to measure the esr of a battery, all you need is a load resistor, compare the unloaded voltage to the loaded voltage, and you can calculate the value of its esr by V=IR, or in your case ESR = Vdroop/I,
really thats the best way to do it, batteries esr is also dynamic, so if you really wanted to characterise it, you would need to record it at points across its discharge curve, as the lower the voltage the higher the ESR (because its based on a chemical reaction)