A method for obtaining satellite laser timing pointing

Abstract

This invention discloses a method for obtaining satellite laser timing pointing. By using the six root numbers of the satellite orbit, the nadir trajectory and foot point trajectory of the satellite are obtained. Combined with the elevation database, the continuous laser pointing of the satellite is calculated, which greatly simplifies the laser pointing calculation process and improves the simulation calculation speed. The input used in this invention does not involve complex parameters such as laser attitude angle. Only TLE ephemeris and elevation data need to be input. The requirements for the function configuration of the scene simulation software are not high, and the calculation cost is low.

Description

Technical Field

[0001] This invention belongs to the field of satellite laser timing pointing technology, and particularly relates to a method for obtaining satellite laser timing pointing. Background Technology

[0002] In the geometric positioning and lidar simulation of spaceborne laser altimeters, the accuracy of the laser pointing angle is crucial to the positioning and calculation results. Currently, the main methods for obtaining the laser pointing angle in orbit for spaceborne laser altimeters are ground-based detector acquisition and airborne infrared camera imaging, but these methods suffer from high costs and low success rates. Therefore, researching efficient on-orbit laser pointing angle acquisition methods is of great significance for improving surveying accuracy.

[0003] Chinese invention patent CN110646782B discloses a method for on-orbit pointing calibration of spaceborne lasers based on waveform matching. The method involves simulating the echo waveform of a spaceborne laser altimeter based on airborne LiDAR data; matching the obtained simulated waveform with the real waveform; determining the centroid coordinates of the spaceborne laser foot point based on the method of matching the simulated waveform with the real waveform; and calibrating the pointing angle of the spaceborne laser based on the geometric calibration model of the spaceborne laser altimeter and the centroid coordinates of the laser foot point.

[0004] The simulated laser pointing angle described above has the following drawbacks:

[0005] High data dependence: This method requires high-quality airborne LiDAR data for waveform simulation, and the acquisition and processing of this data is costly and difficult to obtain.

[0006] High computational complexity: The process involves multiple waveform simulations and matching, requiring a large amount of computational resources and time for layer-by-layer search and surface fitting, resulting in high computational complexity that cannot meet the needs of time-series simulation. Summary of the Invention

[0007] To overcome the shortcomings of the prior art, the present invention aims to provide a method for obtaining satellite laser timing pointing. By using the six root numbers of the satellite orbit, the nadir point trajectory and foot point trajectory are obtained, and the continuous laser pointing of the satellite is calculated by combining the elevation database. This greatly simplifies the laser pointing calculation process and improves the simulation calculation speed. The input used in this invention does not involve complex parameters such as laser attitude angle, but only requires the input of TLE ephemeris and elevation data. It does not have high requirements for the function configuration of the scene simulation software and has low computational cost.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] A method for obtaining satellite laser timing pointing includes the following steps:

[0010] Step 1: Obtain the six-axis data of different satellite orbits at different times. The six-axis data of the satellite orbits includes the orbital inclination. Right ascension of ascending node Orbital eccentricity Perigeal argument , and the near point angle Number of times the Earth orbits each day ;

[0011] Step 2: Calculate the geocentric coordinate system of the satellite orbit at time t based on the six root data of the satellite orbit. ;

[0012] Step 3: Based on the Earth's semi-major axis and Earth's short axis Calculating Earth's oblateness ;

[0013] Step 4: Based on the geocentric and Earth-fixed coordinates of the satellite orbit from Step 2. And the Earth's oblateness in step 3 Calculate the satellite's nadir trajectory coordinates at time t. Satellite's nadir coordinates Using satellite longitude ,latitude express;

[0014] Step 5: Using the satellite's nadir trajectory coordinates from Step 4 Calculate the six-point offset distance of the satellite, including the longitude offset distance of each point. and the distance of the foot point latitude offset ;

[0015] Step 6: Calculate the latitude and longitude coordinates of the six foot points based on the offset distances obtained in Step 5. ;

[0016] Step 7: Obtain the latitude and longitude coordinates of the six foot points at the current time t. Enter the elevation database to query the elevation of the corresponding foot point with latitude and longitude. The elevation of the corresponding footpoint under latitude and longitude was obtained through the query. Calculate the geocentric coordinates of the corresponding foot point. ;

[0017] Step 8: Based on the geocentric and geofixed coordinates of the satellite's footpoint at the current time t in Step 7. Compared with the satellite's geocentric coordinates in step 3 Calculate the laser pointing of the satellite's foot point at time t. .

[0018] In step 2, the geocentric coordinate system of the satellite orbit at the current time t. The specific calculation process is as follows:

[0019] Based on the number of times the Earth orbits each day Calculate the semi-major axis of the track The expression is as follows:

[0020]

[0021] in, Let g be the gravitational constant, and its value is... ;

[0022] Based on the mean angle of the six elements of the satellite orbit. and orbital eccentricity Calculate the near point angle The expression is as follows:

[0023]

[0024] Based on the orbital eccentricity from the six elements of the satellite orbit and the near point angle Calculate the true anterior angle The expression is as follows:

[0025]

[0026] Based on the information of the six roots and the true nearest angle Calculate the geocentric and Earth-fixed coordinates of the satellite orbit at time t. The expression is as follows:

[0027]

[0028] in, For orbital eccentricity, For true near point angle, For the semi-major axis of the track, For the track inclination angle, Right ascension of the ascending node, This is the argument of perigee.

[0029] In step 4, the satellite's nadir trajectory coordinates at the current time t are... The specific calculation process is as follows:

[0030] The geocentric coordinates of the satellite orbit in step 2 Project it onto the z-plane, and then use the satellite's geocentric and Earth-fixed coordinates at the current time t. Calculate the distance from the satellite to the Earth's center at time t. Longitude of the satellite and latitude The expressions are as follows:

[0031]

[0032]

[0033] Calculate the latitude of the satellite using an iterative method. The expression is as follows:

[0034]

[0035]

[0036] in, This represents the initial latitude value of the satellite at time t. For the satellite iteration at time t The latitude value of the second, For the satellite iteration at time t After a certain number of iterations, the latitude value of the satellite can be obtained accurately. The latitude of the satellite at time t. N represents the conversion process coefficient;

[0037] The expression for the coefficient N in the conversion process is as follows:

[0038]

[0039] in, Indicates the Earth's oblateness. Indicates the Earth's semi-major axis. For the satellite iteration at time t The latitude value.

[0040] The specific calculation process for the satellite's six-point offset distance in step 5 is as follows:

[0041] Using the satellite's nadir trajectory coordinates Calculate the direction of the satellite's velocity in latitude and longitude at time t. The expression is as follows:

[0042]

[0043] in, This represents the coordinates of the satellite's nadir trajectory at the current time t+1. This represents the coordinates of the satellite's nadir trajectory at time t. Indicates the time interval of satellite orbits;

[0044] Based on the satellite's velocity direction in latitude and longitude units at time t. and the horizontal displacement of the satellite orbit and vertical displacement The offset distances of the six footpoints in the satellite scan are calculated based on the satellite's trajectory and the geometric positional relationship of the six footpoints. Each footpoint offset distance includes the footpoint longitude offset distance. and the distance of the foot point latitude offset The expression is as follows:

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] in, Represents the velocity vector of the satellite latitudinal component Represents the velocity vector The weight in longitude, velocity vector Size; These represent the horizontal distance between two adjacent strong pulses or two weak pulses during satellite scanning, respectively. These represent the vertical distances between a strong pulse and a weak pulse scanned by the satellite, respectively. This refers to the horizontal distance between strong and weak pulses scanned by the satellite.

[0058] The latitude and longitude coordinates of the six foot points in step 6 The specific calculation process is as follows:

[0059] Based on the offset distances of the six foot points obtained in step 5, calculate the longitude offset of each of the six foot points relative to the nadir point of the satellite. and the latitude offset of the six foot points relative to the satellite's nadir point The expression is as follows:

[0060]

[0061]

[0062] in, It is the distance of the foot point's latitude offset. It is the longitude offset distance of the foot point. It is the latitude value of the satellite's nadir point at the current time t;

[0063] Based on the longitude offset of the six foot points relative to the satellite's nadir point. and the latitude offset of the six foot points relative to the satellite's nadir point Calculate the latitude and longitude coordinates of the six foot points at time t. (i=1, 2, 3, 4, 5, 6), the expression is as follows:

[0064]

[0065] .

[0066] The geocentric coordinates of the corresponding foot point in step 7 The expression is as follows:

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] Where N represents the conversion coefficient, derived from the geometric formula. and These are the latitude and longitude values ​​of the satellite's location at time t. The elevation of the satellite's footpoint at time t is the current elevation.

[0073] In step 8, the laser pointing of the satellite's footpoint at the current time t. The specific expression is as follows:

[0074]

[0075] in, This represents the geocentric and Earth-fixed coordinates of the satellite at time t. This represents the geocentric and geofixed coordinates of the satellite's footpoint at time t.

[0076] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0077] 1. This invention uses the orbital TLE ephemeris to obtain six data points to calculate the nadir point trajectory, resulting in higher accuracy of the calculated time-series ground scan corner point trajectory.

[0078] 2. This invention takes into account the Earth's oblateness and calculates the orbital coordinates of the sub-satellite point using an iterative method, resulting in higher calculation accuracy.

[0079] 3. Based on the accurate calculation of foot trajectory and combined with a highly reliable open-source elevation database, this invention provides accurate results for calculating laser timing direction, with high calculation efficiency and simple method, without relying on on-site scene construction and detection.

[0080] 4. Both spaceborne lidar positioning and laser ranging methods use the transmission and reception time of pulse signals as a basis to calculate the laser direction through satellite attitude. These two methods obtain the laser direction and footprint position through the calculation of data source and laser echo. The calculation process is complex and cannot achieve real-time effect through rapid simulation. Moreover, it has high requirements for the sufficiency and accuracy of data source. Compared with spaceborne lidar positioning and laser ranging methods, this invention uses a geometric method to translate the trajectory to obtain the corresponding footprint trajectory, thereby simulating and calculating the laser direction. The calculation speed is high and the calculation process is simple.

[0081] 5. The method of calculating satellite laser timing pointing based on orbit and elevation data in this invention is not limited by satellite type and has good universality.

[0082] In summary, this invention calculates the laser ground scanning footpoint trajectory using the six-root information of the satellite orbit and combines it with the elevation database to calculate the satellite laser timing direction, which greatly simplifies the laser direction calculation process and improves the simulation calculation speed. The input used in this invention does not involve complex parameters such as laser attitude angles, but only requires the input of TLE ephemeris and elevation data. It does not have high requirements for the functionality of the scene simulation software and has low computational cost. Attached Figure Description

[0083] Figure 1 The flowchart shows the satellite laser timing pointing method provided by the present invention.

[0084] Figure 2 This is a schematic diagram of the satellite's trajectory and the geometric relationship of its six foot points according to the present invention. Detailed Implementation

[0085] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0086] A method for obtaining satellite laser timing pointing includes the following steps:

[0087] Step 1: Obtain TLE ephemeris tables for different satellites at different times from publicly available Celestrak data. Parse the TLE ephemeris tables to obtain the six orbital parameters of the satellites; these parameters include orbital inclination. Right ascension of ascending node Orbital eccentricity Perigeal argument , and the near point angle Number of times the Earth orbits each day ;

[0088] Step 2: Calculate the geocentric coordinate system of the satellite orbit at time t based on the six root data of the satellite orbit. ;

[0089] Based on the number of times the Earth orbits each day Calculate the semi-major axis of the track The expression is as follows:

[0090]

[0091] in, Let g be the gravitational constant, and its value is... ;

[0092] Based on the mean angle of the six elements of the satellite orbit. and orbital eccentricity Calculate the near point angle The expression is as follows:

[0093]

[0094] Based on the orbital eccentricity from the six elements of the satellite orbit and the near point angle Calculate the true anterior angle The expression is as follows:

[0095]

[0096] Based on the information of the six roots and the true nearest angle Calculate the geocentric and Earth-fixed coordinates of the satellite orbit at time t. The expression is as follows:

[0097]

[0098] in, For orbital eccentricity, For true near point angle, For the semi-major axis of the track, For the track inclination angle, Right ascension of the ascending node, Argument of perigee;

[0099] Step 3: Based on the Earth's semi-major axis and Earth's short axis Calculating Earth's oblateness The formula is as follows:

[0100]

[0101] in, It represents the Earth's semi-major axis (equatorial radius). Indicates the Earth's minor axis (polar radius);

[0102] Step 4: Based on the geocentric and Earth-fixed coordinates of the satellite orbit from Step 2. And the Earth's oblateness in step 3 Calculate the satellite's nadir trajectory coordinates at time t. Satellite's nadir coordinates Using satellite longitude ,latitude express;

[0103] The geocentric coordinates of the satellite orbit in step 2 Project it onto the z-plane, and then use the satellite's geocentric and Earth-fixed coordinates at the current time t. Calculate the distance from the satellite to the Earth's center at time t. Longitude of the satellite and latitude The expressions are as follows:

[0104]

[0105]

[0106] Calculate the latitude of the satellite using an iterative method. The expression is as follows:

[0107]

[0108]

[0109] in, This represents the initial latitude value of the satellite at time t. For the satellite iteration at time t The latitude value of the second, For the satellite iteration at time t After a certain number of iterations, the latitude value of the satellite can be obtained accurately. The latitude of the satellite at time t. N represents the conversion process coefficient;

[0110] The expression for the coefficient N in the conversion process is as follows:

[0111]

[0112] in, Indicates the Earth's oblateness. Indicates the Earth's semi-major axis. For the satellite iteration at time t The latitude value;

[0113] Step 5: Using the satellite's nadir trajectory coordinates from Step 4 Calculate the six-point offset distance of the satellite, including the longitude offset distance of each point. and the distance of the foot point latitude offset ;

[0114] Using the satellite's nadir trajectory coordinates Calculate the direction of the satellite's velocity in latitude and longitude at time t. The expression is as follows:

[0115]

[0116] in, This represents the coordinates of the satellite's nadir trajectory at the current time t+1. This represents the coordinates of the satellite's nadir trajectory at time t. Indicates the time interval of satellite orbits;

[0117] Based on the satellite's velocity direction in latitude and longitude units at time t. and the horizontal displacement of the satellite orbit and vertical displacement ,Depend on Figure 2 The geometric positional relationship calculation in the data involves the offset distances of six foot points from the satellite scan, with each foot point offset distance including the longitude offset distance. and the distance of the foot point latitude offset The expression is as follows:

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130] in, Represents the velocity vector of the satellite latitudinal component Represents the velocity vector The weight in longitude, velocity vector Size; These represent the horizontal distance between two adjacent strong pulses or two weak pulses during satellite scanning, respectively. These represent the vertical distances between a strong pulse and a weak pulse scanned by the satellite, respectively. The three parameters—horizontal distance between strong and weak pulses scanned by the satellite—can be obtained from the satellite's design parameters.

[0131] Step 6: Calculate the latitude and longitude coordinates of the six foot points obtained in Step 5 based on their offset distances. ;

[0132] Based on the offset distances of the six foot points obtained in step 5, calculate the longitude offset of each of the six foot points relative to the nadir point of the satellite. and the latitude offset of the six foot points relative to the satellite's nadir point The expression is as follows:

[0133]

[0134]

[0135] in, It is the distance of the foot point's latitude offset. It is the longitude offset distance of the foot point. It is the latitude value of the satellite's nadir point at the current time t;

[0136] Based on the longitude offset of the six foot points relative to the satellite's nadir point. and the latitude offset of the six foot points relative to the satellite's nadir point Calculate the latitude and longitude coordinates of the six foot points at time t. The expression is as follows:

[0137]

[0138]

[0139] Step 7: Obtain the latitude and longitude coordinates of the six foot points at the current time t. Enter the elevation database to query the elevation of the corresponding foot point with latitude and longitude. The elevation database is a publicly available data source, currently downloadable from the University of Bristol's official website. The downloaded images are in GeoTIFF format, ensuring the data source's reliability and high accuracy. The elevation at the corresponding latitude and longitude of the selected point can be determined through the query. Calculate the geocentric coordinates of the corresponding foot point. The expression is as follows:

[0140]

[0141]

[0142]

[0143]

[0144]

[0145] Where N represents the conversion coefficient, derived from the geometric formula. and These are the latitude and longitude values ​​of the satellite's location at time t. The elevation of the satellite's footpoint at time t;

[0146] Step 8: Based on the geocentric and geofixed coordinates of the satellite's footpoint at the current time t in Step 7. Compared with the satellite's geocentric and Earth-fixed coordinates at the current time t in step 3 Calculate the laser pointing of the satellite's foot point at time t. The expression is as follows:

[0147]

[0148] This laser pointing can be used as an important parameter for subsequent footpoint simulation, as well as for satellite lidar scene simulation and on-site model building.

[0149] Simulation experiment:

[0150] First, obtain the six elements of the Icesat-2 satellite orbit from the TLE ephemeris, namely, the orbital inclination is 92.0011° and the right ascension of the ascending node. The orbital eccentricity is 16.2379°. The perigee argument is 0.002349. It is 93.3583°, the angle of approach. It is 266.793°, and the number of times it circles the Earth each day. It is 15.2828;

[0151] The ATL03 data was obtained by verifying the footpoint orbit of the Icesat2 satellite at 00:08:32 on December 30, 2018. The ATL03 data includes 333 points and a total of 367 seconds. In the calculation results, there are some points with significant errors. Considering factors such as cloud cover and minor vibrations of the satellite platform, 10 outlier points were removed. The longitude deviation is 188m and the latitude deviation is 172m. Therefore, the horizontal distance deviation between the measured ground scan footpoint orbit data parsed from the ATL03 data and the data calculated by the theoretical calculation method of this invention is 255m. Based on this, the laser pointing error calculated using the satellite ground scan trajectory and elevation data at any time is approximately 9.80645387893553e-07°, which is within the allowable error range.

Claims

1. A method for obtaining satellite laser timing pointing, characterized in that, Includes the following steps: Step 1: Obtain the six-axis data of different satellite orbits at different times. The six-axis data of the satellite orbits includes the orbital inclination. Right ascension of ascending node Orbital eccentricity Perigeal argument , and the near point angle Number of times the Earth orbits each day ; Step 2: Calculate the geocentric coordinate system of the satellite orbit at time t based on the six root data of the satellite orbit. ; Step 3: Based on the Earth's semi-major axis and Earth's short axis Calculating Earth's oblateness ; Step 4: Based on the geocentric and Earth-fixed coordinates of the satellite orbit from Step 2. And the Earth's oblateness in step 3 Calculate the satellite's nadir trajectory coordinates at time t. Satellite's nadir coordinates Using satellite longitude ,latitude express; Step 5: Using the satellite's nadir trajectory coordinates from Step 4 Calculate the six-point offset distance of the satellite, including the longitude offset distance of each point. and the distance of the foot point latitude offset ; Step 6: Calculate the latitude and longitude coordinates of the six foot points based on the offset distances obtained in Step 5. ; Step 7: Obtain the latitude and longitude coordinates of the six foot points at the current time t. Enter the elevation database to query the elevation of the corresponding foot point with latitude and longitude. ; The elevation of the corresponding foot point under latitude and longitude was obtained through the query. Calculate the geocentric coordinates of the corresponding foot point. ; Step 8: Based on the geocentric and geofixed coordinates of the satellite's footpoint at the current time t in Step 7. Compared with the satellite's geocentric coordinates in step 3 Calculate the laser pointing of the satellite's foot point at time t. .

2. The method for obtaining satellite laser timing pointing according to claim 1, characterized in that, In step 2, the geocentric coordinate system of the satellite orbit at the current time t. The specific calculation process is as follows: Based on the number of times the Earth orbits each day Calculate the semi-major axis of the track The expression is as follows: in, Let g be the gravitational constant, and its value is... ; Based on the mean angle of the six elements of the satellite orbit. and orbital eccentricity Calculate the near point angle The expression is as follows: Based on the orbital eccentricity from the six elements of the satellite orbit and the near point angle Calculate the true anterior angle The expression is as follows: Based on the information of the six roots and the true nearest angle Calculate the geocentric and Earth-fixed coordinates of the satellite orbit at time t. The expression is as follows: in, For orbital eccentricity, For true near point angle, For the semi-major axis of the track, For the track inclination angle, Right ascension of the ascending node, This is the argument of perigee.

3. The method for obtaining satellite laser timing pointing according to claim 1, characterized in that, In step 4, the satellite's nadir trajectory coordinates at the current time t are... The specific calculation process is as follows: The geocentric coordinates of the satellite orbit in step 2 Project it onto the z-plane, and then use the satellite's geocentric and Earth-fixed coordinates at the current time t. Calculate the distance from the satellite to the Earth's center at time t. Longitude of the satellite and latitude The expressions are as follows: Calculate the latitude of the satellite using an iterative method. The expression is as follows: in, This represents the initial latitude value of the satellite at time t. For the satellite iteration at time t The latitude value of the second, For the satellite iteration at time t After a certain number of iterations, the accurate latitude value of the satellite can be obtained. The latitude of the satellite at time t. N represents the conversion process coefficient; The expression for the coefficient N in the conversion process is as follows: in, Indicates the Earth's oblateness. Indicates the Earth's semi-major axis. For the satellite iteration at time t The latitude value.

4. The method for obtaining satellite laser timing pointing according to claim 1, characterized in that, The specific calculation process for the satellite's six-point offset distance in step 5 is as follows: Using the satellite's nadir trajectory coordinates Calculate the direction of the satellite's velocity in latitude and longitude at time t. The expression is as follows: in, This represents the coordinates of the satellite's nadir trajectory at the current time t+1. This represents the coordinates of the satellite's nadir trajectory at time t. Indicates the time interval of satellite orbits; Based on the satellite's velocity direction in latitude and longitude units at time t. and the horizontal displacement of the satellite orbit and vertical displacement The offset distances of the six footpoints in the satellite scan are calculated based on the satellite's trajectory and the geometric positional relationship of the six footpoints. Each footpoint offset distance includes the footpoint longitude offset distance. and the distance of the foot point latitude offset The expression is as follows: in, Represents the velocity vector of the satellite latitudinal component Represents the velocity vector The weight in longitude, velocity vector Size; These represent the horizontal distance between two adjacent strong pulses or two weak pulses during satellite scanning, respectively. These represent the vertical distances between a strong pulse and a weak pulse scanned by the satellite, respectively. This refers to the horizontal distance between strong and weak pulses scanned by the satellite.

5. The method for obtaining satellite laser timing pointing according to claim 1, characterized in that, The latitude and longitude coordinates of the six foot points in step 6 The specific calculation process is as follows: Based on the offset distances of the six foot points obtained in step 5, calculate the longitude offset of each of the six foot points relative to the nadir point of the satellite. and the latitude offset of the six foot points relative to the satellite's nadir point The expression is as follows: in, It is the distance of the foot point's latitude offset. It is the longitude offset distance of the foot point. It is the latitude value of the satellite's nadir point at the current time t; Based on the longitude offset of the six foot points relative to the satellite's nadir point. and the latitude offset of the six foot points relative to the satellite's nadir point Calculate the latitude and longitude coordinates of the six foot points at time t. (i=1, 2, 3, 4, 5, 6), the expression is as follows: 。 6. The method for obtaining satellite laser timing pointing according to claim 1, characterized in that, The geocentric coordinates of the corresponding foot point in step 7 The expression is as follows: Where N represents the conversion coefficient, derived from the geometric formula. and These are the latitude and longitude values ​​of the satellite's location at time t. The elevation of the satellite's footpoint at time t is the current elevation.

7. The method for obtaining satellite laser timing pointing according to claim 1, characterized in that, In step 8, the laser pointing of the satellite's footpoint at the current time t. The specific expression is as follows: in, This represents the geocentric and Earth-fixed coordinates of the satellite at time t. This represents the geocentric and geofixed coordinates of the satellite's footpoint at time t.

Images