1. A battery internal state estimating apparatus that detects a discharge current flowing from a battery to a load including at least an electric motor for starting up an engine and estimates an internal state of the battery based on an equivalent circuit model of the battery as applied on the discharge current, comprising: a memory that stores computer executable instructions corresponding to implementation of the equivalent circuit model comprising a resistance element corresponding to an internal resistance of the battery, the resistance element having a resistance value variable on specification of an inputted parameter; a storing section that stores a plurality of parameters of the equivalent circuit model; a physical detecting section that detects the discharge current flowing from the battery to the load, wherein the load includes at least an electric motor for starting up an engine; a selecting section that selects a parameter indicating a resistance value of the resistance element to be subjected to adaptive learning based on a value of the discharge current detected by the detecting section, wherein the selecting section selects the parameter indicating the resistance value of the resistance element when a peak current which flows at a start-up of the electric motor is detected by the detection section; an adaptive learning section that performs adaptive learning on the parameter indicating the resistance value of the resistance element selected by the selecting section; updating the resistance value of the resistance element of the circuit model, wherein the resistance value of the resistance element is updated in accordance with the adaptive learning and wherein the internal state of the battery is estimated based at least partly on the updated resistance value of the resistance element; and initiating transmission of a signal indicative of the updated resistance value, wherein the signal is used to update the resistance value of the battery.