Objectives Vehicle non-holonomic constraint (NHC) is a commonly used enhancement technique for vehicle positioning global navigation satellite system (GNSS)/strapdown inertial navigation system (SINS) combination positioning. A complex mapping relationship between inertial measurement unit (IMU) output and NHC pseudo-observations can be established by applying machine learning methods, and the NHC pseudo-observations can be directly adjusted from the observation domain, which can improve the constraint accuracy compared with traditional NHC methods to a certain extent. Most existing machine learning methods do not consider the influence of vehicle motion state, resulting in low accuracy and reliability of NHC prediction. The latest researches show that machine learning can predict a vehicle forward speed, as a virtual odometer. However, the current research mainly discusses the prediction of virtual NHC and virtual odometer separately, and fails to fully explore the coupling relationship between them and the full constraint of three-dimensional velocity on vehicles.

Methods We study a long short-term memory (LSTM) neural network based on vehicle speed classification for 3 dimensional (3D) vehicle speed prediction, and adaptively adjust its variance domain by using 3D speed residual. The vehicle GNSS/SINS positioning verifies the effectiveness of the proposed method.

Results and Conclusions Experimental results show that the average accuracy of forward velocity predicted by the proposed method is 0.4 m/s, and the average accuracy of lateral and celestial velocity are 2.4 and 2.1 cm/s, respectively. The simulated GNSS signal is completely missing for 460 s, the horizontal positioning accuracy of 3D velocity constraint is improved by 99.40% compared with the inertial navigation results.