A combined navigation method for a spacecraft using pulsar and starlight refraction

Abstract

The present invention relates to a combined pulsar / starlight refraction navigation method for spacecraft. A navigation system state model of the spacecraft is established according to the Earth orbit dynamics equation; a combined detector of an X-ray detector and a star sensor is used to obtain the pulse arrival time of the pulsar and the starlight refraction angle of the star. A position measurement model is established based on the relationship between the pulse arrival time and the starlight refraction angle and the position of the spacecraft respectively; an implicit UKF filtering method and a BP neural network information fusion method are used to synthesize the data results of the two astronomical navigation methods of pulsar and starlight refraction and suppress the influence of random errors to obtain higher navigation accuracy. The navigation estimation accuracy of the present invention is high and it is applicable to the autonomous navigation of spacecraft. The present invention belongs to the field of space navigation technology and can provide reference for the design of spacecraft navigation systems.

Description

Technical Field

[0001] The present invention belongs to the technical field of aerospace navigation, and particularly relates to a method for combined navigation of a spacecraft using pulsars and starlight refraction. Background Art

[0002] At present, the main navigation method for spacecraft is a combined navigation method that combines inertial navigation (INS) and global navigation satellite system (GNSS). In this combined navigation method, GNSS is used to correct the errors generated by INS navigation. In ordinary low-speed and non-confrontational application scenarios, this navigation method can achieve sufficient navigation accuracy. This combined navigation method depends on the normal and efficient operation of the GNSS system. However, in the context of adversarial navigation warfare, considering that the GNSS system may be affected, resulting in reduced accuracy or even severe damage, the aircraft using this navigation method will lose its autonomous navigation ability. Compared with satellite navigation, celestial navigation has relatively high navigation accuracy and better autonomy, which is an urgently needed navigation method for the development of spacecraft.

[0003] According to different sensitive methods, the celestial navigation methods for spacecraft can be divided into two methods: directly sensitive to the horizon plane and indirectly sensitive to the horizon plane by using starlight refraction. The basic principle of the autonomous celestial navigation method that is directly sensitive to the horizon plane is to use a star sensor to observe navigation stars and obtain the direction of the starlight of the star in the satellite body coordinate system through coordinate transformation, and use an earth sensor or a space sextant to measure the geocentric direction or the horizon direction, and then calculate the direction of the geocentric vector in the satellite body coordinate system. According to the geometric relationship between the satellite, the observed navigation star and the earth, combined with the orbit dynamics model and filtering technology, the autonomous navigation of the spacecraft is realized. This navigation method uses the existing sensors on the spacecraft (such as star sensors and earth sensors) as navigation sensors, and has the advantages of low cost, mature technology and good reliability. However, the accuracy of the geocentric vector directly measured by the earth sensor is relatively low, resulting in limited accuracy of this autonomous navigation method.

[0004] The starlight refraction indirect sensitive horizon method is a low-cost and high-precision satellite autonomous navigation method developed in the early 1980s of the 20th century. It uses a high-precision star sensor to measure the refraction information of starlight when passing through the Earth's atmosphere, and indirectly obtains the horizon information through the mathematical model of refracted starlight in the atmosphere (atmospheric refraction model), thereby realizing the autonomous navigation and positioning of the satellite. Compared with the direct sensitive horizon method, the biggest advantage of the autonomous navigation method based on starlight refraction is that it can complete autonomous navigation only with a star sensor, and the navigation accuracy is not limited by the measurement accuracy of the Earth sensor. However, there are still many theoretical problems and key technologies to be solved for the starlight refraction navigation method to be applied in engineering in our country. The direct measurement information of starlight refraction autonomous navigation is the starlight refraction angle. In practical applications, it is first necessary to ensure that the star sensor can capture and accurately identify the refracted star, and then obtain the refraction angle. That is, the installation of the star sensor and the acquisition of the refraction angle are one of the problems to be solved. In addition, the selection and optimization of navigation observation quantities also need to be studied.

[0005] Pulsars are neutron stars with high-speed rotation, and their X-ray radiation has extremely high-precision periodicity. Pulsar navigation is a process of using the X-ray detector carried by the aircraft to measure the pulse phase and star angle position of the pulsar, and then through the corresponding signal data processing to determine the parameters such as the position, speed, and attitude of the aircraft. The problem with pulsar navigation is that the accuracy of pure pulsar navigation highly depends on the precise measurement of the pulse time. If there is a measurement error outside the allowable range of the pulse time, it will affect the navigation accuracy.

[0006] Kalman filtering (KF) is a linear optimal recursive filtering algorithm developed in the 1960s of the last century. It was initially only applicable to linear systems. With the development of the need to solve nonlinear problems, filtering methods such as extended Kalman filtering (EKF) and Unscented Kalman filtering (UKF) have been gradually proposed and continuously developed. Usually, the measurement models in the KF algorithm all have explicit expressions. However, in many practical problems, the constraints of the state quantity and the measurement quantity are often implicit, and it is difficult or impossible to obtain an explicit measurement model. Such problems are the so-called implicit measurement model filtering problems. The measurement models of the pulsar and starlight refraction navigation systems are such implicit measurement models, and Kalman filtering methods for implicit measurement models are required in the filtering solution. Summary of the Invention

[0007] To overcome the technical difficulty that the starlight refraction-based autonomous navigation cannot perform navigation solution when there is no navigation star, and to overcome the problem of insufficient navigation accuracy caused by time measurement error in pulsar autonomous navigation, the present invention provides a spacecraft pulsar / starlight refraction navigation method, which combines the data of the two navigation methods by means of information fusion, checks each other, and improves the accuracy of the navigation system.

[0008] The technical solution adopted by the present invention to solve its technical problems is as follows:

[0009] A combined pulsar / stellar refraction navigation method for spacecraft, comprising the following steps:

[0010] ① Establish a navigation system state equation based on the orbital dynamics equation of the spacecraft in the Earth's orbit;

[0011] ② Measure the arrival time of pulsar pulses using an X-ray detector, and measure the arrival time of pulsar pulses using an on-board X-ray detector , predict the time of arrival of the same pulse at the origin of the navigation coordinate system using the pulse phase model , and use the time difference to perform system measurement model calculation;

[0012] ③ Respectively establish and calculate the measurement models of the pulsar navigation and stellar refraction navigation systems;

[0013] ④ Adopt an implicit UKF filtering method and a BP neural network information fusion method to synthesize the calculation results of the two navigation methods of pulsar and stellar refraction to improve the system accuracy.

[0014] Further, the step ① includes: considering the gravitational force of the Earth's centroid and the perturbation of the Earth's gravitational field, and equivalently treating the perturbation influence factors of the sun and moon gravitational forces, solar radiation pressure, and atmospheric drag as Gaussian white noise to obtain the state model of the spacecraft in the geocentric inertial coordinate system:

[0015] (1)

[0016]

[0017] In the formula, , are the positions and velocities of the spacecraft in the three directions respectively, is the geocentric gravitational constant, is the Earth's gravitational coefficient, is the Earth's radius; is the numerical magnitude of the position vector of the spacecraft in the geocentric inertial coordinate system, is the comprehensive influence of the high-order perturbation terms of the Earth's non-spherical perturbation and the perturbations of the sun, moon, solar radiation, and atmosphere;

[0018] All variables in formula (1) are variables related to time , and are abbreviated as:

[0019] (2)

[0020] In the formula, is the state variable, is The differentiation with respect to time, is the system's non-linear continuous state transition function, and is the perturbation influence parameter.

[0021] Furthermore, step ③ includes:

[0022] (1) Establishment of the measurement model for the pulsar navigation system: Taking the time of arrival of the pulsar as the observable, considering that the measurement error has a constant error and a random error, the measurement model is expressed as:

[0023] (4)

[0024] In the formula, is the time when the pulsar pulse arrives at the origin of the solar system barycentric coordinate system, is the position vector of the spacecraft relative to the solar system barycentric coordinate system; is the unit vector in the line-of-sight direction of the pulsar; is the position vector of the solar system barycenter in the heliocentric coordinate system ; is the position vector of the pulsar in the heliocentric coordinate system ; respectively represent the magnitudes of the vectors ; is the solar gravitational constant; is the constant measurement error of the time of arrival of the pulsar; is the random measurement error of the time of arrival of the pulsar; is the position vector of the spacecraft relative to the Earth's equatorial inertial coordinate system; is the position vector of the origin of the Earth's equatorial inertial system in the solar system barycentric coordinate system; c is the speed of light in a vacuum;

[0025] (2) Establishment of the measurement model for the starlight refraction navigation system: The essence of establishing the measurement model based on the refraction angle is to construct the functional relationship between the refraction angle and the satellite position. The apparent altitude is expressed as a function of the refraction angle :

[0026] (6)

[0027] The geometric relationship between

[0028] and the satellite position is expressed by the following formula:

[0029] In the formula, ,  is the position vector of the spacecraft in the geocentric inertial coordinate system, is the unit vector of the unrefracted starlight in the inertial frame, 1 is a very small amount and is ignored; if ,but , formula (7) is transformed into:

[0030] (8)

[0031] After solving the above problems together, the refraction angle measurement expression of the starlight refraction navigation system is finally expressed as:

[0032] (9)

[0033] In the formula, is the refraction angle acquisition error, including the measurement error and the model calculation error implied by equation (7).

[0034] Furthermore, the step ④ comprises:

[0035] (1) The state equation of the navigation system is as shown in equation (2). Assume that the covariance matrix of the system state model is ; The measurement model of the pulsar / starlight refraction navigation system is in the form of the following standard observation equation:

[0036] (twenty four)

[0037] In the formula, represents the observed quantity, is a nonlinear observation function, is the measurement noise, and the covariance matrix of the observation noise is , ;

[0038] (2) When a refracting star appears, the BP neural network information fusion method is used to fuse pulsar navigation and starlight refraction navigation: For the pulsar / starlight refraction combined navigation system, the implicit UKF filter is used to process the X-ray detector and star sensor observation data respectively; the filtering results of the two sub-filters are the combined navigation results of pulsar navigation and starlight refraction navigation obtained under the implicit UKF method; on this basis, a neural network fuser is designed using the filtering results of the two sub-filters and their respective error estimates as input, and the output value is the navigation result of the final combined navigation system.

[0039] (3) Beneficial effects:

[0040] In the prior art, pulsar navigation technology is usually used as an independent navigation method to establish an autonomous navigation system. In practical applications, due to some technical limitations, the navigation accuracy achievable by individual pulsar navigation is limited. Among the many methods for improving the accuracy of the navigation system, establishing a combined navigation system is a low-cost and efficient option. The present invention uses the relatively mature indirect sensitive horizon starlight refraction astronomical navigation method in the existing technology and the emerging pulsar navigation method to establish a combined navigation system. Specifically, the pulsar navigation technology is used to make up for the drawback that the indirect sensitive horizon method cannot guarantee real-time observation of navigation stars, and the indirect sensitive horizon method is also used to further improve the navigation accuracy of pulsar navigation. The advantages of the two complement each other. In addition, the present invention abandons the original information fusion method and instead uses the BP neural network information fusion method. The advantage of this method is that at the information fusion level, the entire state vector is no longer used as the statistical object, but the statistical object is refined to each state variable, so as to obtain a higher-precision fusion result. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a flowchart of the pulsar / starlight refraction combined astronomical navigation method for spacecraft of the present invention.

[0042] Figure 2 It is a schematic diagram of starlight refraction navigation in the present invention.

[0043] Figure 3 It is a schematic diagram of pulsar navigation in the present invention.

[0044] Figure 4 It is an algorithm block diagram of the pulsar / starlight refraction combined astronomical navigation method for spacecraft of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0045] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0046] As Figure 1, as shown in Figure 4, the spacecraft pulsar / starlight refraction combined astronomical navigation method of the present invention establishes a navigation system state model of the spacecraft according to the earth orbit dynamics equation; uses an X-ray detector and a double star sensor combined detector to obtain the pulsar pulse arrival time and the starlight refraction angle, and respectively establishes a position measurement model based on the relationship between the pulse arrival time and the starlight refraction angle and the position of the spacecraft; adopts an implicit UKF filtering method and a BP neural network information fusion method to synthesize the data results of the two astronomical navigation methods of pulsar and starlight refraction, and suppresses the influence of random errors to obtain higher navigation accuracy. The specific implementation method is as follows:

[0047] Step 1. Establish a state equation based on the spacecraft navigation system:

[0048] First, initialize the position and velocity, and set the state variables , to be the positions and velocities of the three axes of the spacecraft in the geocentric inertial coordinate system respectively. According to the orbit design of the spacecraft, select the initial values of the position and velocity of the spacecraft .

[0049] Mainly considering the earth's centroid gravity and the perturbation of the earth's gravitational field, and equivalenting other perturbation factors such as the sun and moon gravity, solar radiation pressure and atmospheric drag to Gaussian white noise, the state model of the spacecraft can be obtained:

[0050] (1)

[0051] ;

[0052] In the formula, , are the positions and velocities of the spacecraft in the three directions respectively, is the geocentric gravitational constant, is the earth's gravitational coefficient, is the earth's radius; is the numerical magnitude of the position vector of the spacecraft in the geocentric inertial coordinate system, is the influence of the high-order perturbation term of the earth's non-spherical perturbation and the perturbation forces such as the sun and moon perturbation, solar perturbation and atmospheric perturbation.

[0053] All variables in formula (1) are variables related to time , and can be abbreviated as:

[0054] (2)

[0055] In the formula, is the state variable, is the differential with respect to time, is the system non-linear continuous state transfer function, is the perturbation influence parameter;

[0056] Step 2: Measure the arrival time of the pulsar pulse using an X-ray detector, that is, measure the arrival time of the pulsar pulse using an on-board X-ray detector , predict the time when the same pulse arrives at the origin of the navigation coordinate system using the pulse phase model , use the obtained time difference , the position vector of the spacecraft relative to the barycentric coordinate system of the solar system The projection in the direction of the unit vector in the line of sight of the pulsar can be expressed as:

[0057] (3)

[0058] In the formula, is the speed of light in vacuum. Based on this basic principle, the subsequent pulsar navigation measurement model can be established.

[0059] Step 3: Establishment of the system measurement model. Establish the measurement models of the pulsar navigation and starlight refraction navigation systems respectively, and use the implicit UKF filtering method to improve the system accuracy and calculate the position coordinates of the spacecraft. The specific steps are as follows:

[0060] (1) Establishment of the pulsar navigation system measurement model: As Figure 3 shown, taking the pulse arrival time as the observable, considering that the measurement error has a constant error and a random error, the measurement model can be expressed as:

[0061] (4)

[0062] In the formula, is the time when the pulsar pulse arrives at the origin of the barycentric coordinate system of the solar system, is the position vector of the spacecraft relative to the barycentric coordinate system of the solar system; is the unit vector in the line of sight of the pulsar; is the position vector of the barycenter of the solar system in the heliocentric coordinate system ; is the magnitude of the position vector of the pulsar in the heliocentric coordinate system ; respectively represent the magnitudes of the vectors ; is the solar gravitational constant; is the constant measurement error of the pulse arrival time; is the random measurement error of the pulse arrival time; is the position vector of the spacecraft relative to the Earth's equatorial inertial coordinate system; ​is the position vector of the origin of the Earth's equatorial inertial system in the solar system's mass center coordinate system. By inductively transforming the form of equation (4), we obtain the implicit function form expression:

[0063] (5)

[0064] (2) Establishment of the measurement model of the starlight refraction navigation system: Figure 2 As shown in the figure, the establishment of the measurement model based on the refraction angle is essentially to construct a functional relationship between the refraction angle and the position of the spacecraft, depending on the altitude. It can be expressed as the refraction angle Function:

[0065] (6)

[0066] In the formula, The geometric relationship with the satellite position can be expressed as follows:

[0067] (7)

[0068] In the formula, , is the position vector of the spacecraft in the geocentric inertial coordinate system, is the unit vector of the unrefracted starlight in the inertial frame, 1 is a very small amount and can usually be ignored. ,but , formula (7) can be transformed into:

[0069] (8)

[0070] Solve the problem together. Finally, the implicit function form of the refraction angle of the starlight refraction navigation system can be expressed as:

[0071] (9)

[0072] In the formula, The error in obtaining the refraction angle includes the measurement error and the model calculation error implied by equation (7).

[0073] Step 4: Use the implicit UKF filtering method and the BP neural network information fusion method to combine the calculation results of the two navigation methods to improve the system accuracy.

[0074] The present invention uses a new implicit measurement model filtering method, namely Implicit UKF method. The Implicit UKF method constructs an explicit measurement model, regards the zero vector as an equivalent measurement, and transmits equivalent measurement noise based on UT transformation.

[0075] The following first introduces the construction process of the explicit measurement model. Perform a first-order Taylor expansion at this point and ignore the Lagrange remainder term, we can obtain:

[0076] (10)

[0077] wherein, can be calculated according to Equation (11).

[0078] (11)

[0079] Note that according to the measurement equation, is equal to 0. If the parameters in are formally omitted, Equation (10) can be rewritten as:

[0080] (12)

[0081] wherein, the equation is an explicit equation, is the partial derivative of with respect to , is the measurement noise.

[0082] Therefore, an equivalent explicit measurement model is obtained, as shown in Equation (12). The zero vector can be regarded as the equivalent measurement quantity, and at the same time is regarded as the equivalent measurement noise, and its error covariance matrix can be obtained by the following UT transformation.

[0083] The following introduces the transfer process of the measurement noise based on the UT transformation. At time k, the error covariance matrices of the measurement quantity and its noise are set as and . The error covariance matrix of the equivalent measurement can be obtained through Sigma points. First, these Sigma points are obtained by the following formula:

[0084] (13)

[0085] wherein, is the dimension of the measurement quantity , is the scaling parameter, represents the i-th column vector of the matrix square root , is the weight of the i-th Sigma point.

[0086] The new Sigma points can be calculated from the above Sigma points according to Equation (14) as follows

[0087] (14)

[0088] The calculation of the Sigma points for measurement prediction and the error covariance matrix of the equivalent measurement is as follows:

[0089] (15)

[0090] (16)

[0091] Since the main difficulty of the implicit measurement model lies in how to perform measurement update, the main difference between the classical UKF and Implicit UKF is mainly in the measurement update step.

[0092] The specific algorithm of Implicit UKF is as follows:

[0093] (1)Initialization conditions

[0094] Initialize the state variables and their covariance matrix.

[0095] (2)Time update

[0096] The time update step is the same as the corresponding step in the UKF method.

[0097] (3)Measurement update

[0098] The Sigma points for measurement prediction are calculated according to the following formula:

[0099] (17)

[0100] where is the measurement obtained at time k, is the predicted value of the Sigma point.

[0101] Since the predicted value of the obtained Sigma point is not the true state at time k, that is, Equation (17) is not equal to its true value 0 either. This provides error information about the state estimate and can be used to correct the state variables.

[0102] Then, the predicted value of the measurement can be calculated as:

[0103] (18)

[0104] The corresponding error covariance matrix can be obtained from the following formula:

[0105] (19)

[0106] (20)

[0107] wherein is the measured predicted value, is the point measurement variance matrix, is the point measurement and state covariance matrix, is the covariance matrix of the equivalent measurement error obtained according to Equation (16).

[0108] The filtering gain matrix , the updated state quantity and the corresponding covariance matrix can be calculated respectively by the same method in UKF:

[0109] (21)

[0110] (22)

[0111] (23)

[0112] The state equation of the navigation system is as shown in Equation (2). Let the covariance matrix of the system state model be . After organizing the pulsar / stellar refraction navigation system measurement model according to the above Implicit UKF method, it is written in the following standard observation equation form:

[0113] (24)

[0114] wherein, represents the observed quantity, is the non-linear observation function, is the measurement noise. Let the covariance matrices of the observation noise be respectively , .

[0115] When the refraction star appears, the following BP neural network information fusion method is used: For the pulsar / stellar refraction integrated navigation system, the UKF filter is used to process the observation data of the X-ray detector and the star sensor respectively. The filtering results of the two sub-filters are the integrated navigation results of pulsar navigation and stellar refraction navigation obtained by the UKF method. On this basis, using the filtering results of the 2 sub-filters and their respective error estimates as input quantities, a neural network fusion device is designed, and the output value is the navigation result of the final integrated navigation system.

[0116] The present invention uses a BP neural network to construct a neural network information fusion device, and this neural network information fusion device is a multi-input multi-output system. The specific input data includes:

[0117] (1) The state vector output by the pulsar navigation sub-filter, with a total of 6 elements. These inputs represent the navigation estimates of the pulsar navigation subsystem for the satellite position and velocity states;

[0118] (2) The error covariance determinant output by the pulsar navigation sub-filter, with a total of 1 element. It represents the navigation accuracy of the pulsar navigation subsystem.

[0119] (3) The state vector output by the starlight refraction navigation sub-filter, with a total of 6 elements. These inputs represent the navigation estimates of the starlight refraction navigation subsystem for the satellite position and velocity states;

[0120] (4) The error covariance determinant output by the starlight refraction navigation sub-filter, with a total of 1 element. It represents the navigation accuracy of the starlight refraction navigation subsystem;

[0121] The specific output data is the navigation state vector calculated by the neural network, with a total of 6 elements. It represents the final navigation estimates of the integrated navigation system for the spacecraft position and velocity states.

[0122] The content not described in detail in the specification of the present invention belongs to the prior art well-known to those skilled in the art. It is easy for those skilled in the art to understand that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A spacecraft pulsar / starlight refraction combined navigation method, It is characterized in that The steps include: ① Establish the navigation system state equation based on the spacecraft orbital dynamics equation of the Earth orbit; ②Measure the arrival time of pulsar pulses using an X-ray detector, and measure the arrival time of pulsar pulses using an on-board X-ray detector , predict the time when the same pulse arrives at the origin of the navigation coordinate system using a pulse phase model , and use the time difference to perform system measurement model calculations; ③ Establish the measurement models of pulsar navigation and starlight refraction navigation systems and perform calculations, including: (1) Establishment of the measurement model of the pulsar navigation system: Taking the pulse arrival time as the observed quantity and considering that the measurement error includes constant error and random error, the measurement model can be expressed as: （4） wherein, is the time when the pulsar pulse arrives at the origin of the solar system barycentric coordinate system, is the position vector of the spacecraft relative to the solar system barycentric coordinate system; is the unit vector in the line-of-sight direction of the pulsar; is the position vector of the solar system barycenter in the heliocentric coordinate system ; is the position vector of the pulsar in the heliocentric coordinate system ; respectively represent the magnitudes of the vectors ; is the solar gravitational constant; is the constant measurement error of the pulse arrival time; is the random measurement error of the pulse arrival time; is the position vector of the spacecraft in the geocentric inertial coordinate system; is the position vector of the origin of the Earth's equatorial inertial system in the solar system barycentric coordinate system; c is the speed of light in vacuum; (2) Establishment of the measurement model of the starlight refraction navigation system: The essence of establishing the measurement model based on the refraction angle is to construct the functional relationship between the refraction angle and the satellite position, and the apparent altitude is expressed as a function of the refraction angle : （6） The geometric relationship with the satellite position is expressed by the following formula: （7） In the formula, , is the position vector of the spacecraft in the geocentric inertial coordinate system, is the unit vector of the unrefracted starlight in the inertial system, 1 is a very small quantity and is neglected; If we let , then , and Equation (7) is transformed into: （8） Solve them together, and finally, the expression for measuring the refraction angle of the starlight refraction navigation system is expressed as: （9） In the formula, is the error in obtaining the refraction angle, including the measurement error and the model calculation error implied by Equation (7); ④The implicit UKF filtering method and BP neural network information fusion method are used to integrate the calculation results of pulsar and starlight refraction navigation methods to improve the system accuracy.

2. The spacecraft pulsar / starlight refraction combined navigation method according to claim 1, Features: The step ① includes: considering the gravity of the Earth's center of mass and the perturbation of the Earth's gravitational field, equating the perturbation influencing factors of the Sun-Moon gravity, solar light pressure and atmospheric resistance to Gaussian white noise, and obtaining the state model of the spacecraft in the Earth's center inertial coordinate system: （1） In the formula, , are respectively the position and velocity of the spacecraft in three directions, is the geocentric gravitational constant, is the Earth's gravitational coefficient, is the Earth's radius; is the numerical magnitude of the position vector of the spacecraft in the geocentric inertial coordinate system, is the comprehensive influence of the high-order perturbation terms of the Earth's non-spherical perturbation, the perturbations of the sun, moon, and the perturbations of the sun and the atmosphere; Each variable in Equation (1) is a variable related to time and is abbreviated as: （2） In the formula, is the state variable, is the differential with respect to time, is the system non-linear continuous state transition function, is the perturbation influence parameter.

3. The spacecraft pulsar / starlight refraction combined navigation method according to claim 2, Features: The step ④ comprises: (1) The state equation of the navigation system is as shown in Equation (2). Let the covariance matrix of the system state model be ; The measurement model of the pulsar / stellar refraction navigation system is in the form of the following standard observation equation: （24） In the formula, represents the observable quantity, is the non-linear observation function, is the measurement noise, and the covariance matrices of the observation noises are respectively , ; (2) When a refraction star appears, the BP neural network information fusion method is used to fuse pulsar navigation and starlight refraction navigation: For the pulsar / starlight refraction combined navigation system, the implicit UKF filter is used to process the X-ray detector and star sensor observation data respectively; the filtering results of the two sub-filters are the combined navigation results of pulsar navigation and starlight refraction navigation obtained under the implicit UKF method; on this basis, a neural network fuser is designed using the filtering results of the two sub-filters and their respective error estimates as input, and the output value is the navigation result of the final combined navigation system.

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