GNSS has become a widely accessible technique for vehicle instantaneous velocimetry. GNSS time difference carrier phase (TDCP) velocimetry can provide high-accuracy displacement increments, through which the between-epoch average velocity can be derived. However, there are always so-called modelling errors in such velocity, i.e., the deviation between the average velocity and the instantaneous one. GNSS Doppler velocimetry offers exactly instantaneous velocity, but its measurement is much noisier. In this work, we propose to integrate TDCP with Doppler for estimating vehicle's instantaneous velocity. The TDCP-derived displacements and the Doppler-derived instantaneous velocity are treated as two sets of measurements, whereas the vehicle's kinematics is represented by kernel model. Rather than directly solving for vehicle's velocity, we indirectly seek for the kernel weights to establish an analytical kernel model of vehicle's motion state. Tikhonov regularization is introduced to deal with the ill-conditioned problem in kernel weights estimation, and it can significantly smooth/denoise the noisy Doppler measurements. The hyperparameters involved are optimized using generalized cross validation criterion. The constructed kernel model can provide vehicle's velocity at any instants, not necessarily at the sampling epochs. The static and dynamic vehicle field experiments demonstrate that the proposed TDCP/Doppler integrated velocimetry can provide both high accuracy and efficiency.

In complex urban environments, a single Global Navigation Satellite System (GNSS) is often not ideal for navigation due to a lack of sufficient visible satellites. Additionally, the heading angle error of a GNSS/micro-electro-mechanical system–grade inertial measurement unit (MIMU) tightly coupled integration based on the single antenna is large, and the attitude angle, velocity, and position calculated therein all have large errors. Considering the above problems, this paper designs a tightly coupled integration of GNSS/MIMU based on two GNSS antennas and proposes a singular value decomposition (SVD)-based robust adaptive cubature Kalman filter (SVD-RACKF) according to the model characteristics of the integration. In this integration, the high-accuracy heading angle of the carrier is obtained through two antennas, and the existing attitude angle information is used as the observation to constrain the filtering estimation. The proposed SVD-RACKF uses SVD to stabilize the numerical accuracy of the recursive filtering. Furthermore, the three-stage equivalent weight function and the adaptive adjustment factor are constructed to suppress the influence of the gross error and the abnormal state on the parameter estimation, respectively. A set of real measured data was employed for testing and analysis. The results show that dual antennas and dual systems can improve the positioning performance of the integrated system to a certain extent, and the proposed SVD-RACKF can accurately detect the gross errors of the observations and effectively suppress them. Compared with the cubature Kalman filter, the proposed filtering algorithm is more robust, with higher accuracy and reliability of parameter estimation.

Continuous, reliable, and real-time position information is essential for vehicle navigation. However, Global Navigation Satellite System (GNSS) signals can be easily blocked or interfered with in urban environments, resulting in discontinuous and unreliable positioning. Non-holonomic constraint (NHC) is an effective and low-cost method for vehicle enhancement. However, accurate compensation for the mounting angle and lever arm and reasonable configuration of noise parameters are prerequisites for NHC to perform effectively. Unfortunately, existing studies often focus on only one aspect, neglecting the model’s generalization ability and practicality (ease of implementation). To address this problem, we propose LVB-NHC, a lightweight motion constraint regulator based on variational Bayesian (VB), designed to enhance vehicle navigation in GNSS-constrained environments. The LVB-NHC uses the dead reckoning (DR) method to estimate the mounting angle and lever arm while employing the inverse gamma (IG) distribution to model the time-varying measurement noise covariance matrix (MNCM), thereby effectively addressing NHC inconsistency and uncertainty. Vehicle experiments demonstrate the algorithm’s effectiveness and practicality.

Global navigation satellite system (GNSS) signals will produce outliers when interfered with, which will result in the heavy-tailed characteristics of measurement noise. The traditional Kalman filter based on Gaussian distribution is no longer suitable for this complex scene. The Gaussian-student’s t mixture distribution can be adapted to the state estimation where both Gaussian and non-Gaussian assumptions are present by adjusting the mixture parameters. A novel multidimensional Gaussian-student’s t robust mixture distribution Kalman filter is proposed to improve the robustness of the GNSS/inertial navigation system (INS) integrated system. By introducing a Gaussian classifier, the original variational Bayesian optimization process is divided into the robustness estimation part, the prior weight part, and the classification probability part. The relation between the prior parameters and the optimization results, as well as the relation between the estimated parameters and the iterative process, are revealed. In addition, a multidimensional Gaussian-student’s t mixture distribution-based robust Kalman filter (SIG-MGSTM) is proposed. This method avoids multiple iterations while ensuring estimation accuracy, thus significantly reducing the computational load and complexity of the algorithm, which is conducive to the expansion and application of the algorithm. The simulation results show that compared with other schemes, the proposed SIG-MGSTM algorithm has the best robustness and real-time performance for different levels of heavy-tailed noise scenes. Outdoor vehicle experiments verify the feasibility and practicability of the proposed algorithm in GNSS/INS integrated system.