Attention-enhanced three-dimensional velocity constraint for smartphone GNSS/INS vehicular navigation

In urban canyons, tunnels, and other GNSS signal-blocked environments, the positioning performance of smartphones integrated with consumer-grade GNSS chipsets and inertial measurement unit (IMU) degrades dramatically. Although inertial navigation systems (INS) can continuously provide navigation solutions in GNSS-denied environments, the low-cost IMU embedded in smartphones suffer from rapid error divergence due to low accuracy and high noise. Traditional non-holonomic constraint (NHC) methods experience severe failure when zero-value assumptions are violated during vehicle maneuvers such as turning and U-turns, thereby affecting positioning accuracy. To address these issues, this paper proposes an attention-enhanced three-dimensional velocity constraint method for smartphone-based vehicular positioning. The method constructs a hybrid architecture integrating convolutional neural network (CNN), long short-term memory (LSTM) network, and attention mechanism. Taking raw six-axis IMU observations as input, it directly outputs three-dimensional vehicle velocity, functioning as a three-dimensional virtual odometer during GNSS outages to constrain IMU error accumulation. Specifically, CNN captures local IMU features for noise filtering, LSTM models temporal correlations, and the sliding window-based attention mechanism adaptively weights historical information according to current motion states. Experimental results demonstrate that the proposed method achieves a forward velocity prediction root mean square (RMS) error of 0.48 m/s, representing a 40%—55% reduction compared to existing methods. In GNSS-denied scenarios, the average horizontal positioning RMS is 7.2 m and vertical positioning RMS is 2.3 m, representing reductions of 98.3% and 97.0% respectively compared to the unconstrained scheme, and 79.8% and 39.5% respectively compared to the traditional NHC scheme, significantly improving smartphone positioning performance in GNSS-denied environments.