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Two novel methods to estimate the state of charge (SOC) and state of health (SOH) of a lithium-ion battery are presented. Based on a detailed deduction, a dual filter consisting of an interaction of a standard Kalman filter and an Unscented Kalman filter is proposed in order to predict internal battery states. In addition, a support vector machine (SVM) algorithm is implemented and coupled with the dual filter. Both methods are verified and validated by cell measurements in form of cycle profiles as well as storage and cycle ageing tests. A SOC estimation error below 1% and accurate resistance determination are presented.