A computer-implemented method of estimating a battery state of an electrochemical battery, the method comprising: providing a series of electrical impedance measurements of an electrochemical battery, each electrical impedance measurement being measured at a respective measurement frequency (f s), the series being ordered according to the respective measurement frequencies (f s), characterized in that the method further comprises: calculating electrical impedance gradients from the series of electrical impedance measurements to generate a series of electrical impedance gradients, wherein calculating the electrical impedance gradients includes calculating gradients of a real part and gradients of an imaginary part of the series of electrical impedance measurements, wherein the electrical impedance gradients are calculated with respect to one of the measurement frequency (f s), a logarithm of the measurement frequency (f s), or the index (s) of the elements of the series of electrical impedance measurements, and determining a battery state of the electrochemical battery using computational means configured to receive as inputs at least the series of electrical impedance gradients, wherein the series of calculated electrical impedance gradients is provided to the computational means, wherein the computational means receives and processes at least the provided series of calculated electrical impedance gradients to generate therefrom at least one output signal representing a battery state associated with the electrochemical battery, wherein the computational means include artificial neural network means configured to receive as inputs at least the series of electrical impedance gradients. providing a series of electrical impedance measurements of an electrochemical battery, each electrical impedance measurement being measured at a respective measurement frequency (f s), the series being ordered according to the respective measurement frequencies (f s), characterized in that the method further comprises: calculating electrical impedance gradients from the series of electrical impedance measurements to generate a series of electrical impedance gradients, wherein calculating the electrical impedance gradients includes calculating gradients of a real part and gradients of an imaginary part of the series of electrical impedance measurements, wherein the electrical impedance gradients are calculated with respect to one of the measurement frequency (f s), a logarithm of the measurement frequency (f s), or the index (s) of the elements of the series of electrical impedance measurements, and determining a battery state of the electrochemical battery using computational means configured to receive as inputs at least the series of electrical impedance gradients, wherein the series of calculated electrical impedance gradients is provided to the computational means, wherein the computational means receives and processes at least the provided series of calculated electrical impedance gradients to generate therefrom at least one output signal representing a battery state associated with the electrochemical battery, wherein the computational means include artificial neural network means configured to receive as inputs at least the series of electrical impedance gradients. calculating electrical impedance gradients from the series of electrical impedance measurements to generate a series of electrical impedance gradients, wherein calculating the electrical impedance gradients includes calculating gradients of a real part and gradients of an imaginary part of the series of electrical impedance measurements, wherein the electrical impedance gradients are calculated with respect to one of the measurement frequency (f s), a logarithm of the measurement frequency (f s), or the index (s) of the elements of the series of electrical impedance measurements, and determining a battery state of the electrochemical battery using computational means configured to receive as inputs at least the series of electrical impedance gradients, wherein the series of calculated electrical impedance gradients is provided to the computational means, wherein the computational means receives and processes at least the provided series of calculated electrical impedance gradients to generate therefrom at least one output signal representing a battery state associated with the electrochemical battery, wherein the computational means include artificial neural network means configured to receive as inputs at least the series of electrical impedance gradients.