Increasing of a microsatellite attitude determination accuracy by using several attitude matrix estimates
Batch attitude determination methods allow estimating angular position of a satellite based on two or more vector measurements in two different frames. The TRIAD algorithm is the simplest and fastest one among such methods. It uses information about exactly two direction vectors to obtain a satellite's attitude. In some cases using only two vectors can be an essential restriction but it is common in the of microsatellites. This type of satellites as a rule uses magnetometers and sun sensors to obtain an attitude. These sensors measure vector of Earth magnetic field induction and Sun direction vector respectively. Such approach to attitude determination of microsatellites is called "sun-mag" attitude determination. One of the main drawbacks of the TRIAD algorithm is the information derived by two sensors with different accuracies is taken into consideration equally. Thus an accuracy of attitude estimate derived by the TRIAD algorithm is sensitive to errors of the less accurate sensor. Also there is a group batch attitude determination methods which estimate an attitude by solving Wahba's problem. This problem consists in finding an attitude matrix in optimal way based on the least squares approach. The advantages of these methods are possibility to use more than two reference directions and using information about accuracy of measurements. In this paper two methods of combining attitude matrix estimates derived at some successive points of time by the TRIAD algorithm are considered. It is assumed that angular rates of a microsatellite are low. This is the case of stabilized motion of a spacecraft. The purpose of the combining is to reduce the sensitivity of the TRIAD algorithm to the random errors in direction vector measurements. The first method estimates an attitude matrix on the least squares approach while the second one uses averaging of some estimates. Moving average is used to accumulate attitude matrix estimates. In order to test introduced methods the angular motion of a spacecraft is established by prescribing an exact nominal Euler 3-2-1 angle motion. Rotation angles are extracted from the attitude matrix estimates derived by two methods mentioned above. Vectors of reference directions are modeled in accordance with the QUEST measurement model. Under the considered assumption two methods show equal results. Using of the methods allow reducing the sensitivity of the TRIAD algorithm. The presence or error caused by the satellite's rotation during the accumulation of attitude matrix estimates is pointed. This error can be reduced either the number of estimates which is used or by decreasing time between samples.