This paper describes a numerical robust and computational efficient square-root central difference Kalman filter (SRCDKF) and put it into the application of state estimation of Inertial Navigation System (INS)/GPS integrated navigation for wheeled agricultural robot to overcome the flaws exist in EKF (Extended Kalman Filter). A standard INS mechanization with quaternion form attitude expression is introduced and a GPS antenna position compensated observation model is used. Based on the model above, both EKF and SRCDKF are implemented, and their performances are compared through simulation under several situations. Results indicate that the SRCDKF is much more robust and superior than EKF in the existence of large initial heading errors, short period of GPS outrage and low-cost IMU (Inertial Measurement Unit). It based a good foundation for the accurate and robust control of the agricultural robot.