Cooperative Localisation (CL) technology is required in some situations for Multiple Unmanned Underwater Vehicle (MUUVs) missions. During the CL process, the Relative Localisation Information (RLI) of the master UUV is transmitted to slave UUVs via acoustic communication. In the underwater environment, the RLI is subject to a random time delay. Considering the time delay characteristic of the RLI during the acoustic communication, a Moving Horizon Estimation (MHE) method with a Delayed Extended Kalman Filter (DEKF)-based arrival cost update law is presented in this paper to obtain an accurate and reliable estimation of present location. Additionally, an effective computation method for the MHE method is employed, in which the “Lower Upper” (LU) factorization is used to compute the solution of the Karush-Kuhn-Tucker (KKT) system. At the end of this paper, simulation results are presented to prove the superiority and practicality of the proposed MHE algorithm.
