The integration of multiconstellation global navigation satellite system (GNSS) signals with existing GPS systems enhances integer ambiguity resolution (IAR), a technique essential for achieving continuous and high-precision positioning in real-time kinematic (RTK) systems. However, incorrect IAR can lead to position errors of several meters and reduce system availability. The tight integration of an inertial navigation system (INS) with multi-GNSS significantly improves IAR performance, benefiting from the INS-assisted IAR effect. Building on previous research in INS-assisted IAR, this study focuses on enhancing both IAR performance and computational efficiency for low-cost vehicle-borne applications in complex environments. We propose a robust and efficient two-stage filtering fusion method that combines multi-GNSS and high sampling rate IMU data. This approach integrates time-differenced carrier phase (TDCP) and double-differenced carrier phase (DDCP) measurements within a hybrid model, where TDCP-based GNSS/INS tight integration supports DDCP-based RTK. This method significantly improves IAR performance in challenging scenarios, such as environments with substantial signal interference or strong multipath effects. Moreover, the hybrid model greatly enhances computational efficiency by 45% compared to traditional multi-GNSS RTK/INS tight integration, making it more suitable for real-time applications. The effectiveness of our approach is validated through real-world experiments conducted in both open-sky and urban environments. Results show that the proposed algorithm outperforms conventional RTK/INS tight integration frameworks, achieving more robust and precise positioning in complex settings. Additionally, the proposed method demonstrates a 45% improvement in computational efficiency compared to traditional multi-GNSS RTK/INS integration.

Accurate prediction of slope displacement is an important prerequisite for building an effective geological hazard early warning system for disaster prevention and reduction. However, the inherent nonlinearity and time-varying characteristics of slope displacement evolution greatly affect the prediction accuracy. To improve the slope displacement prediction accuracy, a multi-modal data-driven Bayesian-optimized Convolutional Neural Network and Long Short-Term Memory (Bayes-CNN-LSTM) model was constructed. The performance of the model was evaluated using multi-modal monitoring data from the GuShan mine slope. Experimental results showed that the Bayes-CNN-LSTM model achieved an average coefficient of determination (R²) of 0.971, with a mean absolute error (MAE) of 0.444 mm and a root mean square error (RMSE) of 0.618 mm. Compared with the CNN-LSTM, LSTM, CNN, SVM, TCN, and Transformer models, the MAE of the constructed model was decreased by 25.1%, 31.3%, 32.3%, 24.1%, 24.7%, and 17.7%, respectively, and the RMSE decreased by 20.1%, 26.9%, 29.5%, 18.0%, 20.7%, and 12.4%, respectively. Furthermore, the proper integration of multi-modal data can effectively improve the prediction accuracy when extrapolating slope displacement. Based on rainfall and earth pressure data, the average MAE and RMSE of extrapolation (24-h) prediction using the constructed model were decreased by 30.2% and 24.6%, respectively. The model effectively improves the accuracy of slope displacement prediction and enhances the practicality of the slope safety monitoring system, providing valuable reference for slope safety monitoring.

Integration of global navigation satellite systems (GNSS) with inertial navigation systems (INS) is commonly employed to enhance navigation performance. However, conventional integrated algorithms suffer from low-quality GNSS measurements due to either inaccurate pseudorange or difficulty in ambiguity resolution when utilizing carrier phase (CP) measurements in urban environments. We propose a new time-differenced CP (TDCP-) specified GNSS/INS tightly coupled integration algorithm for low-cost urban applications. The proposed method employs a dual-rate filter scheme, wherein the potential of TDCP observations and INS-derived positions are fully harnessed for state estimation with PR outlier inhibition and CP small cycle slip repair. Field test results in urban environments demonstrate that the integrated navigation scheme proposed is superior to conventional algorithms, with an average improvement of about 13.4%, 19.2%, and 25.5% in position, velocity, and attitude, respectively.

Accurate and continuous outdoor pedestrian positioning using smartphones remains challenging in complex environments like urban canyons, where Global Navigation Satellite System (GNSS) signals are frequently degraded or blocked, and Pedestrian Dead Reckoning (PDR) suffers from cumulative errors. To address this, this paper proposes a novel fusion method based on a Robust Adaptive Cubature Kalman Filter (RACKF). The core of our approach is a two-stage filtering architecture: the first stage employs a quaternion-based RACKF to optimally fuse gyroscope and magnetometer data for robust heading estimation; the second stage performs the core fusion of GNSS observations with an enhanced 3D PDR solution. Key innovations include an adaptive noise estimation strategy combining fading and limited memory weighting, a robust M-estimator-based mechanism to suppress outliers, and the integration of differential barometric height measurements. Experimental results demonstrate that the proposed method achieves a horizontal positioning accuracy of 3.28 m (RMSE), outperforming standalone GNSS and improving 3D PDR by 25.97% and 10.39%, respectively. This work provides a practical, infrastructure-free solution for robust smartphone-based outdoor navigation.

GNSS coordinate series noise modeling is essential for reliable geophysical signal estimation and uncertainty assessment. The generalized Gauss–Markov (GGM) noise model and the Matérn process (MP) noise model are widely used to describe low-frequency spectral flattening in GNSS coordinate series, but they differ in their definition domains, parameterizations and autocovariance function (ACF) structures. These differences may lead to misconceptions, complicate noise model comparison and practical implementation. Building on a systematic review of the theories of GGM and MP, this study proposes a generalized Matérn process (GMP) noise model. By introducing a fractional step size hyperparameter μ into the differencing operator, GMP provides a unified framework that continuously connects the two models: when μ = 1, GMP reduces to GGM; as μ → 0, the spectrum of GMP approaches that of MP. The preferred range of μ is investigated using 420 GNSS coordinate series from 140 global GNSS sites, considering differences in geographical region, coordinate component and length of observations. The results show that the preferred values of μ are robustly concentrated within the interval [0.7, 1]. Large-scale validation is then conducted using 846 GNSS coordinate series from 282 global GNSS sites. The experimental results show that under AIC, BIC and BIC_tp, the proposed WN + GMP family consistently accounts for a large proportion of the optimal models. These results demonstrate that GMP provides a more general noise model family for GNSS coordinate series noise modeling and can improve the fidelity and flexibility of stochastic noise modeling.