## Structured condition number and its application in celestial navigation system with variable observability degree

In the traditional observability analysis methods, much attention is paid to the accuracy of the condition number. However, the authors find the fact that besides the accuracy, the structure of condition numbers is important, such as their range and sequence. A structured condition number method is proposed, which includes the double-reciprocal condition number and the compensation based on the continuous period. As the condition number is in non-linear relation with the navigation error, the mean of condition numbers does not reflect the navigation performance accurately. To solve this problem, the double-reciprocal condition number is proposed, where the impact of a large condition number is small. Considering the fact that the longer the continuous period is, the worse the navigation performance is, the authors develop the compensation method based on the continuous period. Amending the double-reciprocal condition number with the continuous period-based compensation, the authors propose the structured condition number which possesses the advantages of them, and apply it into the celestial direction measurement-based integrated navigation systems which have sharply variable observability degree. The simulation results demonstrate that the structured condition number can reflect the navigation performance and select a proper navigation star effectively.