As an important research field of mobile robot, simultaneous localization and mapping technology is the core technology to realize intelligent autonomous mobile robot. Aiming at the problems of low positioning accuracy of Lidar (light detection and ranging) simultaneous localization and mapping with nonlinear and non-Gaussian noise characteristics, this article presents a mobile robot simultaneous localization and mapping method that combines Lidar and inertial measurement unit to set up a multi-sensor integrated system and uses a rank Kalman filtering to estimate the robot motion trajectory through inertial measurement unit and Lidar observations. Rank Kalman filtering is similar to the Gaussian deterministic point sampling filtering algorithm in structure, but it does not need to meet the assumptions of Gaussian distribution. It completely calculates the sampling points and the sampling points weights based on the correlation principle of rank statistics. It is suitable for nonlinear and non-Gaussian systems. With multiple experimental tests of small-scale arc trajectories, we can see that compared with the alone Lidar simultaneous localization and mapping algorithm, the new algorithm reduces the mean error of the indoor mobile robot in the X direction from 0.0928 m to 0.0451 m, with an improved accuracy rate of 46.39%, and the mean error in the Y direction from 0.0772 m to 0.0405 m, which improves the accuracy rate of 48.40%. Compared with the extended Kalman filter fusion algorithm, the new algorithm reduces the mean error of the indoor mobile robot in the X direction from 0.0597 m to 0.0451 m, with an improved accuracy rate of 24.46%, and the mean error in the Y direction from 0.0537 m to 0.0405 m, which improves the accuracy rate of 24.58%. Finally, we also tested on a large-scale rectangular trajectory, compared with the extended Kalman filter algorithm, rank Kalman filtering improves the accuracy of 23.84% and 25.26% in the X and Y directions, respectively, it is verified that the accuracy of the algorithm proposed in this article has been improved.