State and specifically location estimation is a core concept in automation and is a well-researched field. One such estimation technique is Moving Horizon Estimation (MHE). In this thesis, the MHE variant single-shooting estimation will estimate the location and velocity of a moving object. The moving object is equipped with an  Inertial Measuring Unit (IMU)  measuring acceleration and angular velocity. This thesis will explore pre-integrating the IMU measurement on the device attached to the moving object and using them in another device running the MHE. The acceleration and angular velocity measurements are measured in the local frame of reference of the moving object, rotating the measurement to a global frame of reference requires a known rotation of the tracked object, finding this rotation is also a task in this thesis. This thesis found the presented theory ill-equipped to estimate the object's state without an angle measurement, this thesis assumed any such measurement is made from a magnetometer but the solution presented is not biased towards any other method of measuring angles. With the addition of an angel measurement, the estimation performs at a decimeter-level precision for location.