A battery system, comprising: a battery management system (BMS.); and a secondary battery, comprising: (a) a cathode comprising a first cathode material and a second cathode material, wherein the first and second cathode materials have different operating voltage ranges; (b) an anode comprising an anode material; and (c) a separator, wherein the BMS is electrically connected to the secondary battery and is configured to detect a voltage profile representing a voltage relaxation during operation of the battery system, said voltage relaxation including the transfer of operating ions between the first and second cathode materials when the secondary state comes to an idle state or a no-load state, and estimate a state of the secondary battery corresponding to the voltage profile by using a voltage estimating model derived from the circuit model wherein the circuit model includes: an anode material circuit unit comprising an open-circuit voltage, component changing according to a state of charge of the anode material based on a pre-defined correlation (OCV a (z a [k]) between the open-circuit voltage and the state of charge (z a [k]) of the anode material and an impedance voltage component of the anode material; a cathode material circuit unit connected with the anode material circuit in series and comprising a first cathode materials circuit unit comprising an open-circuit voltage component changing according to a state of charge of the first cathode material based on a pre-defined correlation (OCV c1 (z c1 [k])) between the open circuit voltage component and the state of charge (z c1 [k]) of the first cathode materials and an impedance voltage combonent of the first cathode material and a second cathode material circuit unit connected with the first cathode material circuit in parallel and comprising an open-circuit voltage component changing according to a state of charge of the second cathode material based on a pre-defined correlation (OCVc 2 (z c2 [k])) between the open circuit voltage component and the state of charge of the second cathode material and an impedance voltage component of the second cathode material; and a resistance component (R 0_relax) being proportional to a capacity (1-z c2) of operating ions intercalated into the second cathode material and inversely proportional to a residual capacity (Z c1) of the first cathode material capable of receiving operating ions when the secondary state comes to an idle state or a no-load state and connected in series between the first cathode material circuit unit and the second cathode material circuit unit. a battery management system (BMS.); and a secondary battery, comprising: (a) a cathode comprising a first cathode material and a second cathode material, wherein the first and second cathode materials have different operating voltage ranges; (b) an anode comprising an anode material; and (c) a separator, an anode material circuit unit comprising an open-circuit voltage, component changing according to a state of charge of the anode material based on a pre-defined correlation (OCV a (z a [k]) between the open-circuit voltage and the state of charge (z a [k]) of the anode material and an impedance voltage component of the anode material; a cathode material circuit unit connected with the anode material circuit in series and comprising a first cathode materials circuit unit comprising an open-circuit voltage component changing according to a state of charge of the first cathode material based on a pre-defined correlation (OCV c1 (z c1 [k])) between the open circuit voltage component and the state of charge (z c1 [k]) of the first cathode materials and an impedance voltage combonent of the first cathode material and a second cathode material circuit unit connected with the first cathode material circuit in parallel and comprising an open-circuit voltage component changing according to a state of charge of the second cathode material based on a pre-defined correlation (OCVc 2 (z c2 [k])) between the open circuit voltage component and the state of charge of the second cathode material and an impedance voltage component of the second cathode material; and a resistance component (R 0_relax) being proportional to a capacity (1-z c2) of operating ions intercalated into the second cathode material and inversely proportional to a residual capacity (Z c1) of the first cathode material capable of receiving operating ions when the secondary state comes to an idle state or a no-load state and connected in series between the first cathode material circuit unit and the second cathode material circuit unit.