Method for improving height measurement satellite track intersection point precision based on multi-factor constraint

Abstract

The invention relates to the cross technical field of satellite altimetry, satellite navigation and the like, in particular to a method for improving the accuracy of an altimetry satellite track cross point based on multi-factor constraint, which comprises the following steps of: pre-screening data to reduce invalid calculation; according to the sea surface height data calculation method, a rapid exclusion and straddling test mechanism is introduced, and the calculation efficiency is improved through strategies such as constraint of an accurate intersection calculation window and the like; according to the method, large-area and high-precision satellite data provided by an SWOT satellite task is used for calculation, the capability of efficiently processing the satellite data and obtaining a high-precision intersection point result is achieved, high precision of the intersection point position can be effectively guaranteed, sea surface height calculation verification of different areas is carried out based on the algorithm, and the calculation efficiency is improved. The obtained sea level height has good precision in different latitude areas.

Description

Technical Field

[0001] This invention relates to the interdisciplinary fields of satellite altimetry and satellite navigation, and in particular to a method for improving the accuracy of intersection points of altimetry satellite trajectories based on multiple factor constraints. Background Technology

[0002] The calculation of mean sea level height primarily relies on satellite altimetry data. Since the SEASAT and GEOSAT satellites first achieved continuous observation of global mesoscale sea level changes, dozens of altimetry satellites have been launched. For sea level measurement research, this diverse range of satellite data from different missions provides a crucial data foundation for mean sea level modeling. In the field of sea level measurement, traditional altimetry satellites have continuously optimized observation accuracy through single-beam radar technology. For example, CryoSat has improved its ability to monitor polar ice and the ocean using synthetic aperture radar, while the Jason series has established a high-precision benchmark dataset of global sea level changes through long-term observations from multiple generations of satellites. However, these systems still suffer from limitations such as limited spatial coverage and difficulty in overcoming resolution bottlenecks. In December 2022, the SWOT (SurfaceWater and Ocean Topography) satellite, jointly launched by NASA, CNES, CAS, and UKSA, raised the resolution of sea level height measurement to a new level through its wide-swath observation technology and interferometric synthetic aperture radar (KaRIn). The launch of the SWOT satellite marks a new stage in ocean altimetry technology, moving from traditional single-beam radar altimetry (such as CryoSat and Jason series) to wide coverage and high resolution. It breaks through the limitations of traditional altimetry in terms of spatial coverage and resolution, and achieves seamless, kilometer-level resolution observation of sea surface height globally. This provides key data support for building higher-precision sea level height models.

[0003] Compared to traditional satellite single-track observations, the wide-swath data provided by the SWOT satellite can significantly improve the accuracy of mean sea level height (MSH) model construction. However, to fully realize the potential of the SWOT satellite, the key lies in obtaining accurate satellite trajectory intersections. The intersection is the point where the ascending and descending arcs of the satellite trajectory meet. Within the orbital repetition period, the sea level height parameters measured at the intersection of the ascending and descending arcs should be completely consistent. However, due to factors such as observation system errors, instrument deviations, and environmental interference, the actual data often show significant differences at the intersection. This discrepancy poses a challenge to the reliability of sea level change monitoring, thus affecting the construction of the MSH model. Therefore, researching high-precision intersection location methods is of great significance for the accuracy and reliability of MSH modeling.

[0004] To improve the accuracy of intersection point calculations, scientists have conducted extensive research. In 1989, Tai proposed a FI (Fixed Iteration) algorithm, which solves for intersection point positions through trajectory fitting, but its insufficient fitting accuracy led to significant deviations in the results. In 2012, Zhou Xiaoguang designed a piecewise fitting method with 11 segmentation types, improving the calculation accuracy and applicability, but it required manual judgment of the optimal segmentation type, resulting in low automation. In 2017, Greene proposed the RST (Rapid Rejection and Straddle) algorithm based on computer graphics principles. The test method effectively solves the automation problem, but its algorithm complexity leads to low computational efficiency. In terms of efficiency, the grid method divides the study area into regular grids and regards the grid center point where both ascending and descending measurement points exist as intersection points. It is quite attractive due to its low computation time. In 2024, Zhu found in his research that this method has poor accuracy, which affects the high-precision modeling of sea level. Although the latitude difference method can also reduce some of the computation, it still faces the problem of long computation time when processing large-scale data. In 2021, Zhao Zilong's research found that when the amount of data used is large or the number of intersection points is too large, the computation time of traditional algorithms will increase significantly with the amount of data, further affecting the overall computational efficiency and limiting its application in high-frequency, large-volume satellite data. Summary of the Invention

[0005] This invention addresses the common problem of traditional intersection point algorithms struggling to balance accuracy and efficiency. It proposes a method that balances computational accuracy and efficiency, possesses the ability to efficiently process satellite data and obtain high-precision intersection point results, and effectively guarantees the accuracy of altimetry satellite trajectory intersection points based on multiple factor constraints.

[0006] This invention achieves its purpose through the following measures: A method for improving the accuracy of altimeter satellite trajectory intersections based on multiple factor constraints, characterized by the following steps: Step 1: Data pre-screening. The input ascending and descending orbit data are pre-screened. Based on the boundary of the study area, the data is extended by k° along the latitude and longitude directions. k is set according to the average spacing of the selected satellite observation points to avoid the situation where the orbit crosses the area but there are no observation points in the area due to discrete sampling, which would cause the orbit data to be excluded. In the end, only the orbit data with at least one observation point located in the extended area are retained, and the rest of the orbits are directly removed to reduce invalid calculations. Step 2: Determine if an intersection point exists. First, perform a rapid rejection test: determine whether the diagonal bounding boxes formed by the track endpoints overlap, dividing it into three cases: overlapping rectangles and intersecting tracks, overlapping rectangles but non-intersecting tracks, and non-overlapping rectangles and non-intersecting tracks. Among these, overlapping rectangles do not necessarily indicate that the tracks intersect; however, if the bounding boxes do not overlap, then the two tracks definitely do not have an intersection point, which can effectively avoid including non-intersecting tracks in subsequent calculations. The straddle test determines whether two line segments are straddling each other by calculating the cross product of their vectors. If two line segments straddle each other, they intersect, and the test results in a straddle test. straddle and straddle The conditions are: (1), where, Refer to Starting point For vectors ending at a certain point, and similarly for other vectors, the existence of intersections can be determined by a rapid exclusion crossover experiment, which can avoid a lot of redundant calculations. Step 3: Calculate the intersection point location, which includes: Longitude calculation of approximate intersection point: First, it is necessary to quickly determine the longitude of the approximate intersection point. The ground trajectory of a satellite orbiting the Earth can be divided into two arcs, namely the ascending orbit and the descending orbit. Assuming the ascending orbit and the descending orbit, the ascending orbit and the descending orbit of the same satellite are symmetrical. When the orbit measurement data is complete, based on its symmetrical characteristics, the longitude of the approximate intersection point can be obtained by connecting the four endpoints of the two orbits. Let the endpoints of the ascending and descending orbits be respectively , and , The longitude of the intersection of the lines connecting them This is the approximate longitude of the intersection point: (2), where, , Using the endpoint plane coordinate projection values, the approximate longitude of the intersection point is quickly calculated by leveraging the symmetry between the ascending and descending orbits, with an error of less than 0.5°. For partially missing satellite altimetry data where the approximate longitude of the intersection point cannot be quickly calculated using endpoints, based on the symmetry between the complete ascending and descending orbits, if there is an intersection point between the two orbits, then two points with the same latitude on the two orbits... , The average longitude of the intersection is close to the longitude of the intersection point, and can also be used as a rough estimate of the longitude of the intersection point. The calculation method is as follows: (3), among which, , They are respectively , Longitude values ​​of two points; Precise location calculation of the intersection: Determining the approximate longitude of the intersection through track symmetry. After that, with Centered on the longitude axis, adjacent points on the ascending and descending orbits are selected to form a calculation window, constraining the longitude range of the selected measurement points. Assume the latitude and longitude of the measurement points on the ascending and descending orbits within the calculation window are as follows: , , , Polynomial fitting was used for the ascending trajectory data: (4) After obtaining the fitting result of the ascending trajectory, substitute it into the longitude value of the measuring point of the descending trajectory within the calculation window. Calculate the corresponding ascending orbit latitude value. ,Will and Subtracting the differences yields a set of sorted differences. Within this set, we find two sets of ascending and descending trajectory points with changing signs. Using the data from these two sets of points, we calculate the intersection of line segments, ultimately obtaining the precise latitude and longitude coordinates of the intersection point. (5), among which, , Let these be the longitude and latitude of the intersection point, respectively. Assume the selected ascending point is the [missing value]. The and the first The first ascending point, the selected descending point position. The and the first indivual.

[0007] After calculating the location of the intersection, this invention uses the inverse distance weighting method to interpolate the data from measuring points near the intersection to obtain the sea level height data at the intersection. (7), among which, , This represents the sea level height at a known point, which is the [number]th [point]. The spherical distance between the point and the point to be calculated.

[0008] To avoid the influence of distant points on the sea level height at the intersection, this invention modifies the weighting coefficients to obtain an exponential inverse distance weighting method, which can rapidly reduce the influence of distant measuring points. Specifically, it can be based on the following formula: (8), among which, For the first The weight coefficients of the points, after modification The larger the value, the faster the influence of the distant measuring point on the intersection point decays.

[0009] This invention is based on the principles of polynomial fitting and cross-point calculation, introduces a rapid exclusion and cross-test mechanism, and improves computational efficiency through strategies such as constraining the precise cross-point calculation window. It uses large-area, high-precision satellite data provided by the SWOT satellite mission for calculation. The method has the ability to efficiently process satellite data and obtain high-precision cross-point results, and can effectively ensure the high accuracy of cross-point positions. The sea level height calculation in different regions based on this algorithm has been verified, and the obtained sea level height has good accuracy in different latitude regions. Attached Figure Description

[0010] Appendix Figure 1 This is a flowchart of the present invention.

[0011] Appendix Figure 2 This is a schematic diagram of the rapid rejection test in this invention, wherein... Figure 2 (a) shows the case where rectangles R1 and R2 intersect, and line segments M1M2 and N1N2 intersect; (b) shows the case where rectangles R1 and R2 intersect, and line segments M1M2 and N1N2 do not intersect; (c) shows the case where rectangles R1 and R2 do not intersect, and line segments M1M2 and N1N2 do not intersect.

[0012] Appendix Figure 3 A schematic diagram of the straddle test in this invention, wherein... Figure 3 (a) is a schematic diagram of the case where M1M2 straddles N1N2; (b) is a schematic diagram of the case where M1M2 does not straddle N1N2.

[0013] Appendix Figure 4 This is a schematic diagram of the FCMC calculation of the precise intersection point window in an embodiment of the present invention.

[0014] Appendix Figure 5 In this embodiment of the invention, the intersection point position comparison is calculated, wherein... Figure 5 (a) shows the FCMC method; (b) shows the piecewise fitting method; and (c) shows the grid method, calculated using pass 254 and pass 519 in SWOT L2_LR_SSH cycle 007.

[0015] Appendix Figure 6 This is a schematic diagram illustrating the intersection point calculation results in an embodiment of the present invention, wherein... Figure 6 (a) shows the intersection result of pass 006 and pass 159 in SWOT L3_LR_SSHcycle 006, and (b) is a magnified view of the part, where the red line is the ascending rail, the blue line is the descending rail, and the black dots are the calculated intersection positions.

[0016] Appendix Figure 7 The diagram shows the calculation time of each method in the embodiments of the present invention. Methods 1-3 are FCMC, piecewise fitting method and grid method, respectively.

[0017] Appendix Figure 8 This is a schematic diagram illustrating the time improvement rate of FCMC compared to the piecewise fitting method in an embodiment of the present invention.

[0018] Appendix Figure 9 This is a schematic diagram illustrating the impact of taking different values ​​on the weight of a single point in an embodiment of the present invention.

[0019] Appendix Figure 10 This is a schematic diagram of the contour lines of SDUST2020 MSS (113.5–115°E, 15–16.5°N) in an embodiment of the present invention.

[0020] Appendix Figure 11 The scatter plots show the calculation results of different methods in the present invention in three study regions: Region a: 110°E~120°E, 5°N~25°N; Region b: 120°E~130°E, 5°N~25°N; Region c: 145°E~155°E, 35°N~55°N. Detailed Implementation

[0024] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0025] To ensure the accuracy and efficiency of crossover point calculation, this invention is based on the principles of polynomial fitting and crossover point calculation. It utilizes orbital symmetry to quickly calculate approximate crossover points and improves the accuracy of satellite trajectory by constraining the precise crossover point calculation window, while reducing redundant calculations to improve computational efficiency. This invention constructs a novel Fast Crossover-method under Multi Constraints (FCMC). In previous studies, various cross-point algorithms have been widely used to determine the existence of cross-points. However, these methods have shown significant limitations in processing the ever-increasing volume of satellite altimetry data. For example, piecewise fitting methods suffer from excessive errors in cross-point positioning due to too few segments, while too many segments complicate the calculation process and increase computation time. Therefore, this invention selects SWOT satellites, which are representative of large datasets, and introduces multiple influencing factors for constraint based on polynomial fitting and cross-point calculation principles, thereby significantly improving computational efficiency while ensuring cross-point positioning accuracy. Figure 1 This is a flowchart of the FCMC construction process.

[0026] Figure 1 The flowchart for building FCMC is presented. This method mainly consists of three basic modules, and the implementation steps of each module are described in detail below: (1) Data Pre-screening. To achieve efficient data processing, the input ascending and descending orbit data first need to be pre-screened. Based on the boundary of the study area, the data is extended by k° along the latitude and longitude directions (k is set according to the average spacing of the selected satellite observation points) to avoid the situation where the orbit crosses the area but there are no observation points in the area due to discrete sampling, thus causing the orbit data to be excluded. Finally, only the orbit data with at least one observation point located in the extended area are retained, and the rest of the orbits are directly discarded to reduce invalid calculations.

[0027] (2) Intersection point determination. Rapid rejection test: This determines whether the diagonal bounding boxes formed by the track endpoints overlap. It can be divided into three cases. Figure 2 The three diagrams respectively represent overlapping rectangles and intersecting tracks, overlapping rectangles but non-intersecting tracks, and non-overlapping rectangles and non-intersecting tracks. According to... Figure 2 (a) and Figure 2 (b) shows that overlapping rectangles cannot determine the intersection of tracks; however, from Figure 2 (c) It can be determined that if the bounding boxes do not overlap, the two tracks will definitely not have an intersection point, which can effectively avoid including non-intersecting tracks in subsequent calculations.

[0028] straddle test: Figure 2 (b) illustrates the case where the rectangular bounding boxes overlap but the two tracks do not intersect, while the straddle test can further rule out this situation. Figure 3 (a) and (b) respectively show straddling as well as Not standing on There are two scenarios. For example... Figure 3 As shown, if line segment The two endpoints are located at On both sides, straddle The straddle test determines whether two line segments are straddling each other by calculating the vector cross product. If two line segments straddle each other, then the two line segments intersect.

[0029] Determine line segments straddle and straddle The conditions are: (1), where, Refer to Starting point The vector ending at a certain point is used, and the same applies to other vectors. Determining the existence of intersections through a rapid exclusion crossover experiment avoids a large amount of redundant computation.

[0030] (3) Calculation of the intersection point location. Approximate intersection point longitude calculation: First, the longitude of the approximate intersection point needs to be determined quickly. The ground trajectory of a satellite's orbit around the Earth can be divided into two arc segments: the ascending orbit and the descending orbit. Assuming the distribution of the ascending and descending orbits, the ascending and descending orbits of the same satellite exhibit symmetry. When the orbit measurement data is complete, based on this symmetry, the approximate intersection point's longitude can be obtained by connecting the four endpoints of the two orbits.

[0031] Let the endpoints of the ascending and descending orbits be respectively , and , The longitude of the intersection of the lines connecting them This is the approximate longitude of the intersection point: (2), where, , These are the projection values ​​of the endpoint plane coordinates. The symmetry between the ascending and descending orbits allows for rapid calculation of the approximate longitude of the intersection point, with an error typically less than 0.5°.

[0032] Some satellite altimetry data may be incomplete due to various reasons, making it impossible to quickly calculate the approximate longitude of the intersection point using endpoints. Based on the symmetry between complete ascending and descending orbits, if there is an intersection point between the two orbits, then two points with the same latitude on the two orbits... , The average longitude of the intersection is close to the longitude of the intersection point, and can also be used as a rough estimate of the longitude of the intersection point. The calculation method is as follows: (3), among which, , They are respectively , Longitude values ​​of two points.

[0033] Precise location calculation of the intersection: Determining the approximate longitude of the intersection through track symmetry. After that, with Centered on the longitude axis, neighboring points on the ascending and descending orbits are selected to form a calculation window, constraining the longitude range of the selected measurement points. Assume the latitude and longitude of the measurement points on the ascending and descending orbits within the calculation window are as follows: , , , Polynomial fitting was used for the ascending trajectory data: (4) After obtaining the fitting result of the ascending trajectory, substitute it into the longitude value of the measuring point of the descending trajectory within the calculation window. Calculate the corresponding ascending orbit latitude value. ,Will and Subtracting the differences yields a set of sorted differences. Within this set, we find two sets of ascending and descending trajectory points with changing signs. Using the data from these two sets of points, we calculate the intersection of line segments, ultimately obtaining the precise latitude and longitude coordinates of the intersection point. (5), among which, , Let these be the longitude and latitude of the intersection point, respectively. Assume the selected ascending point is the [missing value]. The and the first The first ascending point, the selected descending point position. The and the first indivual.

[0034] The performance of the novel multi-factor constrained fast crossover algorithm proposed in this example is verified below. The study uses SWOT satellite observation data jointly conducted by NASA, CNES, CSA, and UKSA on December 16, 2022. The SWOT satellite observation plan includes a 1-day rapid sampling phase and a 21-day routine science phase. In this example, the Level 2 low-frequency product (L2_LR_SSH) and Level 3 low-frequency product (L3_LR_SSH) from November 2, 2023 to February 13, 2024 are selected for crossover point positioning and sea surface height calculation. The data used in this invention covers 5 observation periods, each containing approximately 580 valid orbital data points, spatially covering approximately ±78° of global latitude.

[0035] The study areas are: 110°E~120°E, 5°N~25°N, 120°E~130°E, 5°N~25°N, 145°E~155°E, and 35°N~55°N. To verify the reliability of the calculation results of this invention, the present invention conducts cross-point positioning and sea surface height calculation studies in the selected areas. The selection of these areas takes into account the latitudinal span, the diversity of seabed topography, and the complexity of ocean dynamic processes, which can comprehensively verify the adaptability of the algorithm in different environments.

[0036] To avoid the exclusion of certain orbital data due to discrete sampling where the orbit crosses an area but there are no observation points in the area, the absolute values ​​of the latitude and longitude differences between all adjacent measurement points are calculated. The absolute values ​​of all differences are less than 0.3°. The boundary of the study area is expanded, and ascending and descending orbital data related to the study area are screened out to reduce invalid calculations.

[0037] First, the approximate longitude of the intersection point is calculated. The approximate longitude is quickly estimated by connecting the endpoints to the intersection point, providing a reference for constraining the calculation window for the precise intersection point. After obtaining the approximate longitude, constraints are applied to the longitude range to define the calculation window. Figure 4 This is a schematic diagram of a window for calculating precise intersection points based on satellite data.

[0038] like Figure 4 As shown, assuming and Let be the boundary of a segment in the piecewise fitting method, and let the intersection point fall exactly within that segment. Then the window... This refers to the window used for polynomial fitting and precise intersection point calculation in the piecewise fitting method, and this window increases rapidly with the amount of data on the ascending or descending trajectory; while FCMC only needs to maintain a constant size. Performing polynomial fitting and latitude difference calculations within the window ensures both the accuracy of the polynomial fitting and significantly improves computational efficiency.

[0039] After determining the calculation window, polynomial fitting is performed on the ascending orbit data within the window to calculate the ascending orbit latitude value corresponding to the longitude of each descending orbit point. Then, the calculated ascending orbit latitude value is subtracted from the descending orbit latitude value corresponding to the longitude to obtain a set of differences. By judging the change of positive and negative signs, two sets of points that can be used to calculate the intersection point are located, and the longitude and latitude coordinates of the precise intersection point are solved by using the intersection of line segments.

[0040] This example uses piecewise fitting, grid method, and the FCMC proposed in the study to calculate the intersection point position. The piecewise fitting method uses a 12-segment segmentation method with good fitting accuracy (segmentation method: -90° ~ -65° ~ -60° ~ -50° ~ -40° ~ -20° ~ 0° ~ 20° ~ 40° ~ 50° ~ 60° ~ 65° ~ 90°), while the grid method divides the study area into 1′×1′ resolution grids.

[0041] This example uses different methods to calculate the intersection point location, and then plots the intersection point location, the original measurement point location, and the satellite trajectory line on the same graph. Figure 5 This is a partial display of the calculation results using the same SWOT wide-area data from different methods.

[0042] like Figure 5 As shown, black dots represent intersections; blue and red dots represent the measuring points and trajectory lines of the ascending and descending tracks, respectively; and cyan lines represent the grid lines used in the grid method. Regarding accuracy, Figure 5 (c) It can visually show that the deviation between the intersection positions calculated by the grid method and the actual positions is large; according to Figure 5(a) and Figure 5 As shown in (b), the results of FCMC and piecewise fitting demonstrate that FCMC reduces the error to less than 5 seconds, compared to the at least 10 seconds error of the piecewise fitting method. Regarding the number of crossover points, due to the wide-span characteristics of SWOT data, there should theoretically be 4761 valid crossover points. Both FCMC and the piecewise fitting method calculated 4761 points, perfectly matching the theoretical value. However, the grid method calculated 9361 crossover points, far exceeding the theoretical value. This problem was addressed through further analysis... Figure 5 Analysis reveals that when the density of measurement points along the satellite trajectory is high, the grid method incorrectly identifies a large number of non-real intersections. This exposes that while the grid method has the advantage of high computational efficiency, it has significant errors in intersection location. Its characteristics also determine that the grid method is only suitable for preliminary intersection location estimation and cannot support the construction of high-precision sea surface height models. In conclusion, FCMC exhibits the best computational accuracy among the three methods.

[0043] Because the study area selected in this example is relatively large, two trajectories (pass 006 and pass 159 in SWOT L3_LR_SSHcycle006) were chosen to demonstrate the intersection point calculation results, as follows: Figure 6 As shown.

[0044] according to Figure 5 (a) and Figure 6 It can be further verified that the accuracy of FCMC in calculating the intersection point position is stably controlled within 5 seconds, which is sufficient for constructing sea surface height models with higher spatial resolution. In addition to comparing the differences in intersection point positioning accuracy among various methods, this invention summarizes the results in the form of a bar chart for a more comprehensive and intuitive comparative analysis, such as... Figure 7 As shown.

[0045] Figure 7 The time consumption of each method is displayed more intuitively. FCMC achieves a significant improvement in computational efficiency compared to the piecewise fitting method because it avoids redundant calculations, simplifies the calculation steps while ensuring accuracy and avoiding missing intersection points, and greatly reduces computation time. Compared to other methods, although the grid method takes the least time, its calculated position results obviously differ the most from the actual intersection point positions.

[0046] To more intuitively demonstrate the efficiency improvement of FCMC compared to piecewise fitting, this example presents the time improvement rate of FCMC and displays it using a bar chart, such as... Figure 8 As shown, this more intuitively reflects the significant efficiency improvement of the two methods. The time improvement rate is calculated as follows: (6), among which, When using the piecewise fitting method, Used for FCMC.

[0047] The calculation results from the three study areas reveal that the grid method's algorithmic characteristics cause significant deviations between the located intersection points and the actual situation, exceeding 1°. The piecewise fitting method yields better accuracy in calculating intersection point positions, but still exceeds 10 seconds. However, the FCMC method performs significantly better, with its positioning error consistently controlled within 5 seconds. Regarding the number of intersection points, the FCMC method calculates the closest to the actual number. The grid method calculates 2.5 times more points than the FCMC method, indicating that it calculates far more intersection points than actually exist. This results in a large number of invalid points in the results, negatively impacting the efficiency of subsequent calculations. The piecewise fitting method calculates slightly fewer intersection points than the FCMC method, showing some omissions in each region.

[0048] Regarding the efficiency of intersection point calculation, the piecewise fitting method relies on a large number of fitting operations to determine the intersection point location, resulting in significant time consumption. While the grid method is the fastest at obtaining intersection point positions, the significant errors in its calculation results mean that this method is unsuitable for high-precision intersection point positioning and sea surface height calculation. In contrast, FCMC improves computational efficiency by limiting the calculation window, reducing the fitting difficulty and computation, thus achieving a synergistic optimization of efficiency improvement and high accuracy. Calculation results from three study areas show that FCMC is at least 45% more efficient than the piecewise fitting method. Therefore, FCMC significantly improves computational efficiency while ensuring accurate intersection point exploration and positioning, and can still perform the task of determining intersection point positions well even with large amounts of data.

[0049] This example further utilizes a novel multi-factor constrained fast crossover algorithm to calculate the average sea level height: After calculating the crossover point location, the inverse distance weighting method can be used to interpolate the measurement data near the crossover point location to obtain the sea level height data at the crossover point. (7), among which, , This represents the sea level height at a known point. For the first The spherical distance between the point and the point to be calculated.

[0050] To avoid the influence of distant points on the sea level height values ​​at the intersection, the weighting coefficients are modified to obtain an exponential inverse distance weighting method. This method can rapidly reduce the influence of distant measuring points, and can be based on the following formula: (8), among which, For the first The weight coefficients of the points, after modification . Figure 9 The weight of a single point is described by different The impact. The larger the value, the faster the influence of the distant measuring point on the intersection point decays.

[0051] To test in actual calculations The specific impact of the selected values ​​on the calculation results is illustrated using data from the SDUST2020MSS dataset in the region 113.5–115°E, 15–16.5°N, as shown in the contour lines. Figure 10 As shown.

[0052] Due to the influence of seafloor topography, this area has an elliptical protrusion. The MSS value of the point (114°E, 16°N) within the calculated range is obtained using data from this location. The calculated MSS (in meters) for values ​​of 1, 2, 3, 5, 7, and 9 are 15.3453, 15.0872, 14.8876, 14.6493, 14.6370, and 14.6159, respectively. The MSS value for SDUST2020 at this point is 14.6407. Analysis shows that increasing... The value of makes the calculation result gradually approach the expected value and the change gradually level off. When When the value is greater than 5, the influence of distant points on the calculation is significantly reduced; however, excessively large values... Values ​​(e.g.) This can lead to an over-reliance on neighboring data in the calculation, neglecting the overall distribution, which in turn causes the MSS calculation results to deviate from the expected value (e.g., The error is higher than Therefore, the study took... Perform the calculation.

[0053] This example selects three internationally recognized mean sea level (MSS) models for comparative analysis: the DTU MSS model published by the Technical University of Denmark, the CNES-CLS MSS model developed by the French National Centre for Space Studies, and the SDUST2020MSS model developed by Shandong University of Science and Technology. Cross-validation using multi-source data ensures the accuracy and reliability of the sea level calculation results.

[0054] This example compares the average sea level height calculated using different methods with the model described above, using the root mean square error of the difference between the two as the accuracy criterion, as shown in the following formula: (9), This invention selects L3_LR_SSH cycle 006, 007, 009, and 010 data from the SWOT satellite in three study regions, calculates the intersection points using different methods, and then calculates the sea level height at the intersection points using an exponentially decaying inverse distance weighting method. The average sea level height is then used to obtain the following result: Figure 11 The scatter plot shown.

[0055] according to Figure 11 It can be seen that the intersection point distributions obtained by the grid method and the piecewise fitting method deviate significantly from the actual locations, while the intersection point distribution obtained by FCMC is closer to the actual situation. The figure also roughly shows that FCMC exhibits higher accuracy in calculating mean sea level height.

[0056] As can be seen, in calculating the intersection point location under the same sea area and conditions, the FCMC proposed in this invention improves the computational efficiency by at least 45% compared to the piecewise fitting method. In terms of accuracy, compared to the error of the piecewise fitting method (≥10s), the error of FCMC is stably controlled within 5s, with an accuracy improvement of over 50%, thus verifying that FCMC balances accuracy and efficiency in calculating intersection points. Based on FCMC, the mean sea level height is calculated, and the RMSE of the FCMC calculation results are 0.1151m and 0.1179m respectively compared to the SDUST2020 and CLS15MSS models, demonstrating high accuracy and stability. This further verifies that the FCMC method is highly efficient in both accuracy and computation, providing an efficient and feasible means for obtaining sea level height.

Claims

1. A method for improving the accuracy of altimeter satellite trajectory intersection points based on multiple factor constraints, characterized in that, Includes the following steps: Step 1: Data pre-screening. The input ascending and descending orbit data are pre-screened. Based on the boundary of the study area, the data is extended by k° along the latitude and longitude directions. k is set according to the average spacing of the selected satellite observation points to avoid the situation where the orbit crosses the area but there are no observation points in the area due to discrete sampling, which would cause the orbit data to be excluded. In the end, only the orbit data with at least one observation point located in the extended area are retained, and the rest of the orbits are directly removed to reduce invalid calculations. Step 2: Determine if an intersection point exists. First, perform a rapid rejection test: determine whether the diagonal bounding boxes formed by the track endpoints overlap, dividing it into three cases: overlapping rectangles and intersecting tracks, overlapping rectangles but non-intersecting tracks, and non-overlapping rectangles and non-intersecting tracks. Among these, overlapping rectangles do not necessarily indicate that the tracks intersect; however, if the bounding boxes do not overlap, then the two tracks definitely do not have an intersection point, which can effectively avoid including non-intersecting tracks in subsequent calculations. The straddle test determines whether two line segments are straddling each other by calculating the cross product of their vectors. If two line segments straddle each other, they intersect, and the test results in a straddle test. straddle and straddle The conditions are: (1), where, Refer to Starting point For vectors ending at a certain point, and similarly for other vectors, the existence of intersections can be determined by a rapid exclusion crossover experiment, which can avoid a lot of redundant calculations. Step 3: Calculate the intersection point location, which includes: Longitude calculation of approximate intersection point: First, it is necessary to quickly determine the longitude of the approximate intersection point. The ground trajectory of a satellite orbiting the Earth can be divided into two arcs, namely the ascending orbit and the descending orbit. Assuming the ascending orbit and the descending orbit, the ascending orbit and the descending orbit of the same satellite are symmetrical. When the orbit measurement data is complete, based on its symmetrical characteristics, the longitude of the approximate intersection point can be obtained by connecting the four endpoints of the two orbits. Let the endpoints of the ascending and descending orbits be respectively , and , The longitude of the intersection of the lines connecting them This is the approximate longitude of the intersection point: (2), where, , Using the endpoint plane coordinate projection values, the approximate longitude of the intersection point is quickly calculated by leveraging the symmetry between the ascending and descending orbits, with an error of less than 0.5°. For partially missing satellite altimetry data where the approximate longitude of the intersection point cannot be quickly calculated using endpoints, based on the symmetry between the complete ascending and descending orbits, if there is an intersection point between the two orbits, then two points with the same latitude on the two orbits... , The average longitude of the intersection is close to the longitude of the intersection point, and can also be used as a rough estimate of the longitude of the intersection point. The calculation method is as follows: (3), among which, , They are respectively , Longitude values ​​of two points; Precise location calculation of the intersection: Determining the approximate longitude of the intersection through track symmetry. After that, with Centered on the longitude axis, neighboring points of the ascending and descending orbits are selected to form a calculation window, constraining the longitude range of the selected measurement points. Assume the latitude and longitude of the measurement points on the ascending and descending orbits within the calculation window are as follows: , , , Polynomial fitting was used for the ascending trajectory data: (4) After obtaining the fitting result of the ascending trajectory, substitute it into the longitude value of the measuring point of the descending trajectory within the calculation window. Calculate the corresponding ascending orbit latitude value. ,Will and Subtracting the differences yields a set of sorted differences. Within this set, we find two sets of ascending and descending trajectory points with changing signs. Using the data from these two sets of points, we perform line segment intersection calculations to obtain the precise latitude and longitude coordinates of the intersection point. (5), among which, , Let these be the longitude and latitude of the intersection point, respectively. Assume the selected ascending point is the [missing value]. The and the first The first ascending orbit point, the selected descending orbit point position. The and the first indivual.

2. The method for improving the accuracy of altimetry satellite trajectory intersections based on multiple factor constraints according to claim 1, characterized in that, After calculating the location of the intersection, the sea level height at the intersection is calculated by interpolating the data from the measuring points near the intersection using the inverse distance weighting method. (7), among which, , This represents the sea level height at a known point. For the first The spherical distance between the point and the point to be calculated.

3. The method for improving the accuracy of altimetry satellite trajectory intersections based on multiple factor constraints according to claim 2, characterized in that, To avoid the influence of distant points on the sea level height values ​​at the intersection, the weighting coefficients are modified to obtain an exponential inverse distance weighting method, which reduces the influence of distant measuring points. The specific formula is as follows: (8), among which, For the first The weight coefficients of the points, after modification , The larger the value, the faster the influence of the distant measuring point on the intersection point decays.

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