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.

Multi-source fusion constitutes a research focus in the navigation domain. This article focuses on the online estimation of the mounting angles between the body frame and vehicle frame within low-cost embedded vehicle navigation modules and the lever arm between the global satellite navigation system (GNSS) antenna/odometer and the inertial measurement unit (IMU). An online mounting angle error estimation algorithm, using odometers and IMU speeds, has been developed to estimate the angle errors while vehicles are in motion. At the same time, an online estimation algorithm model for the GNSS antenna lever arm and odometer lever arm was constructed. These two types of lever arms are used as the estimated states, and then Kalman filters are used to estimate them. The algorithm can simultaneously estimate the IMU mounting angle error, GNSS antenna arm, and odometer arm online. The experimental outcomes demonstrate that the lever arm estimation algorithm presented herein is effective for tactical and MEMS-level inertial navigation, with an estimation error of less than 2 cm. Meanwhile, the proposed online estimation of the mounting angle algorithm has an accuracy comparable to that of the post-processing algorithm. After making up the mounting angle and lever arm, we found that the position and speed precision of the multi-source fusion navigation systems were significantly improved. The results indicate that the proposed online estimation of mounting angle error and lever arm algorithm are effective and may promote the practical and widespread application of integrated navigation systems in vehicles. It solves the shortcomings of traditional methods, including the cumbersome and inaccurate manual measurement of the lever arm. It provides a technical solution for developing a more accurate and convenient low-cost vehicle navigation module.

Foot-mounted inertial pedestrian navigation is an attractive infrastructure-free solution for pedestrian positioning in environments where Global Navigation Satellite System (GNSS) signals are unavailable, degraded, or intentionally excluded. However, mixed-gait and multi-level motion expose two persistent failure modes: unreliable zero-velocity detection during high-dynamic motion and weak yaw observability after standard zero-velocity-aided filtering. This paper presents a probability-driven adaptive foot-mounted inertial navigation framework that couples a lightweight motion-probability front-end with probability-weighted mode-adaptive zero-velocity detection, local straight-heading constraints, and probability-gated stair-height updates. A 335-dimensional motion-feature LightGBM classifier first outputs six gait probabilities from 128-sample windows of six-axis inertial data. These probabilities continuously determine the zero-velocity detector threshold and the reliability of heading and vertical pseudo-measurements. For planar navigation, a motion-aware local straight-heading constraint (MA-LSHC) establishes local reference headings only over curvature-safe straight segments, and an adaptive heading covariance controls the strength of each heading pseudo-measurement. For stair navigation, height changes are quantized into integer-riser increments only when stair probabilities and vertical inertial evidence agree. All data were collected in outdoor pedestrian environments, and the evaluation includes four parts: motion classification, training and detector diagnostics, closed rectangular planar navigation, and multi-level stair-height reconstruction. The motion-feature classifier achieves 96.24% accuracy and 96.17% macro-F1. In a mixed-gait closed rectangular route, the proposed method obtains a 1.09 m closure error and a 0.68% relative closure error, outperforming fixed SHOE-ESKF, Wang-AWGF, Guo-SIHDC, and Deng-HDR baselines. In stair experiments, the proposed method achieves a grid-node RMSE of 0.13 m and correctly identifies 38 ascending and 38 descending risers. These results demonstrate that motion probabilities can be used not merely as labels, but as continuous reliability cues for adaptive inertial constraints.

Deep learning has achieved notable success in sensor-based human activity recognition (SHAR), yet wearable inertial signals contain activity patterns at different temporal scales while practical deployment imposes strict computational constraints. This paper proposes a three-stage Adaptive CNN-Enhanced Scale-fusion Network (ACESNet) for six-channel accelerometer–gyroscope activity recognition. The Adaptive Kernel Encoder dynamically combines temporal kernels of different sizes, while the CNN-Enhanced Scale-fusion design combines multi-scale temporal mixing, explicit channel mixing and a parallel local CNN path without materializing a global attention matrix. The main benchmark uses a fixed stratified 70/15/15 window-level partition (split seed 42), and all methods in the main comparison are repeated over five training seeds. On REALWORLD, MotionSense, UCI-HAR and SHL, ACESNet achieves accuracies of 95.37 ± 0.09%, 99.33 ± 0.12%, 98.01 ± 0.23% and 93.49 ± 0.10%, with Macro-F1 scores of 95.59 ± 0.09%, 99.12 ± 0.15%, 98.16 ± 0.21% and 94.03 ± 0.08%, respectively. A separate official subject-independent UCI-HAR evaluation yields 94.01 ± 0.84% accuracy and 94.11 ± 0.88% Macro-F1. The adaptive-kernel selector has a mean normalized entropy of 0.9114, providing evidence against severe single-branch collapse rather than strong kernel selectivity. On a Raspberry Pi 5 (Raspberry Pi Ltd., Cambridge, UK), ACESNet requires 8.731 MFLOPs and 1.606 ± 0.014 ms per window in FP32 ONNX Runtime 1.18.1. These results support a favorable performance–efficiency trade-off relative to the selected baselines under the stated protocol.