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.

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