A novel algorithm for simultaneous force estimation and friction compensation of constrained motion of robot manipulators is presented. This represents an extension of the improved extended active observer (IEAOB) algorithm reported earlier and proposes a higher order IEAOB or N−th order IEAOB (IEAOB −N) for a n−DOF robot manipulator. Central to this observer is the use of extra system states modeled as a Gauss-Markov (GM) formulation to estimate the force and disturbances including robot inertial parameters and friction. The stability of IEAOB −N is verified through stability analysis. The IEAOB-1 is validated by applying it to a Phantom Omni haptic device against a Nicosia observer, disturbance observer (DOB)/reaction torque observer (RTOB), and nonlinear disturbance observer (NDO), respectively. The results show that the proposed IEAOB-1 is superior to the compared observers in terms of force estimation. Then, the performance of the IEAOB − N is experimentally studied and compared to the IEAOB-1. Results demonstrate that the IEAOB − N has an improved capability in tracking nonlinear external forces.