Realtime measurements of the drill bit attitude while horizontal directional drilling are the key factors for guiding of directional drilling.A method is introduced to determine the attitude angles and the direct cosine matrix（DCM）.As for nonlinear problems of attitude determination and shortcomings of the existing algorithms

linear observation equation for attitude determination system is established

which uses accelerometers and magnetometers to measure components of the earth’s gravity field and geomagnetic field to construct new observation vectors and takes error vector of attitude quaternion as its input.A solution to the linear observation model

recursive least-squares method is proposed.Simulation results show that the algorithm converges quickly

and can get accurate attitude information

the algorithm can converge to real value

even though the deviation of estimated and real value of initial attitude is large.