The study for degradation of lithium-ion battery is essential to the health management of many applications across various industries. This paper aims to compare the methods of using Extended Kalman Filter, Principle Component Analysis coupled with the Gaussian Process, and Recurrent Neural Network to discover the most reliable and accurate approach for lithium-ion battery state-of-charge and state-of-health estimation. Through the analysis of battery life cycle data, different inputs such as discharging voltage, unit time voltage drop, and discharging time interval are used in different methods to get the best estimation and prediction results. The run-to-failure experiments have been conducted and the battery cycle data has been divided into training set for the construction of the models and the testing set for the validation of constructed models. The advantages and disadvantages of these identified techniques in term of estimation accuracy, robustness and computational complexity are discussed. The study presented in this paper provides a comprehensive comparison towards developing a battery health management solution for lithium-ion batteries under different requirements and conditions.