EKF Estimation of Sensor Installation Parameters for Sensor Fusion in Drones and its Observability Analysis

Since the accuracy of estimation is affected by the characteristics of the sensors and the operating environment, sensor fusion based on self localization using multiple sensor information has been proposed. In sensor fusion, when a new sensor is used, the position and orientation information of that sensor needs to be specified. Normally, these parameters are known by prior measurement or other means, but to improve accuracy through sensor fusion, it is important to know these values as accurately as possible. However, sensor fusion with these parameters unknown has not been discussed so far. This paper aims to improve the accuracy of state estimation by performing sensor fusion while estimating unknown installation parameters. We also examines whether it is possible to evaluate the accuracy of parameter estimation in such cases. The position and orientation of the Time-of-Flight (ToF) sensors are chosen as parameters. The parameters are added as a estimation target as well as the drone's states, and the Extended Kalman filter (EKF) is used to estimate the expanded system which they are added. It is then verified whether the accuracy of the estimation can be assessed by analysing local observability using the Lie derivative and the degree of observability of the system using the condition number of the observability matrix. Simulations show that simultaneous estimation of the state and parameters by EKF is possible, and that the accuracy of the estimation is improved for arbitrary states. And as a result, the degree of observability using the number of conditions allows a quantitative assessment of the accuracy of state and parameter estimation.