A method of estimating at least one of down hole speed and down hole torque of borehole drilling equipment while drilling a borehole in an earth formation, said borehole drilling equipment comprising a rotational drive system , a drill string having a bottom hole assembly comprising a drill bit and a top end coupled to said rotational drive system , and a speed controller arranged for controlling rotational top end drive speed by commanding a top end drive torque, the method being performed in a computer and comprising the steps of: - obtaining transfer matrix components of a two-port spectral domain transfer matrix computational model of said borehole drilling equipment, said computational model including damping properties of said borehole drilling equipment, wherein said down hole speed and down hole torque (T dh ) are dependent variables and said rotational top end drive speed and top end drive torque (T ref ) are independent variables; - obtaining, while drilling, said rotational top end drive speed and top end drive torque, and - calculating, from said obtained transfer matrix components, said top end drive speed and said top end drive torque, at least one of said down hole speed and down hole torque of said borehole drilling equipment, wherein said step of calculating comprises: - reducing spectral bandwidth of said calculation, said reduced bandwidth being selected to include a limited number of higher order spectral modes in said calculation, - applying, in said spectral domain, a time delay term to said calculation, said time delay term being selected to enable a causal time domain solution, and - calculating at least one of said down hole speed and down hole torque of said borehole drilling equipment from applying said reduced bandwidth and added time delay term. - obtaining transfer matrix components of a two-port spectral domain transfer matrix computational model of said borehole drilling equipment, said computational model including damping properties of said borehole drilling equipment, wherein said down hole speed and down hole torque (T dh ) are dependent variables and said rotational top end drive speed and top end drive torque (T ref ) are independent variables; - obtaining, while drilling, said rotational top end drive speed and top end drive torque, and - calculating, from said obtained transfer matrix components, said top end drive speed and said top end drive torque, at least one of said down hole speed and down hole torque of said borehole drilling equipment, wherein said step of calculating comprises: - reducing spectral bandwidth of said calculation, said reduced bandwidth being selected to include a limited number of higher order spectral modes in said calculation, - applying, in said spectral domain, a time delay term to said calculation, said time delay term being selected to enable a causal time domain solution, and - calculating at least one of said down hole speed and down hole torque of said borehole drilling equipment from applying said reduced bandwidth and added time delay term. - obtaining, while drilling, said rotational top end drive speed and top end drive torque, and - calculating, from said obtained transfer matrix components, said top end drive speed and said top end drive torque, at least one of said down hole speed and down hole torque of said borehole drilling equipment, - reducing spectral bandwidth of said calculation, said reduced bandwidth being selected to include a limited number of higher order spectral modes in said calculation, - applying, in said spectral domain, a time delay term to said calculation, said time delay term being selected to enable a causal time domain solution, and - calculating at least one of said down hole speed and down hole torque of said borehole drilling equipment from applying said reduced bandwidth and added time delay term. <EOS>