The integrated navigation system consisting of an inertial navigation system (INS) and Global Navigation Satellite System (GNSS) provides continuous high-accuracy positioning whereas the navigation accuracy during a GNSS outage inevitably degrades owing to INS error divergence. To reduce such degradation, a gated recurrent unit (GRU) and adaptive Kalman filter (AKF)-based hybrid algorithm is proposed. The GRU network, which has advantages of high accuracy and efficiency, is constructed to predict the position variations during GNSS outage. Furthermore, this paper takes the GRU-predicted error accumulation into consideration, and introduces AKF as a supplementary methodology to improve the navigation performance. The proposed hybrid algorithm is trained and tested by practical road datasets and compared with four algorithms, including the standard KF, Multi-Layer Perceptron (MLP)-aided KF, Long Short Time Memory (LSTM) aided KF, and GRU-aided KF. Periods of 180 and 120 s GNSS outage are employed to test the performance of the proposed algorithm in different time scales. The comparison result between the standard KF and neural network-aided KF indicates that the neural network is an effective methodology for bridging GNSS outages. The performance comparison between three kinds of neural networks demonstrate that both recurrent neural networks surpass the MLP in prediction position variation, and the GRU transcends the LSTM in prediction accuracy and training efficiency. Furthermore, it is concluded that the adaptive estimation theory is an effective complement to neural network-aided navigation, as the GRU-aided AKF reduced the horizontal error of GRU-aided KF by 31.71% and 16.12% after 180 and 120 s of GNSS outage, respectively.

Positioning accuracy and power consumption are essential performance indicators of integrated navigation and positioning chips. This paper proposes a single-frequency GNSS/MEMS-IMU/odometer real-time high-precision integrated navigation algorithm with dynamic power adaptive adjustment capability in complex environments. It is implemented in a multi-sensor fusion navigation SiP (system in package) chip. The simplified INS algorithm and the simplified Kalman filter algorithm are adopted to reduce the computation load, and the strategy of adaptively adjusting the data rate and selecting the observation information for measurement update in different scenes and motion modes is combined to realize high-precision positioning and low power consumption in complex scenes. The performance of the algorithm is verified by real-time vehicle experiments in a variety of complex urban environments. The results show that the RMS statistical value of the overall positioning error in the entire road section is 0.312 m, and the overall average power consumption is 141 mW, which meets the requirements of real-time integrated navigation for high-precision positioning and low power consumption. It supports single-frequency GNSS/MEMS-IMU/odometer integrated navigation SiP chip in real-time, high-precision, low-power, and small-volume applications.

Multi-source heterogeneous information fusion based on the Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS)/odometer is an important technical means to solve the problem of navigation and positioning in complex environments. The measurement noise of the GNSS/INS/odometer integrated navigation system is complex and non-stationary; it approximates a Gaussian distribution in an open-sky environment, and it has heavy-tailed properties in the GNSS challenging environment. This work models the measurement noise and one-step prediction as the Gaussian and Student’s t mixture distribution to adjust to different scenarios. The mixture distribution is formulated as the hierarchical Gaussian form by introducing Bernoulli random variables, and the corresponding hierarchical Gaussian state-space model is constructed. Then, the mixing probability of Gaussian and Student’s t distributions could adjust adaptively according to the real-time kinematic solution state. Based on the novel distribution, a robust variational Bayesian Kalman filter is proposed. Finally, two vehicle test cases conducted in GNSS-friendly and challenging environments demonstrate that the proposed robust Kalman filter with the Gaussian–Student’s t mixture distribution can better model heavy-tailed non-Gaussian noise. In challenging environments, the proposed algorithm has position root mean square (RMS) errors of 0.80 m, 0.62 m, and 0.65 m in the north, east, and down directions, respectively. With the assistance of inertial sensors, the positioning gap caused by GNSS outages has been compensated. During seven periods of 60 s simulated GNSS data outages, the RMS position errors in the north, east, and down directions were 0.75 m, 0.30 m, and 0.20 m, respectively.

In vehicle GNSS/INS integrated navigation, robust and adaptive algorithms have become one of the key technologies for achieving a comprehensive PNT due to their ability to control the gross errors of the observation model and dynamic model. The Sage–Husa algorithm is widely used in optimizing the Kalman filter due to its ability to estimate the observation or state covariance without prior information. However, the quality of observations in complex environments is prone to large fluctuations, so the averaging method is not suitable for dynamic navigation. To solve this problem, this article designs a double window structure and introduces a time-dependent fading weighted factor. At the same time, a logarithmic form factor constructor is proposed in order to avoid anomalies in the robust and adaptive factor. The traditional innovation adaptive filter is improved and turned into a multi-factor adaptive filter. In this paper, an improved fault detection algorithm is used to combine a robust algorithm with an adaptive algorithm to adapt to different gross errors in different scenarios. The experimental results of complex scenarios show that the position RMSE of the improved algorithm in the east, north, and height directions is 0.68 m, 0.71 m, and 1.05 m, respectively, which are reduced by 39.3%, 39.3%, and 70.3% compared to the EKF.

Aiming at the problem that the pseudo-velocity measurement noise of non-holonomic constraints (NHCs) in the integrated navigation of vehicle-mounted a global navigation satellite system/inertial navigation system (GNSS/INS) is time-varying and thick-tailed in complex road conditions (turning, sideslip, etc.) and cannot be accurately predicted, an adaptive estimation method for the initial value of NHC lateral velocity noise based on multiple linear regression is proposed. On the basis of this method, a Gaussian Student’s T distribution variational Bayesian filtering algorithm (Ga-St VBAKF) based on NHC pseudo-velocity measurement noise modeling is proposed through modeling and analysis of pseudo-velocity measurement noise. Firstly, in order to adaptively adjust the initial value of NHC lateral velocity noise, a vehicle turning detection algorithm is used to detect whether the vehicle is turning. Secondly, based on the vehicle motion state, the variational Bayesian method is used to adaptively estimate the statistical characteristics of the measurement noise in real time based on modeling of the lateral velocity noise as Gaussian white noise or Student’s T distribution thick-tail noise. The test results show that compared to the traditional Kalman filtering algorithm with fixed noise, the Ga-St VBAKF algorithm with noise adaptation reduces the maximum horizontal position error by 65.9% in the GNSS/NHC/OD/INS (where OD stands for odometer and INS stands for inertial measurement unit) system when the vehicle is in a turning state, and by 42.3% in the NHC/OD/INS system. This indicates that the algorithm can effectively suppress the divergence of positioning errors during turning and improve the performance of integrated navigation.

This study proposes an innovative single-antenna GNSS/MEMS integrated attitude determination system designed to address the challenges of low accuracy and poor robustness in urban complex environments, where conventional multi-antenna GNSS systems and standalone MEMS sensors often fail due to signal obstructions and drift errors. The key innovations include: (1) a hybrid TDCP/TDPR (Time Difference Carrier Phase/Pseudo-Range) technique to enhance GNSS-derived pitch and heading estimation, significantly improving data utilization; (2) a multi-strategy quality control framework incorporating Zero Velocity Detection (ZVD), Magnetic Disturbance Detection (MDD), and Fault Detection and Exclusion (FDE) to suppress outlier contamination and ensure measurement reliability; and (3) an adaptive noise parameter tuning mechanism to optimize filter performance. Experimental results demonstrate that the proposed system outperforms conventional SPP/MEMS, standalone MEMS, and baseline GNSS/MEMS fusion methods, achieving CDF95 attitude errors of 1.2785° (roll), 0.9412° (pitch), and 1.1991° (yaw)-the highest accuracy and robustness reported for single-antenna GNSS/MEMS systems in urban scenarios.