Lithium-ion batteries (LIBs) have emerged as the preferred energy storage systems for various types of electric transports, including electric vehicles, electric boats, electric trains, and electric airplanes. The energy management of LIBs in electric transports for all-climate and long-life operation requires the accurate estimation of state of charge (SOC) and capacity in real-time. This study proposes a multistage
model fusion algorithm to co-estimate SOC and capacity. Firstly, based on the assumption of a normal distribution, the mean and variance of the residual error from the model at different ageing levels are used to calculate the weight for the establishment of a fusion model with stable parameters. Secondly, a differential error gain with forward-looking ability is introduced into a proportional–integral observer
(PIO) to accelerate convergence speed. Thirdly, a fusion algorithm is developed by combining a multistage model and proportional–integral–differential observer (PIDO) to co-estimate SOC and capacity under a complex application environment. Fourthly, the convergence and anti-noise performance of the fusion algorithm are discussed. Finally, the hardware-in-the-loop platform is set up to verify the performance
of the fusion algorithm. The validation results of different aged LIBs over a wide range of temperature show that the presented fusion algorithm can realize a high-accuracy estimation of SOC and capacity with the relative errors within 2% and 3.3%, respectively.