We design and test an algorithm for estimating the bit angular velocity and side forces on a drill string using only topside measurements fed into an adaptive observer. To derive the algorithm gains the drill string is modeled as a distributed wave equation coupled with Ordinary Differential Equations (ODEs) at the boundaries which represent the lumped dynamics of the top-drive and BHA, respectively. Here, the algorithm uses only measurements from the top-drive, while the non-linear side-forces are lumped at the BHA. The obtained observer gains are then implemented on a previously validated torsional drill string model with a distributed BHA model and distributed Coulomb side forces implemented as an inclusion. This design approach combines a high fidelity model with recent theoretical developments on estimation of PDEs to find appropriate feedback gains to ensure a fast and robust tuning. The feasibility of the approach is illustrated by showing convergence in estimated friction factors to the true values when testing on simulated data. When testing on full scale field data, friction factors converge to the same value for different initial values which indicates both good estimates and a robustness of the approach. The estimates produced by the algorithm can be displayed to a driller in real time in an advisory system, and the result can be built on to help optimize the drilling operation, detect faults and unwanted incidents, aid on-site decision making, and improve control of directional drilling.