Accurate measurement of drill bit position and direction is the main technology to realize automation and intelligence in oil drilling field. In recent years, with the rapid development of complex drilling technologies such as high deviation wells, directional wells and horizontal wells, higher requirements have been put forward for measurement technology, especially for real-time monitoring of bit attitude and position during the drilling process. Therefore, for the past few years, the measurement while drilling (MWD) system has been widely recognized and developed rapidly in precision targeted drilling. among them, strapdown inertial navigation system (SINS) consisting of accelerometer and gyroscope is the key of down-hole measurement while drilling. To solve the problem of accumulated errors in SINS, in this paper, a positioning error correction method based on kinematic constraint-aided (KC) SINS zero velocity updated (ZUPT) model is proposed. Firstly, based on the acceleration and angular velocity information measured by SINS, empirical mode decomposition (EMD) and wavelet de-noising reconstruction are performed for MWD signals. Secondly, the static detection model of the drill bit is established by using the reconstructed signal. Thirdly, using drilling technology to analyze the motion attitude of the bit, the KC model of the down-hole bit is established. By analysis the alternating effect of the KC model and the ZUPT model in the process of the bit movement and stop, the ZUPT model of the SINS is established. Finally, experimental verification is performed by building a drilling platform. The experimental results show that the maximum positioning error of the proposed positioning model is 0.15 m within 300 s. Comparing with a single KC model and a single ZUPT model, the bit positioning accuracy is improved to 92.6%, which effectively suppresses the original cumulative error, and verifies the feasibility of the proposed method. INDEX TERMS Measurement while drilling system, strap-down inertial navigation system, empirical mode decomposition, kinematic constraint-aided, zero velocity updated.