Estimation of the behavior of long dynamic systems with limited sensing remains an open question. In this paper, we consider the rotational motion of a deep drilling system and compare three algorithms to estimate the friction factors along the drillstring and thus provide an estimate of bottomhole rotational velocity. These friction terms characterize the interaction between the drill pipe and the wellbore walls (Coulomb source terms) within the curving wellbore. This information is essential to design the next generation of stick-slip mitigation controllers, to develop real-time wellbore monitoring tools, and to enable effective toolface control for directional drilling. We propose two model-based algorithms (an adaptive observer and a recursive dynamics framework) and a machine learning-based algorithm to estimate friction parameters, all of them presenting advantages and drawbacks. The performances of the two model-based estimators are finally compared with the data-driven neural network.