Methods and system for a battery

A method for monitoring a battery, comprising:

• measuring an elapsed time from a starting time;
• computing a remaining capacity of the battery;
• measuring a temperature of the battery;
• and
• computing an updated full charge capacity value based on:
• an initial full charge capacity value, wherein the initial full charge capacity value is a capacity of the battery at the starting time;
• a first fade ratio, wherein the first fade ratio is a function of the measured elapsed time;
• a second fade ratio, wherein the third fade ratio is a function of the measured temperature;
• and
• a third fade ratio, wherein the second fade ratio is a function of the computed remaining capacity.

A system, comprising:

• a battery;
• a temperature sensor to detect a temperature of the battery;
• and
• a fuel gauge circuit connected to the battery and the temperature sensor, and configured to:
• measure an elapsed time from a starting time;
• compute a remaining capacity of the battery at the elapsed time;
• measure a temperature of the battery at the elapsed time;
• compute an updated full charge capacity (UFCC) value at the elapsed time based on:
• known data of faded capacity values of the battery as a function of time, temperature, and remaining capacity;
• an initial full charge capacity (IFCC) value, wherein the IFCC value is a capacity of the battery at the starting time;
• the measured elapsed time;
• the computed remaining capacity;
• and
• the detected temperature;
• and
• estimate a state of health of the battery based on the computed UFCC value.