Accurate, real-time estimation of battery State-of-Charge and State-of-Health represents crucial part of modern battery management systems. Nonlinear and battery degradation-dependent behaviour of output voltage complicates the design of those estimation algorithms, which should be based on parameter-varying models. To this end, the paper proposes a combined state and parameter estimation algorithm, whose performance is experimentally validated for real driving cycles of an electric scooter battery pack. Algorithm is based on nonlinear Kalman filters, and it estimates all relevant parameters of first-order battery equivalent circuit model, such as resistance and open-circuit voltage parameters as well as battery remaining capacity.