Aiming to improve the navigation accuracy during global navigation satellite system (GNSS) outages, an algorithm based on long short-term memory (LSTM) is proposed for aiding inertial navigation system (INS). The LSTM algorithm is investigated to generate the pseudo GNSS position increment substituting the GNSS signal. Almost all existing INS aiding algorithms, like the multilayer perceptron neural network (MLP), are based on modeling INS errors and INS outputs ignoring the dependence of the past vehicle dynamic information resulting in poor navigation accuracy. Whereas LSTM is a kind of dynamic neural network constructing a relationship among the present and past information. Therefore, the LSTM algorithm is adopted to attain a more stable and reliable navigation solution during a period of GNSS outages. A set of actual vehicle data was used to verify the navigation accuracy of the proposed algorithm. During 180 s GNSS outages, the test results represent that the LSTM algorithm can enhance the navigation accuracy 95% compared with pure INS algorithm, and 50% of the MLP algorithm.

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.

Aiming at the GNSS receiver vulnerability in challenging urban environments and low power consumption of integrated navigation systems, an improved robust adaptive Kalman filter (IRAKF) algorithm with real-time performance and low computation complexity for single-frequency GNSS/MEMS-IMU/odometer integrated navigation module is proposed. The algorithm obtains the scale factor by the prediction residual, and uses it to adjust the artificially set covariance matrix of the observation vector under different GNSS solution states, so that the covariance matrix of the observation vector changes continuously with the complex scene. Then, the adaptive factor is calculated by the Mahalanobis distance to inflate the state prediction covariance matrix. In addition, the one-step prediction Kalman filter is introduced to reduce the computational complexity of the algorithm. The performance of the algorithm is verified by vehicle experiments in the challenging urban environments. Experiments show that the algorithm can effectively weaken the effects of abnormal model deviations and outliers in the measurements and improve the positioning accuracy of real-time integrated navigation. It can meet the requirements of low power consumption real-time vehicle navigation applications in the complex urban environment.

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.

Aiming at the problem of high-precision positioning of mass-pedestrians with low-cost sensors, a robust single-antenna Global Navigation Satellite System (GNSS)/Pedestrian Dead Reckoning (PDR) integration scheme is proposed with Gate Recurrent Unit (GRU)-based zero-velocity detector. Based on the foot-mounted pedestrian navigation system, the error state extended Kalman filter (EKF) framework is used to fuse GNSS position, zero-velocity state, barometer elevation, and other information. The main algorithms include improved carrier phase smoothing pseudo-range GNSS single-point positioning, GRU-based zero-velocity detection, and adaptive fusion algorithm of GNSS and PDR. Finally, the scheme was tested. The root mean square error (RMSE) of the horizontal error in the open and complex environments is lower than 1 m and 1.5 m respectively. In the indoor elevation experiment where the elevation difference of upstairs and downstairs exceeds 25 m, the elevation error is lower than 1 m. This result can provide technical reference for the accurate and continuous acquisition of public pedestrian location information.

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.