A spacecraft navigation method based on the combination of pulsars and deep space network

Abstract

The present invention discloses a spacecraft navigation method based on a combination of pulsars and deep space network, which mainly solves the problem that existing technologies are difficult to meet the real-time requirements of complex tasks and have limited coverage capabilities. It includes: establishing a navigation system state model of the spacecraft based on the orbital dynamics equation; using an X-ray detector to obtain the time when the photon arrives at the spacecraft and convert it to the SSB, and establishing a photon arrival phase measurement equation based on the relationship between the photon arrival SSB phase and the spacecraft state; using the deep space network ground station to receive spacecraft signals, and establishing a time difference and Doppler frequency shift measurement equation based on the time collected by multiple ground stations and the frequency information of a single ground station; integrating the data of pulsars and deep space network, and using extended Kalman filtering to calculate the estimated vector of the spacecraft state. The present invention effectively improves the continuity and accuracy of navigation, while enhancing system performance, so that spacecraft can obtain more stable navigation support in complex environments.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace navigation technology, and specifically relates to a spacecraft navigation method based on a combination of pulsars and deep space networks, which can be used for navigation and positioning of spacecraft in complex environments. Background Art

[0002] With the rapid development of aerospace technology, the demand for deep space exploration missions is increasing. To ensure accurate positioning and safe operation of spacecraft in deep space environments, far from the Earth, with limited communications or complex observation conditions, high-precision navigation technology has become an indispensable core support for deep space missions.

[0003] Pulsar-based navigation is an autonomous navigation technology based on the highly periodic and stable pulsar signals in the universe. The pulse signals emitted by pulsars can be considered "cosmic beacons" with extremely stable time periods. Multiple pulsars with known locations can provide an absolute position reference for spacecraft. When a spacecraft receives multiple pulsar signals, it can determine the spacecraft's absolute position in the universe by measuring the arrival phase or arrival time of the signals. This navigation method is highly autonomous and can provide absolute position information in deep space environments. However, pulsar navigation also faces certain limitations. For example, the distribution of pulsar signals is uneven, making it difficult to obtain sufficient observable pulsars in certain locations. Some pulsar signals are weak and easily interfered with in high-noise environments, resulting in a spacecraft being unable to obtain sufficient observation data at specific locations or times. Furthermore, the periodic nature of pulsar signals results in a low data update frequency, making it difficult to meet the real-time and high-frequency update requirements of highly dynamic missions.

[0004] The Deep Space Network (DSN) refers to a deep space communication and tracking network composed of multiple ground stations distributed around the world, used to support communication, navigation, and scientific data transmission for deep space exploration missions. The Deep Space Network uses highly sensitive, large-aperture antennas to receive radio signals emitted by spacecraft. It can measure the position and velocity of spacecraft through radio measurement methods including Time Difference of Arrival (TDOA) and Doppler Shift. Specifically, Time Difference of Arrival measurement calculates the position of the spacecraft relative to the ground station by comparing the time difference between the arrival of signals at different ground stations; Doppler shift measurement calculates the radial velocity of the spacecraft relative to the ground station through the frequency offset of the spacecraft signal. These high-precision radio measurement data provide important support for the precise navigation and orbit adjustment of spacecraft, enabling the Deep Space Network to effectively support exploration missions from Earth orbit to the depths of the solar system. The China Deep Space Net (CDSN) interferometric measurement system currently consists of the Jiamusi Deep Space Station (JM01), the Kashgar Deep Space Station (KS01), the Namibia Deep Space Antenna (NB01), the South American Deep Space Station (NM01), and related processing centers in Beijing. The system's longest baseline reaches 12,000 km. Overall, the CDSN's geographical layout is not optimal, and its coverage of deep space spacecraft tracking and control is only approximately 90%. Furthermore, given the large number of satellite missions currently underway, ground station resources are limited, making it difficult to provide continuous and comprehensive tracking and control support for all satellites. Furthermore, when spacecraft fly to the far side of the moon or enter signal blind spots due to obstruction by other spacecraft and satellites, ground stations will be unable to effectively receive and acquire the signals transmitted by them. Furthermore, for missions in high-latitude orbits or extreme deep space, the ground reception angle for signals may be insufficient, resulting in reduced signal reception efficiency in some directions and the possibility of insufficient signal. Furthermore, Deep Space Network ground stations can be affected by weather (such as storms or snow) or communication interference (such as radio noise or solar activity), resulting in signal degradation or even temporary interruption. Furthermore, due to the Earth's rotation and the maintenance requirements of ground stations, a ground station may be located on the far side of the Earth or require short-term maintenance, forcing spacecraft to rely on other stations. This can limit coverage, especially for spacecraft in extreme locations or remote orbital positions. Summary of the Invention

[0005] The purpose of the present invention is to address the deficiencies of the above-mentioned existing technologies and propose a spacecraft navigation method based on a combination of pulsars and the deep space network, so as to solve the problems of limited data, long processing time, limited tracking and control station resources, weak pulsar navigation signals, and low accuracy in the existing technologies. Pulsar navigation provides absolute positioning for spacecraft, allowing them to navigate autonomously when the deep space network ground station coverage is insufficient or communication is restricted; and when the pulsar signal is interfered with or data is insufficient, the time difference and Doppler frequency shift data of the deep space network are used to provide precise positioning support. The present invention ensures the continuity and high accuracy of navigation in complex environments, while enhancing the autonomy and robustness of the system, enabling spacecraft to obtain more stable navigation support during deep space exploration missions.

[0006] The present invention achieves the above-mentioned purpose by the following specific steps:

[0007] (1) Based on the orbital dynamics equations, the navigation system state equations are established for the uncontrolled motion of the Earth-orbiting satellite in the geocentric equatorial coordinate system;

[0008] (2) Select multiple pulsars as navigation stars to provide pulsar measurement information; use the sequential observation method to observe, and use the phase of the pulse arriving at the solar system center of mass (SSB) as the pulsar navigation quantity measurement; based on the relationship between the time when the pulsar photons arrive at the spacecraft and the phase of the pulsar arriving at the SSB, use the pulsar timing model and time conversion equation to establish the measurement equation of the pulsar navigation system;

[0009] (3) The spacecraft transmits a signal to the ground station, and the time difference between the signal arriving at two different ground stations and its Doppler frequency shift are used as the measurement of the deep space network system, and the measurement equation of the deep space network system is established;

[0010] (4) Combining the measurement equations of the pulsar navigation system with those of the deep space network system to construct a combined navigation system model of pulsars and the deep space network; that is, sequentially observing N pulsars during the motion of the spacecraft, where N is an integer greater than or equal to 1; when one of the navigation pulsars is visible, the navigation measurement of that pulsar is used first; when all N navigation pulsars are not visible, the measurement of the deep space network system is used to fill the gap in the pulsar navigation measurement period; when the navigation pulsar is not visible and the deep space network ground station cannot receive signals, the measurement input of the time period is determined, and the orbital dynamics equation is recursively deduced using the numerical integration method;

[0011] (5) Linearize the state equation of the spacecraft navigation system in step 1, construct the differential equation of the state transfer matrix, and obtain the state transfer matrix using the numerical integration method;

[0012] (6) Linearize the measurement equation of the pulsar navigation system in step 2 near the current time and construct a measurement matrix to describe the conversion relationship from state quantity to measurement quantity;

[0013] (7) Using the state equation of the spacecraft navigation system in step 1 and the measurement equation of the spacecraft navigation system of the pulsar and deep space network combination established in step (4), a pulsar and deep space network combined navigation system model is obtained;

[0014] (8) Based on the combined navigation system model of pulsar and deep space network, the extended Kalman filter (EKF) algorithm is used to estimate the position of the spacecraft, that is, first initialize the state quantity and covariance matrix in the EKF algorithm; then determine whether the pulsar is visible and whether the ground station can receive the signal, determine whether to use pulsar navigation or the deep space network system for measurement, determine the update step size based on the quantity measurement, and extract the quantity measurement through the existing estimation algorithm; use the state equation of the spacecraft navigation system established in step 1, use the numerical integration method to update the spacecraft state, and use the state transfer matrix constructed in step 5 to update the covariance matrix; then calculate the Kalman gain through the measurement matrix constructed in step 6 and the updated covariance matrix, which is used to correct the spacecraft state and covariance matrix; iterate the EKF process to estimate the spacecraft position and complete the spacecraft navigation task.

[0015] Compared with the prior art, the present invention has the following advantages:

[0016] First, when sufficient pulsar signals are received, the present invention first uses pulsar navigation to determine the absolute position of the spacecraft in the universe by measuring the arrival phase or arrival time of the signals. This can provide absolute position reference information in a deep space environment, thereby achieving autonomous positioning of the spacecraft in a deep space environment.

[0017] Second, when pulsar signals are weak, observation conditions are limited, or accuracy is insufficient, the present invention utilizes time difference and Doppler shift observation data from the Deep Space Network to further supplement the accuracy requirements of pulsar navigation in long-term navigation. At the same time, high-frequency measurement updates are performed, and the Deep Space Network provides absolute position information. This maintains navigation stability and effectively improves system reliability.

[0018] Third, because the present invention adopts a combined navigation method based on pulsars and relying on non-continuous observation data from the Deep Space Network, it effectively combines pulsar navigation with Deep Space Network observations, leveraging the complementary advantages of both to improve the accuracy and stability of the entire navigation system. Compared with relying solely on pulsar navigation, the method of the present invention significantly improves navigation accuracy and, to a certain extent, reduces the observation burden on ground stations. When the ground station has the observation conditions, it provides non-continuous observation information and, in combination with pulsar navigation, corrects the position and velocity of the spacecraft, thereby optimizing resource utilization and further improving the accuracy of pulsar navigation.

[0019] The method of the present invention can enable spacecraft to obtain continuous high-precision navigation support during deep space exploration missions, and can achieve accurate orbit determination even in complex space environments, providing reliable technical support for future deep space exploration missions. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 Flowchart for realizing the method of the present invention;

[0021] Figure 2 Schematic diagram of pulsar navigation used in the present invention;

[0022] Figure 3 Schematic diagram of deep space network navigation adopted in the present invention;

[0023] Figure 4 This is a schematic diagram of the implementation process of the extended Kalman filter (EKF) algorithm in the present invention. DETAILED DESCRIPTION

[0024] The present invention proposes a spacecraft navigation method based on the combination of pulsars and the deep space network. The method establishes a navigation system state model of the spacecraft according to the orbital dynamics equation. The method uses an X-ray detector to obtain the time when photons arrive at the spacecraft and converts it to the solar system barycenter (SSB). The photon arrival phase measurement equation is established based on the relationship between the phase of photons arriving at the SSB and the spacecraft state. The method uses a deep space network ground station to receive spacecraft signals. The time difference and Doppler shift measurement equation are established based on the time collected by multiple ground stations and the frequency information of a single ground station. The EKF filtering method is used to integrate the pulsar and deep space network data to obtain an estimated vector of the spacecraft state.

[0025] The present invention will be further described below with reference to the accompanying drawings.

[0026] Example 1: Reference Figure 1 This embodiment proposes a spacecraft navigation method based on the combination of pulsars and the deep space network. This method integrates X-ray pulsar observation information, the time difference of the deep space network, and the Doppler frequency shift. This method studies the combined navigation method based on pulsars and the deep space network, thereby obtaining a more accurate spacecraft state estimate and improving the performance of the navigation system. The specific steps include:

[0027] Step 1. Based on the orbital dynamics equation, establish the navigation system state equation for the satellite in uncontrolled motion in the geocentric equatorial coordinate system; specifically, by analyzing the various perturbations acting on the satellite in uncontrolled motion, establish the navigation system state equation based on a high-precision orbital dynamics model.

[0028] In this embodiment, the position and velocity expressions of the spacecraft relative to the Earth's center of mass at time t are constructed, that is, the navigation system state equation is as follows:

[0029]

[0030] Where X(t)=(r T (t),v T (t)) T represents the spacecraft state vector at time t, T represents the transpose operation, r=r(t)=(x,y,z) T is the position of the spacecraft to the center of the earth at time t, x, y, z are the components of the spacecraft on the three axes in the three-dimensional coordinate system; v = v(t) = (v x ,v y ,v z ) T is the velocity of the spacecraft relative to the center of the earth at time t, v x 、v y 、v z are the components of the spacecraft velocity on the three axes; f(·) is the navigation state equation of the pulsar and deep space network combination, w(t) is the process noise, which can generally be treated as Gaussian noise; μ e =GM ​​is the gravitational constant of the Earth, G is the gravitational constant, and M is the mass of the Earth; a pert is the spacecraft perturbation acceleration, that is, the acceleration vector caused by the perturbation force.

[0031] Step 2. Select multiple pulsars as navigation stars to provide pulsar measurement information; use the sequential observation method to observe, and use the phase of the pulse arriving at the solar system center of mass (SSB) as the pulsar navigation quantity measurement; based on the relationship between the time when the pulsar photons arrive at the spacecraft and the phase of the pulsar arriving at the SSB, use the pulsar timing model and time conversion equation to establish the measurement equation of the pulsar navigation system.

[0032] This embodiment converts the time when pulsar photons arrive at the detector on the spacecraft to the solar system's center of mass (SSB). A pulsar timing model based on the solar system's center of mass is used to predict the phase of the same photon arriving at the SSB. The phase of the photon arriving at the SSB is used as the basic pulsar navigation observable. The relationship between the phase φ(t, X) of the photon arriving at the SSB and the spacecraft state is constructed, namely, the pulsar navigation measurement equation:

[0033] φ(t,X)=φ SSB (t+τ(t,X))

[0034] Where X = X(t) represents the spacecraft state vector at time t; φ SSB(·) is the pulsar timing model at the SSB; τ(t,X) is the optical propagation time of the pulse wave from the detector to the SSB, that is, the time delay of the center of mass correction at time t.

[0035] Step 3. The spacecraft transmits a signal to the ground station. The time difference between the arrival of the signal at two different ground stations and its Doppler shift are used as the measurement of the deep space network system. The measurement equation of the deep space network system is established. The specific method is as follows:

[0036] (3.1) Let the spacecraft transmit a signal to the Deep Space Network ground station at time t, and assume that the positions of ground stations A and B at time t are r A =(x A ,y A ,z A ) T and r B =(x B ,y B ,z B ) T , the time difference Δt between the arrival of the signal at ground station A and ground station B is obtained according to the following formula:

[0037]

[0038] Among them, d A and d B are the distances from the spacecraft to ground stations A and B respectively, c represents the speed of light, and r is the position of the spacecraft to the center of the earth at time t;

[0039] (3.2) Let m = A or B. In the signal received at ground station m, the relationship between the Doppler frequency shift Δf and the radial velocity is:

[0040]

[0041] Where f0 is the base frequency of the signal, v represents the spacecraft speed, and v radial is the radial velocity of the spacecraft relative to the ground station m. In this embodiment, the radial velocity is preferably obtained by velocity projection between the spacecraft and the ground station.

[0042] Step 4. Combine the measurement equations of the pulsar navigation system with those of the Deep Space Network system to construct a combined pulsar and Deep Space Network navigation system model. This involves sequentially observing N pulsars during the spacecraft's motion, where N is an integer greater than or equal to 1. When one of the navigation pulsars is visible, the navigation measurement of that pulsar is prioritized. When all N navigation pulsars are invisible, the measurement of the Deep Space Network system is used to fill the gap in the pulsar navigation measurement period. When the navigation pulsar is invisible and the Deep Space Network ground station cannot receive signals, the measurement input for that period is determined, and the orbital dynamics equations are recursively derived using a numerical integration method.

[0043] The measurement equation of the spacecraft navigation system of the pulsar and deep space network combination in this embodiment is expressed as follows:

[0044]

[0045] where h(·) is the combined navigation system measurement equation, φ(t,X) is the measurement equation corresponding to pulsar navigation, Z(t) is the measurement at time t, and v(t) is the measurement noise at time t.

[0046] Step 5. Linearize the state equation of the spacecraft navigation system in step 1, construct the differential equation of the state transfer matrix, and obtain the state transfer matrix using the numerical integration method. In this embodiment, the state transfer matrix Φ(t+l,t) from time t to time t+l is constructed:

[0047]

[0048] Among them, t0 is the epoch time when the filtering starts, that is, the initial value of t; the reference state is the state quantity extrapolated from time t0 to time ·; l>0 is the filtering step size.

[0049] Step 6. Linearize the measurement equation of the pulsar navigation system in step 2 near the current time and construct a measurement matrix to describe the conversion relationship from state quantity to quantity measurement.

[0050] In this embodiment, the measurement matrix is ​​obtained in the following manner:

[0051] (6.1) When a pulsar is visible, construct the pulsar photon arrival phase measurement matrix H at time t. POA :

[0052]

[0053] in, τ(·) and n are the pulsar timing model, time delay, and pulsar unit direction vector at the SSB of the pulsar, respectively;

[0054] (6.2) When all N navigation pulsars are invisible but the ground station can receive the spacecraft signal, the partial derivative of the state vector is obtained by measuring the time difference and Doppler shift obtained by the deep space network, and the measurement matrix H of the ground station system is obtained. Station :

[0055]

[0056] Step 7. Use the state equation of the spacecraft navigation system in step 1 and the measurement equation of the spacecraft navigation system of the pulsar and deep space network combination established in step (4) to obtain the pulsar and deep space network combined navigation system model;

[0057] Step 8. Based on the pulsar and deep space network combined navigation system model, the extended Kalman filter (EKF) algorithm is used to estimate the spacecraft position. That is, the state quantity and covariance matrix in the EKF algorithm are first initialized; then, whether the pulsar is visible and whether the ground station can receive the signal is determined, and whether to use pulsar navigation or the deep space network system for measurement. The update step size is determined based on the measurement, and the measurement is extracted through the existing estimation algorithm; the state equation of the spacecraft navigation system established in step 1 is used to update the spacecraft state using the numerical integration method, and the state transfer matrix constructed in step 5 is used to update the covariance matrix; the Kalman gain is then calculated using the measurement matrix constructed in step 6 and the updated covariance matrix to correct the spacecraft state and covariance matrix; the iterative EKF process is used to estimate the spacecraft position and complete the spacecraft navigation mission. The specific implementation steps are as follows:

[0058] (8.1) Establish a pulsar and deep space network integrated navigation system model:

[0059]

[0060] (8.2) Initialize the spacecraft's state vector and covariance matrix at the start time t, and set the observation interval length α corresponding to the kth pulsar according to the navigation pulsar flux characteristics. k , set the observation interval length β according to the sampling rate characteristics of the ground station observation data, and set the threshold for judging whether the pulsar is visible;

[0061] (8.3) Sequentially observe the N selected navigation pulsars. When the kth pulsar is visible, set the filter step size l = α k / 2, k = 1, 2, ..., N; when all N navigation pulsars are not visible, set the filter step size l = β; use the spacecraft dynamics model to recursively extrapolate the orbit from t to t + 2l to obtain the predicted orbit for pulse phase extraction; use the estimated state at time t + l in the predicted orbit as the prior state at the current time; calculate the state transition matrix Φ(t + l, t) to update the covariance matrix;

[0062] (8.4) When the kth pulsar is visible, the navigation system measurement equation is Z(t) = φ(t, X) + v(t); the target pulsar photon arrival timestamps recorded from t to t+2l are processed, the predicted orbit of the previous stage is interpolated, the pulsar photon arrival times recorded at the spacecraft are converted to the SSB, and the pulse arrival phase is estimated using the phase estimation algorithm. and use it as a quantity measurement

[0063] When N navigation pulsars are not visible, but the ground station can receive the spacecraft signal, the navigation system measurement equation is: Deep Space Network ground stations A and B respectively accurately record the signal sent by the spacecraft at time t+1, generating a time mark t A and t B , get the time difference between the signal arriving at ground station A and ground station B, and get the arrival time difference Δt=t A -t B Given the reference frequency f0 of the spacecraft signal, the Deep Space Network ground station accurately measures the received spacecraft signal frequency f and records the difference between the received frequency and the reference frequency to obtain the Doppler shift Δf = f - f0. Combining the arrival time difference and the Doppler shift, the measurement quantity Z(t+l) = [ΔtΔf] is constructed. T ;

[0064] When all observed pulsars are not visible and the ground station does not receive signals, that is, there is no measurement input at the current moment, update t = t + l, and return to step (8.3);

[0065] (8.5) Calculate the Kalman gain based on the measurement matrix, use the Kalman gain and the measurement Z(t+l) extracted in (8.4) to correct the prior state at the current moment, obtain the posterior state at the current moment, and update the covariance matrix; let t=t+l, return to execute step (8.3) until the navigation is completed.

[0066] Example 2: Reference Figure 1-4 The overall implementation steps of this embodiment are the same as those of the first embodiment. Now, a specific example is given to further describe the implementation process of the method of the present invention in detail:

[0067] Step 1: Analyze the various perturbations experienced by an Earth-orbiting satellite in uncontrolled motion, taking into account the Earth's gravity, atmospheric drag, the gravitational pull of the Sun and Moon, solar radiation pressure, Earth and ocean tides, and the effects of other celestial bodies on the spacecraft's gravity. Establish the navigation system's state equations based on a high-precision orbital dynamics model in the geocentric equatorial coordinate system:

[0068]

[0069] Wherein, the state vector X(t)=(r T (t),v T (t)) T is the position and velocity of the spacecraft relative to the Earth's center of mass; r is the position of the spacecraft to the Earth's center r = (x, y, z) T , x, y, z are the components of the spacecraft position on the x, y, z axes respectively; v is the velocity of the spacecraft relative to the center of the earth v = (v x ,v y ,v z ) T , v x ,v y ,v z are the components of the spacecraft velocity on the x, y, and z axes; f(·) is the navigation measurement equation for the combination of pulsar and deep space network; μ e =GM ​​is the earth's gravitational constant, G is the gravitational constant, and M is the mass of the earth; w(t) represents the process noise, which can generally be treated as Gaussian noise; a x , a y , a z is the perturbation acceleration a pert The components on the x, y, and z axes, the acceleration vector a caused by the perturbation force pert The calculation formula is:

[0070] a pert =a E +a S +a M +a Pl +a e +a o +a D +a SP +a R ,

[0071] Among them, a E The acceleration is caused by the non-spherical shape and uneven mass distribution of the Earth; a S 、a M 、a Pl is the acceleration caused by the sun, moon and planets; a e 、a o is the acceleration caused by the earth and ocean tides; a Dis the acceleration caused by atmospheric resistance; a SP is the acceleration caused by solar radiation pressure; a R is the acceleration of general relativity. The GGM03C model is used to obtain the high-precision earth gravity and non-spherical shape perturbations. The NRLMSISE-00 atmospheric model is used to calculate the atmospheric density at the satellite's location, thereby calculating the perturbation acceleration caused by atmospheric drag. The DE440 ephemeris provided by JPL is used to obtain the positions of the sun, moon, and planets to determine the acceleration caused by other celestial bodies when the International Space Station orbits the Earth. The spherical harmonic function similar to the static earth gravitational field is used to expand the tidal gravitational potential to calculate the satellite orbit perturbations caused by the solid earth tides of the sun and moon. The solid earth tide and ocean tide related parameters provided by IERS (2010) are used to calculate a e 、a o The actual situation of sunlight propagation, the radius of the sun and the earth, and the distance between the sun and the earth are precisely considered. The conical earth shadow model is used to calculate the shadow factor and the solar light pressure force generated by the absorption or reflection of photons on the satellite under solar radiation. The Runge-Kutta-Felhberg7(8) integrator is used for orbit prediction. The above-mentioned model has a high degree of technical maturity and has been widely used and verified in the aerospace field, showing its effectiveness and reliability.

[0072] Step 2: Establish the navigation measurement equation for the pulsar and deep space network combination:

[0073] The detector on board the spacecraft receives the photon and records the arrival time, converts the photon arrival time to the solar system mass center SSB, and uses the pulsar timing model established in the solar mass center reference system to predict the phase of the same photon arriving at the SSB. The phase of the photon arriving at the SSB is used as the basic observation quantity of pulsar navigation. Figure 2 , the relationship between the photon arrival phase and the spacecraft state is constructed. The phase of the photon arriving at the SSB can be expressed as:

[0074]

[0075] Where t is the MET time of the photon arriving at the spacecraft; φ SSB (·) is the pulsar timing model at the SSB; τ(t) is the optical propagation time of the pulse wave from the detector to the SSB, that is, the time delay of the center of mass correction at time t. Ignoring the effects of parallax and pulsar proper motion, and considering only the first-order Shapiro delay of the sun, the time delay of the center of mass correction is as follows:

[0076]

[0077] Among them, t ssbrepresents the TDB time at the SSB, n is the direction of the given pulsar, v E (t) represents the earth velocity vector, r E (t) is the position vector of the Earth relative to the SSB, r(t) is the position vector of the detector relative to the Earth's center of mass, c is the speed of light, θ is the angle between the pulsar, the sun, and the spacecraft, and the Einstein delay term Δ E Using 127 sinusoidal periodic terms, the accuracy can reach 100ns. This allows us to construct the relationship between the phase φ(t) of the photon arriving at the SSB and the spacecraft position vector r(t).

[0078] The spacecraft transmits signals to the Deep Space Network ground station. Ground stations at different locations receive the signals and record the arrival time and frequency of the signals. Figure 3 , establish the measurement equations for the Deep Space Network system. Calculate the time difference between the spacecraft signal arriving at ground stations A and B, and obtain the corresponding distance difference information, which is used to estimate the lateral position information of the spacecraft.

[0079] Assume that the known positions of ground station A and ground station B are r A =(x A ,y A ,z A ) T and r B =(x B ,y B ,z B ) T , the TDOA measurement Δt represents the time difference between the arrival of the signal at two ground stations:

[0080]

[0081] Among them, d A and d B are the distances from the spacecraft to ground stations A and B respectively.

[0082] In the signal received by ground station A, the frequency offset is measured and the radial velocity information of the spacecraft is calculated based on the Doppler effect to provide accurate velocity data. The relationship between Doppler frequency shift Δf and radial velocity is:

[0083]

[0084] Where f0 is the reference frequency of the signal, and the spacecraft speed v=(v x ,v y ,v z ) T , v radial is the radial velocity of the spacecraft relative to the ground station A, obtained by projecting the velocity between the two points.

[0085] Three pulsars are selected as navigation stars to provide pulsar measurement information. The arrival phases of the pulses of multiple pulsars are used as the pulsar navigation measurement. The relative position information of the spacecraft is measured by combining the time difference of the spacecraft signal received by the Deep Space Network ground station with the radial velocity information measured by the Doppler shift, which can provide the absolute position information of the spacecraft. Combining the three different navigation measurement quantities, the measurement equation of the spacecraft navigation system combined with pulsars and the Deep Space Network is established:

[0086]

[0087] Among them, h(·) pulse arrival phase measurement equation, φ i (t, X) is the measurement equation of the i-th pulsar, i = 1, 2, 3, Z(t) is the pulse phase observation at the detector at time t; v(t) is the pulse phase measurement noise.

[0088] Step 3: Linearize the combined pulsar and deep space network navigation system:

[0089] In the spacecraft navigation system method combining pulsars and deep space networks, the state and observation equations have nonlinear characteristics, making direct solution more complex. Therefore, the nonlinear equations are linearized. During the EKF linearization process, the Jacobian matrix of the state equation and the observation equation is calculated, respectively, to obtain the state transfer matrix and the observation matrix.

[0090] Assume that the state vector of the system at epoch t0 is X(t0)=(r T (t0),v T (t0)) T , then the state transfer matrix is ​​expressed as

[0091]

[0092] It describes how the state vector is transferred from the initial time t0 to the future time t. It is impossible to obtain an analytical solution to the state transfer matrix for the state equation, so a differential equation for the state transfer matrix, namely a variational equation, is constructed and numerical methods are used to solve the variational equation to obtain the state transfer matrix.

[0093]

[0094] Where Φ(t0,t0)=1 6×6 . From this we can get the time from epoch t i-1 To epoch time t i The state transition matrix is:

[0095]

[0096] Among them, the reference state Extrapolate from time t0 to ti The state quantity at the moment. State transfer matrix Φ i It can be obtained by solving the corresponding variational equations.

[0097] The measurement equation is linearized near the current state to construct the measurement matrix H, thereby achieving effective observation update of the nonlinear system. In the calculation of partial derivatives describing the relationship between the pulsar measurement value and the instantaneous position and velocity of the satellite, on the basis of the first-order approximation, all light-time effects can be ignored and only the geometric measurement equation is considered, and the photon arrival phase measurement matrix H at time t is obtained. POA :

[0098]

[0099] Among them, φ SSB,1 , τ i (·), n i are the pulsar timing model, time delay, and unit direction vector at the SSB of the i-th pulsar, i = 1, 2, 3. The time difference and Doppler shift observations obtained through the deep space network are used to obtain the partial derivative of the state vector to obtain the time difference measurement matrix H TDOA and the Doppler frequency shift measurement matrix H Doppler for:

[0100]

[0101] The three types of observation information are expressed uniformly in the same mathematical framework to establish a comprehensive measurement matrix of the system:

[0102]

[0103] Step 4: Based on the navigation system combined with pulsars and deep space network, the extended Kalman filter is used to calculate the estimated vector of the spacecraft state. Specifically, based on the three pulsar observation information received by the spacecraft and the quantity measurements obtained by the deep space network, the navigation system extended Kalman filter is performed to obtain the position and velocity of the spacecraft in the inertial coordinate system. The algorithm block diagram of the spacecraft navigation EKF based on the combination of pulsars and deep space network in this invention is as follows: Figure 4 As shown; it mainly includes two stages: time update and measurement update.

[0104] According to the state equation and measurement equation established above, the pulsar and deep space network integrated navigation system is:

[0105]

[0106] First, initialize the spacecraft's state estimation vector and covariance matrix

[0107]

[0108] Then, in the time update phase of the EKF, the spacecraft’s dynamic model is used to update the state estimate and covariance matrix to predict the spacecraft’s state at the current moment:

[0109]

[0110] Where: t i The forecast status at the moment; P i - t i+1 The moment covariance matrix and t i The covariance matrix of the moment forecast; Q i is the process noise covariance matrix. Use t i-1 The state at the observation time is taken as a priori value, and the orbital dynamics model is used to obtain the i-1 to t i The orbit is recursively calculated at every moment, that is, the predicted state vector is obtained according to the above formula (including position, velocity), and the corresponding covariance matrix P i In addition, according to the set minimum value of the integral step, i-1 to t i+1 The orbit is recursively deduced in the interval to obtain a predicted orbit for the next stage of pulse phase extraction.

[0111] Then, the quantity measurements are extracted from the actual measurements of the spacecraft probes and the Deep Space Network ground stations. i-1 to t i+1 The target pulsar photon arrival timestamp recorded at each moment is processed, and the last stage t i-1 to t i+1 The predicted orbit at the time is interpolated, and the pulsar photon arrival time recorded at the spacecraft is converted to the SSB, and the epoch is folded and compared with the standard profile to obtain the photon arrival phase measurement φ(t i ). Multiple Deep Space Network ground stations accurately record the arrival time of spacecraft signals and generate time stamps t A and t B , get the time difference between the signal arriving at ground station A and ground station B, and get the time difference measurement Δt=t A -t B The signal sent by the spacecraft has a known reference frequency f0. The Deep Space Network ground station accurately measures the received spacecraft signal frequency f and records the difference between the received frequency and the reference frequency to obtain the Doppler frequency shift measurement Δf = f-f0. Combining the three different measurements yields the system comprehensive measurement.

[0112] Z i =[φ1(ti )φ2(t i )φ3(t i )ΔtΔf] T ,

[0113] Finally, the system obtains the quantity Z in actual measurement i After that, it enters the measurement update phase, including Kalman gain calculation and state quantity and covariance matrix correction. i Forecast status at the moment t i The observation quantity is corrected at every moment, and the estimated state is finally obtained. i Estimated state at each moment It is also used as a priori state to participate in the prediction of the next time update stage. By repeating the above three steps of time update, pulse phase extraction, and measurement update, the state estimation result X of each epoch can be obtained. i and its corresponding covariance matrix P i , which is output as the result of navigation.

[0114]

[0115] Where: K i is the filter gain; H i is the measurement matrix; R i is the observation noise covariance matrix.

[0116] Repeat the above three steps of time update, quantity measurement extraction, and state update to obtain the state estimation result X for each epoch i and its corresponding covariance matrix P i , which is output as the result of navigation.

[0117] This invention innovatively combines pulsar navigation with the Deep Space Network (DSN), effectively overcoming the limitations of both. Pulsar navigation utilizes stable pulsar signals in the universe to provide absolute positioning information. This allows spacecraft to achieve autonomous navigation through pulsar signals even when ground station coverage is insufficient or communications are temporarily restricted, alleviating continued reliance on ground stations. When a spacecraft is able to receive sufficient pulsar signals, the system prioritizes pulsar data for absolute position. When pulsar signals are weak, unevenly distributed, or subject to interference, the Deep Space Network (DSN) time difference and Doppler shift information are used to provide precise relative positioning support.

[0118] This combined observation source approach not only ensures continuous and high-precision navigation, but also enhances the system's autonomy and robustness, enabling spacecraft to obtain more stable navigation support in complex environments during deep space exploration missions. This combined navigation system will have irreplaceable application prospects, especially in future interstellar voyages and long-distance exploration missions.

[0119] Portions of the present invention not described in detail are common knowledge to those skilled in the art. The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. It is obvious that, after understanding the content and principles of the present invention, those skilled in the art may make various modifications and changes in form and details without departing from the principles and structure of the present invention. However, such modifications and changes based on the concepts of the present invention shall remain within the scope of protection of the claims of the present invention.

Claims

1. A spacecraft navigation method based on a combination of pulsars and deep space network, characterized in that: The steps include: (1) Based on the orbital dynamics equations, the navigation system state equations are established for the uncontrolled motion of the Earth-orbiting satellite in the geocentric equatorial coordinate system; (2) Select multiple pulsars as navigation stars to provide pulsar measurement information; Observations are made using the sequential observation method, with the phase of the pulse arriving at the SSB of the solar system's center of mass being used as a measurement for pulsar navigation. Based on the relationship between the time it takes for pulsar photons to arrive at the spacecraft and the phase of the pulsar arriving at the SSB, the pulsar timing model and time conversion equations are used to establish the measurement equations for the pulsar navigation system. (3) The spacecraft transmits a signal to the ground station, and the time difference between the signal arriving at two different ground stations and its Doppler frequency shift are used as the measurement of the deep space network system, and the measurement equation of the deep space network system is established; (4) Combine the measurement equations of the pulsar navigation system with those of the deep space network system to construct a combined navigation system model of pulsars and the deep space network; conduct sequential observations of N pulsars during the motion of the spacecraft, where N is an integer greater than or equal to 1; when one of the navigation pulsars is visible, the navigation measurement of that pulsar is used first; when all N navigation pulsars are not visible, the measurement of the deep space network system is used to fill the gap in the pulsar navigation measurement period; when the navigation pulsar is not visible and the deep space network ground station cannot receive signals, determine the measurement input of the time period, and use the numerical integration method to recursively deduce the orbital dynamics equation; (5) linearizing the state equation of the spacecraft navigation system in step (1), constructing the differential equation of the state transfer matrix, and obtaining the state transfer matrix using a numerical integration method; (6) Linearize the measurement equation of the pulsar navigation system in step (2) around the current time, and construct a measurement matrix to describe the conversion relationship from state quantity to measurement quantity; (7) using the state equation of the spacecraft navigation system in step (1) and the measurement equation of the spacecraft navigation system for the pulsar and deep space network combination established in step (4) to obtain a pulsar and deep space network combined navigation system model; (8) Based on the pulsar and deep space network combined navigation system model, the extended Kalman filter (EKF) algorithm is used to estimate the spacecraft position. First, the state quantity and covariance matrix in the EKF algorithm are initialized. Then, it is determined whether the pulsar is visible and whether the ground station can receive the signal, and whether to use pulsar navigation or the deep space network system for measurement. The update step size is determined based on the quantity measurement, and the quantity measurement is extracted through the existing estimation algorithm. The state equation of the spacecraft navigation system established in step (1) is used to update the spacecraft state using the numerical integration method, and the state transfer matrix constructed in step (5) is used to update the covariance matrix. The Kalman gain is then calculated using the measurement matrix constructed in step (6) and the updated covariance matrix to correct the spacecraft state and covariance matrix; the iterative EKF process is used to estimate the spacecraft position and complete the spacecraft navigation mission.

2. The method according to claim 1, wherein: Based on the orbital dynamics equations in step (1), the navigation system state equations are established for the uncontrolled orbiting satellite in the geocentric equatorial coordinate system, and the position and velocity expressions of the spacecraft relative to the Earth's center of mass at time t are constructed, as follows: Where X(t)=(r T (t),v T (t)) T represents the spacecraft state vector at time t, T represents the transpose operation, r = r(t) is the position of the spacecraft relative to the center of the Earth at time t; v = v(t) is the velocity of the spacecraft relative to the center of the Earth at time t; f(·) is the navigation state equation of the pulsar and deep space network combination, w(t) is the process noise; μ e is the Earth's gravitational constant, a pert is the spacecraft perturbation acceleration.

3. The method according to claim 1, wherein: The measurement equation of the pulsar navigation system in step (2) is as follows: The time when the pulsar photon arrives at the detector on the spacecraft is converted to the solar system center of mass SSB. The pulsar timing model established in the solar center of mass reference system is used to predict the phase of the same photon arriving at the SSB. The phase of the photon arriving at the SSB is used as the basic observation of pulsar navigation. The relationship between the phase φ(t,X) of the photon arriving at the SSB and the spacecraft state is constructed. The pulsar navigation measurement equation is: φ(t,X)=φ SSB (t+τ(t,X)) Where X = X(t) represents the spacecraft state vector at time t; φ SSB (·) is the pulsar timing model at the SSB; τ(t,X) is the optical propagation time of the pulse wave from the detector to the SSB, that is, the time delay of the center of mass correction at time t.

4. The method according to claim 3, wherein: The measurement equation of the deep space network system in step (3) is obtained as follows: (3.1) Let the spacecraft transmit a signal to the Deep Space Network ground station at time t, and assume that the positions of ground stations A and B at time t are r A =(x A ,y A ,z A ) T and r B =(x B ,y B ,z B ) T , the time difference Δt between the arrival of the signal at ground station A and ground station B is obtained according to the following formula: Among them, d A and d B are the distances from the spacecraft to ground stations A and B respectively, c represents the speed of light, and r is the position of the spacecraft to the center of the earth at time t; (3.2) Let m = A or B. In the signal received at ground station m, the relationship between the Doppler frequency shift Δf and the radial velocity is: Where f0 is the base frequency of the signal, v represents the spacecraft speed, and v radial is the radial velocity of the spacecraft relative to the ground station m.

5. The method according to claim 4, characterized in that: The radial velocity v of the spacecraft relative to the ground station m radial , which is obtained by velocity projection between the spacecraft and the ground station.

6. The method according to claim 4, characterized in that: The measurement equation of the spacecraft navigation system of the pulsar and deep space network combination in step (4) is expressed as follows: where h(·) is the combined navigation system measurement equation, φ(t,X) is the measurement equation corresponding to pulsar navigation, Z(t) is the measurement at time t, and v(t) is the measurement noise at time t.

7. The method according to claim 2, wherein: The state transfer matrix in step (5) is obtained as follows: Construct the state transition matrix Φ(t+l,t) from time t to time t+l: Among them, t0 is the epoch time when the filtering starts, that is, the initial value of t; the reference state is the state quantity extrapolated from time t0 to time ·; l>0 is the filtering step size.

8. The method according to claim 3, wherein: The measurement matrix in step (6) is obtained as follows: (6.1) When a pulsar is visible, construct the pulsar photon arrival phase measurement matrix H at time t. POA : in, τ(·) and n are the pulsar timing model, time delay, and pulsar unit direction vector at the SSB of the pulsar, respectively; (6.2) When all N navigation pulsars are invisible but the ground station can receive the spacecraft signal, the partial derivative of the state vector is obtained by measuring the time difference and Doppler shift obtained by the deep space network, and the measurement matrix H of the ground station system is obtained. Station :

9. The method according to claim 1, wherein: Step (8) uses the extended Kalman filter (EKF) algorithm to estimate the spacecraft position. The specific steps are as follows: (8.1) Establish a pulsar and deep space network integrated navigation system model: (8.2) Initialize the spacecraft's state vector and covariance matrix at the start time t, and set the observation interval length α corresponding to the kth pulsar according to the navigation pulsar flux characteristics. k , set the observation interval length β according to the sampling rate characteristics of the ground station observation data, and set the threshold for judging whether the pulsar is visible; (8.3) Sequentially observe the N selected navigation pulsars. When the kth pulsar is visible, set the filter step size l = α k / 2, k = 1, 2, ..., N; when all N navigation pulsars are not visible, set the filter step size l = β; use the spacecraft dynamics model to perform orbit recursion in the interval from t to t+2l to obtain the predicted orbit for pulse phase extraction; The estimated state at time t+l in the predicted trajectory is used as the prior state at the current time; Calculate the state transfer matrix Φ(t+l,t) to update the covariance matrix; (8.4) When the kth pulsar is visible, the navigation system measurement equation is Z(t) = φ(t, X) + v(t); the target pulsar photon arrival timestamps recorded from t to t+2l are processed, the predicted orbit of the previous stage is interpolated, the pulsar photon arrival times recorded at the spacecraft are converted to the SSB, and the pulse arrival phase is estimated using the phase estimation algorithm. and use it as a quantity measurement When N navigation pulsars are not visible, but the ground station can receive the spacecraft signal, the navigation system measurement equation is: Deep Space Network ground stations A and B respectively accurately record the signal sent by the spacecraft at time t+1, generating a time mark t A and t B , get the time difference between the signal arriving at ground station A and ground station B, and get the arrival time difference Δt=t A -t B Given the reference frequency f0 of the spacecraft signal, the Deep Space Network ground station accurately measures the received spacecraft signal frequency f and records the difference between the received frequency and the reference frequency to obtain the Doppler shift Δf = f - f0. Combining the arrival time difference and the Doppler shift, the measurement quantity Z(t+l) = [ΔtΔf] is constructed. T ; When all observed pulsars are not visible and the ground station does not receive signals, that is, there is no measurement input at the current moment, update t = t + l, and return to step (8.3); (8.5) Calculate the Kalman gain based on the measurement matrix, use the Kalman gain and the measurement Z(t+l) extracted in (8.4) to correct the prior state at the current moment, obtain the posterior state at the current moment, and update the covariance matrix; let t=t+l, return to execute step (8.3) until the navigation is completed.

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