Method of and a device for estimating down hole speed and down hole torque of borehole drilling equipment while drilling, borehole equipment and a computer program product

A device for estimating at least one of down hole speed and down hole torque of borehole drilling equipment for 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, said device comprising a computer controlled drilling operation observer system arranged for:

• 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, and wherein said down hole speed and down hole torque being dependent variables and said rotational top end drive speed and top end drive torque being 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 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.