Study on the observability analysis based on the trace of error covariance matrix for spacecraft autonomous navigation

In this paper, observability analysis methods for navigation system are considered. The relationships between observability Grammian matrix, error covariance matrix, and fisher information matrix are established. It is shown that the rank of fisher information matrix can be used to test observability and additional measurements can increase the degree of observability. At last, new bounds of trace of error covariance matrix and fisher information matrix are derived, which implies that the bounds of degree of observability can be predicted without implementing the Kalman filter.