ZaVI - State Estimation Solely based on Prior Knowledge and Inertial Sensing

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Inertial Measurement Units (IMUs) allow to determine the position and orientation of a body in space. They were initially mainly used in aerospace applications but are nowadays miniaturized as a single chip and used in every smartphone or fitness tracker. An IMU is a ''relative sensor'' that measures rate of change. It consists of a 3-axes gyrometer, which measures the rotation of a body in space, and a 3-axes accelerometer that measures the acceleration of that body. The bodies' orientation can be obtained by accumulating the rotations measured by the gyrometer and the bodies' velocity and position can be obtained by accumulating the accelerations measured (including gravity). This is the canonical way to obtain the bodies' state, i.e. orientation, velocity, and position from IMU data. While accumulating the measurements, measurement errors accumulate as well, leading to a drift in the state, i.e. the state becomes more and more erroneous over time. Thus, an IMU is usually fused with a complementary ''absolute sensor'' such as GPS or camera. This is a textbook example of sensor-fusion. This project investigates, under which circumstances one can avoid error accumulation without adding a second sensor but by using prior knowledge on the type of motion and type of environment occurring. This can be considered fusion of IMU and prior knowledge. The investigation takes place on two levels:On the one hand, there exist methods from the literature that evaluate IMU data for a specific purpose without involving a second sensor. It shall be examined, how far these can be viewed as fusion with prior knowledge, which prior knowledge they exactly fuse, and whether the algorithm is equivalent to performing Bayes-estimation with the prior knowledge as a-priori distribution.The contribution here is to work out a common framework for understanding the different methods. On the other hand, circumstances that limit the movement occurring are frequent. Here, typical examples shall be investigated in how far these circumstances can be formalized and which consequences they theoretically have on the observability of orientation, velocity, and position, i.e. which of these quantities does not drift any more after being fused with prior knowledge. Further, it shall be investigatedhow this prior knowledge can be modeled as an a-priori distribution in the Bayesian sense, which fusion algorithm is suitable and how precise the result is. The examined examples come from sport science, an area that involves a large variety of movements which are interesting to measure. Examples include frequent ''wait and run'' events, where a prior on velocity shall be used as well as track cycling where the non-planar track geometry presumably even makes the position observable, and bouldering with prior knowledge about the environment.