Today, the problem of timely detection and accommodation to the arising faults in navigation sensors of autonomous underwater robots (AUR) is very topical. Analysis shows that the existing approaches and methods provide a qualitative solution to the accommodation problems of faults only in case of a slow speed motion of AUR. In this paper, a new synthesis method of high-quality continuous accommodation systems to faults a rising in the navigation sensors of AUR is proposed and investigated. This method consists of three main stages. At the first stage, the problem of detection and localization of faults based on the use of a robot's kinematic model and special data fusion from its sensors is solved. It ensures high quality diagnostics data, because the kinematic model connects all the motion parameters of AUR and variables measured by its navigation sensors. At the second stage, the problem of the faults' size identification is solved due to introduction of special feedback in each observer. At the third stage, the additional control signals for AUR guaranteeing expeditious parrying of the arising faults are formed. The advantage of the proposed method is simplicity of its realization and high precision of compensation of the revealed faults in the conditions of uncertainty and essential variability of the environmental parameters. The modeling results prove high efficiency of operation of the synthesized system of accommodation.