Frame-dragging is an important general relativistic effect that has been observed in the weak-field limit by the Gravity Probe B experiment for the gravitational field of the Earth.
Although the effect is relatively small for the Earth, it is prominent for compact objects like black holes and neutron stars. So the observational verification of this effect around such compact objects is important in studies of accretion flows around such compact objects.
I am interested to know whether any attempt has been made for observational verification of frame-dragging in the strong-gravity limit, i.e., around black holes and neutron stars, or any planned NASA mission in future?