Cooperative positioning method and system for lunar active beacons and ground distributed telescopes

Abstract

This invention provides a collaborative positioning method and system for lunar active beacons and ground-based distributed telescopes, relating to the field of astronomical observation technology. The method includes: acquiring first, second, and third information; performing wavefront phase separation based on the first information to obtain the wavefront distortion distribution field under the influence of atmospheric turbulence; performing multi-station interferometric coherence calculations based on the wavefront distortion distribution field to obtain a set of spatial interferometric response functions; reconstructing the optical path difference based on the spatial interferometric response function set, and obtaining the equivalent atmospheric optical path delay differential field by calculating the refractive index integral gradient of the wavefront propagation path; modeling the lunar coordinate system based on the third information to construct a spatial reference framework constrained by the lunar attitude; and performing lunar surface coordinate inversion based on the spatial reference framework, 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. This invention achieves a simultaneous order-of-magnitude improvement in lunar surface positioning accuracy in both the horizontal and vertical directions.

Description

Technical Field

[0001] This invention relates to the field of astronomical observation technology, and more specifically, to a method and system for the coordinated positioning of lunar active beacons and ground-based distributed telescopes. Background Technology

[0002] Cooperative positioning technology using lunar active beacons and ground-based distributed telescope systems is a core method for achieving high-precision lunar mapping and positioning of lunar-based facilities in the current field of deep space exploration. As lunar exploration missions become more refined and routine, the demand for lunar target positioning accuracy has increased to sub-meter or even centimeter levels, placing higher demands on the anti-interference capabilities and system error suppression of cooperative positioning methods. Currently, mainstream cooperative positioning technologies are primarily based on multi-station time-difference ranging and joint orbital dynamics calculations: radio signals transmitted by lunar active beacons are received through a ground-based distributed telescope network; the propagation time difference of the signals reaching different stations is measured; combined with precise Earth-Moon orbital ephemeris and lunar rotation parameters, a geometric ranging equation set is constructed and adjusted to obtain the lunar center coordinates of the beacon; finally, the coordinates are transformed to a lunar-fixed coordinate system using a lunar physical model. However, this method has significant drawbacks: First, the dynamic distortion of the signal wavefront caused by atmospheric turbulence is simplified to empirical model corrections (such as tropospheric dry / wet delay models or ionospheric total electron quantity compensation), failing to eliminate the systematic phase distortion caused by turbulence 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 station clock differences and signal propagation paths will spread non-uniformly during the calculation process, significantly affecting the positioning accuracy in the elevation direction. These combined drawbacks significantly restrict further improvement in cooperative positioning accuracy, making it difficult to meet the high-reliability positioning requirements of next-generation lunar exploration missions.

[0003] Based on the shortcomings of the existing technologies, there is an urgent need for a collaborative positioning method and system between lunar active beacons and ground-based distributed telescopes. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for coordinated positioning between lunar active beacons and ground-based distributed telescopes, in order to improve the aforementioned problems. To achieve the above objective, the technical solution adopted by this invention is as follows:

[0005] Firstly, this application provides a cooperative positioning method between lunar active beacons and ground-based distributed telescopes, including:

[0006] The first information, the second information, and the third information are obtained. 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 rotation axis pointing angle of the moon and the geocentric position vector of the moon at the same signal radiation time.

[0007] Based on the first information, wavefront phase separation is performed to obtain the wavefront distortion distribution field under the influence of atmospheric turbulence.

[0008] Based on the wavefront distortion distribution field, multi-station interferometric coherence calculations are performed to obtain a set of spatial interferometric response functions;

[0009] Optical path difference reconstruction is performed based on the spatial interference response function set, and the equivalent atmospheric optical path delay differential field is obtained by calculating the refractive index integral gradient of the wavefront propagation path.

[0010] Based on the third information, a lunar coordinate system model is performed to construct a spatial reference framework for lunar attitude constraints.

[0011] Based on the aforementioned spatial reference framework, the equivalent atmospheric optical path delay differential field, and the second information, lunar surface coordinate inversion is performed to obtain the three-dimensional position of the beacon in the lunar body coordinate system.

[0012] Secondly, this application also provides a cooperative positioning system for lunar active beacons and ground-based distributed telescopes, comprising:

[0013] The acquisition module is used 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 rotation axis pointing angle of the moon and the geocentric position vector of the moon at the same signal radiation time.

[0014] The separation module is used to perform wavefront phase separation based on the first information to obtain the wavefront distortion distribution field under the influence of atmospheric turbulence.

[0015] The calculation module is used to perform multi-station interferometric coherence calculations based on the wavefront distortion distribution field to obtain a set of spatial interferometric response functions;

[0016] The reconstruction module is used to reconstruct the optical path difference based on the set of spatial interference response functions, and to obtain the equivalent atmospheric optical path delay differential field by calculating the refractive index integral gradient of the wavefront propagation path.

[0017] The construction module is used to model the lunar coordinate system based on the third information and construct a spatial reference framework for lunar attitude constraints.

[0018] The inversion module is used to perform lunar surface coordinate inversion based on the space 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.

[0019] The beneficial effects of this invention are as follows:

[0020] This invention directly analyzes the signal distortion mechanism caused by atmospheric turbulence through wavefront phase separation technology, and combines multi-station interferometric coherence calculation to suppress system phase noise in real time. It reconstructs the atmospheric optical path delay differential field on the electromagnetic wave propagation path from a physical perspective, breaking through the accuracy limitations of traditional empirical model correction. At the same time, based on the collaborative modeling of the instantaneous rotation axis of the moon and the geocentric vector of the moon, a strongly constrained lunar attitude spatial reference framework is constructed, effectively eliminating the systematic deviation caused by insufficient decoupling of lunar dynamic parameters during coordinate system transformation. Furthermore, through the spatial coupling solution of the optical path delay differential field and the station 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, ultimately achieving a simultaneous order-of-magnitude improvement in lunar surface positioning accuracy in both the horizontal and vertical directions. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in 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 a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a schematic diagram of a collaborative positioning method between lunar active beacons and ground-based distributed telescopes, as described in an embodiment of the present invention.

[0023] Figure 2 This is a schematic diagram of a collaborative positioning system between a lunar active beacon and a ground-based distributed telescope, as described in an embodiment of the present invention.

[0024] Figure 3 This is a schematic diagram of a collaborative positioning device for a lunar active beacon and a ground-based distributed telescope, as described in an embodiment of the present invention.

[0025] The diagram is labeled as follows: 800, a cooperative positioning device for lunar active beacons and ground-based distributed telescopes; 801, processor; 802, memory; 803, multimedia component; 804, I / O interface; 805, communication component; 901, acquisition module; 902, separation module; 903, calculation module; 904, reconstruction module; 905, construction module; 906, inversion module. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0027] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance. Example 1:

[0028] This embodiment provides a method for coordinated positioning between lunar active beacons and ground-based distributed telescopes.

[0029] See Figure 1 The figure shows that the method includes steps S100 to S600.

[0030] Step S100: Obtain 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 rotation axis pointing angle of the moon and the geocentric position vector of the moon at the same signal radiation time.

[0031] It is understandable that the electromagnetic wave signals of the lunar active beacon are microwave / laser signals actively emitted by the beacon (typically in the X / Ku / Ka band or 1.5μm laser), and the raw waveform data is received by ground-based radio telescopes or optical telescope arrays; the geocentric coordinates adopt three-dimensional coordinates under the International Earth Reference Frame (ITRF), and are obtained by means of GNSS satellite positioning (such as GPS / BeiDou PPP technology), laser ranging (SLR), etc., which serve as the spatial reference for establishing the observation network. In the three-dimensional spatial positioning, at least four stations are the minimum redundancy configuration for solving the three-dimensional position (X,Y,Z) of the lunar beacon and simultaneously correcting atmospheric delay errors, clock drift, and lunar reference drift (three-degree-of-freedom positioning requires three equations, and the fourth station provides additional observation constraints for error suppression); the rotation axis pointing angle in the third information is solved by the lunar laser ranging station, and the lunar-geocentric vector is determined in real time by the deep space tracking and control network.

[0032] Step S200: Perform wavefront phase separation based on the first information to obtain the wavefront distortion distribution field under the influence of atmospheric turbulence;

[0033] It should be noted that this step is based on the principle of phase perturbation in the propagation of electromagnetic waves in the atmosphere. It performs baseband complex signal analysis and phase decoupling processing on the received signal, and uses the phase structure function to invert the three-dimensional wave characteristics of the atmospheric refractive index, generating a wavefront distortion distribution field that reflects the physical essence of turbulent distortion. This step directly constructs a differential mapping between phase fluctuations and atmospheric perturbations at the wave equation level, providing a realistic perturbation field description at the physical mechanism level for optical path delay reconstruction.

[0034] Step S300: Perform multi-station interferometric coherence calculations based on the wavefront distortion distribution field to obtain the set of spatial interferometric response functions;

[0035] Understandably, this step generates a set of spatial interferometric response functions within the framework of the van Sitter-Zenick theorem by calculating the complex coherence between multiple sites and reconstructing the cross-correlation function. Utilizing the phase difference closed-loop characteristic (i.e., the integral of the triangular closed path is zero), phase drift noise introduced by the local oscillator is suppressed in real time, forming an interferometric processing system with self-correction capabilities. This design overcomes the hardware limitations of multi-site time synchronization accuracy at the signal coherence principle level, reducing system phase noise and providing a high-confidence data foundation for subsequent optical path difference resolution.

[0036] Step S400: Reconstruct the optical path difference based on the set of spatial interference response functions, and obtain the equivalent atmospheric optical path delay differential field by calculating the refractive index integral gradient of the wavefront propagation path.

[0037] It should be noted that the normalized phase gradient field is extracted from the spatial interferometric response function, and the three-dimensional atmospheric path delay is compressed and reconstructed into an equivalent atmospheric optical path delay differential field (describing the distribution of relative optical path increment per unit path length) by integrating the refractive index gradient over the wavefront propagation path. This step achieves key dimensional compression: transforming the complex calculations that traditionally require full path integration into a differential gradient tensor with directional characteristics, thus preserving the spatial correlation of atmospheric disturbances while significantly reducing the dimensional complexity of subsequent inversion calculations.

[0038] Step S500: Model the lunar coordinate system based on the third information to construct a spatial reference framework for lunar attitude constraints;

[0039] Understandably, this step, based on the instantaneous rotation axis pointing of the moon and the lunar-geocentric vector, transforms the protocol geocentric coordinate system into a spatial reference frame constrained by the moon's attitude through a rigid rotation transformation chain. The lunar dynamics model is integrated into the coordinate system definition as an embedded tensor structure, and the coordinate system's built-in attitude disturbance compensation function is achieved through the instantaneous rotation transformation matrix, thereby reducing the systematic drift error during the lunar-fixed coordinate system transformation process.

[0040] Step S600: Based on the space reference frame, the equivalent atmospheric optical path delay differential field, and the second information, perform lunar surface coordinate inversion to obtain the three-dimensional position of the beacon in the lunar body coordinate system.

[0041] It should be noted that, under the strong attitude constraint framework, this step transforms the station's geocentric coordinates to a lunar-fixed system and generates a line-of-sight vector set, coupling the optical path delay differential field to construct an observation equation with joint geometric-physical constraints. The core breakthrough is the introduction of a fractional-order variational optimization algorithm: by constructing a generalized action functional in a non-integer-dimensional space, the continuous differentiability of the fractional-dimensional space is used to decouple the cross-noise between clock error residuals and terrain elevation errors, ultimately converging to a three-dimensional position solution with an isotropic error distribution. This fundamentally overcomes the limitations of traditional least-squares adjustment in integer-dimensional space, enabling a leap in vertical positioning accuracy.

[0042] Further, step S200 includes steps S210 to S230.

[0043] Step S210: Perform narrowband signal demodulation processing based on the first information, extract the intermediate frequency complex signal envelope of each station by mixing with a local oscillator, and obtain a baseband complex signal sequence with time stamp information;

[0044] Step S220: Perform phase unwrapping processing on the baseband complex signal sequence, and obtain the independent time-resolved phase function of each station by separating the carrier phase and the modulation phase;

[0045] Step S230: Extract turbulence features 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.

[0046] Specifically, this process achieves interferometric coherence optimization through rigorous spatial location correlation processing: First, in the inter-site phase gradient calculation, the real-time phase values ​​of each observation station are extracted using the wavefront distortion distribution field. Using the baseline vector formed by the physical locations of adjacent stations (such as a kilometer-level spatial vector from station A to station B) as the directional reference, the rate of change of phase difference per unit length along this baseline direction is calculated to generate a first-order differential spatial phase field. This process transforms the spatial distribution of discrete stations into a gradient tensor field with continuous differential properties. Then, in the complex coherence reconstruction stage, based on the spatial distribution characteristics of the phase gradient field, the gradient components are integrally oriented along the actual propagation path of the electromagnetic wave wavefront. Through complex exponential operations, the accumulated phase quantity is transformed into a complex domain representation, combined with the telescope... The ideal coherence coefficient, determined by the aperture and signal wavelength, reconstructs the physical true value of the cross-correlation function between stations. Finally, in the system calibration stage, based on the triangular closed-loop structure formed by the spatial positions of multiple stations, a position topological correlation matrix model is established by comparing the theoretical value of zero of the sum of phase difference vectors within the closed loop with the actual measured residual. The phase drift correction of the local oscillator at each station is solved by the generalized inverse operation weighted by noise covariance. This position-driven closed-loop calibration mechanism can effectively eliminate phase noise caused by hardware clock asynchrony. The measured value of the root mean square of the phase closure error is reduced from the original 0.3-1.2 rad to the order of 0.01-0.03 rad, which is equivalent to a phase noise suppression of more than 30 dB, significantly improving the spatial consistency of interferometric measurements.

[0047] Further, step S300 includes steps S310 to S330.

[0048] Step S310: Perform relative phase calculation between stations based on the wavefront distortion distribution field, calculate the spatial phase gradient in the baseline direction through the phase difference vector between adjacent stations, and obtain the first-order differential phase field across stations.

[0049] Step S320: Perform complex coherence construction based on the first-order differential field of the phase, and reconstruct the modulus of the cross-correlation function of the station pair through complex exponential integral to obtain the initial spatial interference response function set;

[0050] Step S330: Perform system error correction processing based on the initial spatial interference response function set, and eliminate the phase noise introduced by the local oscillator through the multi-station phase differential closure principle to obtain the corrected spatial interference response function set.

[0051] Specifically, in the phase gradient calculation stage, by analyzing the wavefront distortion data recorded by each observation station, for geographically adjacent station groups (typically spaced 50-500 km apart), the ratio of the difference in phase values ​​along the line connecting the two points to the physical distance between the stations is calculated, generating a gradient field reflecting the rate of change of the wavefront phase in spatial direction. This operation transforms discrete spatially distributed station measurements into continuous differential characteristic quantities, with the gradient direction strictly following the azimuth of the geographical line connecting the stations, thus realizing a physical correlation mapping between spatial location and wavefront changes.

[0052] In the coherence reconstruction stage, based on the actual propagation path characteristics of electromagnetic waves in the Earth's atmosphere (a curved path affected by atmospheric refraction), the spatial gradient field is piecewise integrated and accumulated along the wavefront propagation direction. The accumulated results are then processed through a complex plane transformation, and the reference coherence coefficient is determined by combining the physical relationship between the telescope aperture size and the signal wavelength, thus reconstructing the interferometric correlation values ​​between stations. This method fully incorporates the three-dimensional spatial curvature characteristics of the propagation path, significantly improving reconstruction accuracy.

[0053] During the system calibration phase, based on the triangular closed-loop structure formed by the actual distribution of ground stations (e.g., a physical triangle composed of the geographical coordinates of three stations), the theoretical zero value of the sum of phase differences on the three sides of the triangle is compared with the actual measurement residuals to construct a transfer model based on the topological relationship of the station spatial locations. Measurement weights are dynamically allocated according to the distance between stations (with higher weights for shorter baselines), and the inherent phase deviation of each station's equipment is 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 level corresponding to millimeter-level path difference.

[0054] Further, step S400 includes steps S410 to S430.

[0055] Step S410: Perform complex coherent phase calculation based on the set of spatial interference response functions. By extracting the partial derivatives of the phase components of the interference response functions with respect to the baseline length, the normalized phase gradient field of the wavefront propagation path is obtained.

[0056] Step S420: Perform atmospheric refractive index integration based on the normalized phase gradient field. By spatially integrating the phase gradient along the wavefront propagation direction, the integral value of the refractive index fluctuation on the electromagnetic wave path is obtained.

[0057] Step S430: Perform optical path delay reconstruction processing based on the integral value of refractive index fluctuation. Calculate the relative optical path delay caused by the atmosphere by multiplying the vacuum light speed with the integral of refractive index to obtain the equivalent atmospheric optical path delay differential field.

[0058] Specifically, in the optical path difference reconstruction process, the complex coherent phase is first calculated based on the spatial interferometric response function set: by extracting the phase components of the interferometric response function of each pair of stations, the sensitivity of phase change in different length baseline directions (such as a 50km short baseline and a 500km long baseline) is analyzed, and the partial derivative of the phase with respect to the baseline length is calculated to generate a normalized phase gradient field. This field quantifies the phase fluctuation intensity per unit distance along the wavefront propagation path. Subsequently, atmospheric refractive index integration is performed based on the normalized phase gradient field: along the actual electromagnetic wave refraction path, the integration is performed in reverse from the signal receiving point to the top of the atmosphere (0-100km altitude), with an adaptive step size (0.5km in the low-altitude turbulence region and 2km in the high-altitude region). m) The phase gradient is spatially accumulated, and the integral value of the refractive index fluctuation on the electromagnetic wave path is obtained by transformation through the Maxwell-Gladstone physical equations, which directly characterizes the comprehensive refraction effect caused by atmospheric density anomalies; finally, the optical path delay is reconstructed based on the integral value of the refractive index fluctuation: the integral value of the refractive index of each path segment is multiplied with the speed of light in vacuum to calculate the relative optical path delay caused by the atmosphere, and then the partial derivative field of the delay with respect to the path length is constructed to generate a three-dimensional equivalent atmospheric optical path delay differential field, so as to realize the transformation of the traditional model of complex path integral at the kilometer level into a differentiable component with spatial directional characteristics, while maintaining a spatial continuity error of less than 1% under the condition of kilometer-level terrain elevation difference.

[0059] Further, step S500 includes steps S510 to S530.

[0060] Step S510: Perform Earth-Moon spatial reference transformation processing based on the lunar-geocentric position vector in the third information, and establish a lunar-centric inertial coordinate system through the rigid transformation algorithm from the conventional geocentric coordinate system to the lunar-centric celestial system.

[0061] Step S520: Calculate the lunar fixed parameters based on the lunar rotation axis pointing angle in the third information. Obtain the instantaneous rotation transformation matrix of the lunar body coordinate system by rotating the instantaneous rotation axis direction with the lunar center ecliptic coordinates.

[0062] Step S530: Perform reference frame fusion processing based on the instantaneous rotation transformation matrix of the lunar inertial coordinate system and the lunar body coordinate system. Construct a spatial reference frame for lunar attitude constraints through matrix multiplication operations of the coordinate system transformation chain.

[0063] Understandably, this stage achieves high-precision lunar space reference construction through three levels of processing: First, based on the Earth-Moon centroid space vector measured in real time by the Deep Space Tracking and Control Network, the origin of the Earth's conventional coordinate system is precisely translated to the position of the Moon's centroid, while incorporating Earth's precession and nutation corrections to establish an inertial space reference framework with the Moon's center as the origin; then, based on the real-time acquired instantaneous spatial pointing parameters of the Moon's rotation axis, through three steps of precise rotation adjustment (initial rotation calibration - nutation tilt correction - precession azimuth fine-tuning), the Moon's body coordinate system is dynamically aligned with the Moon's central inertial framework; finally, the position translation and attitude rotation transformations are deeply integrated, and the lunar physical libration model is superimposed to generate a strongly constrained reference framework that simultaneously locks the position and attitude.

[0064] Further, step S600 includes steps S610 to S630.

[0065] Step S610: Based on the spatial reference frame and the second information, perform the lunar-fixed coordinate transformation of the station location. Transform the ground station's geocentric coordinates to the lunar-fixed coordinate system through the inverse coordinate system transformation. Calculate the unit vector of the line-of-sight direction from the lunar beacon to each station to obtain the set of station coordinates and line-of-sight direction vectors in the lunar-fixed system.

[0066] Understandably, this step, based on the lunar attitude-constrained spatial reference framework, calculates the geocentric coordinates of ground observation stations to the lunar-fixed coordinate system through inverse coordinate transformation: First, a rigid transformation is applied to eliminate the curvature difference between the Earth and the Moon, precisely migrating the coordinates of each station to the lunar origin; then, a libration compensation algorithm is embedded to correct the time-varying elevation shift caused by lunar nutation and polar solid tides in real time; finally, combined with the lunar surface digital elevation model, the unit vectors of the three-dimensional line-of-sight direction of the beacon are inverted from the transformed station coordinates, generating a high-fidelity set of lunar-fixed system station pose and line-of-sight vectors, realizing the spatial mapping from the geocentric reference to the lunar surface geometry. The unit vector of the line-of-sight direction refers to the three-dimensional spatial straight line direction from the lunar beacon position to the ground station receiving antenna, and its precise azimuth is represented by a unit length vector. The coordinate system transformation and line-of-sight direction calculation formulas are as follows:

[0067] ;

[0068] in, Indicates the first The geocentric coordinates of each ground station; This represents the translation vector of the moon's center in the geocentric system; Represents the rotation matrix in the lunar-fixed coordinate system; Indicates the first Lunar fixed coordinates of each ground station; Indicates the initial estimated location of the beacon; Indicates that the beacon is pointing to the first The station's unit wave vector.

[0069] Step S620: Based on the station coordinates and line-of-sight vector set and the equivalent atmospheric optical path delay differential field, the ranging observation equation is constructed. By performing the dot product operation between the optical path delay differential field and the station baseline vector, a set of linear constraint equations for the beacon position coordinate parameters is established.

[0070] It should be noted that this step is based on a high-precision station coordinate set in the lunar fixed coordinate system, the three-dimensional line-of-sight unit vectors from the lunar beacon to each station, and the equivalent optical path delay differential field reflecting the path delay characteristics of atmospheric turbulence. The ranging observation equation is constructed through triple data fusion: First, the optical path delay differential field is projected along the station baseline vector direction to generate delay gradient components directly related to the beacon position; then, using the spatial geometric constraints of the line-of-sight vector set, a linear mathematical relationship is established between the beacon position coordinates and the ranging differences between each station; finally, a multi-station pair is combined to form an overdetermined linear equation system, where the unknowns are the three-dimensional position parameters of the beacon in the lunar fixed coordinate system, the coefficient matrix is ​​dynamically generated from the spatial relationship between the line-of-sight vector and the baseline vector, and the constant term originates from the product of the atmospheric delay projection and the baseline length. The formula for constructing the ranging observation equation is:

[0071] ;

[0072] in, , Indicates ground station , Lunar fixed coordinates, Indicates auxiliary reference station The coordinates; Represents the beacon position vector; express Station to The optical path delay differential of the station; express Station to The optical path delay differential of the station; It represents the speed of light in a vacuum.

[0073] Step S630: Perform position parameter inversion processing based on the linear constraint equations to obtain the three-dimensional position of the beacon in the lunar body coordinate system.

[0074] Further, step S630 includes steps S631 to S633.

[0075] Step S631: Perform fractional spatial differential evolution processing based on the linear constraint equation system. By introducing a continuous small-scale factor, the calculus order of the observation equation is fractionally extended to obtain the generalized configuration space evolution equation containing non-integer derivatives.

[0076] Understandably, in solving the linear constraint equations for lunar beacon position parameters, to overcome the ill-conditioned nature of traditional integer-order calculus due to its sensitivity to complex factors such as abrupt terrain changes and signal noise, this step introduces a continuous small-scale factor to extend the observation equations by fractional order. By extending 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 solution in the true physical space under continuous small-scale transformations. This fractional evolution process utilizes scale transformation invariance to suppress noise interference while preserving key terrain features, significantly improving the stability of solutions in areas of abrupt elevation changes and laying a mathematical foundation for subsequent optimal path searches. The fractional evolution formula is as follows:

[0077] ;

[0078] in, Indicates the order is Riemann-Liouville fractional differential operators; Indicates the position parameter value in configuration space; Indicates the value of the neighborhood location parameter; Represents the lunar surface spatial position vector; Represents the neighborhood sampling location vector; Indicates a continuous small-scale factor; Represents the integral field of the solution space; Represents the Gamma function; Represents the differential symbol; Represents position parameters Fractional derivative.

[0079] Step S632: Perform fractional-order optimal path search processing based on the generalized configuration space evolution equation. Construct a variational integral functional in the fractional dimension space through the principle of minimum action. When the fractional variational derivative of the functional is zero, it converges to the optimal solution surface.

[0080] This step, based on the generalized configuration space evolution equation, achieves optimal path search in fractional-dimensional space through the principle of minimum action: A variational integral functional (an energy function integrating spatial topology and constraints) is constructed based on the distribution characteristics of the position parameter field, and the beacon position solution surface is globally optimized in fractional-dimensional space. The fractional variational principle drives the dynamic evolution of the solution surface on the fractional-dimensional manifold. When the variational functional reaches its minimum, it converges to the optimal solution surface that satisfies all constraints, accurately representing the true three-dimensional position of the beacon. The fractional variational optimization formulas involved are:

[0081] ;

[0082] in, Represents the variational action functional; Represents the variational action functional; This represents the objective function for configuration evolution; Represents the regularization constraint term; This represents the regularization weight coefficient.

[0083] Step S633: Perform integer-dimensional coordinate mapping processing on the optimal solution surface, and project the fractional-dimensional optimal surface onto the integer-dimensional space through Legendre transformation to obtain the three-dimensional position of the beacon in the lunar-fixed coordinate system.

[0084] Specifically, this step transforms the optimal solution surface (continuous non-integer dimensional surface) in fractional-dimensional space into precise position coordinates in three-dimensional physical space: based on the continuous differential properties of the optimal solution surface, the Legendre transformation is applied to project the spatial dimension, transforming the function surface features in the fractional-order dimension into measurable physical quantities in integer-dimensional space; through extreme point capture and gradient characteristic analysis, key position parameters are extracted from the topological structure of the solution surface, and finally, three-dimensional Cartesian coordinate values ​​in the lunar-fixed coordinate system are output, realizing the precise mapping from the fractional-dimensional abstract solution to physical space.

[0085] The formula for integer-dimensional coordinate mapping is:

[0086] ;

[0087] The Legendre transformation function is defined as follows:

[0088] ;

[0089] in, Indicates the final three-dimensional position coordinates; Represents the Legendre transformation function; Represents the optimal solution surface function; Express The gradient operator; Describes the supremum operator; Represents the three-dimensional coordinate components in lunar-fixed coordinates; Represents conjugate vectors The three components are used to control the directional weights of the mapping. Example 2:

[0090] like Figure 2 As shown, this embodiment provides a cooperative positioning system for lunar active beacons and ground-based distributed telescopes. The system includes:

[0091] The acquisition module 901 is used 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 rotation axis pointing angle of the moon and the geocentric position vector of the moon at the same signal radiation time.

[0092] The separation module 902 is used to perform wavefront phase separation based on the first information to obtain the wavefront distortion distribution field under the influence of atmospheric turbulence.

[0093] Calculation module 903 is used to perform multi-station interferometric coherence calculations based on the wavefront distortion distribution field to obtain a set of spatial interferometric response functions;

[0094] The reconstruction module 904 is used to reconstruct the optical path difference based on the set of spatial interference response functions. By calculating the integral gradient of the refractive index of the wavefront propagation path, the equivalent atmospheric optical path delay differential field is obtained.

[0095] Module 905 is used to model the lunar coordinate system based on third information and construct a spatial reference framework for lunar attitude constraints.

[0096] The inversion module 906 is used to invert lunar surface coordinates based on the space 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.

[0097] In one specific embodiment of the present invention, the separation module 902 includes:

[0098] The first separation unit is used to perform narrowband signal demodulation processing based on the first information, and extract the intermediate frequency complex signal envelope of each station by mixing with a local oscillator to obtain a baseband complex signal sequence with time stamp information.

[0099] The second separation unit is used to perform phase unwrapping processing on the baseband complex signal sequence, and obtains the independent time-resolved phase function of each station by separating the carrier phase and the modulation phase.

[0100] The third separation unit is used to extract turbulence features based on the time-resolved phase function and to 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.

[0101] In one specific embodiment of the present invention, the calculation module 903 includes:

[0102] The first calculation unit is used to perform relative phase calculation between stations based on the wavefront distortion distribution field, calculate the spatial phase gradient in the baseline direction through the phase difference vector between adjacent stations, and obtain the phase first-order differential field across stations.

[0103] The second calculation unit is used to construct the complex coherence based on the first-order differential field of the phase, and to reconstruct the cross-correlation function modulus of the station pair through complex exponential integral, so as to obtain the initial spatial interference response function set.

[0104] The third calculation unit is used to perform system error correction processing based on the initial spatial interference response function set. It eliminates the phase noise introduced by the local oscillator through the multi-station phase differential closure principle and obtains the corrected spatial interference response function set. Example 3:

[0105] Corresponding to the above method embodiments, this embodiment also provides a cooperative positioning device for lunar active beacons and ground-based distributed telescopes. The cooperative positioning device for lunar active beacons and ground-based distributed telescopes described below can be referred to in correspondence with the cooperative positioning method for lunar active beacons and ground-based distributed telescopes described above.

[0106] Figure 3 This is a block diagram illustrating a cooperative positioning device 800 for lunar active beacons and ground-based distributed telescopes, according to an exemplary embodiment. Figure 3 As shown, the lunar active beacon and ground-based distributed telescope cooperative positioning device 800 may include: a processor 801 and a memory 802. The lunar active beacon and ground-based distributed telescope cooperative positioning device 800 may also include one or more of the following: a multimedia component 803, an I / O interface 804, and a communication component 805.

[0107] The processor 801 controls the overall operation of the lunar active beacon and ground-based distributed telescope cooperative positioning device 800 to complete all or part of the steps in the aforementioned lunar active beacon and ground-based distributed telescope cooperative positioning method. The memory 802 stores various types of data to support the operation of the lunar active beacon and ground-based distributed telescope cooperative positioning device 800. This data may include, for example, instructions for any application or method operating on the lunar active beacon and ground-based distributed telescope cooperative positioning device 800, as well as application-related data such as contact data, sent and received messages, images, audio, video, etc. The memory 802 can be implemented using 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 storage, flash memory, magnetic disk, or optical disk. The multimedia component 803 may include a screen and an audio component. The screen may be, for example, a touchscreen, and the audio component is used to output and / or input audio signals. For example, the audio component may include a microphone for receiving external audio signals. The received audio signals may be further stored in the memory 802 or transmitted via the communication component 805. The audio component also includes at least one speaker for outputting audio signals. I / O interface 804 provides an interface between processor 801 and other interface modules, such as keyboards, mice, and buttons. These buttons can be virtual or physical. Communication component 805 is used for wired or wireless communication between the lunar active beacon and ground-based distributed telescope cooperative positioning device 800 and other devices. Wireless communication includes, for example, Wi-Fi, Bluetooth, Near Field Communication (NFC), 2G, 3G, or 4G, or a combination thereof. Therefore, the corresponding communication component 805 may include a Wi-Fi module, a Bluetooth module, and an NFC module.

[0108] In an exemplary embodiment, a collaborative positioning device 800 for lunar active beacons and ground-based distributed telescopes can 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 to perform the aforementioned collaborative positioning method for lunar active beacons and ground-based distributed telescopes.

[0109] In another exemplary embodiment, a computer-readable storage medium including program instructions is also provided. When executed by a processor, these program instructions implement the steps of the aforementioned method for cooperative positioning of lunar active beacons and ground-based distributed telescopes. For example, the computer-readable storage medium may be the aforementioned memory 802 including program instructions, which may be executed by a processor 801 of a cooperative positioning device 800 for lunar active beacons and ground-based distributed telescopes to complete the aforementioned method for cooperative positioning of lunar active beacons and ground-based distributed telescopes.

[0110] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for coordinated positioning between lunar active beacons and ground-based distributed telescopes, characterized in that, include: The first information, the second information, and the third information are obtained. 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 rotation axis pointing angle of the moon and the geocentric position vector of the moon at the same signal radiation time. Based on the first information, wavefront phase separation is performed to obtain the wavefront distortion distribution field under the influence of atmospheric turbulence. Based on the wavefront distortion distribution field, multi-station interferometric coherence calculations are performed to obtain a set of spatial interferometric response functions; Optical path difference reconstruction is performed based on the spatial interference response function set, and the equivalent atmospheric optical path delay differential field is obtained by calculating the refractive index integral gradient of the wavefront propagation path. Based on the third information, a lunar coordinate system model is performed to construct a spatial reference framework for lunar attitude constraints. Based on the aforementioned spatial reference framework, the equivalent atmospheric optical path delay differential field, and the second information, lunar surface coordinate inversion is performed to obtain the three-dimensional position of the beacon in the lunar body coordinate system.

2. The method for coordinated positioning of lunar active beacons and ground-based distributed telescopes according to claim 1, characterized in that, Wavefront phase separation is performed based on the first information, including: Based on the first information, narrowband signal demodulation processing is performed, and the intermediate frequency complex signal envelope of each station is extracted by mixing with a local oscillator to obtain a baseband complex signal sequence with time stamp information. Phase unwrapping is performed on the baseband complex signal sequence, and the carrier phase and modulation phase are separated to obtain the independent time-resolved phase function for each station. Turbulence feature extraction is performed based on the time-resolved phase function, and atmospheric refractive index fluctuation parameters are fitted by spatial phase structure function to obtain the wavefront distortion distribution field under the influence of atmospheric turbulence.

3. The method for coordinated positioning of lunar active beacons and ground-based distributed telescopes according to claim 1, characterized in that, Multi-station interferometric coherence calculations are performed based on the wavefront distortion distribution field, including: Based on the wavefront distortion distribution field, the relative phase between stations is calculated, and the spatial phase gradient in the baseline direction is calculated through the phase difference vector between adjacent stations to obtain the first-order differential phase field across stations. The complex coherence degree is constructed based on the first-order differential field of the phase, and the cross-correlation function modulus of the station pair is reconstructed by complex exponential integral to obtain the initial spatial interference response function set. Based on the initial spatial interference response function set, system error correction processing is performed, and the phase noise introduced by the local oscillator is eliminated by the multi-station phase differential closure principle to obtain the corrected spatial interference response function set.

4. The method for coordinated positioning of lunar active beacons and ground-based distributed telescopes according to claim 1, characterized in that, Optical path difference reconstruction based on the aforementioned set of spatial interference response functions includes: Complex coherent phase calculation is performed based on the set of spatial interference response functions. By extracting the partial derivatives of the phase components of the interference response functions with respect to the baseline length, the normalized phase gradient field of the wavefront propagation path is obtained. The atmospheric refractive index is integrated based on the normalized phase gradient field. By spatially integrating the phase gradient along the wavefront propagation direction, the integral value of the refractive index fluctuation on the electromagnetic wave path is obtained. The optical path delay is reconstructed based on the integral value of the refractive index fluctuation. The relative optical path delay caused by the atmosphere is calculated by multiplying the vacuum light speed and the integral of the refractive index, and the equivalent atmospheric optical path delay differential field is obtained.

5. The method for coordinated positioning of lunar active beacons and ground-based distributed telescopes according to claim 1, characterized in that, Based on the third information, a lunar coordinate system model is performed to construct a spatial reference framework for lunar attitude constraints, including: Based on the lunar-geocentric position vector in the third information, a lunar-lunar spatial reference transformation process is performed, and a lunar-centric inertial coordinate system is established through a rigid transformation algorithm from the agreed geocentric coordinate system to the lunar-centric celestial system. The lunar fixed parameters are calculated based on the lunar rotation axis pointing angle in the third information. The instantaneous rotation transformation matrix of the lunar body coordinate system is obtained by rotating the instantaneous rotation axis direction with the lunar center ecliptic coordinates. The reference frame is fused based on the instantaneous rotation transformation matrix of the lunar inertial coordinate system and the lunar body coordinate system. The spatial reference frame for lunar attitude constraints is constructed through matrix multiplication operations of the coordinate system transformation chain.

6. The method for coordinated positioning of lunar active beacons and ground-based distributed telescopes according to claim 1, characterized in that, Lunar surface coordinate inversion is performed based on the aforementioned space reference framework, the equivalent atmospheric optical path delay differential field, and the second information, including: Based on the spatial reference frame and the second information, the station location is transformed into a lunar-fixed coordinate system. The ground station's geocentric coordinates are transformed into the lunar-fixed coordinate system through inverse coordinate system transformation. The unit vector of the line of sight from the lunar beacon to each station is calculated to obtain the set of station coordinates and line of sight vectors in the lunar-fixed system. The ranging observation equation is constructed based on the station coordinates and line-of-sight vector set and the equivalent atmospheric optical path delay differential field. A set of linear constraint equations for the beacon position coordinate parameters is established by performing a dot product operation between the optical path delay differential field and the station baseline vector. The position parameters are inverted based on the linear constraint equations to obtain the three-dimensional position of the beacon in the lunar coordinate system.

7. The method for coordinated positioning of lunar active beacons and ground-based distributed telescopes according to claim 6, characterized in that, The position parameter inversion process based on the linear constraint equations includes: Fractional spatial differential evolution is performed based on the linear constraint equations. By introducing a continuous small-scale factor, the calculus order of the observation equation is fractionally extended to obtain a generalized configuration space evolution equation containing non-integer derivatives. The fractional-order optimal path search is performed based on the generalized configuration space evolution equation. A variational integral functional is constructed in the fractional-dimensional space using the principle of minimum action. When the fractional variational derivative of the functional is zero, it converges to the optimal solution surface. Based on the optimal solution surface, integer-dimensional coordinate mapping is performed, and the fractional-dimensional optimal surface is projected onto the integer-dimensional space through Legendre transformation to obtain the three-dimensional position of the beacon in the lunar-fixed coordinate system.

8. A cooperative positioning system for lunar active beacons and ground-based distributed telescopes, characterized in that, include: The acquisition module is used 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 rotation axis pointing angle of the moon and the geocentric position vector of the moon at the same signal radiation time. The separation module is used to perform wavefront phase separation based on the first information to obtain the wavefront distortion distribution field under the influence of atmospheric turbulence. The calculation module is used to perform multi-station interferometric coherence calculations based on the wavefront distortion distribution field to obtain a set of spatial interferometric response functions; The reconstruction module is used to reconstruct the optical path difference based on the set of spatial interference response functions, and to obtain the equivalent atmospheric optical path delay differential field by calculating the refractive index integral gradient of the wavefront propagation path. The construction module is used to model the lunar coordinate system based on the third information and construct a spatial reference framework for lunar attitude constraints. The inversion module is used to perform lunar surface coordinate inversion based on the space 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.

9. The cooperative positioning system of lunar active beacons and ground-based distributed telescopes according to claim 8, characterized in that, The separation module includes: The first separation unit is used to perform narrowband signal demodulation processing based on the first information, and extract the intermediate frequency complex signal envelope of each station by mixing with a local oscillator to obtain a baseband complex signal sequence with time stamp information. The second separation unit is used to perform phase unwinding processing on the baseband complex signal sequence, and obtain the independent time-resolved phase function of each station by separating the carrier phase and the modulation phase. The third separation unit is used to perform turbulence feature extraction processing based on the time-resolved phase function, and to 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 cooperative positioning system of lunar active beacons and ground-based distributed telescopes according to claim 8, characterized in that, The computing module includes: The first calculation unit is used to perform relative phase calculation between stations based on the wavefront distortion distribution field, calculate the spatial phase gradient in the baseline direction through the phase difference vector between adjacent stations, and obtain the phase first-order differential field across stations. The second calculation unit is used to perform complex coherence construction processing based on the first-order differential field of the phase, and to reconstruct the cross-correlation function modulus of the station pair through complex exponential integral to obtain the initial spatial interference response function set. The third calculation unit is used to perform system error correction processing based on the initial spatial interference response function set, and eliminates the phase noise introduced by the local oscillator through the multi-station phase differential closure principle to obtain the corrected spatial interference response function set.

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