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

惯性测量单元（imu）可以确定物体在空间中的位置和方向。它们最初主要用于航空航天应用，但现在被小型化为单个芯片，用于每一个智能手机或健身追踪器。IMU是测量变化率的“相对传感器”。它由一个测量物体在空间中的旋转的三轴陀螺仪和一个测量物体加速度的三轴加速度计组成。将陀螺仪测量到的旋转累加得到物体的方位，将测量到的加速度（包括重力）累加得到物体的速度和位置。这是从IMU数据中获取物体状态（即方向、速度和位置）的规范方法。在积累测量值的同时，测量误差也在积累，导致状态的漂移，即状态随着时间的推移变得越来越错误。因此，IMU通常与互补的“绝对传感器”（如GPS或相机）融合在一起。这是传感器融合的典型例子。该项目研究了在何种情况下可以避免误差积累，而无需添加第二个传感器，而是通过使用关于运动类型和发生环境类型的先验知识。这可以看作是IMU和先验知识的融合。调查发生在两个层面上：一方面，文献中存在评估IMU数据用于特定目的而不涉及第二个传感器的方法。需要考察的是，这些算法在多大程度上可以看作是与先验知识的融合，它们确切融合了哪些先验知识，以及该算法是否等同于将先验知识作为先验分布进行贝叶斯估计。这里的贡献是制定一个用于理解不同方法的通用框架。另一方面，限制运动发生的环境是频繁的。在这里，我们将研究典型的例子，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、速度和位置的可观测性有什么影响，即这些量中哪些在与先验知识融合后不再漂移。进一步，研究如何将这些先验知识建模为贝叶斯意义上的先验分布，哪种融合算法是合适的，以及结果的精度如何。研究的例子来自运动科学，这是一个涉及各种各样的运动的领域，测量起来很有趣。例子包括频繁的“等待并运行”事件，其中先验速度为应使用，以及轨道循环，其中非平面轨道几何形状可能甚至使位置可观察到，以及对环境的先验知识抱石。

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.