To overcome the limitations of traditional evaluation indicators in determining the optimal wavelet decomposition level, this paper proposes an adaptive method for selecting the best decomposition level by combining the Jarque–Bera test and a composite weighting approach. Firstly, in the noise extraction stage, the Jarque–Bera test is employed to ensure that the extracted noise follows Gaussian white noise characteristics, thereby avoiding issues of insufficient denoising or signal distortion. Secondly, in the evaluation stage of the denoised signal, a comprehensive consideration of the geometric and physical meanings of various evaluation metrics, as well as the Pearson correlation coefficients between them, is undertaken. The RMSE and smoothness are selected as evaluation indicators for the denoising performance. Since these two metrics describe signal characteristics from different dimensions, a weighted combination approach is used to generate a single composite evaluation index. Additionally, to overcome the limitations of using a single weighting method, a composite weighting strategy is proposed by combining the entropy weight method and the coefficient of variation method. The composite coefficient between these two weighting methods is calculated using the variance coefficient method, yielding a new composite evaluation metric. A smaller value of this metric indicates better denoising performance, and the corresponding optimal decomposition level is more accurately determined. The simulation results demonstrate that the proposed comprehensive evaluation method can accurately determine the optimal wavelet decomposition level in both known and unknown truth-value cases, exhibiting a high accuracy and good applicability. Furthermore, the experimental results show that using the optimal decomposition level determined by the proposed method for wavelet denoising leads to smoother peak regions, more stable waveforms and significantly improved denoising performance.

With the expanded application scope of the International GNSS Service (IGS) global ionospheric maps (GIMs), it is of great theoretical significance and practical value to evaluate the quality of IGS ionospheric products. A new methodology is proposed to mosaic ionospheric grid maps, and GIMs‐based solutions for global ionosphere vertical total electron content (VTEC)/Root Mean Square (RMS) eigenvalues are put forward for subsequent quality assessment. Moreover, based on the proposed method and the strategy, it is the first time that the quality of IGS GIMs from a macro perspective is assessed using the extracted daily global maxima of ionosphere VTEC/RMS (1998–2016). The results show that there are some abnormal maxima values in the GIMs data between 1998 and 2004, while products from 2005 to 2016 are of relatively better quality and are suitable for use as follow‐up experimental data. In addition, we analyze the statistical characteristics of spatial and temporal distribution of GIMs‐based VTEC/RMS eigenvalues and the correlation between eigenvalues and solar activity, in order to verify the conformity between ionosphere physics characteristic and eigenvalues statistical properties which is for further data quality assessment of GIMs. By analyzing the spatial distribution of VTEC/RMS maxima and minima, we found that VTEC maxima are located on both sides of the geomagnetic equator and there is a “dual‐hump” phenomenon in the distribution, and VTEC minima are concentrated in the high latitudes, while RMS minima are distributed throughout the globe but RMS maxima in the low latitudes. Meanwhile, in terms of time distribution, VTEC maxima distribute mainly in the local time from 13:00 to 17:00, while VTEC minima are mainly at nighttime; for RMS, the maxima are mostly distributed in the daytime, while the minima are of a slightly higher distribution proportion at night than in the daytime. At the same time, it was found that the eigenvalues, except RMS minima, are strongly correlated with solar activity but there are lags of 2 to 3 days. Consequently, the above statistical characteristics of GIMs‐based VTEC/RMS eigenvalues are in conformity with ionospheric physics. It verifies the availability and reliability of GIMs from a macroscopic perspective and provides a favorable support for the further application and promotion of GIMs.

With the development of precise positioning with multi-GNSS, the inter-system bias (ISB) has become an issue that cannot be ignored. ISB is introduced from the differences among satellite reference clocks and different receiver hardware delay biases. To analyze the characteristics of multi-GNSS ISB, the precise point positioning (PPP) with full-rank uncombined model was derived for GLONASS, BDS, GALILEO, while the GPS receiver clock was selected as the reference. In addition, a recommended ISB parameter processing model was adopted. Data of 28-days from the Multi-GNSS Experiment (MGEX) station was used to estimate and analyze the ISB parameters. Based on a statistical analysis of the acquired data, results demonstrate that: (a) The rms of multi-GNSS PPP positional bias can reach 4.6 mm, 3.4 mm and 8.5 mm for E, N and U directions, respectively, which guarantees the reliability and accuracy of the ISB parameter solution. (b) The intra-day ISB time series of the three groups is relatively stable with standard deviations less than 0.6 ns. The ISB parameters between the GALILEO and GPS system are the most stable and the standard deviation was the smallest, at about 0.37 ns, which may be related to the good signal quality of the GALILEO system. (c) The mean of the single-day solution of the ISB parameter is not stable and the amplitude of the jump can be up to 60 ns. However, each station shows a similar variation for the same ISB parameter on the same day. The situation is independent of the type of receiver and antenna; however, it may be affected by the satellite reference clock of different systems. (d) There is a clear relationship between the ISB parameters and receiver types.

In recent years, several Global Navigation Satellite Systems (GNSSs) have begun offering free satellite-based Precise Point Positioning (PPP) services, including Galileo’s High Accuracy Service (HAS), BDS’s PPP-B2b, and Japan’s Quasi–Zenith Satellite System (QZSS) multi-GNSS advanced orbit and clock augmentation (MADOCA). In real-time positioning correction methods, individual services are prone to interruptions and anomalies. This study proposes combining multiple correction services to enhance correction availability and continuity from the user side, thereby fully leveraging observational data from various satellite positioning services. After detecting outliers in clock corrections and standardizing reference frames across services, a Kalman filter is employed to estimate the combined clock corrections. Since GPS is currently the only GNSS supported by these services, this study incorporates GPS correction data from Galileo’s HAS, BDS’s PPP-B2b and Japan’s QZSS MADOCA in a one-week experiment. By combining satellite-based correction products from different services, users can fully utilize GNSS corrections from each. This study demonstrates that combing corrections from multiple services significantly improves their availability and continuity. The average correction availability increased from approximately 75% for a single service to 99% for combined corrections. Static and simulated kinematic experiments at Multi-GNSS Pilot Project stations show that the combination strategy improves positioning accuracy by approximately 52.7%, 10.6% and 59.1% compared to PPP-B2b, MADOCA and HAS, respectively, with convergence time reductions of 48.5%, 37.1% and 67.1%. Marine experiment results with an unmanned underwater vehicle demonstrate that the combination strategy improves horizontal positioning accuracy by 19.7%, 59.1% and 17.8%, and vertical positioning accuracy by 54.1%, 77.8% and 1.2% compared to PPP-B2b, HAS and MADOCA.

This paper proposes an evaluation method for selecting the optimal linear combination coefficients for five-frequency cycle slip detection in BeiDou-3. First, the essence of the optimal linear combination problem for cycle slip detection is analyzed, and two linear combination constraint strategies are introduced: geometry-free ionospheric-free (GFIF) and geometry-free (GF) constraints. For the GFIF combination, a linear combination index is proposed to assess the cycle slip detection performance of different linear combinations, providing a quantitative measure for evaluating the performance of various combination coefficients. By solving the constrained optimization problem, the optimal linear combinations for phase–only geometry-free ionospheric-free (PGFIF) and phase-code geometry-free ionospheric-free (PCGFIF) are determined. For the GF combination, based on phase biases induced by cycle slips, standard deviations of cycle slip detection measurements, ionospheric delay amplification factors, and the success rate of detecting insensitive cycle slips using GFIF, suitable phase-only geometry-free combination (PGF) combinations are selected. The optimal linear combination for PGF is then determined based on the principle of minimizing the condition number. For cycle slip repair, the least squares method is used to solve for the float solution and its covariance matrix, while the LAMBDA algorithm is employed to search for the integer solution of the cycle slip. Finally, the effectiveness of the proposed method is validated through experiments using static, shipborne kinematic, ionospheric active period, and low-sampling-rate data. The experimental results demonstrate that, under five-frequency conditions, the proposed algorithm can accurately detect and repair all simulated cycle slips, confirming the feasibility and effectiveness of the method.