## 3 Navigation
### Fusion Method
#### 3.2.1 Gps + IMU  
The accuracy of GPS cannot meet a robot's movement requirements. For example, parking requires the accuracy at the centimeter level, and the update frequency is approximately 100 Hz. In contrast, for routing and guidance, the required accuracy is reduced to the 10 to 100 m level and the \begin{table}
\begin{tabular}{c c} \hline \hline
**Reference** & **Sensors** \\ \hline
[18; 49; 50] & GPS, IMU \\
[19; 51; 52] & Camera, IMU \\
[36; 53] & Wi-Fi, IMU \\
[54] & GPS, Digital Compass, IMU \\
[37; 55; 56] & UWB, IMU \\
[57; 58] & RFID, IMU \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Some references of navigation system. update frequency is 0.1 Hz approximately. To address GPS measurements' critical problems of low accuracy and susceptibility to interference, the combined use of inertial sensors and GPS will yield a high accuracy in the estimation of a robot's location even when outdoor and indoor placements are mixed [59]. The approach to combine these two types of sensors is mainly based on the estimation method (see Section 4.2) and the tracking system models (see Section 4.1 for details). In Ref. [59], the constant acceleration model was adopted as the process model, along with the linear measurement models of the GPS that are used to obtain the position and those of the IMU that are used to obtain the acceleration--with the assumption that the system has zero-mean Gaussian white noise. By the covariance matrices of the GPS and IMU innovations, the validity domains of the GPS and IMU sensors are determined through the definition of contextual variables. Thresholds are defined considering the confidence level required. As shown in Figure 4, when covariance matrices less than the thresholds are reached, the data are accepted to estimate the trajectory. Another model for the fusion of GPS and IMU is the state space representation of the error vector between the INS and GPS measurements [60; 61]. The Kalman filter attitude correction approach achieves improved performance because of its ability to estimate the attitude errors and gyro bias states. The filter model is made up of two components, a linearized attitude error and gyro bias state model, and a nonlinear attitude quaternion error measurement model. The state model predicts when the attitude errors and gyro bias states will propagate based on input data from the gyros, and the measurement model corrects this prediction with the real world attitude error measurements obtained from an accelerometer. Some of the main inadequacies in the Kalman filter approach for GPS/INS integration are a stochastic error model for every sensor used, which should be predefined, and values like correlation time, variance, and covariance, which should be known accurately. However, it is very difficult to obtain the accurate values of these parameters. [PERSON] and [PERSON] [62] devised an adaptive Kalman filter that is able to adapt to different sensors and circumstances on its own, in which the covariance of  
Figure 4: Sensors validity domains of GPS + IMU [59]. the process noise is adapted based on the state-correction sequence and that of the measurement noise is adapted based on GPS receiver--reported standard deviation. However, GPS and IMU systems have different sampling frequencies, and, in Ref. [63], the so-called time-difference carrier phase (TDCP) problem was solved. Recently, the AI-based techniques have been used to GPS/INS integration. In Ref. [64], the light detection and ranging (LIDAR) point clouds, GPS-IMU information, and Google drivingdirections were integrated by a fully convolutional neural network that jointly learned to carry out perception and path generation from real-world driving sequences. In urban canyon environments, because of the possible operation of the GPS/IMU integrated system, there may be a variable delay between GPS measurement epochs, which makes it more difficult to model the system. [PERSON] and [PERSON] [65] proposed intelligent fusion architecture to take into account this delay. [PERSON] et al.