IMU Alignment Using Maximum Likelihood Estimation

The problem of determining the relative orientation of a personal sensor device and a land vehicle is fundamental to all analysis that aims to use inertial measurements from that same device. In recent years, the rising smartphone penetration rate and growing interest in large-scale intelligent transportation solutions have contributed to further increasing the importance of the problem. Despite this, most methods for IMU alignment presented in the literature rely on heuristics and do not offer any possibility of analysing the problem from an estimation theoretical perspective. This paper addresses this issue by formulating IMU alignment as a maximum likelihood problem. A likelihood function is constructed using two measurement models that connect GNSS and inertial measurements. The small angle error approximation is then applied to the unknown rotation matrix, thereby producing a kinematic model that is linear in the unknown rotation error vector. Combining the kinematic model with the two measurement models, a closed-form expression for the Fisher information is computed and the identifiability properties of the problem are analyzed. The performance of the maximum likelihood estimator is evaluated using CARLA simulations and benchmark comparisons with competing methods.