Spacecraft position and time state joint determination method based on earth-moon reference frame

Abstract

This invention discloses a method for jointly determining the position and time state of a spacecraft by integrating a lunar reference, belonging to the fields of deep space exploration, autonomous navigation, and time synchronization. The method includes: constructing an augmented state vector, which simultaneously includes the spacecraft's position and inertial velocity relative to the Earth's center, its position and inertial velocity relative to the Moon's center, the spacecraft's local clock bias and drift, and the common clock bias and drift of the lunar-based navigation network; acquiring pseudorange and pseudorange rate observation data from the Earth-based and lunar-based base stations, and introducing a precise Earth-Moon ephemeris to construct Earth-Moon position and velocity constraints as virtual observations, combining physical and virtual observations into a unified observation model; constructing a global observation residual vector and configuring a weight matrix; and employing a weighted iterative least squares algorithm to jointly solve the augmented state vector, outputting the synchronization estimation results of the spacecraft's position, velocity, and time state. This invention achieves high-precision autonomous navigation and Earth-Moon time reference synchronization for Earth-Moon spacecraft.

Description

Technical Field

[0001] This invention belongs to the fields of deep space exploration, autonomous navigation and time synchronization technology, and specifically relates to a method for jointly determining the position and time status of a spacecraft by integrating the Earth-Moon reference. Background Technology

[0002] With the advancement of missions such as manned lunar landing, the construction of lunar research stations, and the development of the Earth-Moon space economic circle, the demand for positioning, navigation, and timing (PNT) services in the Earth-Moon space is experiencing explosive growth. In the next decade, hundreds of spacecraft are expected to operate in the Earth-Moon space, encompassing various types including lunar orbiters, landers, rovers, and Earth-Moon libration probes, placing unprecedented demands on the continuity, real-time performance, and accuracy of navigation services. However, existing technological solutions still have significant limitations in practical applications and are insufficient to meet these demands.

[0003] Currently, lunar probes primarily rely on ground-based tracking and control networks and Very Long Baseline Interferometry (VLBI) technology for precise orbit determination. While these ground-based measurement methods offer high accuracy, they are limited by the Earth's rotation and the visible arc of the lunar orbit. Each ground station's continuous tracking arc for the spacecraft typically does not exceed 8 hours, resulting in invisible observation blind spots. When the spacecraft reaches the far side of the moon or is in a specific phase of its Earth-Moon transfer orbit, the ground-based measurement link will be completely interrupted. Furthermore, with the increasing density of Earth-Moon space missions, the scheduling pressure on global deep space tracking and control network resources continues to rise. In scenarios involving multiple targets and high-frequency missions operating in parallel, the existing ground-based tracking and control system struggles to consistently meet the demands for continuous, real-time navigation services.

[0004] In recent years, using Earth GNSS signals for lunar space navigation has become a research hotspot. Theoretically, spacecraft can receive Earth GNSS sidelobe signals to achieve autonomous positioning. However, due to the vast distance between the Earth and the Moon (approximately 380,000 kilometers), signal link attenuation is severe, resulting in extremely low signal power reaching the vicinity of the Moon, placing extremely high demands on receiver sensitivity. More importantly, from the Moon's perspective, the Earth GNSS constellation is concentrated near the Earth's center, with extremely poor observation geometry and a narrow azimuth distribution, leading to an ill-conditioned observation matrix. Single-epoch positioning accuracy is typically on the order of kilometers, which cannot meet the high-precision positioning requirements of lunar landing, rendezvous, and docking missions.

[0005] To address the aforementioned issues, academia and engineering have proposed navigation enhancement schemes such as lunar navigation augmentation satellites, Earth-Moon libration constellations, and lunar surface reference stations. These schemes construct a navigation service system oriented towards the Earth-Moon space by deploying navigation / ranging nodes in lunar orbit, at Earth-Moon libration points, or on the lunar surface. However, these schemes typically require maintaining a unified spatiotemporal reference among the navigation nodes, especially demanding high-precision time synchronization capabilities between orbital nodes, libration point nodes, and lunar surface reference nodes. In practical engineering, the long-term high-precision synchronization between the lunar-based or Earth-Moon navigation network and Earth reference time is costly due to factors such as the lunar surface environment, the long-term autonomous operation conditions of nodes, and the delay, obstruction, and stability of the Earth-Moon link. Furthermore, the synchronization accuracy and stability are difficult to guarantee in the long term. Traditional single-point positioning algorithms usually treat the clock bias of navigation nodes as a known quantity or pre-calibrated by an external system, failing to fully consider the uncertainties of clock bias and clock drift of lunar-based navigation nodes. They also lack a unified estimation framework compatible with different construction stages of navigation nodes, from "independent time synchronization" to "networked synchronization," making it difficult for navigation algorithms to adapt to the practical engineering needs of the gradual deployment of lunar navigation systems.

[0006] Furthermore, when processing mixed observation data from terrestrial and lunar base stations, existing navigation schemes typically force all observations to be transformed into a single coordinate system (such as the geocentric or lunar coordinate system). This "hard transformation" requires the introduction of complex precession, nutation, and libration correction models, as well as high-precision ephemeris data, when processing observation data that crosses the Earth-Moon gravitational center. These model errors and ephemeris errors are directly coupled into the observation equations, affecting each observation, significantly increasing the nonlinearity of the equations, and reducing the navigation solution performance.

[0007] In summary, existing technologies face multiple bottlenecks in lunar space navigation, including insufficient observation coverage, poor signal geometry, difficulty in coordinating spatiotemporal references, and coupling errors in cross-center coordinate transformation. There is an urgent need to propose a new navigation method that can integrate the lunar and Earth references and jointly determine the spacecraft's position and time status in order to overcome the above-mentioned technical limitations and support the future needs of large-scale, high-precision navigation applications in lunar space. Summary of the Invention

[0008] To address the aforementioned technical problems, this invention provides a method for jointly determining the position and time state of a spacecraft based on a lunar reference. By constructing an augmented state vector that simultaneously includes the spacecraft's geocentric state, lunar state, and multiple clock biases and drifts, and by integrating a precise lunar ephemeris as a virtual observation constraint into a unified observation model, the method achieves joint calculation of the spacecraft's position and time within a weighted iterative least squares framework. This avoids the nonlinear error coupling caused by hard transformation of traditional coordinate systems and realizes integrated estimation of navigation and time synchronization based on a lunar reference.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] A method for jointly determining the position and time state of a spacecraft by integrating a lunar reference, comprising:

[0011] Step 1: Construct augmented state vectors, which include the spacecraft's position and inertial velocity vectors relative to the Earth's center, the spacecraft's position and inertial velocity vectors relative to the Moon's center, the spacecraft's local clock bias and clock drift, and the lunar-based navigation network's common clock bias and clock drift.

[0012] Step 2: Obtain ground station observation data and lunar station observation data, and introduce the Earth-Moon precise ephemeris to construct Earth-Moon position constraints and Earth-Moon velocity constraints as virtual observations. Combine the ground station observation data, lunar station observation data and virtual observations to form a unified observation model.

[0013] Step 3: Based on the unified observation model, construct the global observation residual vector and configure the weight matrix according to the observation station type and the accuracy of the Earth-Moon precise ephemeris.

[0014] Step 4: Using the current nominal state as the initial value, calculate the Jacobian matrix of the unified observation model. Use the weighted iterative least squares algorithm to solve for the state increment using the global observation residual vector and weight matrix, update the augmented state vector, and output the joint estimation results of the spacecraft's position, velocity, and time state after the iteration is completed.

[0015] Furthermore, in step 1, the augmented state vector is defined as: the spacecraft's position vector relative to the Earth's center, the spacecraft's velocity vector relative to the Earth's center, the spacecraft's position vector relative to the Moon's center, the spacecraft's velocity vector relative to the Moon's center, the spacecraft's local clock bias, the spacecraft's local clock drift, the lunar-based navigation network's common clock bias, and the lunar-based navigation network's common clock drift, totaling sixteen state variables.

[0016] Furthermore, in step 2, the Earth-Moon position constraint is that the position of the Moon's center relative to the Earth's center is equal to the spacecraft's position relative to the Earth's center minus the spacecraft's position relative to the Moon's center, and the Earth-Moon velocity constraint is that the Moon's inertial velocity relative to the Earth is equal to the spacecraft's velocity relative to the Earth's center minus the spacecraft's velocity relative to the Moon's center; the Moon's position relative to the Earth's center and the Moon's inertial velocity relative to the Earth are provided by the Earth-Moon Precision Ephemeris.

[0017] Furthermore, in step 2, the ground station observation data includes a first pseudorange observation equation and a first pseudorange rate observation equation. The first pseudorange observation equation is that the pseudorange measurement value of the ground station is equal to the first geometric distance between the spacecraft and the ground station plus the speed of light multiplied by the spacecraft's local clock error, plus pseudorange observation noise. The first pseudorange rate observation equation is that the pseudorange rate measurement value of the ground station is equal to the first geometric distance change rate plus the speed of light multiplied by the spacecraft's local clock drift, plus pseudorange rate observation noise. The first geometric distance is given by the magnitude of the difference between the spacecraft's position relative to the Earth's center and the ground station's position. The first geometric distance change rate is obtained by dividing the geometric distance by the dot product of the relative position vector and the relative velocity vector between the spacecraft and the ground station.

[0018] Furthermore, in step 2, the lunar base station observation data includes a second pseudorange observation equation and a second pseudorange rate observation equation. The second pseudorange observation equation is that the pseudorange measurement value of the lunar base station is equal to the second geometric distance between the spacecraft and the lunar base station plus the speed of light multiplied by the difference between the spacecraft's local clock error and the common clock error of the lunar navigation network, plus pseudorange observation noise. The second pseudorange rate observation equation is that the pseudorange rate measurement value of the lunar base station is equal to the second geometric distance change rate plus the speed of light multiplied by the difference between the spacecraft's local clock drift and the common clock drift of the lunar navigation network, plus pseudorange rate observation noise. The second geometric distance is given by the magnitude of the difference between the spacecraft's position relative to the lunar center and the lunar base station's position, and the second geometric distance change rate is obtained by dividing the geometric distance by the dot product of the relative position vector and the relative velocity vector between the spacecraft and the lunar base station.

[0019] Furthermore, in step 3, the global observation residual vector is composed of the ground base station pseudorange residual, the ground base station pseudorange rate residual, the monthly base station pseudorange residual, the monthly base station pseudorange rate residual, and the virtual observation residual.

[0020] Furthermore, in step 3, the pseudorange residual of the ground station is the difference between the measured pseudorange value and the predicted pseudorange value calculated based on the current nominal state, and the pseudorange rate residual of the ground station is the difference between the measured pseudorange rate value and the predicted pseudorange rate value calculated based on the current nominal state; the virtual observation residual includes the Earth-Moon position constraint residual and the Earth-Moon velocity constraint residual, and the Earth-Moon position constraint residual is the difference between the position of the Moon center relative to the Earth center provided by the Earth-Moon precise ephemeris and the Earth center position calculated based on the current nominal state minus the Moon center position.

[0021] Furthermore, in step 4, the weighted iterative least squares solution includes the following steps: using the current nominal state as the initial value, calculating the Jacobian matrix of the unified observation model, wherein the Jacobian matrix contains the partial derivatives of the ground-based observation equation, the lunar-based observation equation, and the virtual observation equation with respect to the relevant state quantities in the augmented state vector; wherein, the partial derivatives corresponding to the ground-based observation equation involve the spacecraft's geocentric position, geocentric inertial velocity, spacecraft local clock error, and local clock drift, and the partial derivatives corresponding to the lunar-based observation equation involve the spacecraft's lunar-based position, lunar-based inertial velocity, and local clock drift. The local clock bias and drift of the spacecraft, the common clock bias and drift of the lunar-based navigation network, and the partial derivatives of the virtual observation equations involve the spacecraft's geocentric position, geocentric inertial velocity, lunar position, and lunar inertial velocity. Based on the global observation residual vector and weight matrix, the weighted least squares formula is used to solve for the state increment. The augmented state vector is updated. The updated state is used as the new nominal state and iterated repeatedly until the preset maximum number of iterations is reached or the state increment magnitude is less than the preset convergence threshold, at which point the joint estimation results of the spacecraft's position, velocity, and time state are output.

[0022] In a second aspect, the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned method for jointly determining the position and time status of a spacecraft based on a fused Earth-Moon reference.

[0023] Thirdly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned method for jointly determining the position and time status of a spacecraft based on a lunar reference.

[0024] The beneficial effects of this invention are as follows:

[0025] This invention avoids the nonlinear error coupling of coordinate transformation across the gravitational center. It simultaneously uses the spacecraft's position and velocity relative to both the Earth's center and the Moon's center as quantities to be estimated, constructing virtual observation constraints through a precise Earth-Moon ephemeris. This eliminates the need to forcibly transform observation data to a single coordinate system, avoiding the coupling of precession, nutation, libration, and ephemeris errors into the observation equations. This significantly reduces the nonlinearity of the solution and improves navigation accuracy and robustness.

[0026] This invention achieves joint depth estimation of position and time. It incorporates the spacecraft's local clock bias and clock drift, as well as the shared clock bias and clock drift of the lunar navigation network, into the augmented state vector, solving the problem synchronously with the space state. This significantly reduces reliance on high-precision external timing links and solves the challenge of long-term high-precision synchronization of time references in the complex dynamic environment of the Earth-Moon space.

[0027] A unified estimation framework compatible with different development stages of lunar base stations was established. By introducing common clock bias parameters of the lunar navigation network, this invention can adaptively process observation data of lunar base stations at different stages from "independent clock" to "networked synchronization," exhibiting good engineering adaptability and scalability.

[0028] The observation geometry and calculation accuracy have been improved. By integrating the joint observation network composed of lunar and terrestrial base stations, the geometric limitations under a single gravitational center have been broken. Combined with adaptive weight configuration, the organic integration of terrestrial pseudorange, lunar pseudorange and virtual observations has been achieved, which has significantly improved the joint calculation accuracy of spacecraft position, velocity and time status. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of a method for jointly determining the position and time status of a spacecraft by integrating the Earth-Moon reference. Detailed Implementation

[0030] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0031] like Figure 1 As shown, this invention proposes a method for jointly determining the position and time state of a spacecraft based on a fusion of Earth and Moon references. The core idea is to address the problem of inconsistent observation references in Earth-Moon space navigation (Ground-based base stations use the Earth's center as the reference, while Moon-based base stations use the Moon's center). Instead of using traditional complex observation equation coordinate transformations, this invention augments the state space, simultaneously treating the spacecraft's position and velocity relative to both the Earth's center and the Moon's center as quantities to be estimated. By introducing a precise Earth-Moon ephemeris as a "virtual observation constraint," a unified augmented state observation model is constructed. Using a weighted iterative least squares algorithm, the high-precision position, velocity, and time deviation between the spacecraft's onboard clock state and the lunar-based navigation network are jointly calculated within this unified framework. Specifically, taking a spacecraft operating in an Earth-Moon DRO (distant retrograde orbit) as an example, the specific implementation process of the method for jointly determining the position and time state of a spacecraft based on a fusion of Earth and Moon references is explained in detail. The method includes:

[0032] Step 1: Construct an augmented state vector, which includes the spacecraft's position and velocity relative to the Earth's center, the spacecraft's position and velocity relative to the Moon's center, the spacecraft's local clock bias and clock drift, and the lunar-based navigation network's common clock bias and clock drift.

[0033] Step 2: Obtain ground station observation data and lunar station observation data, and introduce the Earth-Moon precise ephemeris to construct Earth-Moon position constraints and Earth-Moon velocity constraints as virtual observations. Combine the ground station observation data, lunar station observation data and virtual observations to form a unified observation model.

[0034] Step 3: Based on the unified observation model, construct the global observation residual vector and configure the weight matrix according to the observation station type and the accuracy of the Earth-Moon precise ephemeris.

[0035] Step 4: Using the current nominal state as the initial value, calculate the Jacobian matrix of the unified observation model. Use the weighted iterative least squares algorithm to solve for the state increment using the global observation residual vector and weight matrix, update the augmented state vector, iterate until convergence, and output the joint estimation results of the spacecraft's position, velocity, and time state.

[0036] Furthermore, in step 1:

[0037] First, we define a spatial coordinate system, which involves the geocentric inertial coordinate system (ECI). Lunar Inertial Coordinate System (MCI) Earth-Moon rotating coordinate system ), Geocentric Fixed Coordinate System (ECEF) ) and the lunar fixed coordinate system (MCMF, The geocentric inertial coordinate system typically refers to the J2000 inertial frame, with the Earth's center as its origin and the Earth's mean equatorial plane at 12:00 TDB on January 1, 2000, as its reference plane. Its x-axis points to the vernal equinox. The lunar-centric inertial coordinate system has the Moon's center as its origin, and its three axes are parallel to the geocentric inertial coordinate system. The origin of the Earth-Moon rotating coordinate system is located at the Earth-Moon system's center of mass, with its x-axis pointing to the Moon, its y-axis lying in the orbital plane and pointing in the direction of the Moon's velocity, and its z-axis forming a right-handed rectangular coordinate system with the x and y axes. The origin of the geocentric fixed coordinate system is located at the Earth's center, with its z-axis pointing in the direction of the Earth's rotation axis; its x-axis points to the intersection of the Earth's prime meridian and the equatorial plane; and its y-axis lies in the equatorial plane and forms a right-handed rectangular coordinate system with the x and z axes. The origin of the lunar fixed coordinate system is at the Moon's center, rotating synchronously with the Moon, and its coordinate axes are defined as the principal axes of the diagonal matrix of the Moon's moment of inertia tensor.

[0038] Based on the coordinate system definition, at the start of the navigation calculation, the initial value of the augmented state vector is set according to the spacecraft's prior orbital information. The augmented state vector x is defined as follows:

[0039] ,

[0040] in, These represent the spacecraft's position relative to the Earth's center and its inertial velocity (unless otherwise specified, all velocities mentioned in this article are inertial velocities). These represent the spacecraft's position and inertial velocity relative to the lunar center, respectively. These are the spacecraft's local clock bias and clock drift, respectively. These represent the common clock difference and common clock drift of the lunar-based navigation network relative to the geocentric reference time, respectively, with the superscript T indicating transpose.

[0041] The spacecraft's initial position and velocity relative to the Earth's center can be obtained from the medium-precision orbit determination results provided by the ground-based telemetry and control network. Its initial state relative to the lunar center is obtained by converting the Earth's center state with the lunar precise ephemeris. The initial value of the spacecraft's local clock bias can be set to a coarse deviation between the receiver clock and the system reference time, while the initial value of the lunar-based navigation network's common clock bias can be set to zero.

[0042] Furthermore, in step 2:

[0043] At the current epoch, pseudorange and pseudorange rate data are simultaneously received from ground tracking stations and lunar reference stations. Ground station observation data are described by the following observation equation: for the i-th ground station, its pseudorange observation value... for:

[0044] ,

[0045] in, Let be the geometric distance between the spacecraft and the i-th ground station. Let i be the position of the i-th ground station relative to the Earth's center, with superscript. This indicates that the state is projected onto In coordinate system, At the speed of light, For pseudorange observation noise, This indicates the position of the spacecraft relative to the Earth's center, projected onto... In a coordinate system.

[0046] Taking the time derivative of the pseudorange to reflect the Doppler frequency shift effect, we obtain the observation equation for the pseudorange rate:

[0047] ,

[0048] in, For pseudorange rate observation noise, Let be the pseudorange rate observed by the spacecraft relative to the i-th ground station. The rate of change of geometric distance is calculated using the following formula:

[0049] ,

[0050] in, Represents the dot product of vectors. The velocity projection of the spacecraft relative to the Earth's center is shown in the image. In coordinate system, Let the inertial velocity of the i-th ground station relative to the Earth's center be given by the following formula:

[0051] ,

[0052] in, This indicates the position of the i-th ground station relative to the Earth's center. Projection in coordinate system for relatively angular velocity, in The projection below, symbol This represents the cross product of vectors. for arrive The attitude transformation matrix of the coordinate system. for arrive The attitude transformation matrix of the coordinate system is calculated using the following formula:

[0053] ,

[0054] Where P represents the precession matrix, which corrects for the long-term slow motion of the Earth's rotation axis in inertial space; N represents nutation, which corrects for its periodic small oscillations. Υ represents the rotation transformation (sidereal time) around the z-axis; Υ represents polar motion, correcting the motion of the Earth's poles relative to the crust. The calculation of these matrices can be provided by the IAU 2000 / 2006 protocol standard and the NASA SPICE framework.

[0055] The monthly base station observation data is described by the following observation equation. For the base station in the j-th month, its pseudorange observation value... for:

[0056] ,

[0057] in, Let be the geometric distance between the spacecraft and the base station in the i-th month. This represents the position vector of the spacecraft relative to the center of the moon. Let the position of the base station relative to the center of the moon be in month j, with superscript. This indicates that the state is projected onto In coordinate system, At the speed of light, This represents the observation noise of the pseudorange.

[0058] Correspondingly, the pseudorange rate equation for the monthly base station is written as:

[0059] ,

[0060] in, The equivalent frequency deviation (common clock drift) of the lunar-based navigation network relative to the geocentric reference time. For the pseudorange rate observation noise of the lunar base station, The pseudorange rate observed by the spacecraft relative to the base station in month j. The rate of change of geometric distance between monthly base stations is calculated using the following formula:

[0061] ,

[0062] The velocity of the spacecraft relative to the center of the moon is projected onto... In coordinate system, Let the inertial velocity of the base station relative to the moon in the j-th month be given by the following formula:

[0063] ,

[0064] In the above formula for arrive The attitude transformation matrix of the coordinate system. for relatively angular velocity, in The projection below.

[0065] Considering the changes in the spacecraft's position and velocity relative to the Earth's center and relative to the Moon's center, the following equation gives the result:

[0066] ,

[0067] in, The position of the moon's center relative to the earth's center. The superscript represents the Moon's inertial velocity relative to the Earth. This indicates that the corresponding parameter vector is projected onto... In coordinate system (e.g., This indicates the position of the spacecraft relative to the Earth's center, projected onto... (in coordinate system), because coordinate system and The coordinate system has three parallel axes, and the above formula utilizes... arrive attitude transformation matrix of coordinate system Properties, This represents a 3D identity matrix.

[0068] The DE440 and other precise ephemeris tables are used to obtain the position of the Moon's center relative to the Earth's center and the Moon's inertial velocity relative to the Earth at the current epoch. Based on the geometric relationship of Earth-Moon motion, Earth-Moon position constraints and Earth-Moon velocity constraints are constructed as virtual observations. Specifically:

[0069] The above ground-based station observation equations, lunar-based station observation equations, and virtual observations are combined to form a unified observation model, denoted as the observation vector:

[0070] ,in Let be the number of ground-based stations and lunar-based stations, respectively. Then, from the ground-based station observation equations, lunar-based station observation equations, and the Earth-Moon vector transformation formula, we can obtain:

[0071] ,

[0072] in, and The unified virtual observation equation and virtual noise are given by the following equation:

[0073] ,

[0074] in, These respectively characterize the position and velocity errors caused by ephemeris conversion.

[0075] Furthermore, in step 3:

[0076] First, based on the measured value at the current epoch and the nominal state... The difference between the calculated predictions is used to construct the global observation residual vector Y. To ensure consistency across the central geometry, the residual vector includes not only physical sensor data but also constraint residuals from the Earth-Moon position / velocity transformation.

[0077] ,

[0078] in:

[0079] For the pseudorange and pseudorange rate residual of the ground station.

[0080] The pseudorange and pseudorange rate residuals of the lunar base station.

[0081] To ensure the physical compatibility of the geocentric and lunar states in the augmented state, the residuals based on the precise ephemeris are designed to meet the geometric constraints of the Earth and Moon.

[0082] Next, define the prior weight matrix. This invention measures the inverse of the noise covariance matrix. It employs adaptive weight adjustment based on observation station distance, signal link quality, and node type.

[0083] ,

[0084] in, and They represent peacekeeping An identity matrix with a ground station, due to the influence of the troposphere, has pseudorange noise. It is usually set to the 1m level. Set to 0.5 m / s; the distance to the lunar base station is close and the environment is stable, its pseudorange noise is low. It can be set to 0.5m level. The weight of the virtual observation term is typically set to 0.25 m / s. and The uncertainty can be set according to the Earth-Moon precise ephemeris; when the Earth-Moon precise ephemeris has high accuracy, it can be given a relatively high weight to enhance the geometric consistency constraint between the Earth-centered state and the Moon-centered state.

[0085] Furthermore, in step 4:

[0086] This is a nonlinear equation, which can be solved using the least squares algorithm. This requires calculating the Jacobian matrix, i.e.:

[0087] ,

[0088] in:

[0089] ,

[0090] In the above formula , , , , , They represent the first The partial derivative of the pseudorange of each ground station with respect to the geocentric position vector of the spacecraft, the first The partial derivative of the pseudorange rate of each base station with respect to the geocentric position vector of the spacecraft, the first... The partial derivative of the pseudorange rate of each base station with respect to the geocentric velocity vector of the spacecraft, the first... The partial derivative of the pseudorange of the lunar base station with respect to the lunar center position vector of the spacecraft, the first The partial derivative of the pseudorange rate of the monthly base station with respect to the lunar center position vector of the spacecraft, and the first The partial derivative of the pseudorange rate of the lunar base station with respect to the spacecraft's lunar center velocity vector. This indicates the definition of an operator, that is... and They represent the first The unit line-of-sight vector from each ground station to the spacecraft, and the vector from the first... The unit line-of-sight vector from the monthly base station to the spacecraft.

[0091] The nominal point in the l-th iteration Linearization at that point allows for the calculation of... and According to the observed values Calculated According to the error equation The weighted least squares criterion is adopted, and the state increment is... The solution process is as follows:

[0092] ,

[0093] Therefore, the state update for this iteration can be obtained as follows:

[0094] ,

[0095] This is the value after the l-th iteration, which is also the nominal point of the (l+1)-th iteration. The updated value... As the new nominal point for the next iteration, the Jacobian matrix is ​​recalculated. With residual Set the maximum number of iterations. and convergence threshold If the number of iterations reaches the maximum number of iterations or If the condition is met, the calculation will terminate.

[0096] Example:

[0097] To verify the effectiveness of the proposed method for jointly determining the position and time state of a spacecraft based on a lunar reference, a simulation was conducted using a spacecraft operating in a distant retrograde Earth-Moon (DRO) orbit. The spacecraft's true position and velocity relative to the Earth's center are as follows:

[0098] ,

[0099] The initial navigation errors were set as follows: a standard deviation of 10 km for position error and a standard deviation of 0.01 km / s for speed error. The simulation included 2 ground base stations and 4 monthly base stations. Their geographical location parameters are shown in Table 1 (Ground Base Station Latitude, Longitude, Altitude) and Table 2 (Month Base Station Latitude, Longitude, Altitude).

[0100] Table 1

[0101] Table 2

[0102] The spacecraft's initial clock parameters are:

[0103] ,

[0104] The unified clock parameters for the lunar-based network are:

[0105] ,

[0106] Using the weighted iterative least squares joint estimation method proposed in this invention, the number of iterations is... Set to 20 times and convergence threshold Set to 10 -6After iterative convergence, the spacecraft's position and velocity estimates are as follows:

[0107] ,

[0108] The estimated clock parameters of the spacecraft are as follows:

[0109] ,

[0110] The estimated parameters for the unified lunar network clock are as follows:

[0111] ,

[0112] The estimated results are in high agreement with the actual values, with the spacecraft position error less than 10 meters, the velocity error better than 0.001 km / s, and the clock parameter estimation errors all within acceptable ranges. The simulation results fully verify the effectiveness and high-precision performance of the proposed method in multi-source observation fusion and joint estimation of position and time states in the Earth-Moon space.

[0113] In a second aspect, the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned method for jointly determining the position and time status of a spacecraft based on a fused Earth-Moon reference.

[0114] Thirdly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned method for jointly determining the position and time status of a spacecraft based on a lunar reference.

[0115] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for jointly determining the position and time state of a spacecraft using a lunar reference system, characterized in that, include: Step 1: Construct augmented state vectors, which include the spacecraft's position and inertial velocity vectors relative to the Earth's center, the spacecraft's position and inertial velocity vectors relative to the Moon's center, the spacecraft's local clock bias and clock drift, and the lunar-based navigation network's common clock bias and clock drift. Step 2: Obtain ground station observation data and lunar station observation data, and introduce the Earth-Moon precise ephemeris to construct Earth-Moon position constraints and Earth-Moon velocity constraints as virtual observations. Combine the ground station observation data, lunar station observation data and virtual observations to form a unified observation model. Step 3: Based on the unified observation model, construct the global observation residual vector and configure the weight matrix according to the observation station type and the accuracy of the Earth-Moon precise ephemeris. Step 4: Using the current nominal state as the initial value, calculate the Jacobian matrix of the unified observation model. Use the weighted iterative least squares algorithm to solve for the state increment using the global observation residual vector and weight matrix, update the augmented state vector, and output the joint estimation results of the spacecraft's position, velocity, and time state after the iteration is completed.

2. The method for jointly determining the position and time status of a spacecraft based on a lunar reference as described in claim 1, characterized in that, In step 1, the augmented state vector is defined as: the spacecraft's position vector relative to the Earth's center, the spacecraft's velocity vector relative to the Earth's center, the spacecraft's position vector relative to the Moon's center, the spacecraft's velocity vector relative to the Moon's center, the spacecraft's local clock bias, the spacecraft's local clock drift, the lunar-based navigation network's common clock bias, and the lunar-based navigation network's common clock drift, totaling sixteen state variables.

3. The method for jointly determining the position and time status of a spacecraft based on a lunar reference as described in claim 1, characterized in that, In step 2, the Earth-Moon position constraint is that the position of the Moon's center relative to the Earth's center is equal to the position of the spacecraft relative to the Earth's center minus the position of the spacecraft relative to the Moon's center, and the Earth-Moon velocity constraint is that the Moon's inertial velocity relative to the Earth is equal to the spacecraft's velocity relative to the Earth's center minus the spacecraft's velocity relative to the Moon's center; the Moon's position relative to the Earth's center and the Moon's inertial velocity relative to the Earth are provided by the Earth-Moon Precision Ephemeris.

4. The method for jointly determining the position and time status of a spacecraft based on a lunar reference as described in claim 1, characterized in that, In step 2, the ground station observation data includes the first pseudorange observation equation and the first pseudorange rate observation equation. The first pseudorange observation equation is that the pseudorange measurement value of the ground station is equal to the first geometric distance between the spacecraft and the ground station plus the speed of light multiplied by the spacecraft's local clock error, plus the pseudorange observation noise. The first pseudorange rate observation equation is that the pseudorange rate measurement value of the ground station is equal to the first geometric distance change rate plus the speed of light multiplied by the spacecraft local clock drift, plus the pseudorange rate observation noise. The first geometric distance is given by the magnitude of the difference between the spacecraft's position relative to the Earth's center and the ground station's position, and the rate of change of the first geometric distance is obtained by dividing the geometric distance by the dot product of the relative position vector and the relative velocity vector between the spacecraft and the ground station.

5. The method for jointly determining the position and time status of a spacecraft based on a lunar reference as described in claim 1, characterized in that, In step 2, the lunar base station observation data includes a second pseudorange observation equation and a second pseudorange rate observation equation. The second pseudorange observation equation is that the pseudorange measurement value of the lunar base station is equal to the second geometric distance between the spacecraft and the lunar base station plus the speed of light multiplied by the difference between the spacecraft's local clock error and the common clock error of the lunar navigation network, plus pseudorange observation noise. The second pseudorange rate observation equation is that the pseudorange rate measurement value of the lunar base station is equal to the second geometric distance change rate plus the speed of light multiplied by the difference between the spacecraft's local clock drift and the common clock drift of the lunar navigation network, plus pseudorange rate observation noise. The second geometric distance is given by the magnitude of the difference between the spacecraft's position relative to the lunar center and the lunar base station's position. The second geometric distance change rate is obtained by dividing the geometric distance by the dot product of the relative position vector and the relative velocity vector between the spacecraft and the lunar base station.

6. The method for jointly determining the position and time status of a spacecraft based on a lunar reference as described in claim 1, characterized in that, In step 3, the global observation residual vector is composed of the ground base station pseudorange residual, the ground base station pseudorange rate residual, the monthly base station pseudorange residual, the monthly base station pseudorange rate residual, and the virtual observation residual.

7. The method for jointly determining the position and time status of a spacecraft based on a lunar reference as described in claim 6, characterized in that, In step 3, the pseudorange residual of the ground station is the difference between the measured pseudorange value and the predicted pseudorange value calculated based on the current nominal state, and the pseudorange rate residual of the ground station is the difference between the measured pseudorange rate value and the predicted pseudorange rate value calculated based on the current nominal state. The virtual observation residuals include the Earth-Moon position constraint residuals and the Earth-Moon velocity constraint residuals. The Earth-Moon position constraint residuals are the difference between the position of the Moon's center relative to the Earth's center provided by the precise Earth-Moon ephemeris and the Earth's center position calculated from the current nominal state minus the Moon's center position.

8. The method for jointly determining the position and time status of a spacecraft based on a lunar reference as described in claim 1, characterized in that, In step 4, the weighted iterative least squares solution includes the following steps: using the current nominal state as the initial value, calculate the Jacobian matrix of the unified observation model. The Jacobian matrix contains the partial derivatives of the ground-based observation equation, the lunar-based observation equation, and the virtual observation equation with respect to the relevant state quantities in the augmented state vector. Specifically, the partial derivatives of the ground-based observation equation involve the spacecraft's geocentric position, geocentric inertial velocity, spacecraft local clock bias, and local clock drift; the partial derivatives of the lunar-based observation equation involve the spacecraft's lunar-based position, lunar-based inertial velocity, spacecraft local clock bias, local clock drift, lunar-based navigation network common clock bias, and common clock drift; and the partial derivatives of the virtual observation equation involve the spacecraft's geocentric position, geocentric inertial velocity, lunar-based position, and lunar-based inertial velocity. Based on the global observation residual vector and the weight matrix, solve for the state increment using the weighted least squares formula. Update the augmented state vector. Repeat the iteration with the updated state as the new nominal state until the preset maximum number of iterations is reached or the state increment magnitude is less than a preset convergence threshold, at which point the joint estimation result of the spacecraft's position, velocity, and time state is output.

9. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When one or more programs are executed by the one or more processors, the one or more processors implement the method for jointly determining the position and time status of a spacecraft based on a fused Earth-Moon reference, as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, enable the processor to implement the method for jointly determining the position and time status of a spacecraft based on a fused Earth-Moon reference, as described in any one of claims 1-8.

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