## 3 Navigation
### Sensors
#### 3.1.2 Imu  
An IMU can obtain the moving information of a target. Among dead-reckoning sensors, IMUs are widely used to construct inertial navigation systems (INSs). An IMU usually contains a set of three orthogonally installed accelerometers and three orthogonally installed gyros. An inertial navigation system is a real-time algorithm used to calculate the position, velocity, and attitude of the vehicle that carries the INS by integrating the acceleration and rotation rate signals from an IMU. The position is calculated by double integration of the sum of the the nongravitational acceleration from the three accelerometers. By integrating the rotation rate signals from the three gyros, we can determine the angular orientation of the three accelerometers is determined. Using this orientation information, the calculated acceleration, velocity and position are transformed into the desired navigation coordinate system by this orientation information [18].  
Figure 3 shows the INS process. There are two main phases in INS operation: the initial condition alignment phase and the navigation phase. The alignment phase gives the the rotation matrix \(C_{b}^{n}\), which transforms the measurement in the right-front-up (RFU) coordinate system form the carrier body frame (\(b\)-frame) to the East-North-up (ENU) geographic coordinate system in the navigation frame (\(n\)-frame),  
\[[x_{n},y_{n},z_{n}]^{T}=C_{b}^{n}\left[x_{b},y_{b},z_{b}\right]^{T} \tag{1}\]  
where \(x_{n}\) and \(y_{n}\) represent the geographical coordinate systems of the East and North, respectively; \(z_{n}\) points upward, toward the Earth's surface, antiparallel to the surface's outward normal. Meanwhile, \(x_{b}\), \(y_{b}\), and \(z_{b}\) indicate the front, left, and upward, respectively, according to the movement of the body. The attitude transform matrix \(C_{b}^{n}\) converts the acceleration in the body coordinate system \(b\) to the navigation coordinate system \(n\). [PERSON] and [PERSON] [33] presented the definition and description  
Figure 2: Landmark measurements in the vision navigation [26].  
of these two frames, as well as the method of computing the attitude transform matrix \(C_{b}^{n}\); thus, some details are omitted here.  
Then, for the navigation phase, we can obtain the acceleration of the navigation system \(f\) based on \(C_{b}^{n}\), and the measured acceleration vectors \(accX,accY\) and \(accZ\) as follows:  
\[f=C_{b}^{n}\times[\begin{array}{cccc}accX&accY&accZ\end{array}]^{T}-[\begin{array} []{cccc}0&0&g\end{array}]^{T} \tag{2}\]  
where \(accX\), \(accY\) and \(accZ\) are the accelerations of the body coordinates. \(f\) can be expressed as the vector \(\left[\begin{array}{cccc}f_{xn}&f_{ym}&f_{zn}\end{array}\right]^{T}\), where \(f_{xn}\) represents the acceleration of the \(x_{n}\) axis, \(f_{ym}\) represents the acceleration of \(y_{n}\) axis, and \(f_{zn}\) represents the acceleration of \(z_{n}\) axis, respectively; and \(g\) is the gravitational acceleration. Based on the acceleration of the navigation system, we can obtain pedestrian location and speed information. Therefore, the accuracy of \(C_{b}^{n}\), \(accX\), \(accY\), and \(accZ\) are very important to navigation performance.  
Any errors in either the alignment phase or the navigation phase will be integrated and will propagate over time. These errors greatly reduce the performance and navigational accuracy of the INS. Unfortunately, there is a serious drift in the measured data of an IMU, especially acceleration data, and the trajectory obtained by this method deviates significantly from the real trajectory. Therefore, to mitigate such problems in today's IMU-based navigation systems, integration of multiple sensors is common. Section 3.2 introduces a specific system of this type.