A Novel Inertial Coarse Alignment Method

2This paper proposes an estimator for the initial alignment of a ship strapdown inertial attitude reference system using only IMU measurements for static alignment and IMU measurements with GPS aiding for moving-base alignment. The proposed estimator does not require an initial attitude input and, unlike several current techniques, is effective with large initial attitude errors. The estimator is based on the decomposition of the attitude quaternion into separate earth motion, inertial rate and alignment quaternions. The alignment quaternion is estimated using a minimum variance fit between measured gravitational accelerations and known navigation frame accelerations using solutions to Wahba’s problem. An algebraic expression for the covariance of the resulting attitude estimate as a function of the variance of the navigation frame velocity disturbances is developed and it is shown that resulting attitude covariance estimate can minimised by correctly ordering input velocity data. It is further shown, for a manoeuvring vehicle, that a continuous estimate of the attitude estimate covariance can be generated from the IMU data. Results are presented for static and quasi-static alignment using inertial sensors only and for full in-motion alignment using navigation frame GPS velocity and position aiding. Nomenclature b-frame = Orthogonal reference frame aligned with the orthogonal IMU axis set n-frame = Orthogonal reference frame aligned with the NED navigation axis set e-frame = Earth Centred Earth Fixed (ECEF) orthogonal reference frame i-frame = Earth Centred Inertially Fixed (ECIF) orthogonal reference frame b0-frame = Orthogonal reference frame non-rotating relative to the i-frame n0-frame = Orthogonal reference frame non-rotating relative to the i-frame n b C = Direction cosine matrix representing rotational transform between the b- and n-frames. n b q = Unit quaternion representing rotational transform between the b- and n-frames. n l g = Local gravitational acceleration vector expressed in n-frame. n e v = Velocity vector relative to the earth expressed in the n-frame. 0 n v  = Change of velocity vector expressed in the n0-frame. b i f = Measured inertial acceleration vector expressed in th e b-frame. 0 b i  = Measured inertial angular rate vector expressed in the b0-frame. e  = Geographic latitude. e  = Geographic Longitude. e  = Earth rotation rate.