The fusion of visual and inertial measurements is becoming more and more\npopular in the robotics community since both sources of information complement\nwell each other. However, in order to perform this fusion, the biases of the\nInertial Measurement Unit (IMU) as well as the direction of gravity must be\ninitialized first. Additionally, in case of a monocular camera, the metric\nscale is also needed. The most popular visual-inertial initialization\napproaches rely on accurate vision-only motion estimates to build a non-linear\noptimization problem that solves for these parameters in an iterative way. In\nthis paper, we rely on the previous work in [1] and propose an analytical\nsolution to estimate the accelerometer bias, the direction of gravity and the\nscale factor in a maximum-likelihood framework. This formulation results in a\nvery efficient estimation approach and, due to the non-iterative nature of the\nsolution, avoids the intrinsic issues of previous iterative solutions. We\npresent an extensive validation of the proposed IMU initialization approach and\na performance comparison against the state-of-the-art approach described in [2]\nwith real data from the publicly available EuRoC dataset, achieving comparable\naccuracy at a fraction of its computational cost and without requiring an\ninitial guess for the scale factor. We also provide a C++ open source reference\nimplementation.\n