Attitude and heading reference system (AHRS) can be mounted at Human body to sense and determine the orientation of Human in motion. The algorithms of orientation determination in literature still have problems of insufficient precision. Thus, we design a square root unscented Kalman filter (SRUKF) based on minimum sigma points set with high precision and good rapidity. To cope with the problem of sigma points set determination, we survey the matching method of higher moments than 2 in covariance matrix. As a result, we propose a SRUKF algorithm based on n+2 sigma points set, which retains rapidity of n+1 sigma points set, and also achieves the precision of 2n+1 set. The covariance matrix of sigma points reaches the L / 2 order approximation of original function if the sigma points have L order precision. Particularly, the covariance reaches 2th order if the sigma points have 2th order precision. Furthermore, we analyses the convergence of the filter process step by step with nonlinear drift function. The simulation using a standard experimental data is conducted in comparison with other filters. The orientation precision is similar to that of 2n+1 while the execution time is similar to that of n+1. The results demonstrate that the designed algorithm could achieve stable and reliable orientation determination of AHRS.