NOVELTY - The method involves establishing a reference model of a rechargeable electrochemical system for calculating variations in time of internal electrochemical variables of the system. The model is established by a mathematical representation of kinetics of electrochemical reactions between electrodes and an electrolyte, electrical representation of spatial accumulation of charges at each electrode, charge balance (Bch) in solid and liquid phases, mass balance (BMa) in all phases of the system and by an energy balance (BEn) of the system. An output signal derived from the calculation is generated.    USE - Method for estimating an internal state e.g. charge state, health state and thermal state, of a rechargeable electrochemical system such as electrochemical battery e.g. nickel-metal hybrid battery, in a battery simulator, an impedance spectroscopy simulator and rechargeable electrochemical system thermal state simulator (all claimed) in hybrid and electric vehicles within a framework of a calibration, an optimization or a validation of the management and estimation strategies.    ADVANTAGE - The method estimates the battery characteristics, which are not directly measurable using mathematical models for managing the battery during operation in real time in a synchronous, precise and reliable manner. The method allows reconstruction of the internal characteristics using the mathematical models of the battery by virtue of a reduced or off-line mathematical model within the framework of calibration, optimization or validation of the management and estimation strategies. The method ensures rating of the battery, which is optimized as a function of the energy and thermal management strategies while reducing weight on board and ensuring fuel consumption and reducing cost of the vehicle.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for a battery simulator comprising an input unit.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic block diagram of a nickel-metal hydride battery and a model applied to a rechargeable electrochemical system.    Charge balance (BCh)    Energy balance (BEn)    Mass balance (BMa)    Butler-Volmer equation (EBV)    Charge state (Ech)