The current nonlinear optimization of visual SLAM back-end has disadvantages such as slow optimization speed and poor optimization effect. To overcome these problems, this paper improves the traditional Levenberg-Marquardt algorithm (L-M) based on a framework of Bundle Adjustment (BA) nonlinear optimization. Firstly, the radius and expansion multiplier of the trust region are formulated and a threshold value is set; secondly, the trust region after each iteration is restricted with the pre-defined range for the purpose of improving nonlinear optimization; finally, a comparative analysis is conducted by setting up a comparison experiment with the traditional L-M algorithm, and It is concluded that the improved L-M algorithm can reduce the number of iterations by 16 times and time performance was reduced by an average of 62.30%, which shorens the optimization time, improves the optimization efficiency and has better robustness.

Laser slam usually needs to complete a back-end graph optimization at a fast speed in some specific scenes, such as sharp turns, fast motion, and limited calculation time. Aiming at these problems, this paper proposed a 2D laser slam back-end graph optimization combined with Cholesky decomposition to accelerate a linear solution process and further to achieve a purpose of accelerating graph optimization. In MATLAB simulation experiments, the rate of 2D laser slam back-end graph optimization combined with Cholesky decomposition increased 24%, compared to that of the traditional method without Cholesky decomposition. The result verified the effectiveness of the improved method.