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 thecondition number. However, the authors find the fact that besides the accuracy,the structure of condition numbers is important, such as their range andsequence. A structured condition number method is proposed, which includes thedouble‐reciprocal condition number and the compensation based on the continuousperiod. As the condition number is in non‐linear relation with the navigationerror, the mean of condition numbers does not reflect the navigation performanceaccurately. To solve this problem, the double‐reciprocal condition number isproposed, where the impact of a large condition number is small. Considering thefact that the longer the continuous period is, the worse the navigationperformance is, the authors develop the compensation method based on thecontinuous period. Amending the double‐reciprocal condition number with thecontinuous period‐based compensation, the authors propose the structuredcondition number which possesses the advantages of them, and apply it into thecelestial direction measurement‐based integrated navigation systems which havesharply variable observability degree. The simulation results demonstrate thatthe structured condition number can reflect the navigation performance andselect a proper navigation star effectively.