1. A method for determining an estimated battery state vector and an estimated battery parameter vector, the estimated battery state vector being indicative of a state of a battery at a first predetermined time, the estimated battery parameter vector being indicative of a parameter of the battery at the first predetermined time, the method comprising: determining a plurality of estimated augmented battery state vectors that are indicative of a state of the battery, a battery input noise, a sensor noise associated with a sensor measuring a battery output variable, an uncertainty of the state of the battery, an uncertainty of the battery input noise, and an uncertainty of the sensor noise at a second predetermined time prior to the first predetermined time; determining a plurality of predicted battery state vectors that are indicative of the state of the battery and an uncertainty of the state of the battery at the first predetermined time based on the plurality of estimated augmented battery state vectors; determining a plurality of predicted battery parameter vectors that are indicative of the parameter of the battery and an uncertainty of the parameter of the battery at the first predetermined time; determining a first plurality of predicted battery output vectors that are indicative of at least one output variable of the battery and an uncertainty of the output variable at the first predetermined time based on the plurality of predicted battery parameter vectors; determining a second plurality of predicted battery output vectors that are indicative of at least one output variable of the battery and the uncertainty of the output variable at the first predetermined time based on the plurality of estimated augmented battery state vectors and the plurality of predicted battery state vectors; determining a battery output vector having at least one measured value of a battery output variable obtained at the first predetermined time; determining an estimated battery parameter vector indicative of the parameter of the battery at the first predetermined time based on the plurality of predicted battery parameter vectors, the first plurality of predicted battery output vectors, and the battery output vector; and determining an estimated battery state vector indicative of the state of the battery at the first predetermined time based on the plurality of predicted battery state vectors, the second plurality of predicted battery output vectors, and the battery output vector.