To address the problem that the positioning accuracy is reduced due to the rapid divergence of heading error in the low-cost foot-mounted pedestrian navigation system, from the perspective of reducing the attitude update error, based on the equivalent rotation vector theory and Fourier expansion, a foot-mounted pedestrian navigation algorithm based on the function fitting attitude update algorithm is proposed. Firstly, based on the equivalent rotation vector method, the sine and cosine functions are used to fit the angular velocity of the foot motion. The Taylor expansion and equation transformation are used to obtain the function fitting the attitude update method. Then, combined with the long short-term memory network (LSTM) zero velocity detection method, a foot-mounted pedestrian navigation algorithm suitable for a variety of gait is designed. Finally, WT901BC IMU is used as the hardware platform to carry out the verification experimental of multiple sets of closed-loop paths in different gaits, and the results show that, compared with the traditional foot-mounted pedestrian navigation algorithm based on the quaternion method or the two subsamples equivalent rotation vector method, the positioning error of the proposed method is reduced by 47. 66% and 42. 83% on average, and the heading error is reduced by 49. 99% and 44. 74% on average. Keywords:attitude update; equival