# INS/Vision Integrated Navigation System Based on a Navigation Cell Model of the [PERSON]
## 2 Brain-like Navigation Model
### INS/Vision Brain-like Navigation Model
For other matched points, if their distance is less than two times of Hamming distance, it is concluded that the two points match successfully. Otherwise, the matching between these two points cannot be used. When the distances of all matched points are examined, the next image is read. Figure 3: INS/vision navigation system. INS: Inertial navigation system. As shown in Figure 4, after successfully matching the scene with the vision navigation system [20; 21; 22], the accurate place information \(X_{2}\) of the pre-stored scene is sent to the INS. The INS system is also integrated to obtain place information \(X_{1}\). At the same time, the total time \(t\) from the last place node to the currently successfully matched location is recorded. By subtracting the calculated place information \(X_{1}\) from the accurate place information \(X_{2}\), we can obtain the accumulated error \(X_{err}\) during time interval of \(t\). The accumulated error is obtained by:  
\[X_{err}=X_{2}-X_{1}, \tag{1}\]  
\[X_{2}=V_{1}\!\cdot\!\Delta t+V_{2}\!\cdot\!\Delta t+V_{3}\!\cdot\!\Delta t+V_{4 }\!\cdot\!\Delta t+\cdots+V_{n}\!\cdot\!\Delta t. \tag{2}\]  
The velocity signal is a continuous variation. Since the s collected by the single-chip microcomputer is a discrete signal, the calculated velocity information is also a discrete signal. \(V_{1}\), \(V_{2}\), \(V_{3}\), \(V_{4}\),..., \(V_{n}\) is the velocity of every \(\Delta t\) in \(t\) time, and \(X\) is the travel distance in time \(t\). \[\left\{ \begin{array}{l}V_{2}=V_{1}+a_{1}\!\cdot\!\Delta t\\ V_{3}=V_{2}+a_{2}\!\cdot\!\Delta t=V_{1}+a_{1}\!\cdot\!\Delta t+a_{2}\!\cdot\! \Delta t\\ V_{4}=V_{3}+a_{3}\!\cdot\!\Delta t=V_{1}+a_{1}\!\cdot\!\Delta t+a_{2}\!\cdot\! \Delta t+a_{3}\!\cdot\!\Delta t\\ \cdots\cdots\\ V_{n}=V_{n-1}+a_{n-1}\!\cdot\!\Delta t=V_{1}+a_{1}\!\cdot\!\Delta t+a_{2}\! \cdot\!\Delta t+a_{3}\!\cdot\!\Delta t+\cdots+a_{n-1}\!\cdot\!\Delta t\\ \end{array} \right. \tag{3}\]  
Since there is no regular change of acceleration in the course of motion, the acceleration cannot give a definite relation. \(a_{1}\), \(a_{2}\), \(a_{3}\),..., \(a_{n-1}\) stands for the actual acceleration per \(\Delta t\) in time. We substitute Equation (3) into Equation (2):  
\[ \begin{array}{l}X_{2}=V_{1}\!\cdot\!\Delta t+(V_{1}+a_{1}\!\cdot\!\Delta t) \!\cdot\!\Delta t+(V_{1}+a_{1}\!\cdot\!\Delta t+a_{2}\!\cdot\!\Delta t)\! \cdot\!\Delta t+\cdots\\ \quad\quad+(V_{1}+a_{1}\!\cdot\!\Delta t+a_{2}\!\cdot\!\Delta t+a_{3}\!\cdot\! \Delta t+\cdots+a_{n-1}\!\cdot\!\Delta t)\!\cdot\!\Delta t\\ \end{array}  \tag{4}\]  
The cumulative error of the INS location is mainly caused by the error of accelerometer. \(a_{1}^{\prime}\), \(a_{2}^{\prime}\), \(a_{3}^{\prime}\),..., \(a_{n-1}^{\prime}\) is converted to the geographic coordinates of acceleration, and the error of the accelerometer is assumed to be equal to \(a_{err}\) in a short period of time. Thus the location \(X_{1}\) obtained by the INS is as follows:  
\[\begin{array}{l}X_{2}=V_{1}\!\cdot\!\Delta t+(V_{1}+a_{1}^{\prime}\!\cdot\! \Delta t)\!\cdot\!\Delta t+(V_{1}+a_{1}^{\prime}\!\cdot\!\Delta t+a_{2}^{ \prime}\!\cdot\!\Delta t)\!\cdot\!\Delta t+\cdots\\ \quad\quad+(V_{1}+a_{1}^{\prime}\!\cdot\!\Delta t+a_{2}^{\prime}\!\cdot\!\Delta t +a_{3}^{\prime}\!\cdot\!\Delta t+Hence:  
\[a_{err}=\ X_{err}/\left(\left(\frac{n\cdot(n-1)}{2}\right)\cdot(\Delta t)^{2} \right). \tag{8}\]  
In the STM32 single-chip microcomputer, the calculation frequency of the INS is set to 40 Hz. Thus,  
\[n=t\cdot f_{INS}. \tag{9}\]  
Substituting Equation (9) in Equation (8):  
\[a_{err}=\ X_{err}/\left(\frac{t\cdot(t\cdot f_{INS}-1)}{2\cdot f_{INS}}\right). \tag{10}\]  
Due to the accumulation of errors, the velocity of \(t\) moment has deviated from the true velocity. In order to reduce the error in the later calculation, the velocity \(V_{t}\) of \(t\) time should be calculated again by using the saved acceleration information.