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One of the main issues with KF-based methods is complication of determining the process noise covariance matrix, which is usually obtained by empirical tuning. Here, by using the adaptive observer designed around an arbitrary operating point of a non-linear system, a novel systematic approach is developed for determining the covariance matrix of the parameter noise in the EKF with the aim of jointly estimating the states and unknown parameters of the system. The proposed mixed adaptive observer and EKF method are applied to a Lithium-Ion battery to simultaneously estimate its state of charge (SOC) and internal resistance as well as the state of health (SOH). The dynamical behaviour of the battery is modelled by using a commonly used RC model and is validated by the real data collected from the battery. The proposed method provides a robust performance against the model uncertainties and shows satisfactory parameter convergence properties. Experimental tests are established to certify the capability and effectiveness of the proposed scheme compared to the conventional EKF. Furthermore, a simulation study is carried out to verify the robustness of the proposed method.

A robust non-linear observer is proposed to estimate the state of charge (SoC) of a lithium-ion battery by employing an electrical model of the battery. Considering the non-linear behaviour of the open circuit voltage versus SoC curve, a nonlinear state space model is established. The modelling errors and uncertainties are compensated by the proposed non-linear observer resulting in robustness in the presence of these errors, which is the main feature of the proposed observer. The stability of the observer is proved by the Lyapunov criteria. The effectiveness of the proposed observer is verified by using the experimental test. The test results show that the proposed approach is effective and estimates the SoC with high accuracy. Additional experimental test verifies the robust performance of the proposed observer in the presence of the modelling errors and disturbances. Nomenclature Model parameters V OC open circuit voltage V b , I b terminal voltage and current V 1 polarisation voltage C b , C 1 storage and polarisation capacitances R 0 , R 1 , R d model resistances x, u, y system state, input and output A, B, F 1 , F 2 , f , d system parameters d 0 uncertainties' upper bound γ Lipchitz constant Observer parameters x, ŷ observer state and output P , Q positive definite matrix M observer gain μ , ξ design parameters ρ constant parameter e state estimation error

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