This work investigates a novel approach to joint state-parameter estimation and prediction of the optimal fast-charging current. The approach is based on a global optimisation technique, recently developed in the mathematical field of measure-moment theory. This global (rather than discretised) approach to optimisation offers convergence guarantees even when tackling nonlinear problems with non-convex constraints, which could open the door to using physics-based models in BMS applications. However, the approach is restricted to models with polynomial data and, as with any global method, it is in practice limited by the curse of dimensionality. Here, we benchmark the approach in terms of speed and accuracy for three battery management challenges. As a first example, we use the Thévenin equivalent circuit model of a battery, with two states, one input (current), one output (voltage) and a polynomial open-circuit voltage (OCV) function. We verify that the measure-moment approach can be used to estimate constants, such as the initial state-of-charge and cell capacity, from synthetic data with added measurement noise. For this problem, a local method such as prediction-error minimisation (PEM) achieves higher accuracy for low run time. The advantage of our approach is that it can also be used for ‘grey-box’ estimation, e.g. joint estimation of a time-varying parameter with unknown dynamics along with the states. We show that a sudden rise in the series resistance during a one-minute drive cycle can be accurately retrieved using the measure-moment approach. Finally, we compare the performance of our approach against ‘Bocop’ the nonlinear optimal control solver for the problem of estimating (ahead of time) the optimal input current to achieve the shortest possible charging time, subject to a given set of battery health and safety constraints on the current, voltage and internal states. For our test case, Bocop outperforms the measure-moment approach. Again, the longer run times are to be expected, but only the global method can provide monotonic convergence of the cost function (the total charge time) as shown in the final figure. We therefore conclude that the measure-moment approach is a versatile and robust method which is uniquely suited to tackling nonlinear optimisation problems in the field of battery modelling and control.