# Applying Neural Networks in Aerial Vehicle Guidance to Simplify Navigation Systems
## 2 Vehicle Modeling
### Sensors Models
#### 2.3.3 Semiactive Laser Kit  
Laser guidance may be used to guide a vehicle to a target by means of a laser beam. With this method, a laser is kept pointed at the objective and the laser radiation bobs off the objective and is dispersed every which way. At the point when the vehicle is close enough for a portion of the reflected laser energy from the objective to arrive at it, a laser seeker detects which direction this energy is coming from and provides a signal to correct the trajectory towards the source. The device seeking the laser and providing the signal is a semiactive laser kit. The signal provided by this sensor features the centroid of the laser footprint in the photo-detector of the kit, which is composed of four photodiodes that convert light into an electrical current. To estimate its coordinates, the produced electrical intensities in the photodiodes (\(I_{1},I_{2},I_{3}\) and \(I_{4}\)) are employed, which rely upon the illuminated area. These coordinates can be determined as \([ln\frac{\mu}{I_{2}},ln\frac{I_{1}}{I_{3}}]\)[17], and from them, it is possible to obtain the measured radial distance, \(r_{quad}\). Notwithstanding, real coordinates differ from those calculated, although the transformation is conformal [17]. To obtain the real radial distance, \(r_{c}\), the following mathematical functional relationship may be employed: \(r_{c}=f(r_{quad})\). Then, cubic splines based interpolation is applied to obtain a continuous relationship. Equations (6) are utilized to estimate \(x_{c}\) and \(y_{c}\) (see [17] fore more details on this), which are the real spot center coordinates:  
\[\left[ \begin{array}{c}x_{c}\\ y_{c}\end{array} \right]=R_{quad}\cdot\frac{r_{c}}{r_{quad}}\left[ \begin{array}[ ]{c}ln\frac{I_{4}}{I_{2}}\\ ln\frac{I_{3}}{I_{3}}\end{array} \right], \tag{6}\]  
where the physical radius of the photo-detector of the kit is given by \(R_{quad}\). Consequently, the line of sight vector projected in body axes may be calculated from \(x_{c}\) and \(y_{c}\) and also from the distance of the photo-detector of the kit to the center of mass of the vehicle. Note that the signal of this sensor is only available during the terminal phase of the flight. However, it is during final stages of flight when errors of 3 m in positioning target and vehicle induces enormous errors. In this way, an accurate terminal guidance sensor, for example, a semiactive laser kit,is suggested for these last flight stages. This semiactive laser sensor, in combination with GNSS and accelerometers, will provide an accurate determination of the line of sight, especially in the terminal phase. For that purpose, the signals of these sensors' must be hybridized. Next, GNC algorithms are presented. At their kernel, neural networks are implemented to determine gravity vector in two reference frames in order to determine vehicle attitude. In addition, hybridization algorithms are applied to sensors' signals to improve precision. **3. Guidance, Navigation and Control (GNC) Algorithm Definition**  
This section details the proposed navigation, guidance and control algorithms. A scheme of the overall process is depicted in Figure 2. The navigation function determines the position and attitude of the vehicle by means of the information sensed by the sensors. The position is determined through the integration of the signals provided by the accelerometers and the hybridization of the signal from a GNSS device. The determination of attitude is the core of the research in this paper. From the information provided by the accelerometers and the GNSS, the neural network determines the gravity vector in two different axes systems. Then Euler angles are devised from a triad algorithm. The guidance function compares the information from the navigation function with a reference and computes a desired action to the control function. The control function processes this desired action and transforms it into a command to the actuators of the plant (i.e., the vehicle), which execute the action.