  The fusion of visual and inertial measurements is becoming more and more
popular in the robotics community since both sources of information complement
well each other. 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. Additionally, 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 paper, 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-likelihood 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 approach described in [2]
with real data from the publicly available EuRoC dataset, achieving comparable
accuracy at a fraction of its computational cost and without requiring an
initial guess for the scale factor. We also provide a C++ open source reference
implementation.
