In the simultaneous localization and mapping (SLAM) technology, mobile robots generally has problems such as low state accuracy, poor stability, and complicated calculation, which can not meet the requirements of real-time and accuracy in the SLAM process. In order to improve this problem, an SLAM autonomous positioning algorithm was proposed based on iterated square root central difference Kalman filter (ISRCDKF). The central difference transform was used to deal with the nonlinear problem of SLAM, avoiding complex operations such as Jacobian matrix in the Taylor formula expansion, and directly transmitting the square root factor reduction algorithm of the covariance matrix in the filter update process. In the complexity, the Levenberg-Marquardt (L-M) optimization method was used to introduce the real-time modified covariance matrix of the adjustment parameters in the iterated observation update process to improve the accuracy and stability of the algorithm. The simulation results showed that under the same data model and noise environment, the proposed ISRCDKF-SLAM algorithm was compared with SLAM algorithm based on extended Kalman filter (EKF-SLAM),SLAM algorithm based on unscented Kalman filter (UKF-SLAM) and SLAM algorithm based on cubature Kalman filter (CKF-SLAM), the root mean square error was reduced by 47.3%, 32.7% and 25.0%, respectively. At the same time, compared with the UKF-SLAM algorithm and CKF-SLAM algorithm with the same computational complexity, the running time of the proposed algorithm was reduced by 15.1% and 10.8%, respectively, which proved the effectiveness of the algorithm. Finally, the proposed algorithm was embedded into the mobile robot platform for field experiment verification, which further proved the practicability and effectiveness of the algorithm.