Aligning a robot's trajectory or map to the inertial frame is a critical capability that is often difficult to do accurately even though inertial measurement units (IMUs) can observe absolute roll and pitch with respect to gravity. Accelerometer biases and scale factor errors from the IMU's initial calibration are often the major source of inaccuracies when aligning the robot's odometry frame with the inertial frame, especially for low-grade IMUs. Practically, one would simultaneously estimate the true gravity vector, accelerometer biases, and scale factor to improve measurement quality but these quantities are not observable unless the IMU is sufficiently excited. While several methods estimate accelerometer bias and gravity, they do not explicitly address the observability issue nor do they estimate scale factor. We present a fixed-lag factor-graph-based estimator to address both of these issues. In addition to estimating accelerometer scale factor, our method mitigates limited observability by optimizing over a time window an order of magnitude larger than existing methods with significantly lower computational burden. The proposed method, which estimates accelerometer intrinsics and gravity separately from the other states, is enabled by a novel, velocity-agnostic measurement model for intrinsics and gravity, as well as a new method for gravity vector optimization on $S^2$. Accurate IMU state prediction, gravity-alignment, and roll/pitch drift correction are experimentally demonstrated on public and self-collected datasets in diverse environments.

翻译：将机器人轨迹或地图对准惯性坐标系是一项关键能力，尽管惯性测量单元（IMU）能够观测到相对于重力的绝对横滚角和俯仰角，但精确实现这一目标往往较为困难。IMU初始标定中的加速度计偏置和比例因子误差，通常是机器人里程计坐标系与惯性坐标系对准时的主要误差来源，尤其对于低精度IMU而言。在实际应用中，需同时估计真实重力向量、加速度计偏置和比例因子以提高测量质量，但这些量在IMU未充分激励时不可观测。现有方法虽然能估计加速度计偏置和重力，却未明确解决可观测性问题，也未估计比例因子。我们提出一种基于固定滞后因子图的估计器，以同时解决上述两个问题。除了估计加速度计比例因子外，本方法通过将优化时间窗口扩大至现有方法的量级以上，并显著降低计算负担，从而缓解了可观测性受限的问题。该方法将加速度计内参和重力与其他状态分离估计，其实现依赖于一种新颖的、与速度无关的内参与重力测量模型，以及一种基于$S^2$流形的重力向量优化新方法。通过在多样环境下的公开数据集和自采数据集上的实验，验证了该方法在精确IMU状态预测、重力对准及横滚/俯仰漂移校正方面的有效性。