Relativistic navigation reference bias calibration method based on fusion of star and pulsar information

Abstract

A kind of relative navigation reference deviation calibration method of star and pulsar information fusion is disclosed, which comprises the following steps: configuring a star angular distance measuring sensor and an X-ray detector on a spacecraft; observing stars by the star angular distance measuring sensor to extract navigation information contained in two kinds of relativistic effects, i.e., star aberration caused by the movement of the spacecraft and light deflection caused by celestial gravitational field; observing pulsars by the X-ray detector to obtain pulse arrival time difference observations; combining spacecraft and earth orbit dynamics model to predict the state; processing star angular distance and pulse arrival time difference observations by an extended Kalman filter to correct the state prediction value, and obtaining the estimation of the spacecraft position and velocity, the geocenter position and velocity, and the sensor system error parameters, so as to realize the calibration of two kinds of reference deviations, i.e., earth ephemeris error and sensor system error. The present application provides a new way to improve the performance of relativistic navigation system.

Description

Technical Field

[0001] This invention relates to a relativistic navigation reference deviation calibration method based on the fusion of stellar and pulsar information, belonging to the field of navigation and guidance technology. Background Technology

[0002] Astronomical navigation based on natural celestial observations is a traditional technical means to achieve autonomous navigation of spacecraft, including "starlight + horizon" and X-ray pulsars. The navigation accuracy verified in orbit can only reach the km level, and it is difficult to break through the positioning accuracy level of hundreds of meters.

[0003] The fundamental method of relativistic navigation involves observing stars in different sky regions using multi-aperture stellar angular distance measurement sensors. This yields stellar angular distance observations correlated with stellar aberration and gravitational deflection of light. Based on this, navigation filters process the stellar angular distance observations, and combined with spacecraft orbital dynamics models, the spacecraft's position, velocity, and other motion states are estimated. Relativistic navigation technology can be used for Earth-orbiting communication, navigation, and remote sensing satellite platforms, as well as for lunar spacecraft. It maintains autonomous spacecraft operation without ground station / GNSS (Global Navigation Satellite System) support, providing input information for configuration maintenance, trajectory planning, and maneuver control. Relativistic navigation reference deviations include sensor systematic errors and Earth ephemeris errors. Due to factors such as the space environment, systematic errors exist in the stellar angular distance observations obtained through multi-aperture stellar angular distance measurement sensors, leading to a degraded performance of the relativistic navigation system. However, the relativistic navigation data processing requires the velocity information of the Earth's center relative to the solar system's center of mass. Due to current measurement technology limitations, the geocentric velocity calculated from Earth ephemeris contains errors, adversely affecting the accuracy of relativistic navigation. Reference deviation is one of the main sources of error in relativistic navigation systems, and existing technologies in this field cannot effectively solve the problem of relativistic navigation reference deviation calibration. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and address the issue of reference deviations (including sensor system errors and Earth ephemeris errors) affecting the performance of relativistic navigation systems. It provides a relativistic navigation reference deviation calibration method based on the fusion of stellar and pulsar information, which can be used for Earth orbit spacecraft and can also be extended to deep space exploration missions, and has important application value.

[0005] The technical solution of this invention is: Firstly, a method for calibrating relativistic navigation reference deviations by fusing stellar and pulsar information is provided, wherein:

[0006] S1 uses an extended Kalman filter as the navigation filter and initializes it, setting the initial values ​​of the state vectors that characterize the position and velocity of the Earth orbiting spacecraft relative to the Earth's center, the position and velocity of the Earth's center relative to the solar system's center of mass, and the sensor system error parameters.

[0007] S2 predicts the position and velocity of the spacecraft relative to the Earth's center based on the orbital dynamics model of the Earth orbiting spacecraft and obtains the corresponding predicted values. Based on the Earth's orbital dynamics model, it predicts the position and velocity of the Earth's center relative to the center of mass of the solar system and obtains the corresponding predicted values.

[0008] S3 observes stars and obtains stellar angular distance measurements using a stellar angular distance measurement sensor mounted on an Earth-orbiting spacecraft.

[0009] S4 If the stellar angular distance observation is available, substitute the stellar angular distance observation obtained in step S3 into the extended Kalman filter for calculation, and correct the predicted values ​​of the spacecraft's position and velocity relative to the Earth's center, the predicted values ​​of the Earth's position and velocity relative to the solar system's center of mass, and the sensor system error parameters obtained in step S2.

[0010] S5 observes pulsars using an X-ray detector mounted on an Earth-orbiting spacecraft, obtaining the pulse arrival time difference of the pulsars.

[0011] S6 If the pulse arrival time difference observation is available, substitute the pulse arrival time difference observation obtained in step S5 into the extended Kalman filter for calculation, and correct the predicted values ​​of the spacecraft's position and velocity relative to the Earth's center, the predicted values ​​of the Earth's center's position and velocity relative to the solar system's center of mass, and the sensor system error parameters obtained in step S2.

[0012] S7 returns to step S2 for iteration. When the statistical value of the filtered information is less than a given threshold, the iteration stops. The estimated values ​​of the spacecraft's position and velocity relative to the Earth's center, the Earth's position and velocity relative to the solar system's center of mass, and the estimated values ​​of the sensor system error parameters are obtained, thereby completing the relativistic navigation reference deviation calibration of stellar and pulsar information fusion.

[0013] Preferably, the method for initializing the extended Kalman filter as the navigation filter in step S1 is as follows: set the state vector estimate of the extended Kalman filter at the initial time k=0. for:

[0014]

[0015] in, and These represent the estimated values ​​of the position vector and velocity vector of the Earth-orbiting spacecraft relative to the Earth's center at the initial moment, respectively. and These represent the estimated values ​​of the position vector and velocity vector of the Earth's center relative to the center of mass of the solar system at the initial moment, respectively. This represents the estimated value of the sensor's system error parameter at the initial moment. It is obtained based on prior knowledge of the position and velocity of Earth-orbiting spacecraft, the position and velocity of the Earth's center relative to the solar system's center of mass, and the system error parameters of the stellar angular distance measurement sensor.

[0016] Preferably, the method for predicting the spacecraft's position and velocity relative to the Earth's center, and the position and velocity of the Earth's center relative to the solar system's center of mass in step S2, is as follows: the state vector prediction value of the extended Kalman filter at time k. Calculate according to the following formula:

[0017]

[0018] State transition function The form is:

[0019]

[0020] Where τ represents the time step of prediction in the extended Kalman filter, and the subscript k represents different times. Represents the state vector estimate of the extended Kalman filter at time k-1; nonlinear function The form is:

[0021]

[0022] in, This represents the estimated velocity vector of the Earth-orbiting spacecraft relative to the Earth's center at time k-1. This represents the estimated position vector of the Earth-orbiting spacecraft relative to the Earth's center at time k-1. This represents the estimated velocity vector of the Earth relative to the center of mass of the solar system at time k-1. μ represents the estimated position vector of the Earth's center relative to the center of mass of the solar system at time k-1. E Represents the Earth's gravitational constant. This represents the known spacecraft orbital perturbation function, obtained from the spacecraft's orbital dynamics model, μ. S Represents the solar gravitational constant. This represents the known Earth orbit perturbation function, obtained from the Earth's orbital dynamics model, where m represents the number of sensor system error parameters.

[0023] Preferably, in step S3, the stellar angular distance observation yS,k The calculation method is as follows:

[0024]

[0025] in, Let y represent the angular distance observation of the i-th star at time k, where i = 1, 2, ..., m. S,k It is obtained by observing stars through a star angular distance measurement sensor installed on a spacecraft in Earth orbit.

[0026] Preferably, the method for correcting the predicted values ​​of the spacecraft's position and velocity relative to the Earth's center, the predicted values ​​of the Earth's position and velocity relative to the solar system's center of mass, and the sensor system error parameters in step S4 is as follows:

[0027]

[0028] in, This represents the state vector estimate of the extended Kalman filter at time k. y represents the predicted state vector of the extended Kalman filter at time k. S,k K represents the angular distance observation of stars. S,k The Kalman gain matrix, representing the corresponding stellar angular distance observation, is calculated based on a pre-established relativistic navigation system model. The observation function... The form is:

[0029]

[0030] in, (i = 1, 2, ..., m) represents the angular distance observation corresponding to the i-th star. The observation function is of the following form:

[0031]

[0032]

[0033] Among them, u I ′ Ak and u I ′ Bk This represents the projection of the stellar line-of-sight vector measured by a stationary observer onto an inertial coordinate system. It can be calculated from a pre-established stellar catalog. The subscripts A and B are used to distinguish different stars, and c represents the speed of light. and They represent Predicted values ​​for the velocity of a spacecraft in medium Earth orbit, the geocentric velocity, and the error parameters of the sensor system.

[0034] Preferably, in step S5, the pulse arrival time difference observation y X,k for:

[0035]

[0036] in, Let y represent the observation of the arrival time difference of the j-th pulse at time k, where j = 1, 2, ..., n. X,k Pulsars are observed using X-ray detectors mounted on Earth-orbiting spacecraft and compared with pre-established pulsar timing models.

[0037] Preferably, the method for correcting the predicted values ​​of the spacecraft's position and velocity relative to the Earth's center, the predicted values ​​of the Earth's position and velocity relative to the solar system's center of mass, and the sensor system error parameters in step S6 is as follows:

[0038]

[0039] in, K represents the predicted state vector of the extended Kalman filter at time k. X,k The Kalman gain matrix, representing the observation of the time difference of arrival of the corresponding pulse, is calculated based on a pre-established pulsar navigation system model. X,k The observation function represents the pulse arrival time difference observation. The form is:

[0040]

[0041] in, (j = 1, 2, ..., n) represents the angular distance observation corresponding to the j-th star. The observation function is of the following form:

[0042]

[0043] Where, n (j) This represents the line-of-sight vector of the j-th pulsar. denoted by , represents the distance from the solar system's barycenter to the j-th pulsar, which can be calculated from a pre-established pulsar star catalog. 'b' represents the position vector of the solar system's barycenter relative to the center of the Sun, which can be calculated from a pre-established solar ephemeris. and They represent Predicted positions of spacecraft in medium Earth orbit and their geocentric positions, μ s This represents the solar gravitational constant.

[0044] Preferably, the recursive calculation method for the statistical value of the filtered innovation in step S7 is as follows:

[0045]

[0046] Among them, S k s represents the statistical value of the filtered innovation at time k. k-1 This represents the statistical value of the filtered innovation at time k-1. The initial value S0 of the statistical value of the filtered innovation is set to a positive constant greater than a specified threshold, and l represents the total number of sampled data in the pre-specified time window. The filtered information is represented by the following method:

[0047]

[0048] The method for determining that the statistical value of the filtered innovation is less than a given threshold is: if

[0049]

[0050] Then, it is determined that the statistical value of the filtered innovation is less than a given threshold, where, For a given threshold, it can be preset according to the accuracy index of the stellar angular distance measurement sensor.

[0051] Secondly, a relativistic navigation reference deviation calibration system based on the fusion of stellar and pulsar information is provided, characterized by comprising:

[0052] State initialization module: Initializes the extended Kalman filter, which serves as the navigation filter, and sets the initial values ​​of the state vector representing the position and velocity of the Earth orbiting spacecraft relative to the Earth's center, the position and velocity of the Earth's center relative to the solar system's center of mass, and the sensor system error parameters.

[0053] State prediction module: Based on the orbital dynamics model of the spacecraft orbiting the Earth, predict the position and velocity of the spacecraft relative to the Earth's center, and based on the Earth's orbital dynamics model, predict the position and velocity of the Earth's center relative to the center of mass of the solar system.

[0054] Stellar observation module: Observes stars on the celestial sphere through a stellar angular distance measurement sensor configured on an Earth orbiting spacecraft. Utilizes a multi-aperture optical system on the stellar angular distance measurement sensor to observe multiple stars and obtain the angle between the stellar line-of-sight vectors, i.e., the stellar angular distance observation measurement.

[0055] The correction module based on stellar observations: When the stellar angular distance observations of the stellar angular distance measurement sensor are available, the stellar angular distance observations are processed by an extended Kalman filter to correct the predicted values ​​of the spacecraft's position and velocity relative to the Earth's center, the predicted values ​​of the Earth's position and velocity relative to the solar system's center of mass, and the sensor's system error parameters.

[0056] Pulsar observation module: Pulsars are observed using an X-ray detector on an Earth-orbiting spacecraft. Multiple pulsars are observed using a multi-aperture optical system on the X-ray detector to obtain the difference between the time it takes for the pulse signal emitted by the pulsar to reach the center of the solar system and the time it takes to reach the spacecraft, i.e., the pulse arrival time difference observation.

[0057] The correction module based on pulsar observations: When the pulse arrival time difference observations of the X-ray detector are available, the pulse arrival time difference observations are processed by an extended Kalman filter to correct the predicted values ​​of the spacecraft's position and velocity relative to the Earth's center, the predicted values ​​of the Earth's position and velocity relative to the solar system's center of mass, and the sensor system error parameters.

[0058] Compared with the prior art, the present invention has the following advantages:

[0059] (1) This invention expresses the position and velocity of the geocenter relative to the solar system's center of mass, as well as the error parameters of the stellar angular distance measurement sensor system, in the form of a state vector in the model, and establishes a benchmark deviation calibration model. By expanding the state dimension of the navigation filter, it lays the foundation for implementing geocenter position and velocity estimation and sensor system error parameter identification, effectively solves the problem of relativistic navigation benchmark deviation calibration, and achieves the effect of accurate benchmark deviation estimation and effective compensation.

[0060] (2) This invention introduces pulsar measurement information into the relativistic navigation system. Pulsars are observed by X-ray detectors to provide auxiliary measurement information for on-orbit calibration of the reference deviation. The observations of stellar angular distance and pulse arrival time are fused, and the state vector is accurately estimated by using an extended Kalman filter. This effectively suppresses the influence of the reference deviation, improves the performance of the relativistic navigation system, and achieves navigation and positioning accuracy at the level of hundreds of meters. Attached Figure Description

[0061] Figure 1 This is an overall flowchart of the present invention;

[0062] Figure 2 This is a graph showing the spacecraft position estimation error curve based on the fusion of stellar and pulsar information in an embodiment of the present invention.

[0063] Figure 3 This is a graph showing the spacecraft velocity estimation error curve obtained by fusing stellar and pulsar information according to an embodiment of the present invention.

[0064] Figure 4 This is a graph showing the geocentric position estimation error curve of stellar and pulsar information fusion according to an embodiment of the present invention.

[0065] Figure 5 This is a graph showing the geocentric velocity estimation error curve of stellar and pulsar information fusion according to an embodiment of the present invention.

[0066] Figure 6 This is a system error parameter estimation error curve for the fusion of stellar and pulsar information in an embodiment of the present invention. Detailed Implementation

[0067] The specific embodiments of the present invention will now be described in further detail with reference to the accompanying drawings.

[0068] This invention addresses the issue of relativistic navigation system performance being susceptible to reference deviations. It proposes a relativistic navigation reference deviation calibration method that fuses stellar and pulsar information. This method integrates stellar angular distance observations provided by a stellar angular distance measurement sensor and pulse arrival time difference observations provided by an X-ray detector. Combined with a spacecraft orbital dynamics model, an extended Kalman filter based on a "prediction-correction" structure is designed to achieve accurate estimation of spacecraft position, velocity, and key model parameters used to characterize the reference deviation. This contributes to achieving long-term, high-precision autonomous navigation for spacecraft.

[0069] This invention proposes a relativistic navigation reference deviation calibration method based on the fusion of stellar and pulsar information, such as... Figure 1 As shown, the steps are as follows:

[0070] (1) Initialize the extended Kalman filter used as a navigation filter by setting initial values ​​for the state vectors representing the position and velocity of the Earth-orbiting spacecraft relative to the Earth, the position and velocity of the Earth relative to the center of mass of the solar system, and the sensor system error parameters. The method for initializing the extended Kalman filter as a navigation filter is as follows: set the estimated state vector value of the extended Kalman filter at the initial time k=0 as...

[0071]

[0072] in, and These represent the estimated values ​​of the position vector and velocity vector of the Earth-orbiting spacecraft relative to the Earth at the initial moment, respectively. and Let represent the estimated values ​​of the Earth's position vector and velocity vector relative to the center of mass of the solar system at the initial moment. This represents the estimated value of the sensor system error parameter at the initial time. It is obtained based on prior knowledge of the position and velocity of Earth-orbiting spacecraft, the position and velocity of Earth relative to the center of mass of the solar system, and the system error parameters of the stellar angular distance measurement sensor.

[0073] (2) Based on the orbital dynamics model of the Earth-orbiting spacecraft, the position and velocity of the spacecraft relative to the Earth's center are predicted; based on the Earth's orbital dynamics model, the position and velocity of the Earth relative to the center of mass of the solar system are predicted. The method for predicting the position and velocity of the spacecraft relative to the Earth's center and the position and velocity of the Earth relative to the center of mass of the solar system is as follows: The state vector prediction value of the extended Kalman filter at time k is calculated according to the following formula:

[0074]

[0075] State transition function The form is:

[0076]

[0077] Where τ represents the time step of prediction in one step of the extended Kalman filter, the subscript k is used to distinguish different times, and the nonlinear function... The form is

[0078]

[0079] Where, μ E Represents the Earth's gravitational constant. This represents the known spacecraft orbital perturbation function, obtained from the spacecraft's orbital dynamics model, μ. S Represents the solar gravitational constant. This represents the known Earth orbit perturbation function, obtained from the Earth's orbital dynamics model, where m represents the number of sensor system error parameters.

[0080] (3) Observations of stars on the celestial sphere are made using a stellar angular distance measurement sensor mounted on an Earth-orbiting spacecraft to obtain the stellar angular distance observation; the stellar angular distance observation of the stellar angular distance measurement sensor is...

[0081]

[0082] in, Let y represent the angular distance observation of the i-th star at time k, where i = 1, 2, ..., m. S,k It is obtained by observing stars through a star angular distance measurement sensor installed on a spacecraft in Earth orbit.

[0083] (4) When the stellar angular distance observations of the stellar angular distance measurement sensor are available, the stellar angular distance observations obtained in step (3) are processed by an extended Kalman filter to correct the predicted values ​​of the spacecraft's position and velocity relative to Earth, the Earth's position and velocity relative to the solar system's center of mass, and the sensor's system error parameters obtained in step (2). The method for correcting the predicted values ​​of the spacecraft's position and velocity relative to Earth, the Earth's position and velocity relative to the solar system's center of mass, and the sensor's system error parameters is as follows:

[0084]

[0085] in, K represents the state vector estimate of the extended Kalman filter at time k. S,k The Kalman gain matrix, representing the corresponding stellar angular distance observation, is calculated based on a pre-established relativistic navigation system model. The observation function... The form is

[0086]

[0087] in, (i = 1, 2, ..., m) represents the i-th observation. The observation function is of the form:

[0088]

[0089]

[0090] Among them, u I ′ Ak and u I ′ Bk This represents the projection of the stellar line-of-sight vector measured by a stationary observer onto an inertial coordinate system. It can be calculated from a pre-established stellar catalog. The subscripts A and B are used to distinguish different stars, and c represents the speed of light. and They represent Predicted values ​​for the velocity of spacecraft in medium Earth orbit, Earth velocity, and sensor system error parameters.

[0091] (5) Pulsars are observed using X-ray detectors mounted on Earth-orbiting spacecraft to obtain the pulse arrival time difference observable; the pulse arrival time difference observable of the X-ray detector is...

[0092]

[0093] in, Let y represent the observation of the arrival time difference of the j-th pulse at time k, where j = 1, 2, ..., n. X,k Pulsars are observed using X-ray detectors mounted on Earth-orbiting spacecraft and compared with pre-established pulsar timing models.

[0094] (6) When the pulse arrival time difference observable of the X-ray detector is available, the pulse arrival time difference observable obtained in step (5) is processed by an extended Kalman filter to correct the predicted values ​​of the spacecraft's position and velocity relative to the Earth, the Earth's position and velocity relative to the center of mass of the solar system, and the sensor system error parameters obtained in step (2). The method for correcting the predicted values ​​of the spacecraft's position and velocity relative to the Earth, the Earth's position and velocity relative to the center of mass of the solar system, and the sensor system error parameters is as follows:

[0095]

[0096] Among them, K X,k The Kalman gain matrix, representing the observation of the corresponding pulse arrival time difference, is calculated based on a pre-established pulsar navigation system model. The observation function... The form is

[0097]

[0098] in, (j = 1, 2, ..., n) represents the j-th observation. The observation function is of the form:

[0099]

[0100] Where, n (j) This represents the line-of-sight vector of the j-th pulsar. denoted by , represents the distance from the solar system's barycenter to the j-th pulsar, which can be calculated from a pre-established pulsar star catalog. 'b' represents the position vector of the solar system's barycenter relative to the center of the Sun, which can be calculated from a pre-established solar ephemeris. and They represent Predicted positions of spacecraft in medium Earth orbit and Earth's position.

[0101] (7) Repeat steps (2) to (6) to obtain the estimated values ​​of the spacecraft's position and velocity relative to the Earth, the estimated values ​​of the Earth's position and velocity relative to the center of mass of the solar system, and the estimated values ​​of the sensor system error parameters, thereby completing the relativistic navigation reference deviation calibration of stellar and pulsar information fusion.

[0102] Furthermore, this invention also proposes a relativistic navigation reference deviation calibration system based on the fusion of stellar and pulsar information, comprising:

[0103] State initialization module: Initializes the extended Kalman filter, which serves as the navigation filter, and sets the initial values ​​of the state vector representing the position and velocity of the Earth orbiting spacecraft relative to the Earth, the position and velocity of the Earth relative to the center of mass of the solar system, and the sensor system error parameters.

[0104] State prediction module: Based on the orbital dynamics model of the spacecraft orbiting the Earth, predict the position and velocity of the spacecraft relative to the Earth's center, and based on the Earth's orbital dynamics model, predict the position and velocity of the Earth relative to the center of mass of the solar system.

[0105] Stellar observation module: Observes stars on the celestial sphere through a stellar angular distance measurement sensor configured on an Earth orbiting spacecraft. Utilizes a multi-aperture optical system on the stellar angular distance measurement sensor to observe multiple stars and obtain the angle between the stellar line-of-sight vectors, i.e., the stellar angular distance observation measurement.

[0106] The correction module based on stellar observations: When the stellar angular distance observations of the stellar angular distance measurement sensor are available, the stellar angular distance observations are processed by an extended Kalman filter to correct the predicted values ​​of the spacecraft's position and velocity relative to Earth, the predicted values ​​of Earth's position and velocity relative to the center of mass of the solar system, and the sensor's system error parameters.

[0107] Pulsar observation module: Pulsars are observed using an X-ray detector on an Earth-orbiting spacecraft. Multiple pulsars are observed using a multi-aperture optical system on the X-ray detector to obtain the difference between the time it takes for the pulse signal emitted by the pulsar to reach the center of the solar system and the time it takes to reach the spacecraft, i.e., the pulse arrival time difference observation.

[0108] The correction module based on pulsar observations: When the pulse arrival time difference observations of the X-ray detector are available, the pulse arrival time difference observations are processed by an extended Kalman filter to correct the predicted values ​​of the spacecraft's position and velocity relative to Earth, the predicted values ​​of Earth's position and velocity relative to the center of mass of the solar system, and the sensor system error parameters.

[0109] This invention conducts research on the evolution of relativistic navigation errors, establishes a calibration model for relativistic navigation reference deviation, and designs a relativistic navigation reference deviation calibration method based on the fusion of stellar and pulsar information. By introducing auxiliary measurement information, reconstructing the navigation system model, and optimizing the navigation filter design, the influence of reference deviation is weakened, thereby improving the accuracy of relativistic navigation.

[0110] Example:

[0111] Taking autonomous navigation of a spacecraft in Earth orbit as an example, the effectiveness of the method described in this invention is verified through simulation. The spacecraft is assumed to be orbiting the Earth in a medium Earth orbit (MEO), maintaining a stable attitude relative to the Earth. The spacecraft is equipped with a stellar angular distance measurement sensor with stellar observation capabilities and an X-ray detector with pulsar observation capabilities. In the mathematical simulation, it is assumed that the standard deviation of the random angle measurement error of the stellar angular distance measurement sensor is 1 mas, the systematic error of the sensor is 0.5 mas, and the data update frequency is set to 0.1 Hz; the effective area of ​​the X-ray detector is 1 m². 2 Pointing observations were performed on three pulsars, B0531+21, B1821-24, and B1937+21, with each observation period lasting 1000 seconds; the simulation lasted for 3 days. Using stellar angular distance observations provided by a stellar distance measurement sensor and pulse arrival time difference observations provided by an X-ray detector, the spacecraft's position and velocity relative to Earth, the Earth's position and velocity relative to the solar system's barycenter, and the sensor's system error parameters were determined. The spacecraft position estimation error curve, spacecraft velocity estimation error curve, Earth position estimation error curve, Earth velocity estimation error curve, and sensor system error parameter estimation error curve obtained by the method described in this invention are shown below. Figure 2 , Figure 3 , Figure 4 , Figure 5 and Figure 6 As shown in the figure, the solid line represents the state estimation error curve, and the dashed line represents the 3σ error bound calculated from the corresponding diagonal elements of the error variance matrix estimated by the extended Kalman filter. Mathematical simulation examples show that applying the method described in this invention to the autonomous navigation of Earth-orbiting spacecraft can effectively suppress the adverse effects of Earth ephemeris errors and sensor system errors, achieving a positioning accuracy level on the order of hundreds of meters while maintaining the angular measurement accuracy of the stellar angular distance measurement sensor at the order of mas.

[0112] The main technical content of this invention can open up a new way to improve the performance of relativistic navigation systems for spacecraft, and can meet the technical requirements of "high precision, long duration and autonomy". It has application value on future platforms such as Earth orbit communication, navigation and remote sensing satellites, lunar space cruise vehicles and deep space probes.

[0113] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A method for calibrating relativistic navigation reference deviations by fusing stellar and pulsar information, characterized in that... Includes the following steps: S1 uses an extended Kalman filter as the navigation filter and initializes it, setting the initial values ​​of the state vectors that characterize the position and velocity of the Earth orbiting spacecraft relative to the Earth's center, the position and velocity of the Earth's center relative to the solar system's center of mass, and the sensor system error parameters. S2 predicts the position and velocity of the spacecraft relative to the Earth's center based on the orbital dynamics model of the Earth orbiting spacecraft and obtains the corresponding predicted values. Based on the Earth's orbital dynamics model, it predicts the position and velocity of the Earth's center relative to the center of mass of the solar system and obtains the corresponding predicted values. S3 observes stars and obtains stellar angular distance measurements using a stellar angular distance measurement sensor mounted on an Earth-orbiting spacecraft. S4 If the stellar angular distance observation is available, substitute the stellar angular distance observation obtained in step S3 into the extended Kalman filter for calculation, and correct the predicted values ​​of the spacecraft's position and velocity relative to the Earth's center, the predicted values ​​of the Earth's position and velocity relative to the solar system's center of mass, and the sensor system error parameters obtained in step S2. S5 observes pulsars using an X-ray detector mounted on an Earth-orbiting spacecraft, obtaining the pulse arrival time difference of the pulsars. S6 If the pulse arrival time difference observation is available, substitute the pulse arrival time difference observation obtained in step S5 into the extended Kalman filter for calculation, and correct the predicted values ​​of the spacecraft's position and velocity relative to the Earth's center, the predicted values ​​of the Earth's center's position and velocity relative to the solar system's center of mass, and the sensor system error parameters obtained in step S2. S7 returns to step S2 for iteration. When the statistical value of the filtered information is less than a given threshold, the iteration stops. The estimated values ​​of the spacecraft's position and velocity relative to the Earth's center, the Earth's position and velocity relative to the solar system's center of mass, and the estimated values ​​of the sensor system error parameters are obtained, thereby completing the relativistic navigation reference deviation calibration of stellar and pulsar information fusion.

2. The relativistic navigation reference deviation calibration method based on the fusion of stellar and pulsar information according to claim 1, characterized in that: The method for initializing the extended Kalman filter, which serves as the navigation filter, in step S1 is as follows: set the initial time. State vector estimate of time-extended Kalman filter for: in, and These represent the estimated values ​​of the position vector and velocity vector of the Earth-orbiting spacecraft relative to the Earth's center at the initial moment, respectively. and These represent the estimated values ​​of the position vector and velocity vector of the Earth's center relative to the center of mass of the solar system at the initial moment, respectively. This represents the estimated value of the sensor system error parameter at the initial time. It is obtained based on prior knowledge of the position and velocity of Earth-orbiting spacecraft, the position and velocity of the Earth's center relative to the solar system's center of mass, and the system error parameters of the stellar angular distance measurement sensor.

3. The relativistic navigation reference deviation calibration method based on the fusion of stellar and pulsar information according to claim 1, characterized in that: The method for predicting the spacecraft's position and velocity relative to the Earth's center, and the Earth's position and velocity relative to the solar system's center of mass, in step S2 is as follows: The state vector prediction value of the extended Kalman filter at each time step Calculate according to the following formula: State transition function The form is: in, The subscript indicates the time step of prediction in the extended Kalman filter. Indicates different times, express State vector estimate of the extended Kalman filter at time t; nonlinear function The form is: in, express The estimated velocity vector of a spacecraft in Earth orbit relative to the Earth's center at any given time. express The estimated position vector of a spacecraft in Earth orbit relative to the Earth's center at any given time. express The estimated value of the Earth's velocity vector relative to the center of mass of the solar system at any given time. express The estimated value of the position vector of the Earth's center relative to the center of mass of the solar system at any given moment. Represents the Earth's gravitational constant. This represents the known spacecraft orbital perturbation function, obtained from the spacecraft's orbital dynamics model. Represents the solar gravitational constant. This represents the known Earth orbital perturbation function, obtained from the Earth's orbital dynamics model. This indicates the number of system error parameters of the sensor.

4. The relativistic navigation reference deviation calibration method based on the fusion of stellar and pulsar information according to claim 1, characterized in that: Stellar angular distance observation in step S3 The calculation method is as follows: in, express Time of the first angular distance observations of stars .

5. The relativistic navigation reference deviation calibration method based on the fusion of stellar and pulsar information according to claim 1, characterized in that: The method for correcting the predicted values ​​of the spacecraft's position and velocity relative to the Earth's center, the predicted values ​​of the Earth's position and velocity relative to the solar system's center of mass, and the sensor system error parameters in step S4 is as follows: in, express The state vector estimate of the extended Kalman filter at time step 1. express The state vector prediction value of the extended Kalman filter at each time step. Represents the angular distance observation of stars. The Kalman gain matrix, representing the corresponding stellar angular distance observation, is calculated based on a pre-established relativistic navigation system model. The observation function... The form is: in, , , indicating the corresponding number stellar angular distance observation The observation function is of the following form: in, and This represents the projection of the stellar line-of-sight vector measured by a stationary observer onto the inertial coordinate system, calculated based on a pre-established stellar catalog. The subscript... and Used to distinguish different stars Represents the speed of light. , and They represent Predicted values ​​for the velocity of a spacecraft in medium Earth orbit, the geocentric velocity, and the error parameters of the sensor system.

6. The relativistic navigation reference deviation calibration method based on the fusion of stellar and pulsar information according to claim 1, characterized in that: Pulse arrival time difference observation in step S5 for: in, express Time of the first Observation of pulse arrival time difference .

7. The relativistic navigation reference deviation calibration method based on the fusion of stellar and pulsar information according to claim 1, characterized in that: The method for correcting the predicted values ​​of the spacecraft's position and velocity relative to the Earth's center, the predicted values ​​of the Earth's position and velocity relative to the solar system's center of mass, and the sensor system error parameters in step S6 is as follows: in, express The state vector prediction value of the extended Kalman filter at each time step. The Kalman gain matrix, representing the observation of the time difference of arrival of the corresponding pulse, is calculated based on a pre-established pulsar navigation system model. The observation function represents the pulse arrival time difference observation. The form is: in, , , indicating the corresponding number stellar angular distance observation The observation function is of the following form: in, Indicates the first The line-of-sight vector of a pulsar. Indicates the distance from the center of mass of the solar system to the th The distances to the pulsars were calculated based on a pre-established catalog of pulsars. This represents the position vector of the solar system's barycenter relative to the center of the sun, calculated based on a pre-established solar ephemeris. and They represent Predicted positions of spacecraft in medium Earth orbit and their geocentric positions. This represents the solar gravitational constant.

8. The relativistic navigation reference deviation calibration method based on the fusion of stellar and pulsar information according to claim 1, characterized in that: The recursive calculation method for the statistical value of the filtered innovation in step S7 is as follows: in, express Statistical values ​​of the filtered information at each time step. express The statistical value of the filtered innovation at time step, and the initial value of the statistical value of the filtered innovation. Set to a positive integer greater than a specified threshold. This represents the total number of sampled data within a pre-specified time window. The filtered information is represented by the following method: For stellar angular distance observation, Represents the observation function; The method for determining that the statistical value of the filtered innovation is less than a given threshold is: if Then, it is determined that the statistical value of the filtered innovation is less than a given threshold, where, For a given threshold, it can be preset according to the accuracy index of the stellar angular distance measurement sensor.

9. A relativistic navigation reference deviation calibration system based on the fusion of stellar and pulsar information, characterized in that, include: State initialization module: Initializes the extended Kalman filter, which serves as the navigation filter, and sets the initial values ​​of the state vector representing the position and velocity of the Earth orbiting spacecraft relative to the Earth's center, the position and velocity of the Earth's center relative to the solar system's center of mass, and the sensor system error parameters. State prediction module: Based on the orbital dynamics model of the spacecraft orbiting the Earth, predict the position and velocity of the spacecraft relative to the Earth's center, and based on the Earth's orbital dynamics model, predict the position and velocity of the Earth's center relative to the center of mass of the solar system. Stellar observation module: Observes stars on the celestial sphere through a stellar angular distance measurement sensor configured on an Earth orbiting spacecraft. Utilizes a multi-aperture optical system on the stellar angular distance measurement sensor to observe multiple stars and obtain the angle between the stellar line-of-sight vectors, i.e., the stellar angular distance observation measurement. The correction module based on stellar observations: When the stellar angular distance observations of the stellar angular distance measurement sensor are available, the stellar angular distance observations are processed by an extended Kalman filter to correct the predicted values ​​of the spacecraft's position and velocity relative to the Earth's center, the predicted values ​​of the Earth's position and velocity relative to the solar system's center of mass, and the sensor's system error parameters. Pulsar observation module: Pulsars are observed using an X-ray detector on an Earth-orbiting spacecraft. Multiple pulsars are observed using a multi-aperture optical system on the X-ray detector to obtain the difference between the time it takes for the pulse signal emitted by the pulsar to reach the center of the solar system and the time it takes to reach the spacecraft, i.e., the pulse arrival time difference observation. The correction module based on pulsar observations: When the pulse arrival time difference observations of the X-ray detector are available, the pulse arrival time difference observations are processed by an extended Kalman filter to correct the predicted values ​​of the spacecraft's position and velocity relative to the Earth's center, the predicted values ​​of the Earth's position and velocity relative to the solar system's center of mass, and the sensor system error parameters.

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