## 3 Indoor Positioning Systems
### Systems Based on Inertial Sensors  
Network-based systems estimate user positions by measuring the resources of signals received from a wireless network. This model requires an intervention in the environment with the implementation of physical infrastructure. Systems based on inertial information calculate their positions without having to apply external resources. Estimating a future position given an initial position associated with speed and direction is one of the oldest methods of navigation, generally called \"dead reckoning\" [85]. An obvious problem with this model of dead reckoning is the increase in the progressive accumulation of errors since a small error of direction can mean a huge error over the distance covered [86]. Information about the position of a target must be accurate. Therefore, these models adopt the geographic coordinate model, composed of latitude, longitude, and altitude, to identify the absolute (inertial) position. The sensors allow the absolute (inertial) position to be immediately perceived in the roll, pitch, yaw (RPY) system using the x-, y-, and z-axes, based on the RPY (Figure 5) [87]. In such a system, the x-axis indicates the nominal direction (front), y (slope) is orthogonal to the x-axis and points to the left side, and the z-axis (yaw) points up [88]. Generally, inertial sensors are assembled, forming units of inertial measurement (IMUs), which have an accelerometer, a gyroscope, and a magnetometer, each with three axes [89]. The magnetometer is not an inertial sensor; however, in this work, it will be treated in conjunction with the other sensors because it is part of the IMU. The magnetometer sensor uses the earth's natural magnetic field or artificial magnetic fields of alternating current to establish an address. Another sensor described in this study is the barometer, which indicates changes in the floor due to changes in atmospheric pressure. Accelerometers can be used to determine changes in the user's position when acceleration in each direction is detected. This is a very rough estimate, which can be improved using a gyroscope to observe changes in a course [90; 91; 7]. The evidence of initial acceleration can be confirmed by the fact that a user is walking, recognizing (also with an accelerometer) the typical tremor associated with walking [86]. In general, the pedestrian dead reckoning (PDR) algorithm behaves, as shown in Figure 6.  
[PERSON] and [PERSON] reported the construction of inertial IPSs. They showed different strategies to reduce the accumulation of errors typical of inertial systems, refining the navigation with particle filtering and Kalman filter [88; 91]. The system reported by [PERSON] et al. deals with a navigation map in which the user's position is tracked continuously [88]. The filtering algorithms refine the  
Figure 5: Roll, pitch, yaw (RPY) system reference. general location by discarding impossible paths within the limits of the map, reducing the immediate errors, and accumulated errors over time. Location and inertial navigation systems can be classified into two types [10]: strapdown systems and step and heading systems (SHSs). Strapdown systems use a person's acceleration to estimate position. SHSs estimate the person's location by the direction the head is pointing (direction) and by the length of the stride the person applies. Regardless of the approach used, the first step in an inertial navigation system is to calculate the relative orientation of the sensor and the user's body. IMU measurements are expressed in the sensor coordinate table and, depending on where the device is used, the user's body. They may not correspond to the axes of the navigation frame. Any misalignment in the axes produces errors of location and direction, necessary to estimate the relative orientation to keep the user's displacement within a tolerable error field.