A lunar probe precise orbit determination method and system based on ground-based one-way measurement

Abstract

The present application relates to deep space exploration and spacecraft autonomous navigation technical field, specifically, it relates to a kind of lunar probe precision orbit determination method and system based on ground-based one-way measurement.The ground deep space network multi-station launches uplink carrier according to intermittent tracking plan, and the probe end receives to form limited counting one-way uplink Doppler measurement;Execute periselene priority scheduling, and concentrate tracking window in the most violent arc segment of velocity change;Construct augmented state vector containing three-dimensional position, three-dimensional velocity, clock drift and three-direction empirical acceleration, and sequentially estimate with square root unscented Kalman filter;With fixed parameter first-order Gauss-Markov process to compensate absorption force model mismatch deviation;Through the normalized innovation square gate screening measurement, with normalized innovation square and normalized estimation error square double test to assess covariance calibration nature.The present application realizes meter-level orbit determination accuracy under intermittent tracking covering one-third of arc segment, and reduces the dependence on downlink coherent link and continuous tracking resources.

Description

Technical Field

[0001] This invention relates to the field of deep space exploration and autonomous spacecraft navigation technology, and more specifically, to a precise orbit determination method and system for a lunar probe based on ground-based unidirectional measurement. Background Technology

[0002] Currently, lunar probe orbit determination primarily relies on ground-based methods. Ground-based deep space stations transmit uplink carrier signals to the probe, which then relays phase-coherent downlink signals via a transponder. Ground stations compare the transmit and receive frequencies to generate two-way Doppler measurements. The navigation team then uses a dynamic model and ground-based precision orbit determination software to calculate the probe's orbit. This method has been successfully applied in missions such as the Lunar Reconnaissance Orbiter (LRO) and Tianwen-1, but it has the following inherent limitations: 1. It relies on the detector to forward downlink coherent signals, which consumes two-way satellite-to-ground link resources. Each orbit update requires waiting for the signal round trip and ground processing cycle, thus limiting real-time performance. 2. Measurement updates cannot be obtained when the probe is on the far side of the moon or when it is out of sight of the ground station.

[0003] To reduce reliance on ground-based telemetry and control resources, several autonomous orbit determination schemes for lunar probes have been proposed. One scheme utilizes inter-satellite link measurements, deploying navigation satellites in a distant retrograde orbit (DRO) to broadcast ranging signals to lunar user satellites. The user satellites then calculate their own orbits based on inter-satellite pseudorange and carrier phase observations. Another scheme utilizes lunar beacons, determining the probe's orbit by measuring the distance between the probe and beacons at known locations on the lunar surface, combined with filtering algorithms. However, the inter-satellite link scheme requires pre-deploying a navigation constellation, resulting in high system complexity and cost; the lunar beacon scheme requires pre-deploying and maintaining beacons on the lunar surface, which is currently not feasible.

[0004] One-way Doppler measurement—where a ground station transmits a carrier wave of a known frequency, the spacecraft receives it, and the frequency offset is compared with a local oscillator—allows the measurement processing to be performed on the spacecraft, eliminating the need to relay downlink signals. The US Deep Space Atomic Clock (DSAC) mission conducted flight verification of this system in low Earth orbit, equipped with a high-performance onboard atomic clock (daily stability of 3 × 10⁻⁶). Under conditions of a 15-meter mercury ion trap clock, orbit determination accuracy ranging from meters to tens of meters can be achieved. However, the following core challenges remain unresolved: (1) Clock-orbit coupling is difficult to separate: receiver clock drift and spacecraft velocity along the line of sight are fully coupled in scalar Doppler measurement - the measurement effect caused by clock drift error Δd is related to the line of sight velocity error c. Δd (where c is the speed of light) is completely equivalent, and a single count cannot distinguish between the two. Current methods primarily rely on high-performance spaceborne atomic clocks to suppress clock errors to acceptable levels, but this is insufficient for medium- to low-performance clocks (e.g., those with a daily stability of 10). The adaptability of the 12 levels has not been fully studied, and the information provided by orbital geometry features (such as eccentricity) to assist separation has not been fully utilized.

[0005] (2) Lack of effective compensation and evaluation for force model mismatch: The lunar low-orbit probe is significantly affected by perturbations such as the high-order lunar gravitational field (above order 100) and solar radiation pressure. Due to limitations in computing resources and time, the onboard computer usually adopts a truncated order (e.g., order 100) gravitational field model and a simplified radiation pressure model (e.g., taking a fixed reflection coefficient Cr=1.0), which has a systematic deviation from the real mechanical environment (gravitational field up to order 420, real Cr=1.5). Under scalar measurement conditions, the existing adaptive compensation scheme is prone to over-amplifying the navigation covariance due to insufficient observation capability of three-dimensional acceleration, resulting in overconfidence or divergence of the filter; the actual effect and limitations of the fixed parameter compensation scheme lack systematic quantification.

[0006] (3) Lack of measurement scheduling strategy for limited tracking resources: In actual missions, ground deep space network tracking resources are limited and allocated in a time-sharing manner. Existing methods usually assume continuous tracking or fixed-interval measurement availability, and do not design measurement scheduling for the constraints of "limited window, intermittent tracking", which leads to the accumulation of orbit and clock errors during tracking gaps due to the lack of measurement constraints.

[0007] (4) Lack of independent verification of navigation covariance calibration: Existing methods usually use the normalized innovation square approaching 1 as a criterion for the statistical consistency of the filter, but the variance calibration of scalar measurement residuals is not equivalent to the calibration of the joint covariance of multidimensional navigation states. The filter may perform well in the measurement space but be seriously overconfident in the state space - this "pseudo-calibration" phenomenon has not been revealed and tested in the existing technology.

[0008] In summary, all existing unidirectional Doppler orbit determination schemes are based on 3×10 The verification of high-performance spaceborne atomic clocks at level 15 (such as the DSAC mercury ion trap clock) has not yet been conducted, and the verification of medium- and low-performance clocks (such as those with a daily stability of 10) has not yet been carried out. 12 to 10 Feasibility study of orbit determination under the conditions of a Class 13 conventional rubidium clock or a miniaturized cesium clock—the latter being a more realistic and economical spaceborne frequency reference option for current and near-term lunar exploration missions.

[0009] Therefore, how to provide a precise orbit determination method and system for lunar probes based on ground-based unidirectional measurement is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0010] In view of this, the present invention provides a method and system for precise orbit determination of a lunar probe based on ground-based unidirectional measurement, aiming to solve the above-mentioned technical problems.

[0011] To achieve the above objectives, the present invention adopts the following technical solution: A precise orbit determination method for a lunar probe based on ground-based unidirectional measurement includes the following steps: S1. Multiple ground stations of the Deep Space Network transmit uplink carrier signals of known frequencies to the lunar probe within the tracking window according to the intermittent tracking plan. The lunar probe receives the uplink carrier signals and compares the frequencies with the local oscillator. After deducting the modelable relativistic effects, the residual frequency offset is obtained. S2. Integrate the residual frequency offset over a finite counting interval and convert it into the average geometric distance change rate. Iteratively solve the optical travel time to determine the signal transmission time and take into account the relativistic propagation delay correction. Convert the differential optical travel time into an equivalent value of the distance change rate including the receiver clock residual drift to form a scalar Doppler measurement value. S3. Under the constraint of total tracking resources, the tracking window is preferentially allocated to the visible arc segment where the orbital altitude of the lunar probe is in the lowest preset proportion range of the nominal altitude range. When multiple ground stations are visible at the same time, the ground station with the highest elevation angle is selected to perform the measurement, and elevation angle mask test and lunar occlusion test are performed on the candidate measurement epochs. S4. Construct an augmented state vector, which includes three-dimensional position, three-dimensional velocity, receiver clock residual drift, and empirical acceleration components in three directions under the radial-lateral-normal orbital coordinate system. Use a fixed diagonal scaling matrix to transform the state components of different dimensions to dimensionless coordinates, obtain the square root Cholesky factor of the initial covariance matrix, and initialize the square root unscented Kalman filter. S5. Execute a prediction-update loop with the finite counting interval as the filtering period: When no measurement is available, only the prediction step is executed, the sigma point is propagated through the spaceborne simplified force model and process noise is merged; when a measurement is available, the prediction step is executed first and then the normalized innovation square is calculated; when the normalized innovation square is less than a preset threshold, the measurement is received and the covariance is reduced at the square root factor level; when the normalized innovation square is greater than or equal to the preset threshold, the measurement is rejected and the prediction state and covariance are retained; the empirical acceleration components in the three directions are propagated according to a first-order Gaussian-Markov process with fixed parameters, and the receiver clock residual drift is propagated according to a random walk process; S6. During the filtering process, the normalized innovation square and the normalized estimation error square are calculated simultaneously. When the median of the normalized innovation square is close to 1 and the normalized estimation error square deviates significantly from 1, it is determined that the filter is consistent in the measurement space but overconfident in the navigation state space, and the navigation covariance does not have calibration properties. The determination result is then output as the input for the integrity monitoring of the navigation system.

[0012] Furthermore, in S1, the subtracted relativistic effects include the gravitational potential difference between the ground station and the lunar probe and the second-order Doppler shift. The target orbit of the lunar probe is configured as an eccentric orbit with a perigee altitude of 100 km and an apogee altitude of 500 km to 5000 km, and an eccentricity of 0.1 to 0.5. This causes the lunar probe to generate rapid and significant line-of-sight velocity changes near the perigee. The time scale and amplitude characteristics of these line-of-sight velocity changes cannot be represented by the random walk process of the receiver clock residual drift, thereby achieving separation of the receiver clock residual drift from the orbital motion in the prediction-update cycle.

[0013] Furthermore, in S2, the signal transmission time is iteratively solved using the reception time as a known condition. The relativistic propagation delay correction includes Shapiro delay corrections for the Sun's and Jupiter's mass centers. The count is marked at the end of the count to ensure causality. The measurement noise variance of the scalar Doppler measurement adopts a multi-source hierarchical model, consisting of the sum of carrier phase extraction noise and finite count numerical effect noise, receiver clock white frequency noise, instrument noise and margin fixed terms, and tropospheric and ionospheric propagation medium residuals. The sum of carrier phase extraction noise and finite count numerical effect noise increases as the counting interval shortens. The receiver clock white frequency noise is proportional to the square of the receiver clock's daily stability and increases as the counting interval shortens. The tropospheric and ionospheric propagation medium residuals increase as the elevation angle decreases.

[0014] Furthermore, in S3, the total tracking resource constraint is as follows: M tracking windows are allocated within the N-day orbit determination arc, each tracking window lasts for 60 minutes, the interval between adjacent tracking windows is not less than 120 minutes, and the total tracking duration covers one-third of the orbit determination arc; the ground deep space network includes at least three deep space stations distributed at geographical longitude intervals, the positions of each deep space station are calibrated in the Earth-fixed coordinate system and converted to the J2000 inertial frame through Earth orientation parameters; the scheduling result remains fixed throughout the entire orbit determination arc.

[0015] Furthermore, in step S4, the radial-lateral-normal orbital coordinate system is defined by the instantaneous state of the lunar probe, with the radial direction along the position vector direction, the normal direction along the orbital angular momentum direction, and the lateral direction being the orbital direction after deducting the radial velocity component; the diagonal elements of the fixed diagonal scaling matrix take the initial one standard deviation uncertainty of each state component, where the position uncertainty is 1 km, the velocity uncertainty is 1 m / s, and the clock drift and empirical acceleration uncertainty are taken as preset initial uncertainties; the parameters of the square root unscented Kalman filter adopt the standard recommended values, generating 21 sigma points for the augmented state vector; in step S5, when no measurements are available, the process noise is incorporated into the square root covariance factor through QR decomposition, and when receiving measurements, covariance reduction at the square root factor level is achieved through Cholesky degradation.

[0016] Furthermore, in step S4, the augmented state vector does not include clock bias, and the clock bias is converted to coordinate time through uplink time synchronization; in step S5, the correlation time of the first-order Gauss-Markov process corresponds to three consecutive finite counting intervals, enabling the empirical acceleration to span multiple consecutive measurements of accumulated orbital response, while avoiding smooth confusion between the high dynamic region of the perilunar point and the low dynamic region of the apolunar point due to an excessively long memory window; the root mean square difference between the steady-state amplitude and the acceleration difference of the onboard simplified force model along the reference trajectory is on the same order of magnitude; the diffusion intensity of the random walk process of the receiver clock residual drift is determined by the daily Allan deviation of the receiver clock according to the standard relationship between the double-sampled Allan variance and the white-frequency noise diffusion coefficient.

[0017] Furthermore, in S5, the spaceborne simplified force model includes: a lunar gravitational field model truncated to the 100th order; Earth's point mass gravity and Sun's point mass gravity; a solar radiation pressure projectile model with a fixed reflection coefficient; and first-order relativistic corrections for the Sun's center of mass and Jupiter's center of mass. The spaceborne simplified force model and the actual mechanical environment have higher-order gravitational field truncation biases (from the 101st to the 420th order) and solar radiation pressure reflection coefficient biases. These higher-order gravitational field truncation biases and radiation pressure reflection coefficient biases are not directly provided to the filter, but are absorbed from the Doppler measurement sequence through the empirical acceleration components propagating according to the first-order Gauss-Markov process, absorbing their cumulative effect after dynamic propagation. The preset threshold is the quantile of a chi-square distribution with 1 degree of freedom under a preset tail probability.

[0018] Furthermore, in S6, the navigation state measured by the normalized estimation error square is a seven-dimensional navigation state, which includes three-dimensional position, three-dimensional velocity, and receiver clock residual drift. The normalized estimation error square is divided by seven and compared with 1. When the median of the normalized innovation square is close to 1 and the normalized estimation error square is significantly deviated from 1 after being divided by seven, it is determined that the navigation covariance does not have calibration properties.

[0019] Furthermore, the finite counting interval is between 5 seconds and 60 seconds; when the finite counting interval is shorter, the Doppler measurement time resolution is improved, but the carrier phase extraction noise and the finite counting numerical effect noise increase; when the finite counting interval is longer, the measurement noise is reduced, but the number of available measurements decreases.

[0020] A precise orbit determination system for a lunar probe based on ground-based unidirectional measurement includes a ground segment subsystem and a probe terminal system. The ground segment subsystem includes: multiple geographically distributed ground deep space station modules, used to transmit uplink carrier signals within the tracking window; and a tracking scheduling module, used to prioritize the allocation of the tracking window to the visible arc segment of the lowest preset proportion interval of the lunar probe's orbital altitude under the constraint of total tracking resources, select the station with the highest elevation angle when multiple stations are visible, and perform elevation angle masking and lunar occlusion checks. The detector terminal system is deployed on the lunar probe and includes: a carrier receiving and frequency comparison module, used to receive the uplink carrier signal and compare it with the local oscillator, outputting the residual frequency offset after subtracting modelable relativistic effects; a finite-count Doppler forming module, used to integrate the residual frequency offset over the counting interval and convert it into the average geometric distance change rate, iteratively solve for the optical travel time and take into account the relativistic propagation delay, and output a scalar Doppler measurement; a spaceborne simplified force model propagation module, used to propagate the orbital state during the prediction step; and a square-root unscented Kalman filter module, used to maintain an augmented state vector including three-dimensional position, three-dimensional velocity, receiver clock residual drift, and three-directional empirical acceleration, and after transforming to dimensionless coordinates using a fixed diagonal scaling matrix, perform sigma point generation, propagation, and... The system includes: a square root factor update and a gating filter for effective measurements using the normalized innovation square; a fixed dynamic model compensation module to propagate empirical acceleration in three directions using a first-order Gaussian-Markov process with fixed parameters, absorbing the cumulative effect of systematic deviations between the onboard simplified force model and the real mechanical environment in the Doppler measurement sequence; a clock drift estimation module to propagate the receiver clock residual drift using a random walk process, with the diffusion intensity determined by the one-day Allan deviation of the receiver clock; and a dual consistency evaluation module to simultaneously calculate the normalized innovation square and the normalized estimation error square. When the normalized innovation square is close to 1 while the normalized estimation error square deviates significantly from 1, the filter is determined to be consistent in the measurement space but overconfident in the navigation state space, and the determination result is output as input for navigation system integrity monitoring.

[0021] Compared with the prior art, the present invention has the following beneficial effects: (1) Achieving autonomous and precise orbit determination at the detector end without relying on the downlink coherent link. By fully deploying the unidirectional uplink Doppler measurement and processing at the detector end, the detector can autonomously determine its orbit without transmitting phase-coherent downlink signals. Compared with bidirectional Doppler orbit determination that requires forwarding downlink signals, it reduces the occupation of the two-way satellite-to-ground link, and the orbit update is shortened from relying on the ground processing cycle (minutes to hours) to the on-board real-time filtering cycle (10 seconds). Under the reference configuration (100km×2000km eccentric orbit), the orbit determination accuracy of 3.03m root mean square error, 2.57m median, and 4.66m 95th percentile of the three-dimensional position is achieved by intermittent tracking covering only one-third of the arc segment, with a velocity root mean square error of 1.28mm / s and a position convergence time of 3.57 hours.

[0022] (2) Practical separation of clock drift and line-of-sight velocity is achieved using orbital eccentricity. Unlike existing methods that rely solely on high-performance spaceborne atomic clocks to suppress clock errors, this invention fully utilizes the rapid and significant changes in line-of-sight velocity generated near the lunar perihelion by the eccentric orbit. The time scale and magnitude of these changes cannot be represented by the slowly evolving clock drift random walk model, thus achieving practical separation of the two during the filtering process. When the performance of the spaceborne clock degrades to a daily stability of 10... -12 Even at the exponential level, the median position error on the eccentric orbit remains at 11.04m. This level of accuracy can still meet the orbit determination requirements of most lunar exploration missions, indicating that this orbit determination system is also applicable under low-to-medium performance onboard clock conditions.

[0023] (3) A fixed-parameter dynamic model is used to compensate for the mismatch in the effective absorbing force model. A first-order Gaussian-Markov process with fixed parameters is used to absorb the unmodeled perturbation force, avoiding the defect of excessive amplification of covariance in the adaptive compensation scheme due to insufficient three-dimensional acceleration observation capability under scalar measurement. Under the condition that there are significant deviations in the force model (gravitational field truncation from 420th order to 100th order, solar radiation pressure reflection coefficient deviation from 1.5 to 1.0), the root mean square error of position under the fixed dynamic model compensation assistance is only 3.03m, and the convergence time is 3.57 hours.

[0024] (4) Improve the efficiency of measurement information acquisition under limited resources by using a near-lunar point priority scheduling strategy. Under the constraint of tracking resources covering only one-third of the arc segment, the window is preferentially allocated to the low-altitude range of the near-lunar point to concentrate on acquiring high-information Doppler measurements of the arc segment with the most dramatic velocity changes. Under the reference configuration, meter-level accuracy is achieved with only 33.3% of the epochs having available measurements.

[0025] (5) Establish a dual consistency verification mechanism for measurement space and state space. By simultaneously calculating the normalized innovation square and normalized estimation error square statistic in unidirectional Doppler autonomous orbit determination, the phenomenon that scalar measurement residual variance calibration does not guarantee multidimensional navigation state covariance calibration is revealed. When the receiver clock degrades to 10 -12 At the exponential level, the median of the normalized squared innovation can be maintained at 0.99 (superficially consistent), while the normalized estimation error squared divided by seven is as high as 9.09 (actually severely overconfident), verifying the risk of relying solely on the normalized squared innovation to judge the filter calibration.

[0026] (6) Significantly reduces the demand for spaceborne atomic clock performance and tracking resources while maintaining the same or better orbit determination accuracy. Compared with existing deep space atomic clock schemes, this invention achieves comparable orbit determination accuracy using intermittent tracking resources in a more complex gravitational field environment (lunar 420th order relative to Earth's lower order) and under more stringent force model mismatch conditions. Furthermore, it provides a more comprehensive means of evaluating covariance calibration than relying solely on innovation statistics through a dual verification mechanism. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0028] Figure 1 A flowchart of a precise orbit determination method for a lunar probe based on ground-based unidirectional measurement, provided in an embodiment of the present invention. Detailed Implementation

[0029] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] This invention provides a precise orbit determination method for a lunar probe based on ground-based unidirectional measurement, comprising the following steps: Step S1: Construct a ground-based unidirectional uplink Doppler measurement link; Multiple ground stations of the Deep Space Network transmit X-band uplink carrier signals of known frequencies to the lunar probe within a selected tracking window according to a pre-set intermittent tracking plan. After receiving the uplink carrier signals, the probe compares the frequencies with those of the local oscillator and subtracts modelable relativistic effects (including the gravitational potential difference between the ground stations and the probe and the second-order Doppler frequency shift) to obtain the residual frequency offset.

[0031] To enhance the separability of clock drift and line-of-sight velocity in step S5, the lunar probe's target orbit was configured as an eccentric orbit—the perigee altitude was maintained at 100 km, the apogee altitude was configured to be between 500 km and 5000 km, and the eccentricity was configured to be between 0.1 and 0.5, causing the probe to generate rapid and significant changes in line-of-sight velocity near the perigee. The timescale and magnitude characteristics of this change cannot be represented by the slowly evolving clock drift random walk model (step S5d), thus achieving practical separation of clock drift and orbital motion in the filter's prediction-update loop.

[0032] Step S2: Forming a unidirectional upward Doppler measurement with a finite counting interval; The residual frequency offset obtained in step S1 is integrated over a preset finite counting interval Tc and converted into the average geometric distance change rate to form a scalar Doppler measurement value. The signal transmission time is determined using iterative optical timing calculation—based on the reception time. Given the conditions, iteratively solve for the launch time. Make it satisfy ,in For the detector position, This represents the location of the ground station. Calculate the one-way light travel time, including the Shapiro delay corrections for the Sun and Jupiter's barycenters. The differential optical travel time is converted into an equivalent value of the distance change rate, including clock drift, using the following observation model: , in At the speed of light, For the first Each count ends at a specific time (the count is marked at the end time to ensure causality). For receiver clock residual drift, Measurement noise variance for hierarchical modeling.

[0033] The measurement noise variance Rk in hierarchical modeling consists of the following components: , The first term is the sum of carrier phase extraction noise and finite count numerical effect noise (and...). The second term is the receiver clock white frequency noise (proportional to clock daily stability). Proportional to the square and with The third item is the instrument noise and margin fixed item, and the fourth item is the residual of the tropospheric and ionospheric propagation media (according to...). Inverse scaling).

[0034] Step S3: Perform multi-station intermittent tracking scheduling with priority given to near-lunar points; Under the total tracking resource constraint (M 60-minute windows allocated within an N-day arc segment, with a window interval of no less than 120 minutes, and the total tracking duration covering 1 / 3 of the arc segment), tracking windows are preferentially allocated to visible arc segments where the detector's orbital altitude is within the lowest preset proportion range of the nominal altitude (e.g., the lowest 20%). When multiple ground stations are simultaneously visible to the detector, the ground station with the highest elevation angle is selected to perform this measurement to minimize atmospheric path propagation error. An elevation angle mask test (threshold 10) is performed for each candidate measurement epoch. And lunar obstruction verification. The scheduling results remain constant throughout the entire orbit determination arc.

[0035] The total tracking resource constraints are as follows: M tracking windows are allocated within the N-day orbit determination arc, each window lasts for 60 minutes, the interval between adjacent windows is no less than 120 minutes, and the total tracking duration covers 1 / 3 of the arc; the multi-station network includes at least three deep space stations with geographical longitude intervals.

[0036] Step S4: Construct an augmented state vector containing clock drift and empirical acceleration, and initialize the square root UKF filter; Construct a 10-dimensional state vector ,in and These represent the position and velocity vectors of the three-dimensional lunar-centered J2000 inertial frame. For receiver clock residual drift (clock bias is not included in the estimate, the measurement model assumes that the counting endpoint has been converted to coordinate time through uplink time synchronization). , , These are the empirical acceleration components in the instantaneous radial-lateral-normal (RTN) orbital coordinate system of the detector. The RTN coordinate system is defined by the instantaneous state of the detector. (Radial), (Normal direction) (Transverse direction, along the track after deducting the radial velocity component).

[0037] Using a fixed diagonal scaling matrix (The diagonal element takes the initial 1 of each state component) Uncertainties: 1 km for position in each direction, 1 m / s for velocity in each direction, and clock drift. Empirical acceleration in all directions (km / s²) Transform state components of different dimensions to dimensionless coordinates. Obtain the square root Cholesky factor of the initial covariance matrix P. ,satisfy .

[0038] As a further improvement of the present invention, the UKF parameters are set to the standard recommended values, and 21 sigma points are generated for the 10-dimensional state according to the UKF standard formula.

[0039] Step S5: Perform a prediction-update loop based on the square root UKF, including information filtering and fixed DMC compensation; By counting interval For each filter epoch, perform the following sub-steps: S5a: If no measurements are available (the current epoch is not within the tracking window, or the target station is not visible due to insufficient elevation angle / lunar obstruction), only the prediction step is performed—the sigma point is propagated to the current epoch via the onboard simplified force model, and the process noise is merged to the square root covariance factor through QR decomposition.

[0040] The simplified force model for spaceborne systems includes: (a) a lunar gravitational field model truncated to the 100th order; (b) the gravitational forces of Earth and the Sun; and (c) a model with reflection coefficients. (d) A fixed-coefficient solar radiation pressure projectile model; and (e) first-order relativistic corrections to the mass centers of the Sun and Jupiter. This simplified spaceborne force model exhibits higher-order gravitational field truncation bias (orders 101 to 420) and radiation pressure reflection coefficient bias (true value) compared to the actual mechanical environment. This systemic bias is not directly provided to the filter, but rather its cumulative effect after dynamic propagation is absorbed from the Doppler measurement sequence through the DMC state in step S5d.

[0041] S5b: If a measurement is available, perform the prediction step first, then calculate the normalized innovation square. ,in To measure the new information, For the new information variance; S5c: When The measurement update is received in a timely manner, and covariance reduction at the square root factor level is achieved through Cholesky degradation; when The measurement is rejected at that time, but the predicted state and covariance are retained; among which The quantiles of a chi-square distribution with 1 degree of freedom under a preset tail probability are given.

[0042] S5d: Regardless of measurement updates, all three RTN empirical acceleration components propagate according to a first-order Gaussian-Markov process. , The relevant time and steady-state amplitude The km / s² value remains constant across each axis throughout the filtering process. After discretization, the mean acceleration is calculated as follows: Attenuation, process noise variance is The discrete covariance matrix is ​​calculated using the standard method for a first-order Gaussian-Markov process, and then incorporated into the process noise covariance after a rotation matrix transformation from RTN to J2000. .

[0043] Receiver clock drift propagates according to a random walk model: The diffusion intensity is determined by the day-to-day Allan deviation of the clock. The variance of the double-sampled Allan variance is determined according to the standard relationship between the white-frequency noise diffusion coefficient, i.e. ( ).

[0044] Step S6: Evaluate the navigation covariance calibration based on the NIS-NEES dual test; During the filtering process, two statistics are calculated simultaneously: the normalized squared innovation. (Measures the consistency between scalar measurement residuals and their predicted variance) and the squared error of the normalized estimate. (Measures the consistency of the joint error and covariance of the seven-dimensional navigation state—three-dimensional position, three-dimensional velocity, and clock drift). When the median NIS is close to 1 and NEES / 7 deviates significantly from 1, the decision filter is consistent on the measurement space surface but overconfident in the navigation state space. The navigation covariance lacks calibrability, and this decision result is output as input for navigation system integrity monitoring. NIS≈1 should not be used as an independent criterion for meeting navigation accuracy requirements.

[0045] Among them, the simplified force model mentioned in step S5 includes at least a truncated lunar gravitational field model and a simplified solar radiation pressure model, which are used to approximate orbital propagation at the probe end with a force model fidelity lower than the true orbit, given the limited computational resources.

[0046] The present invention also provides a precise orbit determination system for a lunar probe based on ground-based unidirectional measurement. This system is used to implement the above method and includes: The ground segment subsystem includes: Multiple geographically distributed ground deep space station modules are used to transmit X-band uplink carrier signals within a preset tracking window. The location of each station is accurately calibrated in the Earth-fixed coordinate system and converted to the J2000 inertial frame through Earth orientation parameters. The tracking and scheduling module is used to perform multi-station intermittent tracking scheduling with a focus on the nearest point to the moon. Under the constraint of total tracking resources, the tracking window is preferentially allocated to the visible arc segment of the lowest preset proportion interval of the probe's orbital altitude. When multiple stations are visible, the station with the highest elevation angle is selected, and elevation angle masking and lunar occlusion checks are performed. The probe terminal system, deployed on the lunar probe, includes: The carrier receiving and frequency comparison module is used to receive the X-band uplink carrier signal, compare it with the local oscillator, and output the residual frequency offset after subtracting the modelable relativistic effects. A finite-count Doppler forming module is used to convert the residual frequency offset within a preset counting interval. Integrate internally and convert to the average geometric distance change rate, perform iterative optical travel time solving and take into account relativistic propagation delay, and output scalar Doppler measurements. ; The onboard simplified force model propagation module, which includes truncated lunar gravitational field, point mass gravity, fixed-coefficient solar radiation pressure, and relativistic corrections, is used to propagate orbital states in the filter prediction step. The square root UKF filtering module is configured to: maintain a 10-dimensional augmented state vector containing three-dimensional position, three-dimensional velocity, clock drift, and empirical acceleration in the three RTN directions; transform to dimensionless coordinates using a fixed diagonal scaling matrix, and then perform sigma point generation, propagation, and square root factor update; during measurement updates, filter effective measurements by normalized innovation square gating and reduce covariance by Cholesky degradation; The fixed DMC compensation module is configured to use fixed parameters ( , The first-order Gauss-Markov process (km / s² per axis) propagates empirical acceleration in three RTN directions, absorbing the cumulative effect of systematic deviations between the simplified spaceborne force model and the real mechanical environment in the Doppler measurement sequence. The clock drift estimation module is configured to propagate the receiver clock residual drift by a random walk process, with the propagation intensity determined by the one-day Allan deviation of the clock. The dual consistency assessment module is configured to simultaneously calculate the normalized innovation square (NIS) and the normalized estimation error square (NEES / 7). When NIS ≈ 1 and NEES / 7 significantly deviates from 1, the filter is determined to be consistent on the measurement space surface but overconfident in the navigation state space. This determination result is then output as input for navigation system integrity monitoring.

[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment uses a lunar eccentric orbiter as the application object to construct an autonomous orbit determination system for a lunar probe based on ground-based unidirectional measurements. The system consists of two main parts: a ground segment and a probe segment. The ground segment includes three geographically distributed deep space stations and a tracking and scheduling module; the probe segment is deployed on the lunar probe and includes a carrier reception and frequency comparison module, a finite-count Doppler formation module, a spaceborne simplified force model propagation module, a square-root UKF filter module, a fixed DMC compensation module, a clock drift estimation module, and a dual consistency evaluation module. The ground stations transmit X-band uplink carrier signals within the allocated tracking window according to a perigee priority scheduling strategy. After receiving the signals, the probe generates 10-second finite-count Doppler measurements, which are then sequentially processed by a square-root UKF filter to output an orbital state estimate.

[0048] I. System Composition and Workflow Reference Figure 1 The method in this embodiment is performed according to the following six steps: Step S1 – Constructing a ground-based unidirectional uplink Doppler measurement link: The ground deep space station transmits an X-band uplink carrier signal (carrier frequency 7.17 GHz) to the detector within the selected tracking window according to a preset intermittent tracking plan. After receiving the signal, the detector compares the frequency with the local oscillator and subtracts the modelable relativistic effects (gravitational potential difference and second-order Doppler frequency shift) to obtain the residual frequency offset.

[0049] Step S2 – Forming a unidirectional upward Doppler measurement with finite counting intervals: The residual frequency offset is counted at 10-second intervals. The inner integral is converted into the average geometric distance change rate to form a scalar Doppler measurement. The signal transmission time is determined by solving the optical timing equation using the Newton-Raphson iterative method, taking into account the Shapiro delay correction for the Sun and Jupiter's barycenters. The observation model is shown in Equation (1), and the measurement noise variance adopts a multi-source hierarchical model.

[0050] Step S3 – Execute multi-station intermittent tracking scheduling with a focus on the perigee: Allocate 24 60-minute tracking windows within a three-day arc (adjacent intervals no less than 120 minutes, total tracking time covering 1 / 3 of the arc), prioritizing the allocation of windows to visible arcs where the orbital altitude is at least 20% of the nominal altitude range. When multiple stations are visible, select the station with the highest elevation angle and execute… Elevation angle masking and lunar obstruction checks were performed. The scheduling results remained constant throughout the entire orbit determination arc.

[0051] Step S4 – Constructing the augmented state vector and initializing the square root UKF filter: Constructing a 10-dimensional state vector A fixed diagonal scaling matrix D is used to transform the state components of different dimensions to dimensionless coordinates, and the square root Cholesky factor of the initial covariance matrix is ​​obtained.

[0052] Step S5 – Execute the prediction-update loop: The filtering period is 10 seconds. When no measurements are available, the 21 sigma points are propagated to the current epoch via the onboard simplified force model, and process noise is merged through QR decomposition. When measurements are available, prediction is performed first, followed by updating – the normalized innovation square is calculated. ,when Timely measurement reception and covariance reduction via Cholesky degradation, when Measurements are rejected to preserve the predicted state. Regardless of measurement updates, the three RTN empirical acceleration components propagate according to a first-order Gaussian-Markov process with fixed parameters. , (km / s²), receiver clock drift propagates via a random walk process.

[0053] Step S6 – Perform the NIS-NEES dual test: Simultaneously calculate the NIS and NEES statistics. When the NIS is close to 1 and the NEES significantly deviates from 1, it is determined that the filter is consistent on the measurement space surface but overconfident in the navigation state space, and the navigation covariance is not calibrated. This determination result is then output as the input for navigation system integrity monitoring.

[0054] II. Dynamic Model Configuration In this embodiment, a high-fidelity force model is used to propagate the detector reference trajectory, while a simplified force model is used for the onboard filter to propagate the orbital state. The systematic deviation between the two constitutes the force model mismatch condition for the filter. The configuration is shown in Table 1.

[0055] Table 1 Dynamic Model Configuration

[0056] As shown in Table 1, there are two types of systematic biases between the spaceborne filter force model and the reference trajectory force model: the truncation bias of higher-order terms of the lunar gravitational field (orders 101 to 420) and the bias of the solar radiation pressure reflection coefficient (reference value). Spaceborne model These biases are not directly provided to the filter, but are absorbed from the Doppler measurement sequence through the fixed DMC state in step S5, where they have accumulated after propagation by dynamics.

[0057] III. Track Parameters and Clock Configuration The reference orbit for this embodiment is a 100km × 2000km lunar eccentric orbit. The simulation epoch is January 8, 2022, 00:00:00 (UTC), and the arc segment lasts for three days (72 hours). The initial orbital elements are shown in Table 2.

[0058] Table 2 Initial elements of the reference orbit (lunar center J2000 inertial frame)

[0059] Initial angle of approach By bringing the probe close to the lunar perihelion at the start of the simulation, filtering can begin directly from the complex dynamic range of low altitude and high speed—at which point the probe's orbital altitude is lowest and its speed is highest. The filter needs to converge during the phase of most dramatic dynamic changes, allowing for a conservative assessment of the method's performance.

[0060] The receiver clock daily stability is configured as follows: Under this clock configuration, the total Doppler measurement noise at the mask elevation angle is... The propagation intensity of the clock drift noise is 0.299 mm / s. ( )Sure.

[0061] IV. Measurement Model and Ground Station Configuration 1. Doppler measurement model This embodiment uses a 10-second finite-count unidirectional upward Doppler measurement with a carrier frequency of 7.17 GHz (X-band). The k-th count ends at... Coverage area The observation equation is: , in The unidirectional light travel time, including the Shapiro delay of the Sun and Jupiter's barycenters, is solved using the Newton-Raphson iterative method. Sure.

[0062] The Shapiro delay of the Sun and Jupiter's barycenters is included in the unidirectional light travel time according to the Moyer (2003) standard formula.

[0063] Measurement noise variance Using a multi-source hierarchical model, in Angle of elevation Total noise under certain conditions It is 0.299 mm / s.

[0064] Regarding the clock skew assumption: This measurement model assumes that when the counting endpoints have been transformed to coordinates via uplink time synchronization, clock skew is not included in the estimation state. Typical uplink time synchronization residuals are on the order of milliseconds, and the Doppler error introduced by this residual skew is far lower than the total noise at the mask elevation angle. (0.299 mm / s), and this is already covered by the fixed margin term in the measurement noise budget. This assumption is acceptable under the accuracy target of this embodiment.

[0065] 2. Ground stations and tracking / dispatch The ground-based deep space network consists of three stations, whose coordinates are precisely calibrated in the ITRF93 Earth-fixed system and converted to the J2000 inertial system using SPICE Earth orientation parameters. The three stations are distributed at approximately 120° intervals in longitude, forming global coverage.

[0066] The tracking and scheduling parameters are as follows: 24 tracking windows of 60 minutes each are allocated within a three-day arc segment, with an interval of no less than 120 minutes between adjacent windows; near-lunar point priority scheduling—windows are preferentially allocated to visible arc segments where the orbital altitude is at least 20% of the nominal altitude range; when multiple stations are visible, the station with the highest elevation angle is selected; elevation angle mask threshold is 10. Perform lunar obstruction testing. The scheduling results remain constant throughout the entire orbit determination arc.

[0067] V. Filter Configuration The complete parameter configurations for the square root UKF and DMC are shown in Table 3.

[0068] Table 3 Filter Parameter Configuration

[0069] The selection of the above DMC parameters is based on the following technical reasons: (i) relevant time Corresponding to three consecutive 10s counting intervals, the empirical acceleration can span multiple consecutive measurements to accumulate orbital responses, while avoiding smoothing confusion between the high dynamic region of the perigee and the low dynamic region of the apogee caused by an excessively long memory window; (ii) steady-state acceleration km / s² and the RMS difference between the force model acceleration along the reference trajectory (approximately) (km / s²) are in the same order of magnitude, ensuring that the noise amplitude of the DMC process matches the typical amplitude of this deviation; (iii) driving noise intensity From the above and The parameters were determined using the standard relations of a first-order Gauss-Markov process. The above parameter values ​​are designed for a 10-second counting interval and the low lunar orbit mechanical environment, and remain unchanged throughout the filtering process. This fixed parameter design differs from the adaptive DMC scheme, avoiding excessive covariance amplification caused by the adaptive scheme when scalar Doppler measurements are insufficient for three-dimensional acceleration observation.

[0070] The orbit propagation uses a DOP853 variable step integrator with relative and absolute tolerance configurations of... .

[0071] VI. Technical Effects Achieved by the Embodiments Based on the above reference configuration (100×2000km track, clock) Monte Carlo simulations were performed to statistically evaluate orbit determination accuracy. The statistical results of the final segment (the last 24 hours of the arc segment) are shown in Table 4.

[0072] Table 4. Track determination accuracy of the embodiment (statistics in the last 24 hours)

[0073] The above results show that this embodiment achieves meter-level orbit determination accuracy—position RMS 3.03m, median 2.57m, and convergence time 3.57 hours—under intermittent tracking conditions covering only 1 / 3 of the arc segment.

[0074] It is noteworthy that the results of the double test are as follows: the median NIS of 1.01 indicates that the scalar measurement residual variance is well calibrated, but NEES / 7 = 2.27 indicates that the joint covariance of the seven-dimensional navigation states (three-dimensional position, three-dimensional velocity, and clock drift) has not been fully calibrated. This inconsistency between NIS and NEES verifies the risk of relying solely on NIS to judge the filter calibration and demonstrates the necessity of the double test mechanism in step S6.

[0075] Unlike the first embodiment, the perigee altitude can be maintained at 100 km, the apogee altitude can be selected within the range of 500 km to 5000 km, and the eccentricity can be selected within the range of 0.1 to 0.5. The eccentric orbit causes the probe to produce rapid and large-amplitude changes in line-of-sight velocity near the perigee. The time scale and amplitude characteristics of this change cannot be represented by the slowly evolving clock drift random walk model, thus achieving practical separation of clock drift and orbital motion during the filtering process.

[0076] The receiver clock's daily stability can be achieved to Within the selected range, the noise propagation intensity during the clock drift process is determined by... The clock white frequency term in the measured noise variance is determined based on the selected daily stability S. Adjust in sync.

[0077] Finite counting interval The time interval can be selected from 5 to 60 seconds—when a shorter counting interval is used, the Doppler measurement time resolution is improved, but the carrier phase extraction noise and finite count numerical effect noise are reduced. Increased noise levels are a trade-off when using longer counting intervals, but the number of available measurements decreases. This trade-off can be determined by those skilled in the art based on task requirements.

[0078] Compared with the prior art, the present invention has the following beneficial effects: (1) Achieving autonomous and precise orbit determination at the detector end without relying on the downlink coherent link: By fully deploying the unidirectional uplink Doppler measurement and processing at the detector end, the detector can autonomously determine its orbit without transmitting phase-coherent downlink signals. Compared with bidirectional Doppler orbit determination that requires forwarding downlink signals, this reduces the occupation of the satellite-to-ground bidirectional link, and the orbit update is shortened from relying on the ground processing cycle (minutes to hours) to the on-board real-time filtering cycle (10 seconds). In the reference configuration (100km × 2000km eccentric orbit, receiver daily stability 3× Under these conditions, intermittent tracking covering only 1 / 3 of the arc segment achieved a three-dimensional position RMS of 3.03m, a median of 2.57m, and a 95th percentile of 4.66m for the final segment, with a velocity RMS of 1.28mm / s and a position convergence time of 3.57 hours.

[0079] (2) Practical separation of clock drift and line-of-sight velocity using orbital eccentricity: Unlike existing methods that rely solely on high-performance spaceborne atomic clocks to suppress clock errors, this invention fully utilizes the rapid and significant changes in line-of-sight velocity generated near the lunar perihelion by the eccentric orbit—the time scale and magnitude of which cannot be represented by the slowly evolving clock drift random walk model—to achieve practical separation of the two during the filtering process. When the performance of the spaceborne clock degrades to a daily stability... At that time, the median position error on the eccentric orbit remained at 11.04m—this level of accuracy can still meet the orbit determination requirements of most lunar exploration missions, indicating that this orbit determination system is also applicable under low-to-medium performance onboard clock conditions.

[0080] (3) Mismatch in effective absorption force model using fixed parameters DMC: using fixed parameters ( , The first-order Gaussian-Markov process (km / s²) absorbs unmodeled perturbations, avoiding the over-amplification of covariance caused by insufficient three-dimensional acceleration observation capability in the adaptive DMC scheme under scalar measurements. Under conditions of significant bias in the force model (gravitational field truncation from 420th to 100th order, solar radiation pressure reflection coefficient Cr bias from 1.5 to 1.0), the position RMS with fixed DMC assistance is only 3.03 m, and the convergence time is 3.57 hours.

[0081] (4) Improve the efficiency of measurement information acquisition under limited resources by prioritizing the near-lunar point scheduling strategy: Under the constraint of tracking resources covering only 1 / 3 of the arc segment, the window is preferentially allocated to the low-altitude range of the near-lunar point—concentrating on acquiring high-information Doppler measurements of the arc segment with the most dramatic velocity changes. Under the reference configuration, meter-level accuracy is achieved with only 33.3% of the epochs having available measurements.

[0082] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0083] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A precise orbit determination method for a lunar probe based on ground-based unidirectional measurement, characterized in that, Includes the following steps: S1. Multiple ground stations of the Deep Space Network transmit uplink carrier signals of known frequencies to the lunar probe within the tracking window according to the intermittent tracking plan. The lunar probe receives the uplink carrier signals and compares the frequencies with the local oscillator. After deducting the modelable relativistic effects, the residual frequency offset is obtained. S2. Integrate the residual frequency offset over a finite counting interval and convert it into the average geometric distance change rate. Iteratively solve the optical travel time to determine the signal transmission time and take into account the relativistic propagation delay correction. Convert the differential optical travel time into an equivalent value of the distance change rate including the receiver clock residual drift to form a scalar Doppler measurement value. S3. Under the constraint of total tracking resources, the tracking window is preferentially allocated to the visible arc segment where the orbital altitude of the lunar probe is in the lowest preset proportion range of the nominal altitude range. When multiple ground stations are visible at the same time, the ground station with the highest elevation angle is selected to perform the measurement, and elevation angle mask test and lunar occlusion test are performed on the candidate measurement epochs. S4. Construct an augmented state vector, which includes three-dimensional position, three-dimensional velocity, receiver clock residual drift, and empirical acceleration components in three directions under the radial-lateral-normal orbital coordinate system. Use a fixed diagonal scaling matrix to transform the state components of different dimensions to dimensionless coordinates, obtain the square root Cholesky factor of the initial covariance matrix, and initialize the square root unscented Kalman filter. S5. Execute a prediction-update loop with the finite counting interval as the filtering period: When no measurement is available, only the prediction step is executed, the sigma point is propagated through the spaceborne simplified force model and process noise is merged; when a measurement is available, the prediction step is executed first and then the normalized innovation square is calculated; when the normalized innovation square is less than a preset threshold, the measurement is received and the covariance is reduced at the square root factor level; when the normalized innovation square is greater than or equal to the preset threshold, the measurement is rejected and the prediction state and covariance are retained; the empirical acceleration components in the three directions are propagated according to a first-order Gaussian-Markov process with fixed parameters, and the receiver clock residual drift is propagated according to a random walk process; S6. During the filtering process, the normalized innovation square and the normalized estimation error square are calculated simultaneously. When the median of the normalized innovation square is close to 1 and the normalized estimation error square deviates significantly from 1, it is determined that the filter is consistent in the measurement space but overconfident in the navigation state space, and the navigation covariance does not have calibration properties. The determination result is then output as the input for the integrity monitoring of the navigation system.

2. The precise orbit determination method for a lunar probe based on ground-based unidirectional measurement according to claim 1, characterized in that, In S1, the subtracted relativistic effects include the gravitational potential difference between the ground station and the lunar probe and the second-order Doppler shift. The target orbit of the lunar probe is configured as an eccentric orbit with a perigee altitude of 100 km and an apogee altitude of 500 km to 5000 km, and an eccentricity of 0.1 to 0.

5. This causes the lunar probe to generate rapid and significant line-of-sight velocity changes near the perigee. The time scale and amplitude characteristics of these line-of-sight velocity changes cannot be represented by the random walk process of the receiver clock residual drift, thereby achieving separation of the receiver clock residual drift from the orbital motion in the prediction-update cycle.

3. The precise orbit determination method for a lunar probe based on ground-based unidirectional measurement according to claim 1, characterized in that, In S2, the signal transmission time is iteratively solved using the reception time as a known condition. The relativistic propagation delay correction includes Shapiro delay corrections for the solar and Jupiter's mass centers. The count is marked at the end of the count to ensure causality. The measurement noise variance of the scalar Doppler measurement adopts a multi-source hierarchical model, consisting of the sum of carrier phase extraction noise and finite count numerical effect noise, receiver clock white frequency noise, instrument noise and margin fixed terms, and tropospheric and ionospheric propagation medium residuals. The sum of carrier phase extraction noise and finite count numerical effect noise increases as the counting interval shortens. The receiver clock white frequency noise is proportional to the square of the daily stability of the receiver clock and increases as the counting interval shortens. The tropospheric and ionospheric propagation medium residuals increase as the elevation angle decreases.

4. The precise orbit determination method for a lunar probe based on ground-based unidirectional measurement according to claim 1, characterized in that, In S3, the total tracking resource constraint is as follows: M tracking windows are allocated within the N-day orbit determination arc, each tracking window lasts for 60 minutes, the interval between adjacent tracking windows is not less than 120 minutes, and the total tracking time covers one-third of the orbit determination arc; the ground deep space network includes at least three deep space stations distributed at geographical longitude intervals, the positions of each deep space station are calibrated in the Earth-fixed coordinate system and converted to the J2000 inertial frame through Earth orientation parameters; the scheduling result remains fixed throughout the entire orbit determination arc.

5. The precise orbit determination method for a lunar probe based on ground-based unidirectional measurement according to claim 1, characterized in that, In step S4, the radial-lateral-normal orbital coordinate system is defined by the instantaneous state of the lunar probe, with the radial direction along the position vector direction, the normal direction along the orbital angular momentum direction, and the lateral direction being the orbital direction after deducting the radial velocity component. The diagonal elements of the fixed diagonal scaling matrix take the initial one standard deviation uncertainty of each state component, where the uncertainty is 1 km for each position direction, 1 m / s for each velocity direction, and preset initial uncertainties for each clock drift and empirical acceleration direction. The parameters of the square root unscented Kalman filter adopt the standard recommended values, generating 21 sigma points for the augmented state vector. In step S5, when no measurements are available, the process noise is merged into the square root covariance factor through QR decomposition. When receiving measurements, covariance reduction at the square root factor level is achieved through Cholesky degradation.

6. The precise orbit determination method for a lunar probe based on ground-based unidirectional measurement according to claim 1, characterized in that, In step S4, the augmented state vector does not include clock bias, and the clock bias is converted to coordinate time through uplink time synchronization; in step S5, the correlation time of the first-order Gauss-Markov process corresponds to three consecutive finite counting intervals, so that the empirical acceleration can span multiple consecutive measurement cumulative orbital responses, while avoiding smooth confusion between the high dynamic region of the perilunar point and the low dynamic region of the apolunar point caused by an excessively long memory window; the root mean square difference between the steady-state amplitude and the acceleration difference of the onboard simplified force model along the reference trajectory is on the same order of magnitude; the diffusion intensity of the random walk process of the receiver clock residual drift is determined by the daily Allan deviation of the receiver clock according to the standard relationship between the double-sampled Allan variance and the white frequency noise diffusion coefficient.

7. The precise orbit determination method for a lunar probe based on ground-based unidirectional measurement according to claim 1, characterized in that, In S5, the spaceborne simplified force model includes: a lunar gravitational field model truncated to the 100th order; Earth's point mass gravity and Sun's point mass gravity; a solar radiation pressure projectile model with a fixed reflection coefficient; and first-order relativistic corrections for the Sun's center of mass and Jupiter's center of mass. The spaceborne simplified force model and the actual mechanical environment have higher-order gravitational field truncation biases (from the 101st to the 420th order) and solar radiation pressure reflection coefficient biases. These higher-order gravitational field truncation biases and radiation pressure reflection coefficient biases are not directly provided to the filter, but are absorbed from the Doppler measurement sequence through the empirical acceleration components propagating according to the first-order Gauss-Markov process, absorbing their cumulative effect after dynamic propagation. The preset threshold is the quantile of a chi-square distribution with 1 degree of freedom under a preset tail probability.

8. The precise orbit determination method for a lunar probe based on ground-based unidirectional measurement according to claim 1, characterized in that, In step S6, the navigation state measured by the normalized estimation error square is a seven-dimensional navigation state, which includes three-dimensional position, three-dimensional velocity, and receiver clock residual drift. The normalized estimation error square is divided by seven and compared with 1. When the median of the normalized innovation square is close to 1 and the normalized estimation error square is significantly deviated from 1 after being divided by seven, it is determined that the navigation covariance does not have calibration properties.

9. The precise orbit determination method for a lunar probe based on ground-based unidirectional measurement according to claim 1, characterized in that, The finite counting interval is between 5 and 60 seconds. When the finite counting interval is shorter, the Doppler measurement time resolution is improved, but the carrier phase extraction noise and the finite count numerical effect noise increase. When the finite counting interval is longer, the measurement noise is reduced, but the number of available measurements decreases.

10. A precise orbit determination system for a lunar probe based on ground-based unidirectional measurement, used to implement the precise orbit determination method for a lunar probe based on ground-based unidirectional measurement as described in any one of claims 1 to 9, characterized in that, Including ground segment subsystem and detector terminal system: The ground segment subsystem includes: multiple geographically distributed ground deep space station modules, used to transmit uplink carrier signals within the tracking window; and a tracking scheduling module, used to prioritize the allocation of the tracking window to the visible arc segment of the lowest preset proportion interval of the lunar probe's orbital altitude under the constraint of total tracking resources, select the station with the highest elevation angle when multiple stations are visible, and perform elevation angle masking and lunar occlusion checks. The detector terminal system is deployed on the lunar probe and includes: a carrier receiving and frequency comparison module, used to receive the uplink carrier signal and compare it with the local oscillator, outputting the residual frequency offset after subtracting modelable relativistic effects; a finite-count Doppler forming module, used to integrate the residual frequency offset over the counting interval and convert it into the average geometric distance change rate, iteratively solve for the optical travel time and take into account the relativistic propagation delay, and output a scalar Doppler measurement; a spaceborne simplified force model propagation module, used to propagate the orbital state during the prediction step; and a square-root unscented Kalman filter module, used to maintain an augmented state vector including three-dimensional position, three-dimensional velocity, receiver clock residual drift, and three-directional empirical acceleration, and after transforming to dimensionless coordinates using a fixed diagonal scaling matrix, perform sigma point generation, propagation, and... The system includes: a square root factor update and a gating filter for effective measurements using the normalized innovation square; a fixed dynamic model compensation module to propagate empirical acceleration in three directions using a first-order Gaussian-Markov process with fixed parameters, absorbing the cumulative effect of systematic deviations between the onboard simplified force model and the real mechanical environment in the Doppler measurement sequence; a clock drift estimation module to propagate the receiver clock residual drift using a random walk process, with the diffusion intensity determined by the one-day Allan deviation of the receiver clock; and a dual consistency evaluation module to simultaneously calculate the normalized innovation square and the normalized estimation error square. When the normalized innovation square is close to 1 while the normalized estimation error square deviates significantly from 1, the filter is determined to be consistent in the measurement space but overconfident in the navigation state space, and the determination result is output as input for navigation system integrity monitoring.

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