An agricultural implement includes a sensor supported on the frame. The sensor, in turn, is configured to emit output signals for refection off of a field surface of a field and detect reflections of the output signals as return signals. Moreover, the agricultural implement includes a computing system communicatively coupled to the sensor. In this respect, the computing system configured to receive data associated with the detected reflections from the sensor and fit a line or plane to received data. In addition, the computing system is configured to determine at least one of an orientation of the frame or a distance between the frame and the field surface based on the fitted line or plane.