## 1 Introduction  
A successful outdoor positioning system based on the global positioning system (GPS) has been developed. However, satellite signals are weakened indoors, such as underground and inside large buildings, making GPS useless for positioning. Indoor navigation and positioning services can be made available to users through indoor location-based services, which can boost pedestrian travel efficiency and make it easier for managers to prioritize pedestrian traffic. The demand for indoor positioning is increasing as personalized networks become more popular. Indoor positioning technologies rely on various technologies, such as Bluetooth [1, 2], WiFi [3], machine vision [4], ultra-wide band (UWB) [5] and inertial navigation [6]. The first four technologies are highly precise and relatively mature. However, each of these technologies has its own challenges to consider. Bluetooth and WiFi can be affected by electromagnetic interference and indoor obstacles. Machine vision needs to take into account user privacy concerns. UBW requires advanced facility deployment. Finally, inertial navigation can be challenged by drift during extended operation. Despite these limitations, no single positioning technology can provide a stable high-accuracy positioning service. Multisensor fusion technology is currently under development to address this challenge. In the complex indoor environment, high-precision inertial navigation can provide a reliable positioning service for pedestrians for a short period of time when other positioning technologies are temporarily disabled by electromagnetic interference. Additionally, it can provide correction information for other positioning technologies because inertial navigation is not disturbed by external factors and does not rely on any external signals. Therefore, high-precision pedestrian inertial navigation has a high research value. The development of microelectro mechanical technology has led to the inclusion of inertial measurement units (IMUs) based on these systems in smart devices such as mobile phones, watches and wristbands. The use of IMU sensors in these devices for inertial navigation is very convenient and does not require the purchase of additional expensive equipment. However, compared to platform-based inertial guidance, IMU sensors in smart devices have several limitations due to their lower cost and other factors. Specifically, they generally have lower accuracy and higher noise levels. Conventional techniques frequently use double-integration methods to solve for position coordinates based on acceleration data, in which positioning errors caused by sensor measurement errors can quickly increase and accumulate, in addition to the direct solution process itself generating some errors. How to effectively eliminate the cumulative error of positioning has been a hot research topic in the field of pedestrian inertial navigation positioning. Better localization accuracy can be attained using the Kalman filter and zero velocity update (ZUPT) algorithm together [7], but these methods require pedestrians to fix IMUs on their feet, which is not compatible with the usage scenarios of most smart devices. In addition, these methods require high measurement accuracy of IMU, resulting in the requirement of more expensive sensors [8], which has kept such algorithms in the laboratory stage. Data-driven methods have been recognized in recent years as the most effective means to suppress error drift by transforming the inertial tracking problem into a data sequence learning problem. The algorithms simultaneously collect IMU data and ground truth trajectory data over a short period to regress motion parameters (e.g., velocity vector and heading) and are proven to outperform traditional heuristics in terms of navigation accuracy and robustness. Among them, RIDI [9] made a breakthrough in coordinate system normalization by using SVM to regress the walking velocity vector and achieve the first accurate estimation of pedestrian velocity in a real indoor environment.