Reliability of lithium-ion (Li-ion) rechargeable batteries has been recognized as of high importance from a broad range of stakeholders, including battery manufacturers, manufacturers of battery-powered devices, regulatory agencies, researchers, and the public. Assessing the current and future health of Liion batteries is essential to ensure the batteries operate safely and reliably throughout their lifetime. This paper presents a new data-driven approach for prediction of battery remaining useful life (RUL) in the presence of corruptions (or errors) in capacity features. The approach leverages bilinear kernel regression to build a nonlinear mapping between the capacity feature space and the RUL state space. Specific innovations of the approach include: i) a general framework for robust sparse prognostics that effectively incorporates sparsity into kernel regression and implicitly compensates for errors in capacity features; and ii) two numerical procedures for error estimation that efficiently derives optimal values of the regression model parameters. Results of 10 years' continuous cycling test on Li-ion prismatic cells suggest that the proposed approach achieves robust RUL prediction despite random noise in the capacity features.