Abstract: For the simultaneous localization and mapping (SLAM) problem of mobile robots in the three-dimensional space, a fast and adaptive SLAM algorithm based on the improved strong tracking filter (STF) is proposed. Firstly, the noise covariance matrixes of STF are adaptively estimated on line to suppress the effects of noises on system state estimation, which makes the system state estimation converge to real values quickly. Secondly, singular value decomposition (SVD) is used to decompose the state covariance matrix which can help the algorithm get better numerical stability. This algorithm can improve the adaptive ability of time-varying systems and the state estimation precision, and the comparative simulation results with STF-SLAM algorithm illustrate the effectiveness and the superiority of the proposed algorithmon on the denoising performance and the estimation precise.