The error estimation of X-ray pulsar navigation in circular orbit

The posterior covariance matrix of the Kalman filter, whose lower bound is commonly estimated by Posterior Cramer-Rao Bound (PCRB), reflects the accuracy of the filter result. For X-ray Pulsar Navigation (XPNAV) system with linear measurement equations, this paper proves the calculating process of PCRB is the same as iterative calculating the posterior covariance matrix directly. Besides that, this paper estimates the error of XPNAV in circular orbit based on solving Riccati equation by Schur decomposition, which is more efficient and simpler than the iterative algorithm. Simulation results validate the effectiveness of the proposed method.