## 1 Introduction
To enhance the autonomous navigation capability of the deep space probes, many FEKF integrated navigation methods based on multiple measurement models have been proposed [34]. [PERSON] et al. [35] applied the XNAV and ultraviolet sensor to measure the position, velocity, and attitude of the deep space probe. The researchers also designed the FEKF integrated navigation system based on the X-ray pulsar and ultraviolet sensor, and the system could perform clock time prediction, attitude determination, and orbit determination concurrently during the deep space probe in-orbit flight. It could supply high-precision error state estimations. In order to eliminate the influence of the unstable solar spectra on Doppler velocity measurements and given that Doppler difference navigation might accumulate position errors over time, [PERSON] et al. [36] combined the solar Doppler difference velocity measurement and the XNAV method to propose integrated X-ray pulsar/Doppler differential velocity measurement navigation based on FEKF for deep space exploration. This method has high robustness for Doppler velocity measurement deviation brought by the solar spectral instability and also ensures high-accuracy state estimation of the deep space probe in orbit. The intelligent autonomous navigation algorithm combined with the reinforcement \(Q\)-learning algorithm has been favored by researchers at present [37]. In particular, it hasa very good application in estimating the accuracy of in-orbit spacecraft, providing high precision for spacecraft navigation systems [38]. [PERSON] et al. [39] proposed the state error estimation algorithm that combines the reinforcement \(Q\)-learning algorithm and the EKF and tried to use reinforcement learning (RL) to restrain the influence of the uncertain noise error covariance matrix on the estimation performance of the EKF navigation algorithm, in which the covariance adaptive adjustment strategy based on \(Q\)-learning was designed to enhance the state estimation performance of the autonomous nonlinear navigation systems for the spacecraft. In addition, they also adopted the astronomical integrated navigation based on an ultraviolet earth sensor and optical interferometer and introduced QLEKF to integrate the information from the two measurements to estimate the position, velocity, and attitude state error of the spacecraft [40]. They also assessed the optical path delay bias in the optical interferometer, and the proposed QLEKF demonstrates superior estimation performance compared to the conventional EKF. [PERSON] et al. [41] adopted RL to enhance the position estimation of the spacecraft and proposed the state estimation algorithm based on the combination of RL and the Kalman filter to acquire the optimal solution of the state and observation noise covariance, which improved the PVSE accuracy for the spacecraft navigation. [PERSON] et al. [42] recently developed an improved \(Q\)-learning EKF optical autonomous navigation based on their own previous research by measuring the line of sight (LOS) direction of the non-cooperative spacecraft targets, which improved the PVSE precision of the spacecraft navigation based on the space target LOS by fine-tunning the process noise error covariance matrix filtering parameters. Based on the above research conducted by others, this paper presents a combined navigation scheme based on the X-ray pulsar and two-dimensional Doppler velocity measurements to improve the high accuracy of autonomous integrated navigation for the SSBE cruise phase, which can make up for the accumulated position estimation error in the Doppler velocity measurements. The FEKF algorithm is designed to correct the position information obtained from the two-dimensional Doppler velocity-measuring in real-time by the position information estimation of the XNAV, and eliminate the accumulated position errors caused by Doppler velocity-measuring at the same time.