On Observability and Identifiability of Tightly-coupled Ultrawideband-aided Inertial Localization

The combination of ultrawideband (UWB) radios and inertial measurement units (IMU) can provide accurate positioning. To ensure reliable communication, the radios are generally mounted at the extremities of a mobile system whereas the IMUs are located closer to the center of gravity for use in control, resulting in a spatial offset between the IMU and the UWB radio. Additionally, data from heterogeneous sensors can arrive at different time instants. The systematic fusion of data from multiple sources requires the temporal offset and spatial offset between the sensors to be known. An important aspect of calibration is the observability of the system state and identifiability of the system parameters. Estimating the state or parameters of a system that is otherwise unobservable or unidentifiable, can result in poor estimates. In this report, the local weak observability of the state and the identifiability of the temporal offset for a tightly-coupled UWB-aided inertial localization system is studied.