This paper discusses two ways to estimate the interaction force at the end-effector of a robot. The first approach that is presented combines filtered dynamic equations with a recursive least squares estimation algorithm to provide a smoothened force signal, which is useful in the (common) case of noisy torque measurements. The second approach, which uses a generalized momentum based disturbance observer, is mainly discussed to compare it to the first approach. Although very different in appearance, it is shown that a close connection exists between both approaches. Simulation results for both algorithms are shown, and experimental results derived from a sensorless admittance controller that was implemented using the algorithms are presented.