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

惯性测量单元(IMU)可以确定物体在太空中的位置和方向。它们最初主要用于航空航天应用，但现在被微型化为单芯片，用于每一部智能手机或健身跟踪器。IMU是一个测量变化率的“相对传感器”。它由一个三轴陀螺仪和一个三轴加速度计组成，三轴陀螺仪测量物体在太空中的旋转，三轴加速度计测量物体的加速度。通过对陀螺仪测量的旋转进行累加，可以得到物体的方位；通过对测量的加速度(包括重力)进行累积，可以得到物体的速度和位置。这是从IMU数据中获取物体状态的规范方法，即方向、速度和位置。在累积测量的同时，测量误差也累积，导致状态漂移，即随着时间的推移，状态变得越来越错误。因此，IMU通常与互补的“绝对传感器”融合在一起，例如GPS或相机。这是传感器融合的典型例子。这个项目研究，在这种情况下，人们可以避免误差累积，而不需要增加第二个传感器，而是通过使用关于运动类型和发生的环境类型的先验知识。这可以被认为是IMU和先验知识的融合。调查在两个层面上进行：一方面，文献中存在评估IMU数据用于特定目的的方法，而不涉及第二个传感器。应检查这些方法在多大程度上可以被视为与先验知识的融合，它们准确地融合了哪些先验知识，以及算法是否等价于以先验知识为先验分布执行贝叶斯估计。另一方面，限制移动发生的情况是频繁的。在这里，典型的例子应该调查这些情况可以形式化到什么程度，以及它们在理论上对方向、速度和位置的可观性有什么影响，即这些量中的哪些在与先验知识融合后不再漂移。此外，还应研究如何将这些先验知识建模为贝叶斯意义下的先验分布，哪种融合算法适用，以及结果的精度如何。研究的例子来自体育科学，这一领域涉及到各种有趣的测量动作。例子包括频繁的“等待和奔跑”事件，其中应优先使用速度，以及场地自行车，其中非平面轨道几何结构可能甚至使位置可见，以及具有关于环境的先验知识的抱石。

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.