In this paper, a co-estimation scheme of the state of charge (SOC) and available capacity is proposed for lithium-ion batteries based on the adaptive model-based algorithm. A three-dimensional response surface (TDRS) in terms of the open circuit voltage, the SOC and the available capacity in the scope of whole lifespan, is constructed to describe the capacity attenuation, and the battery available capacity is identified by a genetic algorithm (GA), together with the parameters related to SOC. The square root cubature Kalman filter (SRCKF) is employed to estimate the SOC with the consideration of capacity degradation. The experimental results demonstrate the effectiveness and feasibility of the co-estimation scheme.Energies 2020, 13, 1410 2 of 15 initial values, and the latter is not suitable for online estimation, as it usually costs long shelving time to acquire the OCV value. With the development of computation technologies and machine learning, a variety of artificial intelligence-based, data-driven methods, such as neural networks [6] and support vector machines [7], are proposed for SOC estimation by establishing black-box models. Data-driven methods feature a strong nonlinear mapping capability with high accuracy; however, these approaches show high complexity, and require a considerable amount of training data. Alternatively, model-based methods have been widely investigated and applied for SOC estimation, thanks to the capabilities of online application, high precision and the independence of initial values. Conventional modeling manners mainly include electrochemical models and the equivalent circuit models (ECMs). Compared with complicated electrochemical models, ECM is commonly used to describe the electrical behavior of batteries, and subsequently to estimate the SOC due to its simplification and preferable precision. Yanwen Li et al. proposed a multi-model probability fusion algorithm to describe the battery's electrical characteristics, and subsequently estimate the SOC [8]. In model-based methods, the combination of the battery model and the intelligent filtering algorithm is a hotspot in SOC estimation research. The frequently used filtering algorithms include Kalman filtering (KF) [9], the H-infinity filter (HIF) [10], particle filter (PF) [11], and their various extensions. In particular, the extended KF (EKF) is widely employed to execute SOC estimation using a first-order Taylor expansion on the basis of the battery's nonlinear model [12]. Nonetheless, the second and higher order expansion is usually neglected, thus leading to slow a convergence rate, and even divergence. The unscented KF (UKF) is exploited to estimate battery SOC, based on the recursive unscented transformation to approximate the nonlinear observation without Taylor polynomial expansions [13]. The UKF shows better estimation precision and robustness than the EKF in strong, nonlinear systems [14]. On the basis of the radial-spherical cubature criterion, the cubature Kalman filter (CKF) leverages a set of volume points to appro...