ABSTRACT
Is Constant ........................................................................................................... 119 7.3.2 Deterministic Observability of the Model When the Angular Velocity Is
Time-Varying ............................................................................................................ 120 7.4 Consistency Analysis ............................................................................................................ 121 7.5 Simulation Testing ................................................................................................................ 121
7.5.1 Consistency Test ....................................................................................................... 121 7.5.2 Convergence Test ...................................................................................................... 122 7.5.3 Sensitivity Test .......................................................................................................... 122
7.6 Experimental Results ............................................................................................................124 7.6.1 Gravity and External Acceleration Estimation ......................................................... 124 7.6.2 Attitude Estimation ................................................................................................... 124
7.7 Concluding Remarks ............................................................................................................ 125 Appendix A .................................................................................................................................... 126 References ...................................................................................................................................... 127
IMUs contain a three-axis gyroscope and a three-axis accelerometer for measuring the angular velocity and acceleration of the rigid body, respectively. The attitude can be computed by integrating the gyroscope output from known initial conditions. However, the integration process is heavily influenced by errors that grow unbounded over time due to low-frequency drifts and wideband measurement noise affecting the gyroscope output. The accelerometer output can be used either to compute the initial conditions or to support the attitude estimation process thanks to sensor fusion approaches, which are oftentimes mechanized with some sort of Kalman filter (KF). The problem with a three-axis accelerometer being used for attitude estimation is that it is sensitive to both the reaction to the Earth’s gravitational field and to the changes of velocity occurring because of the own motion of the body (external acceleration). The usual approach to deal with the problem of external accelerations consists of gating accelerometer measurements, which amounts to discard acceleration samples whose magnitude deviates too much from the gravity value that would be valid in conditions of slow motion. Recently, a new approach has been proposed, in which the two signal components contained in the accelerometer output (i.e., gravity and external acceleration) are both included in the system’s state (source-separation problem). In this chapter, we show that the main advantage of the source separation approach is the possibility to design truly linear KFs, with a twofold benefit: on the one hand, linear and time-invariant measurement models are introduced for better convergence and less computational demand of the attitude estimator; on the other hand, robust model-based rejection of external acceleration can be performed for improved accuracy in attitude estimation. Part of the chapter will be devoted to analyze consistency and observability properties of the attitude estimator working on inertial data generated from a proprietary IMU simulator. Moreover, the results of some real-life experiments concerning the performance of basic motor tasks, including walking, will be presented and discussed to highlight the feasibility of the proposed approach.
