# Glove Prototype for Feature Extraction Applied to Learning by Demonstration Purposes
## 2 Literature Review
Crossbow Technology originally proposed a quaternion-based extended Kalman filter for the navigation IMU [4]. Developers of the UAV have used this approach on their specific platform. The system state variables include both the unit quaternion (q) and the gyro biases (\(\text{b}_{\text{p}}\), \(\text{b}_{\text{q}}\), \(\text{b}_{\text{r}}\)). The measurements or observation of the system are the accelerations: \(\text{a}_{\text{x}}\), \(\text{a}_{\text{y}}\), \(\text{a}_{\text{z}}\), and the yaw angle derived from the magnetometer [16]. * Q-Method Extended Kalman Filter The proposed method smoothly incorporates the nonlinear estimation of the attitude quaternion with the [PERSON]'s q-method and the estimation of the nonattitude states through an extended Kalman filter [21]. Other methods of attitude estimation in attitude heading reference systems (AHRS) [22] are very common:* Algebraic Quaternion Algorithm (AQUA) Aside from extended Kalman filter approaches, there are other types of nonlinear filters such as complementary filters. They fuse the estimation of, for example, the gyroscope and the accelerometer with a confident gain approach where the trust in each sensor can be adjusted. The AQUA filter estimates and fuses the data in quaternion representation [23; 24]. It consists of estimating the orientation from the angular rate and corrects that estimation with accelerometer and magnetometer readings. It computes two quaternions, the \"tilt\" quaternion and the \"heading\" quaternion from the magnetometer [25]. * Fast Accelerometer-Magnetometer Combination The accelerometer-magnetometer combination (AMC) is the most typical low-cost sensor system. It integrates the local gravity and the Earth's magnetic field together to form a full-attitude estimation system [26]. The matrix operations are the main focus of attention in this method which are analytically simplified, where the accuracy is maintained, while the time consumption is reduced, hence the name fast accelerometer-magnetometer combination (FAMC) [27; 28]. * Madwick Orientation Filter [PERSON] introduced the sensor fusion algorithm [PERSON] named after him [29] in 2010. The proposed method is applicable to IMUs consisting of a triaxial gyroscope and accelerometer, and MARG sensor arrays that also include a tri-axial magnetometer. The advantages of this filter are: computationally inexpensive, requiring 109 (IMU) or 277 (MARG) arithmetic operations for each filter update, efficient at low sampling rates, and better performance than Kalman-based algorithms. * Mahony Orientation Filter This method proposed by [PERSON] [30] is formulated as a deterministic kinematic observer on the special orthogonal group SO(3) based on the instantaneous attitude and angular velocity measurements. By taking advantage of the geometry of the special orthogonal group, a related observer, the passive complementary filter, decouples the gyroscope measurements from the reconstructed attitude in the observer [31]. The algorithm also estimates the gyroscope bias online with gyroscope and accelerometer outputs and an explicit complementary filter [31].