A method of maintaining a phased array antenna of an earth bound device pointed at a satellite, the method comprising; (a) obtaining a first position in an earth centered coordinate system, ECCS, of the earth bound device by reading global positioning system coordinates of the phased array antenna; (b) looking up a second position in the ECCS of the satellite based on a stored model of satellite location as a function of time; (c) determining (1014, 1016) an angle of arrival expressed within a local earth coordinate system, LECS, of a signal from the satellite to the phased array antenna based on i) the second position of the satellite looked up in said step (b), ii) the first position of the phased antenna array of the earth bound device obtained in said step (a), and iii) an orientation of the earth bound device; (d) determining an estimated direction in a vehicle coordinate system, VCS, of a local vector quantity at the first position of the phased array antenna of the earth bound device and for determining said orientation using locally sensed values at the earth bound device chosen from the group consisting of a direction of gravity, a direction to a celestial object, and magnetism of the earth; (e) performing a local search using the angle of arrival estimate in the VCS determined in said step (d) to find a pointing angle of the phased array antenna having a highest gain and said orientation; (f) determining an orientation of the phased array antenna in the LECS based on the angle of arrival expressed within the LECS of the signal coming from the satellite determined in said step (c) and the estimated direction of the vector quantity determined in said step (d); (g) correcting the orientation of the antenna array in the LECS determined in said step (f) using the angle of arrival in the LECS determined in said step (c) to produce a corrected orientation of the antenna array in the LECS; (h) translating the corrected orientation of the phased array antenna in the LECS into a pointing direction of the antenna array within the VCS; and (i) pointing the antenna array to the pointing direction within the VCS. (a) obtaining a first position in an earth centered coordinate system, ECCS, of the earth bound device by reading global positioning system coordinates of the phased array antenna; (b) looking up a second position in the ECCS of the satellite based on a stored model of satellite location as a function of time; (c) determining (1014, 1016) an angle of arrival expressed within a local earth coordinate system, LECS, of a signal from the satellite to the phased array antenna based on i) the second position of the satellite looked up in said step (b), ii) the first position of the phased antenna array of the earth bound device obtained in said step (a), and iii) an orientation of the earth bound device; (d) determining an estimated direction in a vehicle coordinate system, VCS, of a local vector quantity at the first position of the phased array antenna of the earth bound device and for determining said orientation using locally sensed values at the earth bound device chosen from the group consisting of a direction of gravity, a direction to a celestial object, and magnetism of the earth; (e) performing a local search using the angle of arrival estimate in the VCS determined in said step (d) to find a pointing angle of the phased array antenna having a highest gain and said orientation; (f) determining an orientation of the phased array antenna in the LECS based on the angle of arrival expressed within the LECS of the signal coming from the satellite determined in said step (c) and the estimated direction of the vector quantity determined in said step (d); (g) correcting the orientation of the antenna array in the LECS determined in said step (f) using the angle of arrival in the LECS determined in said step (c) to produce a corrected orientation of the antenna array in the LECS; (h) translating the corrected orientation of the phased array antenna in the LECS into a pointing direction of the antenna array within the VCS; and (i) pointing the antenna array to the pointing direction within the VCS.