 This paper proposes a novel approach to monitoring and estimating the capacity of a lithium-ion battery online in satellite applications. It extracts a health indicator, HI, from the operating parameters of the battery, which can then be used to quantify battery degradation. Additionally, the gray correlation analysis, GCA, is employed to evaluate the similarities between the extracted HI and the battery's capacity. This shows the effectiveness of using the HI for fading indication. An enhanced monotonic ECHO state networks and underscore monosin algorithm is also proposed, which incorporates a monotonic constraint into the adaptive degradation trend estimation process. Experimental results demonstrate the accuracy and efficiency of the proposed method in RUL estimation and degradation, modeling for the satellite lithium-ion battery application. This article was authored by Haitao Yao, Wei Xia, Yupeng, and others.