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

# Is also a function of airspeed magnitude and pitch

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is also a function of airspeed magnitude and pitch rate ˙ θ . For the sake of simplicity, the details of these air-related relations are not presented here and readers are encouraged to see the reference [Mahony et al., 2011] for more information. The block diagram of the overall filter can be seen in Fig. (4.3), with ω y = ω meas . Figure 4.3: Block diagram of the complementary filter with airspeed measurements, from [Mahony et al., 2011] . Although the authors give no stability proofs for the proposed filter, the experimen- tal results for the filter behavior show a performance comparable to that of an Extended

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C hapter 4. D ynamic A ttitude F iltering and E stimation 96 Kalman Filter with GPS measurements. The advantage of their strategy, however, is that the problem of GPS data requirement for velocity compensation was overcome by using an additional measurement of another variable (here, airspeed). This is a considerable im- provement for the vehicles that fly in environments without having access to GPS data or with poor reception. An example of such indoor attitude observers is the extended Kalman filter designed in [Vissiere et al., 2007], where an orthogonal trihedron structure of four magnetometers is used to take advantage of the positional variations of surrounding mag- netic field of a flying small UAV. The magnetic field is a function of position and comparing the four magnetometers readings results in an estimate of vehicles position. This compen- sates the lack of GPS data in indoor or covered spaces. 4.8 Nonlinear Observers on SE(3) Extending the attitude estimation problem to pose estimation by using nonlinear observers has attracted the attention of the research community in the last decade. Some researchers have tried to design nonlinear observers using the GPS data fused with IMU measurements (see e.g., [Vik and Fossen, 2001], [Baldwin et al., 2007], [Vasconcelos et al., 2008b]), while others tried to develop techniques to take advantage of vision-based camera measurements. Computer vision applications in the estimation of the pose have long been known and studied by many researchers, reported in the survey papers of [Huang and Netravali, 1994], and [Olensis, 2000]. In this section, we try to present the latest developments in the field of pose estimation with visual and vectorial measurements. One of the pioneering works in the nonlinear observer design for pose estimation was proposed in [Rehbinder and Ghosh, 2003], where vision-based measurements along with inertial measurements were used to develop a locally convergent observer for attitude esti- mation. The observer evolves on the Special Orthogonal group S O (3) and does not include position and velocity estimation, but provides a theoretical framework for the combination of IMU measurements and camera recordings to estimate translational motion.
C hapter 4. D ynamic A ttitude F iltering and E stimation 97 Consider a set of fixed lines l i , i = 1 , ..., N , known in the inertial frame. The lines are represented by l i = { x I R 3 : x I = ξ i , I + d i , I s , s R } , (4.141) where ξ i
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