Device for charging an electrical storage battery comprising a filtering stage, which is intended to be connected to an electrical network, a voltage buck stage, which is connected to the filtering stage, and a voltage boost stage, which is coupled to the voltage buck stage and is intended to be connected to an electrical storage battery, said charging device comprising a system for controlling the voltage buck and boost stages (18, 26) of the charging device, said filtering stage including two inputs, to each of which there are connected two parallel branches, one of which includes a series assembly of a first inductor and a resistor, and the other one of which includes a second inductor, an output capacitor of the filtering stage being connected between the nodes common to the branches that are connected in parallel, characterized in that the control system comprises: - a voltage and current measurement module, - a first observer, which is connected to said measurement module and uses a Kalman filter, for observing at least two state variables (x i), said state variables comprising an output voltage (V F) of the filtering stage and a current (i 2) flowing through an inductor of said filtering stage, said observer being capable of transmitting the estimated state variables to a control generation module, and - a phase-locked loop, which is connected to said voltage and current measurement module, generating a sinusoidal signal that has the same frequency and phase as the first harmonic of the voltage of said electrical network (V R) and is connected both to a second observer, which uses a Kalman filter and is capable of estimating a derivative of the voltage of said electrical network (V R), the output of said second observer being connected to a low-pass filter, an output of which is connected to said control generation module, and to a differentiator, which is capable of calculating the first derivative and the second derivative of a setpoint current of the electrical network, and the output of which is connected to said control generation module, said control generation module being capable of generating the control functions (u, z) for controlling the voltage buck and boost stages so as to regulate the charging current (i n) according to a charging current setpoint while limiting the harmonic content of the current (i R) delivered by the network to its fundamental. - a voltage and current measurement module, - a first observer, which is connected to said measurement module and uses a Kalman filter, for observing at least two state variables (x i), said state variables comprising an output voltage (V F) of the filtering stage and a current (i 2) flowing through an inductor of said filtering stage, said observer being capable of transmitting the estimated state variables to a control generation module, and - a phase-locked loop, which is connected to said voltage and current measurement module, generating a sinusoidal signal that has the same frequency and phase as the first harmonic of the voltage of said electrical network (V R) and is connected both to a second observer, which uses a Kalman filter and is capable of estimating a derivative of the voltage of said electrical network (V R), the output of said second observer being connected to a low-pass filter, an output of which is connected to said control generation module, and to a differentiator, which is capable of calculating the first derivative and the second derivative of a setpoint current of the electrical network, and the output of which is connected to said control generation module,