Methods of operating a control system of a vehicle and vehicle systems

A vehicle system, comprising:

• a longitudinal accelerometer adapted to sense an acceleration of a vehicle and to provide an output signal including a vehicle acceleration component, a gravity component, and a bias offset component;
• a speed sensor adapted to sense a vehicle speed and to provide an output signal including a wheel speed component;
• and
• a controller in operable communication with the longitudinal accelerometer and the speed sensor and adapted to (1) receive a first output signal from the longitudinal accelerometer while the vehicle is subjected to a first travel condition, the first travel condition including a first vehicle speed of the vehicle and a first road grade, wherein the first vehicle speed is a substantially constant speed, the first road grade is substantially equal to zero, and the first output signal represents a first measurement including a first vehicle acceleration component and a bias offset component, (2) receive a second output signal from the longitudinal accelerometer while the vehicle is subjected to a second travel condition, the second travel condition including a second vehicle speed of the vehicle and a second road grade, wherein the second output signal represents a second measurement including a second vehicle acceleration component and the bias offset component, (3) subtract the bias offset component from the second output signal to obtain an intermediate longitudinal acceleration output signal, and (4) determine a first gravity component included in the intermediate longitudinal acceleration output signal by calculating a derivative of a wheel speed component included in a third measurement represented by a first output signal from a wheel speed sensor and calculating a difference between the intermediate longitudinal acceleration and the derivative of the wheel speed component, wherein the difference of represents the first gravity component.