Prognostics and health management (PHM) for electronic devices is intricate yet crucial in an era of electricity. The impending future of electric vehicles and clean energy requires more in-depth scrutiny and monitoring of their storage elements, lithium-ion batteries. State-of-health (SOH), as one of the most evident indicators for battery degradation quantifications, is a matter of vital importance that worths more attention. In this regard, this paper proposes a novel SOH prognostics framework for lithium-ion batteries considering the limitations in the recorded measurements through the use of linear statistical knearest neighbors (LSKNN) data interpolation, maximal information entropy search (MIES), and collective sparse variational Gaussian process regression (CSVGPR). First, the incomplete charging measurements are processed by LSKNN to infer the missing data points and suppress the unanticipated noises in the extracted temporal features, which indicate the trend of degradation. Then, the MIES scheme is proposed to filter the features that are extraneous to the SOHs of the corresponding batteries and that greatly correlate to the other features in the feature set. Finally, the CSVGPR model, considering the uncertainties within each of the sparse variational Gaussian processes, is utilized to implement SOH prognosis. The proposed framework is verified by a subset of the repository from NASA. In the test, multiple prognostics comparisons of innerbattery tests, cross-battery tests, and tests with other statistical learning methods are presented. The experiment results lend support to the superiority and effectiveness of the work. INDEX TERMS Lithium-ion batteries, prognostics and health management (PHM), maximal information entropy (MIE), sparse variational Gaussian process, k-nearest neighbors, state-of-health.