A method for error correction and precision analysis of laser ranging data of lunar satellite

Abstract

The application discloses a lunar-orbit satellite laser ranging data error correction and precision analysis method, and belongs to the technical field of deep space measurement, and comprises the following steps: setting inner coincidence error and outer coincidence error of the whole laser ranging process; calibrating and modeling the system error and random error in the inner coincidence error, correcting the system delay by using the calibration target in real time, and synthesizing the standard deviation of random error to evaluate the data precision; establishing a physical model for the relativistic effect, atmospheric refraction, earth tide, station offset and corner reflector offset in the outer coincidence error to correct the outer coincidence error; and finally comparing with external reference values, calculating the root mean square error of residual error to evaluate the data accuracy. The application realizes systematic correction and precision quantitative analysis of the whole link error of the lunar-orbit satellite laser ranging, significantly improves the ranging data quality, and provides reliable data support for high-precision lunar-orbit orbit determination.

Description

Technical Field

[0001] This invention belongs to the field of deep space measurement technology, specifically relating to a method for error correction and accuracy analysis of lunar orbit satellite laser ranging data. Background Technology

[0002] With the increasing demands of various lunar exploration missions, the requirements for high-precision determination of lunar orbit satellite orbits are also rising. Currently, traditional lunar orbit determination technologies rely on ground-based radio observation techniques, including S-band / X-band ranging and velocimetry, and Very Long Baseline Interferometry (VLBI). These technologies have been widely applied in lunar exploration projects both domestically and internationally. However, radio orbit determination techniques have relatively low accuracy, ranging only from kilometers to hundreds of meters, which cannot meet the needs of some high-precision lunar exploration missions. With the development of new-era lunar exploration technologies, there is a need to expand the means of high-precision lunar orbit determination for satellites.

[0003] Laser ranging is currently the most accurate distance measurement method on the Earth-Moon distance scale. With its high precision and long-range capabilities, laser ranging is an ideal supplement to lunar orbit satellite orbit determination. However, laser ranging for lunar orbit satellites is subject to various errors, which affect its accuracy. To improve the accuracy of laser ranging data and thus further enhance the orbit determination accuracy of lunar orbit satellites, it is necessary to correct these errors.

[0004] Chinese invention patent CN115840232B proposes a method for correcting drift errors in satellite laser ranging. It incorporates the calculated ground target drift error and satellite drift error into the result of signal recognition, yielding a corrected satellite laser ranging data. However, this patent does not address error correction during the satellite laser ranging process.

[0005] Chinese invention patent CN101915926B proposes a method for determining one-way distance in satellite laser ranging. It utilizes a satellite laser ranging telescope to acquire SLR (Satellite Laser Ranging) data from artificial satellites and calculates the relatively accurate uplink or downlink distance using the measured values. However, this patent primarily addresses error correction methods for near-Earth satellites and does not cover error correction methods for lunar orbit satellites.

[0006] The paper "Research and Application of Lunar Laser Ranging Observation Model" (Huang Kai, Sun Shangbiao, Yang Yongzhang, et al. Research and Application of Lunar Laser Ranging Observation Model [J]. Progress in Laser & Optoelectronics, 2022, 59(19): 197-203.) models solid tides, ocean tides, atmospheric delay, and general relativistic effects in lunar laser ranging, and establishes an LLR (Lunar Laser Ranging) observation model. However, this paper does not involve the internal coincidence error correction method or the lunar orbit satellite observation model. Summary of the Invention

[0007] To address the issues of error correction and accuracy analysis in lunar orbit satellite laser ranging, this invention provides a method for error correction and accuracy analysis of lunar orbit satellite laser ranging data. This method considers and corrects errors throughout the entire laser flight process, analyzes the accuracy of ranging data, aligns with engineering practice, and provides a reference for various analyses of lunar orbit satellite laser ranging experimental data.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A method for error correction and accuracy analysis of lunar orbit satellite laser ranging data includes the following steps:

[0010] Step 1: Set the laser error term. The laser error term is the internal coincidence error and external coincidence error of the laser uplink and downlink during the entire process of laser transmission and reception. The internal coincidence error includes systematic error and random error. The external coincidence error includes errors introduced by relativistic effects, tropospheric refraction, Earth's tidal deformation, station coordinate deviation, and corner reflector centroid offset.

[0011] Step 2: Process the systematic and random errors of the internal consistency error and analyze the internal consistency accuracy; the internal consistency accuracy reflects the dispersion between observations and is measured by error or standard deviation.

[0012] Step 3: Process external compliance errors;

[0013] Step 4: Analyze the external compliance accuracy of the laser ranging data based on the processed external compliance error. The external compliance accuracy is compared with the externally provided reference value, reflecting the degree of deviation between the laser ranging data and the reference value, and reflecting the actual reliability of the positioning result. It is measured by the root mean square of the error.

[0014] Beneficial effects:

[0015] 1. This invention achieves a systematic correction of the end-to-end error in laser ranging for lunar-orbiting satellites. It systematically corrects both internal and external coincidence errors, and employs a series of specific techniques, including real-time calibration of the target system delay, Mendes-Pavlis model correction for atmospheric delay, and physical model correction for gravitational delay and Earth tides, to construct a complete error correction model. This overcomes the shortcomings of existing technologies that fail to adequately consider the complex error environment of lunar-orbiting satellites.

[0016] 2. This invention proposes a reliable method for quantitatively evaluating the accuracy of ranging data. Data precision is assessed by measuring the composite standard deviation of random errors such as laser pulses and detector jitter; data accuracy is assessed by calculating the root mean square of the residuals between observed values ​​and external reference values. This analytical framework provides a clear and reproducible quantitative basis for quality assessment and reliability judgment of lunar orbit satellite laser ranging data.

[0017] 3. This invention significantly improves the accuracy of measured data used for determining the orbits of lunar-orbiting satellites. By applying this method, errors in the raw laser data of lunar-orbiting satellites are corrected, improving the accuracy to the meter level, thus providing a more reliable data foundation for high-precision orbit determination of lunar-orbiting satellites. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the method for correcting errors and analyzing accuracy of lunar orbit satellite laser ranging data according to the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0020] like Figure 1 As shown in the figure, this invention discloses a method for error correction and accuracy analysis of lunar orbit satellite laser ranging data, including the following steps:

[0021] Step 1: Define the error term for laser ranging of lunar orbit satellites. During the entire process of laser transmission and reception, it is necessary to consider the internal coincidence error and external coincidence error of the uplink and downlink lasers.

[0022] Internal coincidence error includes both systematic and random errors in the laser ranging system. The event timer in the laser ranging system has a systematic error when recording the laser emission and reception times (i.e.,...). Figure 1The system delay of the timer can be calibrated and eliminated by placing a calibration target near the reference point of the laser station. Random errors come from internal equipment, external environment and corner reflectors, and are used to analyze the ranging accuracy. Specifically, they include laser pulse jitter, superconducting detector rising edge jitter, event timer timing jitter, main wave probe rising edge jitter, fiber dispersion, corner reflector surface shape error, atmospheric turbulence, etc.

[0023] External coincidence error is the error introduced by physical effects, including relativistic effect error, tropospheric refraction error, Earth's tidal deformation, station coordinate deviation, and the error introduced by the centroid offset of the corner reflector. A physical model can be established to eliminate this part of the error.

[0024] Step Two: Propose methods for handling internal consistency errors and analyzing internal consistency accuracy. Systematic and random errors within the internal consistency error are processed and analyzed. Internal consistency accuracy mainly reflects the dispersion between observations, i.e., precision, which is generally measured by error or standard deviation (STD). Figure 1 Internal review accuracy of the analysis: using STD to characterize data precision, including:

[0025] Step 2.1: Perform systematic error processing:

[0026] Errors in the equipment, environment, measurement methods, and personnel can all cause systematic errors. Laser ranging systems often share a single optical path for transmitting and receiving laser light. A calibration target is placed near the secondary mirror of the telescope. During ranging tests, the calibration target is measured simultaneously to measure and calibrate the system delay in real time. Multiple observations can be repeated to calibrate and analyze the stability of the system's internal delay. The system delay obtained through calibration is then subtracted from the laser ranging data.

[0027] Step 2.2: Perform random error processing:

[0028] Random errors are caused by a combination of factors, including internal equipment, external environment, and corner reflectors. Taking a typical laser station and corner reflector as an example, the random error parameters are as follows:

[0029] Laser pulse jitter ;

[0030] jitter of rising edge of superconducting detector ;

[0031] Event timer timing jitter ;

[0032] jitter of the rising edge of the main wave probe ;

[0033] Time jitter introduced by fiber dispersion ;

[0034] Jitter introduced by laser corner reflector surface shape error ;

[0035] Random errors introduced by atmospheric turbulence .

[0036] Here, ps represents picosecond.

[0037] Step 2.3: Calculate the standard deviation of the sum of the above random errors. The formula is as follows:

[0038] ;

[0039] Under typical laser station and corner reflector conditions, the total random error is 99.7 ps, which means that the internal coincidence accuracy of lunar orbit satellite laser ranging data under these typical conditions is 3 cm.

[0040] Step 3: Propose methods for handling external compliance errors, including:

[0041] Step 3.1: Correct for the electromagnetic signal delay caused by celestial gravity. Within the Earth's framework, based on the gravitational constant of the celestial body and the distances between the Earth's center, the measuring station, and the satellite, the gravitational delay of the beam propagation due to the celestial body's gravitational field is calculated. The correction model is as follows:

[0042] ;

[0043] in, Indicates gravitational time delay error; Represents the gravitational constant; Represents the speed of light; Let A and B represent the mass of celestial body A and the mass of the Sun, respectively. These represent the distances from celestial body A to the corner reflector and the distance from the sun to the corner reflector, respectively. These represent the distance from celestial body A to the ground station and the distance from the sun to the ground station, respectively. This indicates the distance from the ground station to the corner reflector.

[0044] Step 3.2: Correct for atmospheric-induced optical path deflection and optical path lengthening.

[0045] Using the Mendes-Pavlis model, a zenith retardation model and projection function were constructed and fitted using ray tracing. The relevant function coefficients were obtained. Atmospheric retardation at any elevation angle was calculated using the zenith retardation model and projection function based on atmospheric refraction. The corrected model is as follows:

[0046] ;

[0047] in, This represents the atmospheric delay error along the integration path; This represents atmospheric delay error; the subscripts ray and vac in the integral indicate the optical path and vacuum path of the signal, respectively. Indicates the integration path; Indicates atmospheric refractive index; This represents the projection function.

[0048] Step 3.3: Correct the Earth solid tides, ocean tides, and atmospheric load tides caused by external gravitational forces, as well as the solid polar tides and ocean polar tides caused by the Earth's rotation. The errors mainly come from the Earth solid tides. The main model for the Earth solid tides is as follows:

[0049] ;

[0050] in, This represents the station offset caused by solid tides. The gravitational constants representing the Moon (j=1) and the Sun (j=2); Represents the Earth's gravitational constant; This represents the unit vectors of the Moon and the Sun relative to the Earth's center, as well as the magnitude of those vectors. This indicates the distance of the station relative to the Earth's center; Represents the second-order Love number; This represents the unit vector of the Earth station relative to the Earth's center.

[0051] Step 3.4: Address the measurement deviation caused by the inconsistency between the measurement center position and the station's calibration coordinates due to continental plate drift. The model has been revised as follows:

[0052] ;

[0053] in, This represents the coordinate offset of the measuring station caused by continental plate drift. This represents the components of the satellite position vector in the ENU (East, North, Sky) coordinate system; This represents the component of the measurement deviation in the station coordinate system.

[0054] Step 3.5: Correct the distance offset from the satellite corner reflector to the satellite's center of mass. The correction model is as follows:

[0055] ;

[0056] in, This represents the distance offset from the satellite's corner reflector to its center of mass. This represents the attitude rotation matrix from the inertial frame to the satellite's body coordinate system; The position vector of the satellite in the inertial frame at the observation station at the time of observation; This represents the satellite's position vector in the body coordinate system.

[0057] Step 4: Analyze the external consistency accuracy of the laser ranging data. External consistency accuracy uses an externally provided reference value as the comparison benchmark and mainly reflects the degree of deviation between the observed value and the reference value, i.e., the precision. It reflects the actual reliability of the positioning result and is generally measured using the root mean square (RMS) of the error (i.e., the accuracy of the positioning result). Figure 1 Analytical accuracy (using RMS standard data accuracy), including:

[0058] Step 4.1: Process the laser ranging data and remove the external compliance error term. Compare the data after error removal with the external reference value and calculate the residual between the laser ranging data and the external reference value;

[0059] Step 4.2: Set a residual threshold to remove invalid data from the laser ranging data whose residuals exceed the threshold;

[0060] Step 4.3: Calculate the total root mean square error (RMS) for all data based on the residuals of each valid data point. The formula for calculating the root mean square error (RMS) is as follows:

[0061] ;

[0062] in, Indicates the total amount of data; This represents the calculated value of the i-th data point; This represents the observation value of the i-th data point.

[0063] The root mean square error of all data can be calculated as the external consistency accuracy of the laser ranging data.

[0064] In summary, this study achieves accuracy analysis of lunar orbit satellite laser ranging data.

[0065] Example:

[0066] Taking a typical lunar orbit satellite as an example, the error of its laser ranging data is corrected:

[0067] Corresponding to step 3.1, addressing the relativistic errors caused by the gravitational field of celestial bodies. The corrections are primarily made considering the influence of the sun's gravitational field, among which... ; ; ; ; The second part of the formula can be ignored; substituting it into the formula above yields the result. ;

[0068] Corresponding to step 3.2, regarding the error caused by tropospheric refraction. Make corrections, among which , Therefore, we can obtain Influence factors of projection function Substituting into the formula above, we get... ;

[0069] Corresponding to step 3.3, regarding the error caused by Earth's solid tides. Make corrections, among which , , , , , , , , , , Substituting into the formula above, we get... ;

[0070] Corresponding to step 3.4, regarding the error caused by station offset. Corrections are made, generally based on the station offset. ;

[0071] Corresponding to step 3.5, the distance offset from the satellite corner reflector to the satellite's center of mass can be obtained. .

[0072] After the above steps, the total error was corrected to 7.82m. When compared with VLBI (Very Long Baseline Interferometry) laser ranging data, the accuracy of the corrected data was improved by orders of magnitude to the meter level.

[0073] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for error correction and accuracy analysis of lunar orbit satellite laser ranging data, characterized in that, Includes the following steps: Step 1: Set the laser error term. The laser error term is the internal coincidence error and external coincidence error of the laser uplink and downlink during the entire process of laser transmission and reception. The internal coincidence error includes systematic error and random error. The external coincidence error includes errors introduced by relativistic effects, tropospheric refraction, Earth's tidal deformation, station coordinate deviation, and corner reflector centroid offset. Step 2: Process the systematic and random errors of the internal consistency error and analyze the internal consistency accuracy; the internal consistency accuracy reflects the dispersion between observations and is measured by error or standard deviation. Step 3: Process external compliance errors; Step 4: Analyze the external compliance accuracy of the laser ranging data based on the processed external compliance error. The external compliance accuracy is compared with the externally provided reference value, reflecting the degree of deviation between the laser ranging data and the reference value, and reflecting the actual reliability of the positioning result. It is measured by the root mean square of the error.

2. The method for error correction and accuracy analysis of lunar orbit satellite laser ranging data according to claim 1, characterized in that, In step one, the system error is the error that exists in the event timer of the laser ranging system when recording the laser emission and reception time.

3. The method for error correction and accuracy analysis of lunar orbit satellite laser ranging data according to claim 2, characterized in that, Random errors originate from internal devices, the external environment, and corner reflectors.

4. The method for error correction and accuracy analysis of lunar orbit satellite laser ranging data according to claim 1, characterized in that, Step two includes: Step 2.1: When processing system errors, since the laser ranging system uses a single optical path for transmitting and receiving lasers, a calibration target is placed near the secondary mirror of the telescope. During the ranging experiment, the calibration target is measured simultaneously to measure and calibrate the system delay in real time. Repeated observations are performed to calibrate and analyze the stability of the internal delay of the system. The system delay obtained through calibration is then subtracted from the laser ranging data. Step 2.2: Process random errors and calculate the discrepancies in laser ranging data caused by laser pulse width, superconducting detector, event timer, and target broadening, in order to analyze the absolute accuracy of laser ranging data.

5. The method for error correction and accuracy analysis of lunar orbit satellite laser ranging data according to claim 4, characterized in that, Step two also includes: Step 2.3: Calculate the standard deviation of the sum of random errors in Step 2.

2. This standard deviation is the internal consistency accuracy of the lunar orbit satellite laser ranging data.

6. The method for error correction and accuracy analysis of lunar orbit satellite laser ranging data according to claim 1, characterized in that, Step three includes: Step 3.1: Correct the delay in electromagnetic signals caused by celestial gravity; Step 3.2: Correct for atmospheric-induced optical path deflection and optical path lengthening.

7. The method for error correction and accuracy analysis of lunar orbit satellite laser ranging data according to claim 6, characterized in that, Step 3.1 includes: within the Earth framework, calculating the gravitational time delay of the celestial body's gravitational field on the propagation of the light beam based on the gravitational constant of the celestial body and the distances between the Earth's center, the measuring station, and the satellite.

8. The method for error correction and accuracy analysis of lunar orbit satellite laser ranging data according to claim 6, characterized in that, Step 3.2 includes: using the Mendes-Pavlis model, employing ray tracing to construct a zenith delay model and projection function, obtaining function coefficients through fitting, and calculating the atmospheric delay at any elevation angle using the atmospheric refraction zenith delay model and projection function; the Mendes-Pavlis model is the Mendes-Pavlis model.

9. The method for error correction and accuracy analysis of lunar orbit satellite laser ranging data according to claim 6, characterized in that, Step three also includes: Step 3.3: Correct the Earth's solid tides, ocean tides, atmospheric load tides caused by external gravitational forces, as well as the solid polar tides and ocean polar tides caused by the Earth's rotation; Step 3.4: Correct the measurement deviation caused by the inconsistency between the measurement center position and the calibration coordinates of the station due to continental plate drift; Step 3.5: Correct the distance offset between the corner reflector and the satellite's center of mass.

10. The method for error correction and accuracy analysis of lunar orbit satellite laser ranging data according to claim 1, characterized in that, Step four includes: Step 4.1: Process the laser ranging data and deduct the external compliance error term; compare the data after error deduction with the external reference value and calculate the residual between the laser ranging data and the external reference value; Step 4.2: Set a residual threshold to remove invalid data from the laser ranging data whose residuals exceed the residual threshold, and retain valid data; Step 4.3: Calculate the root mean square error of all valid data based on the residual of each valid data point, and use it as the external consistency accuracy of the laser ranging data.

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