## 1 Introduction  
With the spread of mobile devices such as smartphones and tablets in recent years, applications that provide users with location information obtained by using the devices' sensors have become popular, and the demand for such applications has been increasing. In general applications, Global Positioning System (GPS) and Light Detection And Ranging (LiDAR) are mainly used for position estimation. However, because GPS uses the transmission time and reception of radio waves, accurate location estimation requires an outdoor location. On the other hand, LiDAR requires nonmoving objects and the presence of obstructions or objects in the vicinity. GPS is unreliable in underground and indoor facilities due to the presence of obstacles that block or attenuate radio waves. It can also be difficult to estimate position using LiDAR due to the presence of humans around the facility. Although there are methods that use machine learning, it is difficult to solve the problem of non-periodic geomagnetic interference from other devices, and the need for pretraining makes high introduction costs a challenge for general users. In indoor location estimation, a method called Pedestrian Dead Reckoning (PDR) is particularly applicable to pedestrians. PDR is a method of calculating relative position from a certain point based on information such as acceleration, angular velocity, geomagnetism,and atmospheric pressure. There are various approaches to position estimation. Essentially, there are three steps: step number estimation, step length estimation, and direction estimation. In step count estimation, methods include record acceleration and determining the number of steps by the magnitude of the acceleration value [1; 2; 3]. In stride estimation, different methods use fixed values [4; 5; 6; 7] or acceleration [8; 9; 10]. In direction estimation, methods use the acceleration, angular velocity, and geomagnetism [3]. A number of the above methods have actually already been implemented in factories and commercial facilities; however, these often require a dedicated terminal to be attached to the pedestrian. Previous studies have obtained measurements with an Inertial Measurement Unit (IMU) attached to the foot [11] or a PDR with a dedicated sensor unit attached to the belt [12; 13]. Most of these methods require fixation to the body or the use of a dedicated terminal. As mentioned at the beginning of this paper, applications that provide location information to users have become popular because they are easy to operate and use, with no cost and no complicated operations. Therefore, these currently introduced applications are unlikely to be accepted by general users. In order for the system to be usable by anyone, it is necessary to eliminate restrictions such as the need for it to be fixed to the body or reliance on a dedicated terminal. Although PDR using mobile terminals has been studied in the past, it is difficult to perform unconstrained self-position estimation because it is necessary to perform estimation in hand-held walking and hand-swinging walking conditions. In addition, although geomagnetic sensors are suitable for estimating absolute direction, they are difficult to use in practical situations because other electronic devices and structures affect the geomagnetic field and cause errors. Device-based positioning estimation uses the geomagnetic values [10; 11; 14]. However, previous studies have often failed to consider the influence of structures and other electronic devices. In a recent trend, indoor positioning fingerprints such as RSSI using BLE or WiFi are sometimes used to correct estimated positions [15; 16; 17; 18]. However, when using BLE it is necessary to install beacons in the indoor environment where estimation is performed, and even WiFi-based methods require prior setup. Additionally, estimation methods that use markers or indoor images [13; 19] require directing the camera to a specified position, and also require pretraining when utilizing machine learning.