An apparatus and method for compensation of the effects of various bias errors encountered by inertial rate gyroscopes, particularly vibrating element gyroscopes, configured to detect heading relative to true north. Certain embodiments are suitable for reducing rotational dynamic errors associated with rotating gyroscopes. Other embodiments may include compensation of biases not related to rotational dynamics, such as thermal drift. The various methods disclosed may also account for the bias by sampling the rotational vector of the earth at an arbitrary heading, and at a heading that is 180° offset from the arbitrary heading. The sequence may be repeated numerous times to compensate for bias drift. The bias drift may be constant with respect to time (linear) or changing over time (non-linear) during the data acquisition sequence. Some embodiments include methods that utilize data from accelerometers to infer the bank and elevation angles as well as earth latitude location relative to the equator.