Spacecraft navigation method based on pulsar and deep space network combination

Abstract

The invention discloses a spacecraft navigation method based on combination of a pulsar and a deep space network, and mainly solves the problems that the real-time requirement of a complex task is difficult to meet and the coverage capability is limited in the prior art. Comprising the following steps: establishing a navigation system state model of a spacecraft according to an orbital kinetic equation; obtaining the time when photons arrive at the spacecraft by using an X-ray detector, converting the time to the SSB, and establishing a photon arrival phase measurement equation according to the relationship between the phase when the photons arrive at the SSB and the state of the spacecraft; the method comprises the following steps: receiving a spacecraft signal by using a deep space network ground station, and establishing a time difference and Doppler frequency shift measurement equation through time acquired by a plurality of ground stations and frequency information of a single ground station; and integrating the data of the pulsar and the deep space network, and calculating an estimation vector of the state of the spacecraft by using extended Kalman filtering. According to the invention, the continuity and accuracy of navigation are effectively improved, and the system performance is enhanced, so that the spacecraft can obtain more stable navigation support in a complex environment.

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 a deep space network, 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. In order to ensure that spacecraft can still achieve accurate positioning and safe operation in deep space environments, far away 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 strong periodic and stable pulsar signals in the universe. The pulse signals emitted by pulsars can be regarded as "cosmic beacons" with extremely stable time periods. Multiple pulsars with known positions can provide absolute position references for spacecraft. When a spacecraft receives multiple pulsar signals, it can determine the absolute position of the spacecraft in the universe by measuring the arrival phase or arrival time of the signals. This navigation method has a high degree of autonomy 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, and it is impossible to obtain enough observable pulsars in some locations. The signals of some pulsars are weak, and the signals are easily interfered in a high-noise environment, resulting in the spacecraft being unable to obtain sufficient observation data at a specific location or time. In addition, the periodic characteristics of pulsar signals lead to a low frequency of data updates, which makes it difficult to meet the real-time and high-frequency update requirements of high-dynamic tasks.

[0004] The Deep Space Network (DSN) refers to a deep space communication and tracking network composed of multiple ground stations distributed around the world, which is 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, and can measure the position and velocity of spacecraft through radio determination methods including Time Difference of Arrival (TDOA) and Doppler Shift. Specifically, the time difference of arrival measurement calculates the position information of the spacecraft relative to the ground station by comparing the time difference between the arrival of the signal at different ground stations; the 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 interferometric measurement system of China Deep Space Net (CDSN) is currently composed of Jiamusi Deep Space Station (JM01), Kashgar Deep Space Station (KS01), Namibia Deep Space Antenna (NB01) and South America Deep Space Station (NM01) and related processing centers in Beijing. The longest baseline of the system reaches 12,000 km. In terms of overall layout, China's deep space tracking and control network is not the best geographical layout. The coverage rate of China's deep space network for tracking and control of deep space spacecraft is only close to 90%. Secondly, given the current large number of satellite missions and limited ground station resources, it is difficult to provide continuous and comprehensive tracking and control support for all satellites. Furthermore, when a spacecraft flies to the back of the moon or is in a signal blind spot due to obstruction by other spacecraft and satellites, the ground station will not be able to effectively receive and obtain the signal it transmits. In addition, for high-latitude orbits or extreme deep space missions, the ground reception angle of the signal may be insufficient, resulting in a decrease in the signal reception efficiency in some directions, and insufficient signals may occur. Furthermore, the Deep Space Network's ground stations may also 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. In addition, due to the rotation of the Earth and the maintenance requirements of ground stations, a ground station may be on the back of the Earth or require short-term maintenance, resulting in spacecraft relying on other stations, especially for spacecraft in extreme orientations or remote orbital locations, where coverage capabilities may be limited. Summary of the invention

[0005] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and propose a spacecraft navigation method based on a combination of pulsars and 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 precision in the prior art. Pulsar navigation provides absolute positioning for spacecraft, so that it can still navigate autonomously when the deep space network ground station coverage is insufficient or communication is limited; 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 accurate positioning support. The present invention ensures the continuity and high precision of navigation in complex environments, while enhancing the autonomy and robustness of the system, enabling spacecraft to obtain more stable navigation support in 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 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; according to the relationship between the time when the pulsar photons arrive at the spacecraft and the phase when the pulsar arrives 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 uses the time difference between the signal reaching two different ground stations and its Doppler frequency shift as the measurement of the deep space network system, and establishes the measurement equation of the deep space network system;

[0010] (4) Combining the measurement equations of the pulsar navigation system with the measurement equations of the deep space network system, a pulsar and deep space network combined navigation system model is constructed; that is, sequential observations are made on 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 the pulsar is used first; when all N navigation pulsars are not visible, the measurement of the deep space network system is used to make up for the vacant time period of the pulsar navigation without measurement; when the navigation pulsar is not visible and the deep space network ground station cannot receive signals, the without measurement input of this 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 quantity measurement;

[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, the state quantity and covariance matrix in the EKF algorithm are first 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 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 covariance matrix is ​​updated using the state transfer matrix constructed in step 5. 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 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 signal, and can provide absolute position reference information in a deep space environment, thereby realizing autonomous positioning of the spacecraft in a deep space environment;

[0017] Second, when the pulsar signal is weak, the observation conditions are limited or the accuracy is insufficient, the present invention uses the time difference and Doppler frequency shift observation data of the deep space network to further supplement the accuracy requirements of pulsar navigation in long-term navigation, and at the same time performs high-frequency measurement updates to provide absolute position information with the deep space network; thereby maintaining the stability of navigation and effectively improving the reliability of the system;

[0018] Third, since the present invention adopts a combined navigation method based on pulsars and relying on non-continuous observation data of the deep space network, pulsar navigation and deep space network observation are effectively combined, and the complementary advantages of the two are used 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 reduces the observation burden of ground stations to a certain extent; when the ground station has the observation conditions, it provides non-continuous observation information, and combines pulsar navigation to correct the position and speed of the spacecraft, thereby optimizing resource utilization and further improving pulsar navigation accuracy;

[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 Flow chart for realizing the method of the present invention;

[0021] Figure 2 This is a schematic diagram of pulsar navigation used in the present invention;

[0022] Figure 3 A schematic diagram of deep space network navigation used in the present invention;

[0023] Figure 4 The figure 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 pulsar and deep space network, establishes a navigation system state model of the spacecraft according to the orbital dynamics equation; uses an X-ray detector to obtain the time when photons arrive at the spacecraft, and converts it to the solar system barycenter SSB (Solar System Barycenter, SSB), and establishes a photon arrival phase measurement equation based on the relationship between the photon arrival SSB phase and the spacecraft state; uses the deep space network ground station to receive spacecraft signals, and establishes a time difference and Doppler frequency shift measurement equation through the time collected by multiple ground stations and the frequency information of a single ground station; adopts an EKF filtering method to integrate the data of pulsar and deep space network to obtain an estimated vector of the spacecraft state.

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

[0026] Example 1: Reference Figure 1 This embodiment proposes a spacecraft navigation method based on the combination of pulsars and deep space network, which integrates the observation information of X-ray pulsars, the time difference of deep space network and Doppler frequency shift, and studies the navigation method based on the combination of pulsars and deep space network, so as to obtain a more accurate spacecraft state estimation value and improve the performance of the navigation system. Specifically, it includes the following steps:

[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, analyze the various perturbations acting on the satellite in uncontrolled motion and establish the navigation system state equation based on the high-precision orbital dynamics model.

[0028] In this embodiment, the position and velocity expressions of the spacecraft relative to the center of mass of the earth at time t are constructed, that is, the state equation of the navigation system 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, 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 measurement quantity of pulsar navigation; according to 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 the pulsar photon arrives at the detector on the spacecraft to the solar system mass center SSB, uses the pulsar timing model established in the solar mass center reference system, predicts the phase of the same photon arriving at SSB, takes the phase of the photon arriving at SSB as the basic pulsar navigation observation, and constructs the relationship between the phase φ(t,X) of the photon arriving at SSB and the spacecraft state, that is, 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 light 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, and uses the time difference of the signal reaching two different ground stations and its Doppler frequency shift as the measurement of the deep space network system, and establishes the measurement equation of the deep space network system; specifically, it is obtained 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 station A and ground station 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 by ground station m, the relationship between Doppler frequency shift Δf and 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 the measurement equations of the deep space network system to construct a pulsar and deep space network combined navigation system model; that is, sequentially observe 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 the pulsar is used first; when all N navigation pulsars are not visible, the measurement of the deep space network system is used to make up for the vacant time period of the pulsar navigation without measurement; when the navigation pulsar is not visible and the deep space network ground station cannot receive signals, the without measurement input of this time period is determined, and the orbital dynamics equation is recursively deduced using the numerical integration method;

[0043] In this embodiment, the measurement equation of the spacecraft navigation system of the above-mentioned pulsar and deep space network combination is expressed as follows:

[0044]

[0045] Among them, 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 above 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 the N navigation pulsars are not visible, 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 frequency 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 a pulsar and deep space network combined navigation system model;

[0057] Step 8. According to 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 deep space network system for measurement, determine the update step size based on the measurement, and extract the 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. 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 state vector and covariance matrix of the spacecraft at the start time t, and set the observation interval length α corresponding to the kth pulsar according to the navigation pulsar flow 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 selected N 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 dynamic model of the spacecraft 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 transfer 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 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+l, 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 frequency shift Δf = f-f0; combining the arrival time difference and the Doppler frequency shift, the measurement quantity Z(t+l) = [ΔtΔf] 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 execute 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 of the satellite in uncontrolled motion, taking into account the gravity of the earth, atmospheric drag, the gravity of the sun and the moon, the solar radiation pressure, the earth and ocean tides, and the influence of other celestial bodies on the gravity of the spacecraft. In the geocentric equatorial coordinate system, establish the navigation system state equation based on the high-precision orbital dynamics model:

[0068]

[0069] Among them, the state vector X(t) = (r T (t),v T (t)) T is the position and velocity of the spacecraft relative to the center of mass of the earth; r is the position of the spacecraft to the center of the earth 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 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 drag; 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 earth's gravity and non-spherical shape perturbations with high accuracy. 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 in the International Space Station's orbit around the earth. The tidal gravitational potential is expanded using spherical harmonics similar to the static earth's gravitational field to calculate the satellite orbit perturbations caused by the sun and moon's solid earth tides. 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 accurately 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 selected 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 SSB at the solar system mass center, 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 of pulsar navigation. Figure 2 , the relationship between the photon arrival phase and the spacecraft state is constructed, and 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 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. Thus, the relationship between the phase φ(t) of the photon arriving at the SSB and the spacecraft position vector r(t) is constructed.

[0078] The spacecraft transmits signals to the Deep Space Network ground station. Ground stations at different locations receive the signals and record the signal arrival time and frequency. Figure 3 , establish the measurement equation of the deep space network system. Calculate the time difference between the spacecraft signal reaching ground station A and ground station 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 the Doppler frequency shift Δf and the 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, and the pulse arrival phases of multiple pulsars are used as the measurement of pulsar navigation. The relative position information of the spacecraft and the radial velocity information of the Doppler frequency shift measurement are measured by combining the time difference of the spacecraft signal received by the Deep Space Network ground station, which can provide the absolute position information of the spacecraft. Combining three different navigation measurement quantities, the measurement equation of the spacecraft navigation system combined with pulsars and Deep Space Network is established:

[0086]

[0087] Where h(·) is the 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 of pulsar and deep space network combination, due to the nonlinear characteristics of the state and observation equations, it is more complicated to solve them directly, so the nonlinear equations are linearized. In the linearization process of EKF, 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 of the state transfer matrix, namely a variational equation, is constructed and the variational equation is solved using a numerical method to obtain the state transfer matrix.

[0093]

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

[0095]

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

[0097] The measurement equation is linearized near the current state to construct the measurement matrix H, thereby realizing effective observation update of the nonlinear system. In the calculation of partial derivatives describing the relationship between the instantaneous position and velocity of the pulsar measurement value and 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, respectively, i = 1, 2, 3. The time difference and Doppler frequency shift observations obtained by 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 uniformly expressed in the same mathematical framework to establish a comprehensive measurement matrix of the system:

[0102]

[0103] Step 4: Based on the navigation system of the combination of pulsar 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 measurement 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 pulsar and deep space network in the present 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 combined navigation system is:

[0105]

[0106] First, the spacecraft state estimation vector and covariance matrix are initialized

[0107]

[0108] Then, in the time update phase of the EKF, the dynamic model of the spacecraft is used to update the state estimate and covariance matrix to predict the state of the spacecraft 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 i The orbit is recursively calculated at each 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 size, for t i-1 to 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 actual measurements made by spacecraft probes and Deep Space Network ground stations. i-1 to i+1 The photon arrival timestamp of the target pulsar recorded at each moment is processed to i-1 to 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 the spacecraft signal and generate a time mark t A and t B , get the time difference between the signal reaching 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. The three different measurements are combined to obtain 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 the 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 observed quantity is corrected at every moment, and the estimated state is finally obtained. i Estimated state at any 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] The present invention innovatively proposes to combine pulsar navigation with the deep space network, thereby effectively making up for the limitations of both. Pulsar navigation uses stable pulsar signals in the universe to provide absolute positioning information, so that even when the ground station coverage is insufficient or the communication is temporarily limited, the spacecraft can still achieve autonomous navigation through pulsar signals, reducing the continuous dependence on the ground station. When the spacecraft is able to receive enough pulsar signals, the system gives priority to using pulsar data to provide absolute position; when the pulsar signal is weak, unevenly distributed or interfered with by the signal, the deep space network time difference and Doppler frequency shift information are used to provide accurate relative positioning support.

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

[0119] The parts of the present invention that are not described in detail belong to the common knowledge of those skilled in the art. The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Obviously, after understanding the content and principle of the present invention, professionals in this field may make various modifications and changes in form and details without departing from the principle and structure of the present invention, but these modifications and changes based on the idea of ​​the present invention are still 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 orbiting satellite in the geocentric equatorial coordinate system; (2) Selecting multiple pulsars as navigation stars to provide pulsar measurement information; Observation is performed using the sequential observation method, and the phase of the pulse arriving at the SSB of the solar system center of mass is used as the measurement of pulsar navigation; based on the relationship between the time when the pulsar photons arrive at the spacecraft and the phase when the pulsar arrives at the SSB, the pulsar timing model and time conversion equation are used to establish the measurement equation of the pulsar navigation system; (3) The spacecraft transmits a signal to the ground station, and uses the time difference between the signal reaching two different ground stations and its Doppler frequency shift as the measurement of the deep space network system, and establishes the measurement equation of the deep space network system; (4) Combining the measurement equations of the pulsar navigation system with the measurement equations of the deep space network system, a pulsar and deep space network combined navigation system model is constructed; that is, sequential observations are made on 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 the pulsar is used first; when all N navigation pulsars are not visible, the measurement of the deep space network system is used to make up for the vacant time period of the pulsar navigation without measurement; when the navigation pulsar is not visible and the deep space network ground station cannot receive signals, the without measurement input of this time period is determined, and the orbital dynamics equation is recursively deduced using the numerical integration method; (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) linearizing the measurement equation of the pulsar navigation system in step (2) near the current time, and constructing a measurement matrix to describe the conversion relationship from state quantity to quantity measurement; (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) to obtain a pulsar and deep space network combination navigation system model; (8) According to 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, firstly, the state quantity and covariance matrix in the EKF algorithm are initialized; then, whether the pulsar is visible and whether the ground station can receive the signal is determined, and whether the pulsar navigation or the deep space network system is used for measurement, the update step size is determined according to the quantity measurement, and the quantity measurement is extracted by 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 covariance matrix is ​​updated using the state transfer matrix constructed in step (5); 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 estimates the spacecraft position and completes the spacecraft navigation mission.

2. The method according to claim 1, characterized in that: In step (1), based on the orbital dynamics equation, the navigation system state equation is established for the satellite orbiting the earth in uncontrolled motion in the geocentric equatorial coordinate system, that is, the position and velocity expression of the spacecraft relative to the center of mass of the earth at time t is constructed, which is specifically as follows: Where X(t) = (r T (t),v T (t)) T represents the spacecraft state vector at time t, T represents the transposition operation, r = r(t) is the position of the spacecraft to the center of the earth at time t; v = v(t) is the speed of the spacecraft relative to the center of the earth at time t; f(·) is the navigation state equation of the combination of pulsar and deep space network, 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, characterized in that: 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 SSB at the mass center of the solar system. The pulsar timing model established in the solar mass center 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 state of the spacecraft is constructed, that is, the pulsar navigation measurement equation: 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 light 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, characterized in that: The measurement equation of the deep space network system in step (3) is obtained in the following manner: (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 station A and ground station 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 by ground station m, the relationship between Doppler frequency shift Δf and 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: Among them, 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, characterized in that: The state transfer matrix in step (5) is obtained as follows: Construct the state transfer 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, characterized in that: 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 the N navigation pulsars are not visible, 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 frequency 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, characterized in that: Step (8) uses the extended Kalman filter (EKF) algorithm to estimate the position of the spacecraft, and the specific implementation steps are as follows: (8.1) Establish a pulsar and deep space network integrated navigation system model: (8.2) Initialize the state vector and covariance matrix of the spacecraft at the start time t, and set the observation interval length α corresponding to the kth pulsar according to the navigation pulsar flow 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 selected N 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 dynamic model of the spacecraft to recursively calculate the orbit 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 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+l, 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 frequency shift Δf = f-f0; combining the arrival time difference and the Doppler frequency shift, the measurement quantity Z(t+l) = [ΔtΔf] 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 execute 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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