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

410 discussion in this chapter some of the dynamic

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4.10 Discussion In this chapter, some of the dynamic attitude estimation algorithms, including the latest nonlinear attitude observers, are discussed and simulation results were presented. The study of the structure of each filter and the provided simulations help in making comparisons between di ff erent techniques. The Invariant EKF and Unscented EKF have been chosen for simulations. Since the
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C hapter 4. D ynamic A ttitude F iltering and E stimation 120 Figure 4.17: Error Euler angles of the invariant observer with ideal measurements (Accel- erated mode) IEKF can be regarded as a generalization of the Multiplicative EKF and the probability- analysis-based Particle filters techniques can be simplified to the UKF, the two choices seem to provide a good representation of the class of attitude estimators of the Kalman- type. The simulation results for the extended Kalman filters show good performance of in estimating the attitude with noisy measurements. This is due to the fact that these filters are specifically designed to compensate for the e ff ect of noise. Once the noise characteristics of the sensor readings are determined, the filter can be simply tuned. It should be noted that real-time noise cannot be assumed to be white noise with zero mean. Non-Gaussian noise is long known to have e ff ects on sensor measurements and its existence in the system measurements can degrade the filter output. The initial value issue was also noticed during the simulations. The Kalman filters are derived through linearizition processes and this makes large initial errors a potential threat to the performance of the filter. For the unscented filter, it was seen that large initial errors in the state vector and the covariance matrix led to a non-positive predicted covariance matrix. Unlike the Kalman filters, the studied nonlinear observers did not show vulnerability to initial state values.
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C hapter 4. D ynamic A ttitude F iltering and E stimation 121 Figure 4.18: Error Euler angles of the invariant observer with noisy measurements (Accel- erated mode) For most of the nonlinear observers, the results are semi-global and for some even global. This means that the choice of the initial filter states did not have an e ff ect on the ultimate performance and the filter remains stable under di ff erent initial conditions. The simulations with noise-free measurements show how perfectly these observers obtain the true rigid body attitude. By adding measurement noise to sensor readings, however, the performance was degraded to a relatively acceptable level. However, this is not the case for all nonlinear attitude observers. In fact, the simulations for the nonlinear observers with global results, that do not evolve on S O (3), show how a relatively small noise can have an important negative impact on the estimated attitude.
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