Abstract
The analysis of the observability of system states is very important in the design of an optimal filter estimation algorithm. A relative attitude estimation algorithm is developed based on a stereo vision system and a gyroscope, and the observability of this algorithm is studied. First, we build the error model of the relative attitude determination system. Second, the observability of every state of the filter is studied. Third, by choosing different variables as the states of the error model, the unobservable subspace of the system is confirmed. Furthermore, the system structural decomposition reveals that this type of relative attitude determination system can only determine the relative attitude between the deputy and the chief and that their gyro drift errors are unobservable. In addition, the structural decomposition also tells us that when the feature points measured by the stereo vision system are greater than two, increasing the number of feature points provides little benefit for improving the observability of the gyro drift errors. Considering the incomplete observability of the original system, the star sensor is added into the system to enable it to be completely observable. The final simulation result indicates that after adding the star sensor, the system, which becomes completely observable, can estimate the body attitude, the relative attitude and the gyro error while providing improved accuracy.
Highlights
To form a constellation with small satellites, the relative attitude among each of the satellites must be determined independently
The purpose of this paper is to study the observability of the relative attitude determination system based on stereo vision
Under the assumption that the former two stages are accomplished by a stereo vision system, this paper only considers the situation in which the coordinate values of the feature points are given by the stereo vision system
Summary
To form a constellation with small satellites, the relative attitude among each of the satellites must be determined independently. The optimal filter estimation algorithm can evaluate the attitude parameters of a small satellite and the uncertain parameters in the observations. In this way, we can use smaller and cheaper sensors to achieve higher relative attitude determination accuracy. Maessen and Gill (2012) presented an investigation of the relative state estimation and observability for two formation flying satellites using two different relative navigation sensor sets. When applying the PWCS theory to the relative attitude determination system based on stereo vision system with gyros, the observability of every state in the filter cannot be evaluated clearly. The purpose of this paper is to study the observability of the relative attitude determination system based on stereo vision.
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