# S-PDR: SBAUPT-Based Pedestrian Dead Reckoning Algorithm for Free-Moving Handheld Devices
## 1 Introduction  
Navigation is a service that we rely on during our daily activities and is defined as the task of successfully providing directions from a starting point to a destination. The goal of any navigation system is finding the time-varying navigation states: position, velocity, and attitude of a moving platform with high precision [1]. Existing navigation technologies and techniques can be categorized into absolute measurements (also known as reference-based) systems, relative measurements (also known as Dead Reckoning) systems, or a combination of both [2]. Global navigation satellite system (GNSS) is one of the main technologies used for navigation with the global positioning system (GPS) being the prevalent system. GNSS is a reference-based system that uses a set of satellites for the purpose of positioning and attitude estimation. Although GNSS is always expanding and improving with the presence of many constellations such as GPS, BEIDOU, GALILEO, and QZSS, and the increasing number of satellites per constellation providing wide coverage, GNSS navigation is not always accurate and stable, and in many cases it can fail to provide a positional solution [3]. This results from degraded GNSS services in certain environments such as urban canyonsand indoors. To compensate for the shortcomings of GNSS, relative navigation techniques are used as an alternative or aiding in the case of a combined system. Relative navigation techniques cannot measure the position and attitude directly and rely on other techniques to evaluate the navigation states. Inertial navigation is one of the prominent relative navigation techniques that can aid GNSS systems to achieve a continuous navigation solution. An inertial navigation system (INS) is a self-contained navigation system that relies on inertial measurements provided by an inertial measurements unit (IMU) to compute position, velocity, and attitude information [2, 4]. The bases of inertial navigation are based on [PERSON]'s 1 st and 2 nd laws of motion and uses a technique known as dead reckoning (DR) [2]. The inertial measurements are provided from an IMU that consists of a combination of 3-axis accelerometers and 3-axis gyroscopes to measure the acceleration and angular rate vectors. In some cases, extra sensors are available and used in conjunction with an IMU to provide more information for navigational purposes such as a three-axis magnetometer to provide magnetic field measurements and a barometer for pressure measurements. The sensor measurements provided by the IMU are processed using DR to track the changing navigation states of the platform, where the position is updated by knowing the distance traveled and the direction of motion [5]. An initialization process for obtaining the initial position is required along with an alignment process for finding the initial attitude difference between the navigation platform and the navigation frame--local level frame (LLF)--[6]. The miniaturization and power efficiency of IMU sensors made possible by micro-electro-mechanical systems (MEMS) technology advancements [7, 8, 9, 10, 11, 12] led to their inclusion in many of the consumer-based devices such as smartphones and wearable devices. The availability of sensor-enabled smart devices led to an increasing interest in MLBS applications such as military applications, gaming, personal navigation and localization [13], and emergency service providers tracking [14] especially when GNSS services are degraded. Indoor MLBS applications fall under three main sectors: government, business, and individual [15], and can fall in multiple sectors at a time. These sectors are considered to be the commercial drivers of MLBS market, and they dictate the level of required services [16]. On the other hand, MEMS IMU tend to suffer from high measurement errors which makes them less reliable. IMUs are categorized based on their performance and underlying fabrication technologies.