Minimum Error Entropy Robust Delay Filter for Multi-AUV Cooperative Localization

This article proposes a minimum error entropy (MEE) based robust delay filter for cooperative localization (CL) of autonomous underwater vehicles (AUVs). The underwater environment is complex and dynamic, which can lead to unreliable measurements and pose unpredictable risks during the CL process. So, first, we design two hierarchical delay-augmented models to, respectively, mitigate the impact of measurement biases induced by delay in the processes of position estimation and unknown input estimation. Using this model, the cost function based on MEE criterion is then constructed. Meanwhile, an improved kernel function is introduced to improve its response sensitivity to non-Gaussian noise. By doing so, the adaptive updating of the gain matrix and error variance matrices is realized in the iterative process, which enhances the ability of capturing and processing outliers, alleviates the loss of valid observations, and mitigates the effect of time delays and unknown inputs on posterior state estimation. The effectiveness and advancement of the algorithm are verified by simulations and lake trials.