Rigid Body Attitude Estimation- An Overview and Comparative Stud.pdf

# From an application perspective the ability of the

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From an application perspective, the ability of the attitude observer to work without inertial measurements and sensors such as magnetometers and accelerometers and relying only on the position measurements can be regarded as a positive point of the estimation technique. However, in practice, some of their assumptions are di ffi cult to satisfy. For example, the exact positioning of the landmark centroid as origin of the inertial frame may not be a rational assumption. In fact, the accuracy of the estimation is in a way dependent on the distance of the flying vehicle from the centre of the inertial frame. This “dependency” of the estimation method on a non-moving set of landmarks poses an obstacle in practical applications of such technique. On the other hand, the authors other previously discussed work [Vasconcelos et al., 2008b] on the attitude and position estimation gives a greater region of mobility for the vehicle’s pose observer to properly function.

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C hapter 4. D ynamic A ttitude F iltering and E stimation 106 4.9 Simulations In this section, some of the attitude observers and filters discussed in this chapter are sim- ulated. The known inertial-frame vectors of gravity and magnetic field are taken similar to those in section (3.8). For this part, the trajectory of the rigid body position in the inertial frame is specified as p ( t ) = [200 sin(0 . 1 t ) , 150 cos(0 . 1 t ) , 6 t ] T m , (4.173) from the first and second derivatives of which the velocity v and linear acceleration ˙ v of the rigid body are obtained v ( t ) = [20 cos(0 . 1 t ) , - 15 sin(0 . 1 t ) , 6] T m / s , ˙ v ( t ) = [ - 2 sin(0 . 1 t ) , - 1 . 5 cos(0 . 1 t ) , 0] T m / s 2 . (4.174) Figure (4.4) illustrates the trajectory of the rigid body position obtained from (4.173) in a 100 seconds time interval. Figure 4.4: The trajectory of the rigid body position in a 100 seconds time interval.
C hapter 4. D ynamic A ttitude F iltering and E stimation 107 In these simulations, all the estimators are tested with the same initial conditions for orientation and velocity. The initial attitude of the actual system is taken as R (0) = 1 0 0 0 - 1 0 0 0 - 1 , and the initial conditions for estimators were chosen to be ˆ R (0) = I 3 × 3 or equivalently ˆ Q (0) = [1 , 0 , 0 , 0] T . For simulations in which a constant gyro bias is assumed, the bias vector is chosen as ω b = [0 . 5 , - 0 . 5 , 1] T deg / s . For velocity-aided estimators, the initial velocity was taken as ˆ v = [0 , 1 , 0] T m / s . While the previous noise assumptions for accelerometer and magnetometer measure- ments in section (3.8) hold here, the following noise variances were considered Gyroscope noise = 1 deg / s GPS-velocity noise = 0 . 01 m / s . 4.9.1 Invariant EKF The Invariant Extended Kalman Filter in (4.38) is simulated. This filter is designed based on an accelerated motion assumption and takes the accelerometer, magnetometer and gyro measurements, in the body frame, well as the linear velocity, in the inertial frame, as the filter inputs. The constant accelerometer scaling factor is taken as a s = 0 . 9 .
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