  Existing inertial motion capture techniques use the human root coordinate
frame to estimate local poses and treat it as an inertial frame by default. We
argue that when the root has linear acceleration or rotation, the root frame
should be considered non-inertial theoretically. In this paper, we model the
fictitious forces that are non-neglectable in a non-inertial frame by an
auto-regressive estimator delicately designed following physics. With the
fictitious forces, the force-related IMU measurement (accelerations) can be
correctly compensated in the non-inertial frame and thus Newton's laws of
motion are satisfied. In this case, the relationship between the accelerations
and body motions is deterministic and learnable, and we train a neural network
to model it for better motion capture. Furthermore, to train the neural network
with synthetic data, we develop an IMU synthesis by simulation strategy to
better model the noise model of IMU hardware and allow parameter tuning to fit
different hardware. This strategy not only establishes the network training
with synthetic data but also enables calibration error modeling to handle bad
motion capture calibration, increasing the robustness of the system. Code is
available at https://xinyu-yi.github.io/PNP/.
