# GPS is used to determine the attitude and relative position of formation constellation

Where is the phase difference between the main antenna m and antenna j of the satellite i to the GPS satellite fc, and the unit vector from the satellite * to the line of sight of the GPS satellite fc (calculated using the pseudo-range positioning value of the satellite main antenna), is from The transformation matrix from the body coordinate system of the satellite i to the geocentric inertial coordinate system (ECEI) is the baseline vector formed by the main antenna m and the antenna j of the satellite i in the body coordinate system, A is the carrier wave length of the GPS signal, which is a single difference Weekly ambiguity.

Let the coordinate transformation matrix of the satellite i's body coordinate system to the local horizontal coordinate system (NED, the coordinates pointing to north, east, and earth) be, among them, s, also be the three attitude angles of satellite i, which is the coordinate system around The elementary transformation matrix of rotation angle.

The coordinate transformation matrix of the local horizontal coordinate system to the geocentric inertial coordinate system is called, which are respectively the right ascension and declination of the satellite's center of mass (calculated by the pseudorange positioning value of the satellite's main antenna).

Then, the transformation matrix from the satellite i's body coordinate system to the geocentric inertial coordinate system is the double-difference mathematical model of inter-satellite CDGPS. It is assumed that the formation constellation is composed of 3 satellites, with the main antennas of satellites 1, 2 and satellites 1, 3 The linearly independent inter-satellite single-difference equations that make up the synchronous observation are: Aim2, A are the phase difference between the main antennas of satellites 1, 2 and 1, 3 respectively to the GPS satellite, and Slfcl is the main antenna rm of the satellite 1 to the GPS satellite Unit vector of the line of sight direction (can be calculated from the pseudorange positioning value of the main antenna of satellite 1), n2 and t13 are the difference between the receiver clock difference of satellite 1 and satellites 2 and 3, c is the speed of light; Bmim2 and Bmim3 are satellite 1 The main antennas of the main antenna mi and the main antenna m2 of the satellite 2 and the main antenna of the satellite 3 constitute the baseline vector, ami, am2, am3 are the main antennas m :, m2, and m3 of the satellites 1, 2, and 3 in their respective body coordinate systems. The position vector in (a: i 2/1 further composes the main antennas of each satellite into an inter-satellite double-difference, the equation is the combination of all single and double-difference equations, where e is the error correction number, which is the satellite to GPS The position vector of St, Min, is the main antenna of satellite 1, satellite i The line-of-sight unit vectors to the GPS satellites are calculated from the pseudorange positioning results.

2.4 The solution method (11) formula reflects the adjustment problem of a GPS carrier phase measurement network (space network). In order to avoid rank deficit in its normal equation, the positioning criterion of the network must be given. There are two options to choose from: one is to select a point in the network as the origin; the other is not to specify a certain point as the origin, but to assign certain weights to the absolute coordinate values â€‹â€‹of all points in the network and participate in the adjustment The number of orbits for T (main antenna), T, T and T GPS satellites are taken from. The receiver carrier phase measurement noise, antenna phase center error, and multipath effect error are generally 2mm, 5mm, and 5mm respectively Yan Ye, Xi Xiaoning, and Ren Xuan. Using inter-satellite ranging to achieve satellite network autonomous positioning, Journal of Space Science, 2000, 20 (1): 54-60 1 Space Science and Technology Youth Fund (8632.00.2), National Natural Science Foundation (10072076) co-funded project 2001-08 -09 received manuscript, 2002-01-31 received revised manuscript

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