Multi-orbit lunar GNSS constellation design with distant retrograde orbit and Halo orbit combination.

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.

Improved GNSS integer ambiguity resolution method based on the column oriented Cholesky decomposition.

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.