An Analytical Solution to the IMU Initialization Problem for Visual-Inertial Systems

The fusion of visual and inertial measurements is becoming more and more popular in the robotics community since both sources of information complement each other well. However, in order to perform this fusion, the biases of the Inertial Measurement Unit (IMU) as well as the direction of gravity must be initialized first. In case of a monocular camera, the metric scale is also needed. The most popular visual-inertial initialization approaches rely on accurate vision-only motion estimates to build a non-linear optimization problem that solves for these parameters in an iterative way. In this letter, we rely on the previous work in [1] and propose an analytical solution to estimate the accelerometer bias, the direction of gravity and the scale factor in a maximum-a-posteriori framework. This formulation results in a very efficient estimation approach and, due to the non-iterative nature of the solution, avoids the intrinsic issues of previous iterative solutions. We present an extensive validation of the proposed IMU initialization approach and a performance comparison against the state-of-the-art approaches described in [2] and [3] with real data from the publicly available EuRoC dataset. Our approach achieves better accuracy without requiring an initial guess for the scale factor and incorporates a prior for the accelerometer bias in order to avoid observability issues. In terms of computational efficiency, it is as fast as the first work and two times faster than the second. We also provide a C++ open source reference implementation.