1. A system 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 system comprising: a sensor configured to generate a first signal indicative of an output variable of the battery; and a computer operably coupled to the sensor, the computer configured to determine 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, the computer further configured to determine 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, the computer further configured to determine 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, the computer further configured to determine 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, the computer further configured to determine 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, the computer further configured to determine a battery output vector based on the first signal, the computer further configured to determine 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, the computer further configured to determine 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.