medium hard to very hard rock formations. This ROP which depends on the bit-rock contact conditions at the well bottom to
efficiently transfer the impact energy to an intact rock can be maximized for certain parameter sets, including the static weight
on bit (WOB, also known as thrust force/feed force). Indeed, recent experimental and numerical investigations of the bit-rock
interface (BRI) have revealed an optimum WOB which is rooted in the dependence of the BRI law on theWOB force. That is an
optimal state of pseudo-stiffness at the BRI can be obtained with the appliedWOB for which the impact energy transmitted to rock
is maximized. Therefore, accurate estimation and control of the BRI stiffness is crucial in order to optimize drilling operation.
In this paper, a numerical solution is proposed which can estimate the state of drilling dynamics and evolving BRI stiffness. This
approach combines a 1D phenomenological percussive drilling model accounting for the longitudinal wave transmission during
bit-rock interaction and a joint Unscented Kalman Filter (UKF) designed to simultaneously estimate the unknown parameters in
the nonlinear BRI stiffness expression as well as the inaccessible states at the BRI. The results show that this approach has the
potential to provide an accurate estimation of the percussive drilling dynamics and nonlinear BRI stiffness evolution over a wide
range of initial conditions and static deformations that induced from changing WOB.