  In this paper, we define and solve the Inverse Stochastic Optimal Control
(ISOC) problem of the linear-quadratic Gaussian (LQG) and the linear-quadratic
sensorimotor (LQS) control model. These Stochastic Optimal Control (SOC) models
are state-of-the-art approaches describing human movements. The LQG ISOC
problem consists of finding the unknown weighting matrices of the quadratic
cost function and the covariance matrices of the additive Gaussian noise
processes based on ground truth trajectories observed from the human in
practice. The LQS ISOC problem aims at additionally finding the covariance
matrices of the signal-dependent noise processes characteristic for the LQS
model. We propose a solution to both ISOC problems which iteratively estimates
cost function and covariance matrices via two bi-level optimizations.
Simulation examples show the effectiveness of our developed algorithm. It finds
parameters that yield trajectories matching mean and variance of the ground
truth data.
