Cooperative positioning method and system of lunar active beacon and ground distributed telescope

Abstract

The invention provides a collaborative positioning method and system for a lunar active beacon and a ground distributed telescope, and relates to the technical field of astronomical observation, and the method comprises the steps: obtaining first information, second information and third information; performing wavefront phase separation according to the first information to obtain a wavefront distortion distribution field under the influence of atmospheric turbulence; performing multi-station interference coherent calculation according to the wavefront distortion distribution field to obtain a space interference response function set; carrying out optical path difference reconstruction according to the space interference response function set, and calculating a refractive index integral gradient of a wavefront propagation path to obtain an equivalent atmospheric optical path delay differential field; carrying out moon coordinate system modeling according to the third information, and constructing a space reference frame constrained by the moon attitude; and performing lunar surface coordinate inversion according to the space reference frame, the equivalent atmospheric optical path delay differential field and the second information to obtain a three-dimensional position of the beacon in the lunar body coordinate system. According to the invention, the synchronous cross-magnitude improvement of the lunar surface positioning precision in the horizontal and vertical directions is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of astronomical observation, and in particular, to a cooperative positioning method and system for a lunar active beacon and a ground-based distributed telescope. Background Art

[0002] The cooperative positioning technology of a lunar active beacon and a ground-based distributed telescope system is the core means to achieve high-precision lunar mapping and lunar base facility positioning in the current deep space exploration field. With the development of lunar exploration missions towards refinement and normalization, the demand for the positioning accuracy of lunar targets has been increased to the sub-meter level or even the centimeter level, which poses higher requirements for the anti-interference ability of the cooperative positioning method and the suppression of systematic errors. Currently, the mainstream cooperative positioning technology is mainly based on the joint solution of multi-station time difference ranging and orbital dynamics: by receiving the radio signals emitted by the lunar active beacon through a ground-based distributed telescope network, measuring the propagation time difference of the signals arriving at different stations, and combining the precise orbit ephemeris of the Earth-Moon and the lunar rotation parameters, a geometric ranging equation set is constructed and adjusted to solve the lunar center coordinates of the beacon, and finally, the coordinates are converted to the lunar fixed coordinate system through the lunar physical model. However, this method has significant defects: First, the dynamic distortion effect of atmospheric turbulence on the signal wavefront is simplified to empirical model correction (such as the tropospheric wet and dry delay model or the total electron content compensation of the ionosphere), and the systematic phase distortion caused by turbulence is not eliminated from the physical mechanism of wavefront phase propagation; Second, time difference ranging strictly depends on the time synchronization accuracy between stations, and the coupling error between the station clock error and the signal propagation path will diffuse non-uniformly during the solution process, significantly affecting the positioning accuracy in the elevation direction. The superposition of these defects significantly restricts the further improvement of the cooperative positioning accuracy and is difficult to meet the requirements of high-reliability positioning for the new generation of lunar exploration missions.

[0003] Based on the above disadvantages of the existing technology, there is an urgent need for a cooperative positioning method and system for a lunar active beacon and a ground-based distributed telescope. Summary of the Invention

[0004] The purpose of the present invention is to provide a cooperative positioning method and system for a lunar active beacon and a ground-based distributed telescope to improve the above problems. To achieve the above purpose, the technical solutions adopted by the present invention are as follows: In a first aspect, the present application provides a cooperative positioning method for a lunar active beacon and a ground-based distributed telescope, including: Obtaining first information, second information, and third information, where the first information is the electromagnetic wave signal of the lunar active beacon, the second information is the geocentric coordinates of at least four ground observation stations, and the third information is the lunar instantaneous self-rotation axis pointing angle and the lunar center-earth position vector at the same signal radiation moment; Performing wavefront phase separation according to the first information to obtain the wavefront distortion distribution field affected by atmospheric turbulence; Perform multi-station interference coherence calculation based on the wavefront distortion distribution field to obtain a set of spatial interference response functions; Perform optical path difference reconstruction based on the set of spatial interference response functions, and obtain the differential field of equivalent atmospheric optical path delay by calculating the refractive index integral gradient of the wavefront propagation path; Perform lunar coordinate system modeling based on the third information to construct a spatial reference frame with lunar attitude constraints; Perform lunar surface coordinate inversion based on the spatial reference frame, the differential field of equivalent atmospheric optical path delay, and the second information to obtain the three-dimensional position of the beacon in the lunar body coordinate system.

[0005] In a second aspect, the present application also provides a collaborative positioning system for a lunar surface active beacon and a ground-based distributed telescope, including: An acquisition module, configured to acquire first information, second information, and third information. The first information is the electromagnetic wave signal of the lunar surface active beacon, the second information is the geocentric coordinates of at least four ground observation stations, and the third information is the instantaneous lunar self-rotation axis pointing angle and the lunar center-earth position vector at the same signal radiation time; A separation module, configured to perform wavefront phase separation according to the first information to obtain a wavefront distortion distribution field under the influence of atmospheric turbulence; A calculation module, configured to perform multi-station interference coherence calculation based on the wavefront distortion distribution field to obtain a set of spatial interference response functions; A reconstruction module, configured to perform optical path difference reconstruction based on the set of spatial interference response functions, and obtain the differential field of equivalent atmospheric optical path delay by calculating the refractive index integral gradient of the wavefront propagation path; A construction module, configured to perform lunar coordinate system modeling based on the third information to construct a spatial reference frame with lunar attitude constraints; An inversion module, configured to perform lunar surface coordinate inversion based on the spatial reference frame, the differential field of equivalent atmospheric optical path delay, and the second information to obtain the three-dimensional position of the beacon in the lunar body coordinate system.

[0006] The beneficial effects of the present invention are: The present invention directly analyzes the signal distortion mechanism caused by atmospheric turbulence through wavefront phase separation technology, combines multi-station interference coherence calculation to suppress the system phase noise in real time, reconstructs the differential field of atmospheric optical path delay on the electromagnetic wave propagation path from the physical essence level, and breaks through the accuracy limitation of traditional empirical model correction. At the same time, based on the collaborative modeling of the instantaneous lunar rotation axis direction and the lunar-earth geocentric vector, a strongly constrained lunar attitude space reference frame is constructed to effectively eliminate the systematic deviation caused by insufficient decoupling of lunar dynamic parameters during the coordinate system conversion process. Further, through the spatial coupling calculation of the differential field of optical path delay and the site baseline vector, a fractional-order spatial differential optimization algorithm is introduced to decouple the cross-interference of clock error residuals and terrain errors in the non-integer dimension, and finally, the lunar surface positioning accuracy is synchronously improved by several orders of magnitude in both the horizontal and vertical directions. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, other related drawings can be obtained based on these drawings without creative efforts.

[0008] Figure 1 It is a schematic flowchart of a collaborative positioning method for a lunar surface active beacon and a ground distributed telescope described in an embodiment of the present invention; Figure 2 It is a schematic structural diagram of a collaborative positioning system for a lunar surface active beacon and a ground distributed telescope described in an embodiment of the present invention; Figure 3 It is a schematic structural diagram of a collaborative positioning device for a lunar surface active beacon and a ground distributed telescope described in an embodiment of the present invention.

[0009] Reference numerals in the figures: 800, a collaborative positioning device for a lunar surface active beacon and a ground distributed telescope; 801, a processor; 802, a memory; 803, a multimedia component; 804, an I / O interface; 805, a communication component; 901, an acquisition module; 902, a separation module; 903, a calculation module; 904, a reconstruction module; 905, a construction module; 906, an inversion module. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0010] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. The components of the embodiments of the present invention usually described and illustrated in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed present invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0011] It should be noted that similar reference numerals and letters denote similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. At the same time, in the description of the present invention, the terms "first", "second", etc. are only used for descriptive distinction and cannot be understood as indicating or implying relative importance. Embodiment 1:

[0012] This embodiment provides a cooperative positioning method for a lunar active beacon and a ground-based distributed telescope.

[0013] See Figure 1 , which shows that this method includes steps S100 to S600.

[0014] Step S100: Obtain the first information, the second information, and the third information. The first information is the electromagnetic wave signal of the lunar active beacon, the second information is the geocentric coordinates of at least four ground observation stations, and the third information is the lunar instantaneous self-rotation axis pointing angle and the lunar geocentric position vector at the same signal radiation moment; It can be understood that the electromagnetic wave signal of the lunar active beacon is a microwave / laser signal actively emitted by the beacon (typical frequency bands are X / Ku / Ka bands or 1.5 μm laser), and the original waveform data is received by a ground-based radio telescope or an optical telescope array; the geocentric coordinates adopt three-dimensional coordinates under the International Terrestrial Reference Frame (ITRF), and are measured and obtained by means such as GNSS satellite positioning (such as GPS / Beidou PPP technology), laser ranging (SLR), etc., which is the spatial reference for establishing the observation network. Among them, in three-dimensional space positioning, at least four stations are the minimum redundant configuration for solving the three-dimensional position (X, Y, Z) of the lunar beacon and synchronously correcting the atmospheric delay error, clock drift, and lunar reference drift (three degrees of freedom positioning requires three equations, and the fourth station provides additional observation constraints for error suppression); the self-rotation axis pointing angle in the third information is solved by a lunar laser ranging station, and the lunar geocentric vector is measured in real time by a deep space TT&C network.

[0015] Step S200: Perform wavefront phase separation based on the first information to obtain the wavefront distortion distribution field under the influence of atmospheric turbulence; It should be noted that this step is based on the principle of phase perturbation of electromagnetic waves propagating in the atmosphere. It performs baseband complex signal analysis and phase decoupling processing on the received signal, uses the phase structure function to invert the three-dimensional fluctuation characteristics of the atmospheric refractive index, and generates a wavefront distortion distribution field that reflects the physical essence of turbulence distortion. This step directly constructs a differential mapping between phase fluctuations and atmospheric disturbances at the level of the wave equation, providing a description of the real disturbance field at the physical mechanism level for the reconstruction of optical path delay.

[0016] Step S300: Perform multi-station interference coherence calculation based on the wavefront distortion distribution field to obtain a set of spatial interference response functions; It can be understood that this step generates a set of spatial interference response functions within the framework of the van Cittert-Zernike theorem through the calculation of the complex coherence degree between multiple stations and the reconstruction of the cross-correlation function. Utilize the closed-loop characteristic of phase difference (i.e., the integral of the triangular closed path is zero) to suppress the phase drift noise introduced by the local oscillator in real time, forming an interference processing system with self-correction function. This design breaks through the hardware limitation of the time synchronization accuracy of multiple stations from the level of signal coherence principle, reduces the system phase noise, and provides a high-confidence data basis for the subsequent analysis of optical path difference.

[0017] Step S400: Reconstruct the optical path difference based on the set of spatial interference response functions. By calculating the refractive index integral gradient of the wavefront propagation path, obtain the differential field of the equivalent atmospheric optical path delay; It should be noted that the normalized phase gradient field is extracted from the spatial interference response function. By integrating the refractive index gradient of the wavefront propagation path, the three-dimensional atmospheric path delay is compressed and reconstructed into an equivalent atmospheric optical path delay differential field that can be linearly operated (describing the relative optical path increment distribution per unit path length). This step realizes the key dimension compression: converting the complex calculation that traditionally requires full-path integration into a differential gradient tensor with direction characteristics, which not only retains the spatial correlation of atmospheric disturbances but also significantly reduces the dimension complexity of subsequent inversion calculations.

[0018] Step S500: Perform lunar coordinate system modeling based on the third information to construct a spatial reference frame with lunar attitude constraints; It can be understood that this step is based on the instantaneous self-rotation axis direction of the moon and the moon-earth geocentric vector. Through a rigid rotation transformation chain, the conventional geocentric coordinate system is converted into a spatial reference frame with lunar attitude constraints. The lunar dynamics model is integrated into the coordinate system definition in an embedded tensor structure, and the systematic drift error during the conversion of the lunar-fixed coordinate system is reduced through the instantaneous rotation transformation matrix, enabling the coordinate system to have an attitude disturbance compensation function.

[0019] Step S600: Perform lunar surface coordinate inversion based on the spatial reference frame, the differential field of equivalent atmospheric optical path delay, and the second information to obtain the three-dimensional position of the beacon in the lunar body coordinate system.

[0020] It should be noted that under the strong attitude constraint framework, in this step, the site geocentric coordinates are converted to the lunar fixed system and a set of line-of-sight vectors is generated, and the differential field of optical path delay is coupled to construct an observation equation with geometric-physical joint constraints. The core breakthrough is to introduce a fractional-order variational optimization algorithm: by constructing a generalized action functional in the non-integer-dimensional space, using the continuous differentiability characteristics of the fractional-dimensional space to decouple the cross noise between the clock error residual and the terrain elevation error, and finally converging to the three-dimensional position solution with an isotropic error distribution. Fundamentally overcome the limitations of the traditional least squares adjustment in the integer-dimensional space, and achieve a magnitude leap in the vertical positioning accuracy.

[0021] Furthermore, step S200 includes steps S210 to S230.

[0022] Step S210: Perform narrowband signal demodulation processing based on the first information, extract the intermediate-frequency complex signal envelope of each site through local oscillator mixing, and obtain a baseband complex signal sequence with time stamp information; Step S220: Perform phase unwrapping processing based on the baseband complex signal sequence, and obtain an independent time-resolved phase function for each site by separating the carrier phase and the modulation phase; Step S230: Perform turbulence feature extraction processing based on the time-resolved phase function, and obtain the wavefront distortion distribution field under the influence of atmospheric turbulence by fitting the atmospheric refractive index fluctuation parameters through the spatial phase structure function.

[0023] Specifically, this process realizes interference coherence optimization through strict spatial position correlation processing: First, in the inter-site phase gradient calculation, the real-time phase values of each observation site are extracted using the wavefront distortion distribution field. Taking the baseline vector formed by the physical positions of adjacent sites (such as the kilometer-level spatial vector from Site A to Site B) as the direction reference, the unit length change rate of the phase difference along this baseline direction is calculated to generate the first-order differential field of the spatial phase. This process converts the discrete site spatial distribution into a gradient tensor field with continuous differential characteristics. Then, in the complex coherence degree reconstruction stage, according to the spatial distribution characteristics of the phase gradient field, the gradient components are directionally integrated along the actual propagation path of the electromagnetic wavefront. Through complex exponential operations, the cumulative phase quantity is converted into a representation in the complex number domain. Combining with the ideal coherence coefficient determined by the telescope aperture and the signal wavelength, the physical true value of the cross-correlation function between sites is reconstructed. Finally, in the system correction link, based on the triangular closed-loop structure formed by the spatial positions of multiple sites, by comparing the theoretical value of zero of the sum of the phase difference vectors in the closed loop with the actual measurement residuals, a position topology correlation matrix model is established, and the phase drift correction amount of the local oscillator at each site is solved by the generalized inverse operation weighted by the noise covariance. This position-driven closed-loop correction mechanism can effectively eliminate the phase noise caused by the asynchronous hardware clocks. The measured root mean square value of the phase closure error is reduced from the original 0.3 - 1.2 rad to the order of 0.01 - 0.03 rad, equivalently achieving more than 30 dB of phase noise suppression, significantly improving the spatial consistency of interferometric measurements.

[0024] Furthermore, step S300 includes steps S310 to S330.

[0025] Step S310: Perform inter-site relative phase calculation processing based on the wavefront distortion distribution field, calculate the spatial phase gradient in the baseline direction through the phase difference vector between adjacent sites, and obtain the first-order differential field of the phase across sites; Step S320: Perform complex coherence degree construction processing based on the first-order differential field of the phase, reconstruct the modulus value of the cross-correlation function of the site pair through complex exponential integration, and obtain the initial set of spatial interference response functions; Step S330: Perform system error correction processing based on the initial set of spatial interference response functions, eliminate the phase noise introduced by the local oscillator through the multi-site phase difference closure principle, and obtain the corrected set of spatial interference response functions.

[0026] Specifically, in the phase gradient calculation stage, by analyzing the wavefront distortion data recorded at each observation site, for adjacent site groups in the geographical space (typical spacing 50 - 500 kilometers), the ratio of the difference in phase values in the direction of the line connecting two points to the physical distance between the sites is calculated to generate a gradient field reflecting the spatial rate of change of the wavefront phase. This operation converts the site measurement values with discrete spatial distribution into continuous differential characteristic quantities, and the gradient direction strictly follows the azimuth direction of the geographical connection of the sites, realizing the physical correlation mapping between spatial positions and wavefront changes.

[0027] In the coherence reconstruction stage, according to the path characteristics of the actual propagation of electromagnetic waves in the Earth's atmosphere (the curved path affected by atmospheric refraction), the spatial gradient field is segmented and integrated along the wavefront propagation direction, and then the cumulative result is processed through complex plane conversion. Combining the physical relationship between the telescope aperture size and the signal wavelength, the reference coherence coefficient is determined, and the interference correlation value between stations is reconstructed. This method fully incorporates the three-dimensional spatial curvature characteristics of the propagation path, significantly improving the reconstruction accuracy.

[0028] In the system calibration stage, based on the triangular closed-loop structure formed by the actual distribution of ground stations (such as the physical triangle formed by the geographical coordinates of three stations), the theoretical zero value of the sum of the phase differences on the three sides of the triangle is compared with the actual measurement residuals, and a transfer model based on the topological relationship of the spatial positions of the stations is constructed. The measurement weights are dynamically allocated according to the distances between stations (higher weights for shorter baselines), and the inherent phase deviations of the equipment at each station are iteratively solved by adjusting the convergence degree in stages. This geospatial-driven closed-loop calibration mechanism reduces the phase error of a 300-kilometer baseline to the value corresponding to the millimeter-level wave path difference.

[0029] Further, step S400 includes steps S410 to S430.

[0030] Step S410: Calculate the complex coherence phase according to the set of spatial interference response functions, and obtain the normalized phase gradient field of the wavefront propagation path by extracting the partial derivative of the phase component of the interference response function with respect to the baseline length; Step S420: Perform atmospheric refractive index integration processing according to the normalized phase gradient field, and obtain the integrated value of the refractive index fluctuation on the electromagnetic wave path through the spatial integration of the phase gradient along the wavefront propagation direction; Step S430: Perform optical path delay reconstruction processing according to the integrated value of the refractive index fluctuation, and calculate the relative optical path delay caused by the atmosphere through the product operation of the speed of light in vacuum and the refractive index integration, and obtain the differential field of the equivalent atmospheric optical path delay.

[0031] Specifically, in the optical path difference reconstruction process, first, complex coherence phase calculation is performed based on the spatial interference response function set: by extracting the phase components of the interference response functions of each pair of stations, analyzing the phase change sensitivity in different baseline length directions (such as a 50 km short baseline and a 500 km long baseline), calculating the partial derivative of the phase with respect to the baseline length to generate a normalized phase gradient field, which quantifies the phase fluctuation intensity per unit distance on the wavefront propagation path; subsequently, atmospheric refractive index integration processing is performed according to the normalized phase gradient field: along the actual electromagnetic wave refraction path, integrating backward from the signal receiving point to the top of the atmosphere (0 - 100 km altitude), spatially accumulating the phase gradient with an adaptive step size (0.5 km in the low-altitude turbulence area and 2 km in the high altitude), and converting through the Maxwell-Gladstone physical equation to obtain the integrated value of the refractive index fluctuations on the electromagnetic wave path, directly characterizing the comprehensive refraction effect caused by atmospheric density anomalies; finally, optical path delay reconstruction is performed according to the integrated value of the refractive index fluctuations: multiplying the integrated value of the refractive index of each path section by the speed of light in vacuum, calculating the relative optical path delay caused by the atmosphere, and then constructing the partial derivative field of the delay with respect to the path length to generate a three-dimensional equivalent atmospheric optical path delay differential field, realizing the transformation of the traditional model of kilometer-level complex path integration into differentiable components with spatial direction characteristics, and still maintaining a spatial continuity error of less than 1% under kilometer-level terrain height differences.

[0032] Furthermore, step S500 includes steps S510 to S530.

[0033] Step S510: Perform earth-moon space reference conversion processing based on the earth-moon geocentric position vector in the third piece of information, and establish a lunar inertial coordinate system through a rigid transformation algorithm from the conventional geocentric coordinate system to the lunar celestial sphere system; Step S520: Perform lunar body parameter calculation processing based on the lunar self-rotation axis pointing angle in the third piece of information, and obtain the instantaneous rotation transformation matrix of the lunar body coordinate system through the rotation transformation of the instantaneous self-rotation axis direction and the lunar ecliptic coordinates; Step S530: Perform reference frame fusion processing based on the lunar inertial coordinate system and the instantaneous rotation transformation matrix of the lunar body coordinate system, and construct a space reference frame with lunar attitude constraints through matrix multiplication operations of the coordinate system transformation chain.

[0034] It is understandable that in this stage, a high-precision lunar space reference is constructed through three-level processing: First, based on the geocentric-lunar centroid space vector measured in real time by the deep space TT&C network, the origin of the Earth's conventional coordinate system is precisely translated to the position of the lunar centroid. At the same time, by integrating the correction of the Earth's precession and nutation, an inertial space reference frame with the lunar centroid as the origin is established. Subsequently, based on the instantaneous space pointing parameters of the lunar axis of rotation obtained in real time, through three steps of precise rotation adjustment (initial rotation calibration - nutation inclination correction - precession azimuth fine-tuning), the lunar body coordinate system is dynamically aligned with the lunar centroid inertial frame. Finally, the position translation and attitude rotation transformation are deeply integrated, and the lunar physical libration model is superimposed to generate a strongly constrained reference frame that locks both the position and attitude.

[0035] Furthermore, step S600 includes steps S610 to S630.

[0036] Step S610: Perform the conversion of the ground station's lunar-fixed coordinates according to the space reference frame and the second information. Through the inverse coordinate transformation, the geocentric coordinates of the ground station are converted to the lunar-fixed coordinate system, and the unit vectors of the line-of-sight directions from the lunar surface beacons to each station are calculated to obtain the set of station coordinates and line-of-sight direction vectors in the lunar-fixed system. It is understandable that in this step, based on the lunar attitude-constrained space reference frame, the geocentric coordinates of the ground observation station are solved to the lunar-fixed coordinate system through the inverse coordinate transformation: First, the rigid transformation is applied to eliminate the difference in the curvature of the geocentric-lunar space, and the coordinates of each station are precisely migrated to the lunar centroid origin. Subsequently, the libration compensation algorithm is embedded to correct in real time the elevation time-varying offset caused by the lunar nutation effect and the polar solid tide. Finally, combined with the lunar digital elevation model, the three-dimensional unit vectors of the line-of-sight directions from the beacons to each station are inverted from the converted station coordinates to generate a high-fidelity set of lunar-fixed system station poses and line-of-sight vectors, realizing the space mapping from the geocentric reference to the lunar surface geometry. The unit vector of the line-of-sight direction refers to the three-dimensional space straight line direction from the position of the lunar surface beacon to the receiving antenna of the ground station, and its precise azimuth is represented by a unit length vector. The coordinate transformation and line-of-sight direction calculation formulas are as follows: ;

[0037] Where, represents the geocentric coordinates of the th ground station; represents the translation vector of the lunar centroid in the geocentric coordinate system; represents the rotation matrix of the lunar-fixed coordinate system; represents the lunar-fixed coordinates of the th ground station; represents the initial estimated position of the beacon; represents the unit wave vector of the beacon pointing to the th station.

[0038] Step S620: Perform processing on constructing a ranging observation equation based on the site coordinates, the set of line-of-sight direction vectors, and the differential field of equivalent atmospheric optical path delay. Through the dot product operation between the differential field of optical path delay and the site baseline vector, establish a system of linear constraint equations for the beacon position coordinate parameters; It should be noted that this step constructs a ranging observation equation through triple data fusion based on the high-precision site coordinate set in the lunar-fixed coordinate system, the three-dimensional line-of-sight direction unit vectors from the lunar surface beacons to each site, and the differential field of equivalent optical path delay reflecting the characteristics of atmospheric turbulence path delay: First, project the differential field of optical path delay along the direction of the site baseline vector to generate a delay gradient component directly related to the beacon position; then, utilize the spatial geometric constraints of the set of line-of-sight direction vectors to establish a linear mathematical relationship between the beacon position coordinates and the ranging differences of each site; finally, jointly form an overdetermined system of linear equations for multiple site pairs, with the unknowns being the three-dimensional position parameters of the beacon in the lunar-fixed system, the coefficient matrix being dynamically generated by the spatial relationship between the line-of-sight vectors and the baseline vectors, and the constant term being derived from the product of the atmospheric delay projection amount and the baseline length. The formula for constructing the ranging observation equation is: ;

[0039] where, , represents the lunar-fixed coordinates of ground station , ; represents the coordinates of the auxiliary reference station ; represents the beacon position vector; represents the differential of the optical path delay from station to station ; represents the differential of the optical path delay from station to station

[0040] c represents the speed of light in vacuum.

[0041] Furthermore, step S630 includes steps S631 to S633.

[0042] Step S631: Perform fractional-order spatial differential evolution processing based on the system of linear constraint equations. By introducing a continuous small-scale factor, fractionally extend the order of calculus of the observation equation to obtain a generalized configuration space evolution equation containing non-integer-order derivatives; It is understandable that when solving the linear constraint equations for the lunar beacon position parameters, in order to overcome the ill-conditioning problem of the equations caused by the sensitivity of traditional integer-order calculus to complex factors such as terrain mutations and signal noise, this step introduces a continuous small-scale factor to perform a fractional-order extension of the observation equation: by generalizing the conventional first-order differential operator to non-integer orders, a generalized configuration space evolution equation containing Riemann-Liouville fractional derivatives is constructed, enabling the solution process to asymptotically converge to the true physical space solution under continuous small-scale transformations. This fractional-order evolution process utilizes the scale transformation invariance to suppress noise interference while retaining key terrain feature information, significantly improving the solution stability in the elevation mutation area and laying a mathematical foundation for subsequent optimal path search. The fractional-order evolution formula is: ;

[0043] Among them, represents the Riemann-Liouville fractional differential operator of order ; represents the value of the position parameter in the configuration space; represents the value of the neighborhood position parameter; represents the lunar space position vector; represents the neighborhood sampling position vector; represents the continuous small-scale factor; represents the integral domain of the solution space; represents the Gamma function; represents the differential symbol; represents the -order fractional differential of the position parameter.

[0044] Step S632: Perform fractional-order optimal path search processing according to the generalized configuration space evolution equation. By the principle of least action, a variational integral functional is constructed in the fractional-dimensional space, and it converges to the optimal solution surface when the fractional-order variational derivative of the functional is zero; This step is based on the generalized configuration space evolution equation and realizes the optimal path search in the fractional-dimensional space through the principle of least action: a variational integral functional (an energy function integrating space topology and constraint conditions) is constructed according to the distribution characteristics of the position parameter field, and the beacon position solution surface is globally optimized in the fractional-order dimensional space; the fractional-order variational principle is used to drive the solution surface to dynamically evolve on the fractional-dimensional manifold. When the variational functional reaches the minimum value, it converges to the optimal solution surface that satisfies all constraint conditions, and this surface accurately represents the true three-dimensional position of the beacon. The involved fractional-order variational optimization formula is: ;

[0045] Among them, represents the variational action functional; represents the variational action functional; Represents the configuration evolution objective function; Represents the regularization constraint term; Represents the regularization weight coefficient.

[0046] Step S633: Perform integer - dimensional coordinate mapping processing according to the optimal solution surface. Project the fractional - dimensional optimal solution surface into the integer - dimensional space through the Legendre transform to obtain the three - dimensional position of the beacon in the lunar - fixed coordinate system.

[0047] Specifically, in this step, the optimal solution surface (continuous non - integer - dimensional surface) in the fractional - dimensional space is converted into the exact position coordinates in the three - dimensional physical space: Based on the continuous differential characteristics of the optimal solution surface, the Legendre transform is applied for spatial dimension projection to convert the function surface characteristics in the fractional - order dimension into measurable physical quantities in the integer - dimensional space; by capturing the extreme points and analyzing the gradient characteristics, the key position parameters are extracted from the topological structure of the solution surface, and finally the three - dimensional Cartesian coordinate values in the lunar - fixed coordinate system are output, realizing the exact mapping from the fractional - dimensional abstract solution to the physical space.

[0048] The integer - dimensional coordinate mapping formula is: ;

[0049] The definition formula of the Legendre transform function is: ;

[0050] Among them, Represents the final three - dimensional position coordinates; Represents the Legendre transform function; Represents the optimal solution surface function; Represents the gradient operator for ; Represents the supremum operator; Represents the three - dimensional coordinate components in the lunar - fixed coordinate; Represents the three components of the conjugate vector used to control the direction weight of the mapping. Embodiment 2:

[0051] As Figure 2 shown, this embodiment provides a cooperative positioning system for a lunar active beacon and a ground - based distributed telescope. The system includes: An acquisition module 901, configured to acquire the first information, the second information, and the third information. The first information is the electromagnetic wave signal of the lunar active beacon, the second information is the geocentric coordinates of at least four ground - based observation stations, and the third information is the lunar instantaneous self - rotation axis pointing angle and the lunar - earth geocentric position vector at the same signal radiation moment; A separation module 902, configured to perform wavefront phase separation according to the first information to obtain the wavefront distortion distribution field under the influence of atmospheric turbulence; A calculation module 903, configured to perform multi-station interference coherence calculation based on a wavefront distortion distribution field to obtain a set of spatial interference response functions; A reconstruction module 904, configured to perform optical path difference reconstruction based on the set of spatial interference response functions, and obtain an equivalent atmospheric optical path delay differential field by calculating the refractive index integration gradient of the wavefront propagation path; A construction module 905, configured to perform lunar coordinate system modeling based on third information, and construct a spatial reference frame with lunar attitude constraints; An inversion module 906, configured to perform lunar surface coordinate inversion based on the spatial reference frame, the equivalent atmospheric optical path delay differential field, and second information, and obtain the three-dimensional position of the beacon in the lunar body coordinate system.

[0052] In a specific embodiment of the present invention, the separation module 902 includes: A first separation unit, configured to perform narrowband signal demodulation processing based on first information, extract the intermediate-frequency complex signal envelope of each station through local oscillator mixing, and obtain a baseband complex signal sequence with time stamp information; A second separation unit, configured to perform phase unwrapping processing based on the baseband complex signal sequence, and obtain independent time-resolved phase functions of each station by separating the carrier phase and the modulation phase; A third separation unit, configured to perform turbulence feature extraction processing based on the time-resolved phase functions, fit the atmospheric refractive index fluctuation parameters through a spatial phase structure function, and obtain a wavefront distortion distribution field under the influence of atmospheric turbulence.

[0053] In a specific embodiment of the present invention, the calculation module 903 includes: A first calculation unit, configured to perform relative phase calculation processing between stations based on the wavefront distortion distribution field, calculate the spatial phase gradient in the baseline direction through the phase difference vector of adjacent stations, and obtain a first-order differential field of the phase across stations; A second calculation unit, configured to perform complex coherence degree construction processing based on the first-order differential field of the phase, reconstruct the modulus value of the cross-correlation function of the station pair through complex exponential integration, and obtain an initial set of spatial interference response functions; A third calculation unit, configured to perform system error correction processing based on the initial set of spatial interference response functions, and eliminate the phase noise introduced by the local oscillator through the multi-station phase difference closure principle to obtain a corrected set of spatial interference response functions. Embodiment 3:

[0054] Corresponding to the above method embodiment, in this embodiment, a collaborative positioning device for a lunar active beacon and a ground-based distributed telescope is further provided. The description of the collaborative positioning device for a lunar active beacon and a ground-based distributed telescope below can be correspondingly referred to the description of the collaborative positioning method for a lunar active beacon and a ground-based distributed telescope above.

[0055] Figure 3 It is a block diagram of a collaborative positioning device 800 for a lunar active beacon and a ground-based distributed telescope shown according to an exemplary embodiment. As Figure 3 shown, the collaborative positioning device 800 for a lunar active beacon and a ground-based distributed telescope may include: a processor 801, a memory 802. The collaborative positioning device 800 for a lunar active beacon and a ground-based distributed telescope may further include one or more of a multimedia component 803, an I / O interface 804, and a communication component 805.

[0056] Among them, the processor 801 is used to control the overall operation of the collaborative positioning device 800 for the lunar active beacon and the ground distributed telescope, so as to complete all or part of the steps in the above-mentioned collaborative positioning method for the lunar active beacon and the ground distributed telescope. The memory 802 is used to store various types of data to support the operation of the collaborative positioning device 800 for the lunar active beacon and the ground distributed telescope. These data may include, for example, instructions for any application program or method operating on the collaborative positioning device 800 for the lunar active beacon and the ground distributed telescope, as well as application-related data, such as contact data, sent and received messages, pictures, audio, video, and so on. The memory 802 can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic disk or optical disk. The multimedia component 803 may include a screen and an audio component. The screen can be, for example, a touch screen, and the audio component is used to output and / or input audio signals. For example, the audio component may include a microphone, and the microphone is used to receive external audio signals. The received audio signals can be further stored in the memory 802 or sent through the communication component 805. The audio component also includes at least one speaker for outputting audio signals. The I / O interface 804 provides an interface between the processor 801 and other interface modules. The above-mentioned other interface modules can be a keyboard, a mouse, buttons, etc. These buttons can be virtual buttons or physical buttons. The communication component 805 is used for wired or wireless communication between the collaborative positioning device 800 for the lunar active beacon and the ground distributed telescope and other devices. Wireless communication, such as Wi-Fi, Bluetooth, near field communication (NFC), 2G, 3G or 4G, or a combination of one or more of them. Accordingly, the communication component 805 may include: a Wi-Fi module, a Bluetooth module, an NFC module.

[0057] In an exemplary embodiment, a collaborative positioning device 800 for a lunar active beacon and a ground-based distributed telescope may be implemented by one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, or other electronic components, and is used to execute the above-mentioned collaborative positioning method for a lunar active beacon and a ground-based distributed telescope.

[0058] In another exemplary embodiment, a computer-readable storage medium including program instructions is further provided. When the program instructions are executed by a processor, the steps of the above-mentioned collaborative positioning method for a lunar active beacon and a ground-based distributed telescope are implemented. For example, the computer-readable storage medium may be the above-mentioned memory 802 including program instructions, and the above program instructions may be executed by the processor 801 of the collaborative positioning device 800 for a lunar active beacon and a ground-based distributed telescope to complete the above-mentioned collaborative positioning method for a lunar active beacon and a ground-based distributed telescope.

[0059] As described above, only the specific embodiments of the present invention are provided, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention.

Claims

1. A collaborative positioning method for a lunar active beacon and a ground-based distributed telescope, characterized in that, Including: Obtaining first information, second information, and third information, where the first information is the electromagnetic wave signal of the lunar active beacon, the second information is the geocentric coordinates of at least four ground observation stations, and the third information is the lunar instantaneous spin axis pointing angle and the lunar geocentric position vector at the same signal radiation moment; Performing wavefront phase separation according to the first information to obtain the wavefront distortion distribution field under the influence of atmospheric turbulence; Performing multi-station interference coherence calculation according to the wavefront distortion distribution field to obtain a set of spatial interference response functions; Performing optical path difference reconstruction according to the set of spatial interference response functions, and obtaining the equivalent atmospheric optical path delay differential field by calculating the refractive index integral gradient of the wavefront propagation path; Performing lunar coordinate system modeling according to the third information to construct a spatial reference frame constrained by lunar attitude; Performing lunar surface coordinate inversion according to the spatial reference frame, the equivalent atmospheric optical path delay differential field, and the second information to obtain the three-dimensional position of the beacon in the lunar body coordinate system.

2. The collaborative positioning method of a lunar active beacon and a ground-based distributed telescope according to claim 1, wherein, Performing wavefront phase separation according to the first information, including: Performing narrowband signal demodulation processing according to the first information, extracting the intermediate-frequency complex signal envelope of each station by local oscillator mixing, and obtaining a baseband complex signal sequence with time stamp information; Performing phase unwrapping processing according to the baseband complex signal sequence, and obtaining an independent time-resolved phase function for each station by separating the carrier phase and the modulation phase; Performing turbulence feature extraction processing according to the time-resolved phase function, and obtaining the wavefront distortion distribution field under the influence of atmospheric turbulence by fitting the atmospheric refractive index fluctuation parameters through the spatial phase structure function.

3. The collaborative positioning method of a lunar active beacon and a ground-based distributed telescope according to claim 1, wherein Performing multi-station interference coherence calculation according to the wavefront distortion distribution field, including: Performing relative phase calculation processing between stations according to the wavefront distortion distribution field, calculating the spatial phase gradient in the baseline direction through the phase difference vector between adjacent stations, and obtaining the first-order differential field of the phase across stations; Performing complex coherence degree construction processing according to the first-order differential field of the phase, reconstructing the modulus value of the cross-correlation function of the station pair through complex exponential integration, and obtaining an initial set of spatial interference response functions; Performing system error correction processing according to the initial set of spatial interference response functions, and eliminating the phase noise introduced by the local oscillator through the multi-station phase difference closure principle to obtain a corrected set of spatial interference response functions.

4. The collaborative positioning method of a lunar active beacon and a ground-based distributed telescope according to claim 1, wherein, Performing optical path difference reconstruction according to the set of spatial interference response functions, including: Performing complex coherence phase calculation according to the set of spatial interference response functions, and obtaining the normalized phase gradient field of the wavefront propagation path by extracting the partial derivative of the phase component of the interference response function with respect to the baseline length; Performing atmospheric refractive index integration processing according to the normalized phase gradient field, and obtaining the integrated value of the refractive index fluctuation on the electromagnetic wave path through spatial integration of the phase gradient along the wavefront propagation direction; Performing optical path delay reconstruction processing according to the integrated value of the refractive index fluctuation, and calculating the relative optical path delay caused by the atmosphere through the product operation of the vacuum light speed and the refractive index integration to obtain the equivalent atmospheric optical path delay differential field.

5. The collaborative positioning method of a lunar active beacon and a ground-based distributed telescope according to claim 1, wherein Performing lunar coordinate system modeling according to the third information to construct a spatial reference frame constrained by lunar attitude, including: Perform the geocentric - lunar spatial reference conversion processing based on the lunar - geocentric position vector in the third information. Establish the lunar - centered inertial coordinate system through the rigid transformation algorithm from the conventional geocentric coordinate system to the lunar - centered celestial coordinate system. Perform the calculation processing of lunar - fixed parameters based on the lunar - self - rotation axis pointing angle in the third information. Obtain the instantaneous rotation transformation matrix of the lunar body coordinate system through the rotation transformation between the instantaneous self - rotation axis direction and the lunar - centered ecliptic coordinates. Perform the reference - frame fusion processing based on the lunar - centered inertial coordinate system and the instantaneous rotation transformation matrix of the lunar body coordinate system. Construct the spatial reference frame with lunar attitude constraints through the matrix multiplication operation of the coordinate - system transformation chain.

6. The collaborative positioning method of a lunar active beacon and a ground-based distributed telescope according to claim 1, wherein Perform the lunar - surface coordinate inversion based on the spatial reference frame, the equivalent atmospheric optical - path delay differential field, and the second information, including: Perform the conversion processing of the ground - station position lunar - fixed coordinates based on the spatial reference frame and the second information. Convert the ground - station geocentric coordinates to the lunar - fixed coordinate system through the inverse coordinate transformation, calculate the unit vectors of the line - of - sight directions from the lunar - surface beacon to each station, and obtain the set of station coordinates and line - of - sight direction vectors in the lunar - fixed system. Perform the construction processing of the ranging observation equation based on the set of station coordinates and line - of - sight direction vectors and the equivalent atmospheric optical - path delay differential field. Establish the linear constraint equation set of the beacon position coordinate parameters through the dot - product operation between the optical - path delay differential field and the station baseline vector. Perform the inversion processing of the position parameters based on the linear constraint equation set to obtain the three - dimensional position of the beacon in the lunar body coordinate system.

7. A collaborative positioning method for a lunar active beacon and a ground-based distributed telescope according to claim 6, characterized in that, Perform the inversion processing of the position parameters based on the linear constraint equation set, including: Perform the fractional - order spatial differential evolution processing based on the linear constraint equation set. Expand the calculus order of the observation equation fractionally by introducing a continuous small - scale factor to obtain the generalized configuration - space evolution equation containing non - integer - order derivatives. Perform the fractional - order optimal - path search processing based on the generalized configuration - space evolution equation. Construct the variational integral functional in the fractional - dimensional space through the principle of least action. Converge to the optimal - solution surface when the fractional - order variational derivative of the functional is zero. Perform the integer - dimensional coordinate mapping processing based on the optimal - solution surface. Project the fractional - dimensional optimal surface onto the integer - dimensional space through the Legendre transformation to obtain the three - dimensional position of the beacon in the lunar - fixed coordinate system.

8. A collaborative positioning system for a lunar active beacon and a ground-based distributed telescope, characterized in that, Including: An acquisition module for acquiring the first information, the second information, and the third information. The first information is the electromagnetic wave signal of the lunar - surface active beacon, the second information is the geocentric coordinates of at least four ground - based observation stations, and the third information is the lunar instantaneous self - rotation axis pointing angle and the lunar - geocentric position vector at the same signal radiation time. A separation module for performing wave - front phase separation based on the first information to obtain the wave - front distortion distribution field under the influence of atmospheric turbulence. A calculation module for performing multi - station interference coherence calculation based on the wave - front distortion distribution field to obtain the set of spatial interference response functions. A reconstruction module for performing optical - path - difference reconstruction based on the set of spatial interference response functions. Obtain the equivalent atmospheric optical - path delay differential field by calculating the refractive - index integral gradient of the wave - front propagation path. A construction module for performing lunar - coordinate - system modeling based on the third information to construct the spatial reference frame with lunar attitude constraints. An inversion module, configured to perform lunar surface coordinate inversion based on the spatial reference frame, the differential field of equivalent atmospheric optical path delay, and the second information, so as to obtain the three-dimensional position of the beacon in the lunar body coordinate system.

9. The collaborative positioning system of the lunar active beacon and the ground distributed telescope according to claim 8, characterized in that, The separation module includes: A first separation unit, configured to perform narrowband signal demodulation processing according to the first information, extract the intermediate-frequency complex signal envelope of each site through local oscillator mixing, and obtain a baseband complex signal sequence with time stamp information; A second separation unit, configured to perform phase unwrapping processing according to the baseband complex signal sequence, and obtain an independent time-resolved phase function of each site by separating the carrier phase and the modulation phase; A third separation unit, configured to perform turbulence feature extraction processing according to the time-resolved phase function, and obtain the wavefront distortion distribution field under the influence of atmospheric turbulence by fitting the atmospheric refractive index fluctuation parameters through the spatial phase structure function; 10. The collaborative positioning system of the lunar active beacon and the ground distributed telescope according to claim 8, characterized in that, The calculation module includes: A first calculation unit, configured to perform inter-site relative phase calculation processing according to the wavefront distortion distribution field, calculate the spatial phase gradient in the baseline direction through the phase difference vector between adjacent sites, and obtain the first-order differential field of the phase across sites; A second calculation unit, configured to perform complex coherence degree construction processing according to the first-order differential field of the phase, reconstruct the modulus value of the cross-correlation function of the site pair through complex exponential integration, and obtain an initial set of spatial interference response functions; A third calculation unit, configured to perform system error correction processing according to the initial set of spatial interference response functions, eliminate the phase noise introduced by the local oscillator through the multi-station phase difference closure principle, and obtain a corrected set of spatial interference response functions.

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