## 1 Introduction
The radial velocity of the probe relative to the navigation stellar objects can be calculated based on the Doppler frequency offset of the probe with respect to the stellar object, and then the velocity state of the probe can be estimated. [PERSON] et al. [23] adopted Doppler measurements generated by the relative motion of the spacecraft and Sun as the key measurement, which realized the autonomous navigation of the spacecraft for deep space exploration, but the positioning accuracy is not particularly high. [PERSON] et al. [24] introduced the celestial navigation algorithm assisted by the differential Doppler measurements, which used the difference between Doppler radial velocity measured in two adjacent observation periods as the measured value to mitigate the effects of solar spectrum frequency instability and enhance autonomous celestial navigation accuracy. Since deep space probes operate in long-endurance, highly dynamic, and extreme environments, it is difficult for the single navigation pattern to satisfy the navigation demands of excellent accuracy and great dependability for the deep space probe. The integrated navigation formed by the combination of multiple navigation modes is an irresistible trend for deep space exploration navigation systems in the future. [PERSON] et al. [25] proposed an autonomous integrated navigation scheme based on Doppler/XNAV, and the Doppler autonomous navigation provides high-accuracy velocity error estimation information by measuring the radial velocity information relative to the Sun. The complementary of the two navigation methods can make up for the problem of low-accuracy navigation caused by shrinking the pulse signal receiving area size for the X-ray pulsar detection sensor. [PERSON] et al. [26] used the stability of the solar Doppler differential navigation to put forward the solar time difference of arrival (TDOA)/Doppler difference joint observation and integrate it with Mars angle navigation. This approach allows fully observable Mars angle and solar light joint observation navigation, providing higher accuracy and stability of the navigation. [PERSON] et al. [27] proposed the integrated navigation scheme based on the X-ray pulsars and Doppler to advance the error estimation precision of the probe during the final approach phase entry state of Mars exploration, and the navigation scheme adopted the X-ray pulsar observations and Doppler velocity measurements to complement each other to eliminate the problem of the reduced velocity state estimation performance of the XNAV for this phase. During the design of the autonomous navigation system for the SSBE cruise phase, compared with other filtering estimators [28; 29], the extended Kalman filter (EKF) is the preferred state estimator for the cruise phase navigation system because of the nonlinearity of the orbital dynamics model [30]. The EKF is widely used in various scenarios involving navigation systems and has a very stable navigation performance [31; 32]. This state estimation algorithm has also been favored by researchers from the field of astronomical autonomous navigation. In addition, for the navigation system, the measurement noise is usually based on the measurement error of the sensor used in actual tasks. The environment disturbances mainly come from micrometeoroids, cosmic rays, and solar wind in the space environment, which all have an impact on the navigation accuracy of the deep space probe, and it is necessary to set the noise according to the scene in the different phases during the simulation analysis. [PERSON] et al. [33] combined Doppler velocity measurements and the XNAV and proposed the integrated navigation method of the Doppler velocity measurements based on the double measurement model and X-ray pulsar. The EKF was used to achieve continuous high-accuracy state estimation, which effectively suppressed the accumulative state errors in the Doppler velocity measurements and improved the PVSE precision of the autonomous navigation system for the deep space exploration spacecraft.