Water-depth-oriented photon counting lidar slope-aware adaptive filtering method

Abstract

The application discloses a water depth-oriented photon counting laser radar slope perception adaptive filtering method, acquires water body point cloud data of a photon counting laser radar, determines an instantaneous water surface elevation based on an elevation kernel density estimation, so as to form a candidate underwater photon data set; a local window is moved along a track direction, a local slope surface direction and a corresponding slope angle are estimated in each local window by using PCA, a slope surface alignment coordinate system is constructed, and the candidate underwater photons are uniformly converted to the slope surface alignment coordinate system; in the slope surface alignment space, kernel density peak value detection is performed on each local window by using a large-scale window and a small-scale window respectively, and double-scale soft decision fusion is performed based on a signal saliency index, so as to generate underwater terrain seed points; the underwater terrain seed points are taken as centers, adaptive elliptical filtering neighborhoods are constructed according to local photon density and slope geometric constraints, candidate underwater photons are filtered and extracted, and continuous water depth results are acquired through refraction correction.

Description

Technical Field

[0001] This invention belongs to the technical field of laser cutting, specifically relating to an adaptive filtering method for slope sensing in a photon counting lidar system for water depth applications. Background Technology

[0002] Photon-counting lidar is a novel laser detection technology that has emerged in recent years. Compared to traditional lidar, photon-counting lidar uses a high-sensitivity detector to detect individual echo photons, featuring high repetition rate, high efficiency, lightweight design, and long-range detection capabilities. When acquiring effective signals, this type of system no longer relies solely on high-energy emission to obtain high signal-to-noise ratio waveforms. Instead, it fully utilizes each echo photon and improves data processing methods to achieve effective signal extraction even under low signal-to-noise ratio conditions.

[0003] Current research indicates that photon-counting lidar possesses a certain depth detection capability. However, when the target area is water, the photon point cloud typically exhibits different distribution characteristics compared to land-based detection data. Surface-returned photons, water column-scattered photons, underwater topographic photons, and solar background noise often coexist, and the number of effective underwater photons decreases with increasing water depth, resulting in uneven distribution of surface and underwater photon signals and a low signal-to-noise ratio. Traditional filtering methods for land-based or fixed-density point clouds are prone to problems such as missed detection of weak underwater signals, false detection of background noise, and breakage of underwater topographic signals when processing water photon point clouds, making it difficult to simultaneously extract effective photons from both the surface and the bottom to form continuous depth results.

[0004] Currently, photon extraction methods for shallow seawater topography using photon-counting lidar mainly include photon density-based clustering, sliding window methods, kernel density estimation, and adaptive filtering. Spatial clustering methods such as DBSCAN and OPTICS can eliminate discrete noise photons based on local density differences, but their effectiveness is usually affected by parameters such as neighborhood scale and minimum number of points. When underwater photon density decreases rapidly with water depth or local background noise increases, it can easily lead to missed detections of weak signals in deep water. To adapt to changes in underwater photon density, adaptive elliptic filtering methods such as AVEBM improve seabed photon extraction capabilities by adjusting the search neighborhood size. Furthermore, orientation and scale adaptive filtering methods attempt to match local topographic orientation by rotating the search kernel, while sliding window and KDE methods generate topographic seed points through local density peaks to enhance extraction stability under varying photon density conditions.

[0005] However, existing photon counting lidar methods for shallow-sea topographic photon extraction still have the following problems: ① In complex reef slopes, deep channels, and locally undulating areas, underwater topographic photons are often tilted or non-horizontally distributed. Fixed-direction or single-scale filtering methods are difficult to stably adapt to local topographic orientation, which can easily cause topographic signal breaks; ② High background photons in shallow water and weak topographic signals in deep water often coexist. Fixed thresholds, fixed windows, or search neighborhoods that rely solely on local density are prone to imbalance between noise false detection and weak signal missed detection

[15] ,

[16] ; ③ When the adaptive elliptical neighborhood is controlled only by photon density, the search range may be overextended in areas with large slope changes, thereby increasing the risk of water column scattered photons being misidentified as topographic photons. The above problems directly affect the continuity, stability, and reliability of shallow-sea topographic photon extraction and depth measurement results of ICESat-2.

[0006] Therefore, to address the challenges of high noise levels, uneven distribution of effective photons, and difficulty in extracting photons from continuous terrain under complex underwater slope conditions in photon-counting lidar water point clouds, it is necessary to propose an adaptive filtering method that can simultaneously utilize statistical features of photon elevation, geometric features of local slope, and changes in local photon density, thereby improving the continuity and stability of underwater terrain photon extraction. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a slope-sensing adaptive filtering method for photon counting lidar in water depth. This method can adaptively extract effective photon signals from the water surface and underwater topography, and acquire continuous water depth data, even in situations with high photon signal noise, uneven distribution of photon signals between the water surface and underwater, and complex underwater topographic changes.

[0008] To achieve the above objectives, the present invention provides the following technical solution: An adaptive filtering method for slope sensing in a photon-counting lidar system for water depth includes the following steps: Step 1: Acquire the raw water point cloud data of the photon counting lidar and determine the instantaneous water surface elevation based on the elevation kernel density estimation to form a candidate underwater photon dataset; Step 2: Move the local window along the trajectory direction with a fixed step size, and use the principal component analysis algorithm (PCA) to estimate the local slope direction and the corresponding slope angle in each local window. In this way, construct a slope alignment coordinate system consistent with the local slope, and uniformly transform the candidate underwater photons to the slope alignment coordinate system. Step 3: Within the slope alignment space, kernel density peak detection is performed for each local window using both large-scale and small-scale windows, and dual-scale soft decision fusion is performed based on the signal significance index to generate underwater terrain seed points. Step 4: Using the underwater topography seed point as the center, construct an adaptive elliptical filter neighborhood based on the local photon density and slope geometric constraints, filter and extract candidate underwater photons, and obtain continuous water depth results after refraction correction.

[0009] Furthermore, the local center of the current local window is taken as the origin of the coordinate system, and the local slope direction is taken as the coordinate system. The axis is defined by a direction perpendicular to the local slope. Establish a coordinate system aligned with the slope axis.

[0010] In step three, the current sliding position of the local window is first determined. Establish large windows for the center and small window Gaussian kernel density estimation was performed on all candidate underwater photon elevations within each window, and the vertical slope coordinates corresponding to the maximum value of the kernel density curve were taken as the peak values ​​of the large window. and small window peak , Then in the small window peak Set half a width on both sides The vertical slope to the neighborhood is used to count the number of candidate underwater photons in the small window. The signal significance index is obtained. : in, The symbol # indicates the number of photons within the curly braces that simultaneously satisfy both conditions. This represents the pre-set peak reliability reference photon count; Then the Sigmoid function is used to express the significance index of the signal. Continuous conversion to small window weights : The vertical slope coordinates of the underwater topography seed point are then calculated using the following formula. , Finally, the sliding position of the current local window is... Transform to a slope-aligned coordinate system, using the slope-side coordinates of the underwater topography seed point. This forms the slope-aligned coordinates of the underwater topographic seed point. .

[0011] Furthermore, in step four, the first... Align the slope surfaces of the underwater terrain seed points with coordinates. As the first The center of the ellipse, with The axial direction is the direction of the major semi-axis, with The axial direction is the direction of the minor semi-axis, and its minor semi-axis Set to a fixed value, major half-axis It is determined by the candidate photon density near the seed point and the slope constraint; For the Alignment coordinates of the slope surface of any candidate underwater photon within a local window Align the coordinates of the underwater terrain seed point with the slope surface. Calculate the distance along the slope and the distance perpendicular to the slope between the two objects in a coordinate system aligned on the same slope: If a candidate underwater photon satisfies the following formula, then the candidate underwater photon is determined to be located at the underwater terrain seed point. Within the central ellipse, photons are identified and preserved as underwater terrain signal photons; If a candidate underwater photon does not satisfy the following formula, it shall be eliminated; .

[0012] Furthermore, in determining the major semi-axis First, using the orbital coordinates of the underwater terrain seed point as the center, set a width of... The window is used to count the total number of candidate underwater photons within the window. The semi-major axis of density control is calculated using the following formula. : In the formula, For reference density, For local candidate photon density, The maximum permissible semi-major axis under slope conditions can be calculated using the following formula. : In the formula, This represents the maximum permissible half-span of the ellipse along the original elevation direction. It is the short half-axis; For the first The slope angle corresponding to each underwater terrain seed point; Then the first The actual semi-major axis of the ellipse Pick and The smaller value in: .

[0013] Furthermore, using the inverse transformation of the coordinate transformation in step two, the slope-aligned coordinates of the underwater terrain signal photons after elliptical filtering are restored to the original track distance-elevation coordinates. Let the inverse transformation yield the first The original elevation of the underwater terrain signal photon is Then, the water depth information after refraction correction is calculated using the following formula. In the formula, For the first Water depth after refraction correction for underwater topographic signal photons and The refractive indices of air and seawater are respectively. This indicates the water surface elevation at the instant the underwater topographic signal photon is emitted.

[0014] Furthermore, in step two, the covariance matrix of the current local window is first calculated. And for the covariance matrix Perform eigenvalue decomposition, take the unit eigenvector corresponding to the largest eigenvalue as the main direction, i.e. the local slope direction, and calculate the slope angle from the unit eigenvector corresponding to the main direction.

[0015] Furthermore, let the first... There are a total of [number] local windows. The candidate underwater photon, the first The two-dimensional profile coordinates of the candidate underwater photons are ( The orbital distance of all candidate underwater photons within this local window is used as a reference. average and elevation average This indicates the local center of the local window. , ), First, use the following formula to calculate the covariance matrix of the current local window. , Then consider the covariance matrix Perform eigenvalue decomposition and solve ,get eigenvalues and its corresponding unit eigenvector Let the unit eigenvector corresponding to the largest eigenvalue be . ,in, and Let represent the components of the principal direction along the track distance and elevation directions, respectively. The slope angle is then calculated using the following formula. , Then, using the following formula, the candidate underwater photons are uniformly transformed to a slope-aligned coordinate system. In the formula, Candidate underwater photons Slope-direction coordinates relative to the local center; Candidate underwater photons Vertical coordinates.

[0016] Furthermore, in step one, the Gaussian kernel density is estimated for the elevation of all photons using the following formula: In the formula, For elevation The KDE value at that location is the kernel density value. The number of photons used for water surface identification. For the first The elevation of a photon For elevation KDE bandwidth, The elevation corresponding to the maximum value of the kernel density curve is defined as the instantaneous water surface elevation. : Photons that satisfy the following formula are classified as underwater photons. Let it be denoted as the candidate underwater photon set. In the formula, For the first One photon, Indicates the lower boundary and upper boundary. From instantaneous water surface elevation Searching for the KDE value in the direction of increasing elevation until it decreases to the instantaneous water surface elevation. of The elevation corresponding to the time multiplier. This represents the proportion of the water surface boundary.

[0017] Compared with the prior art, the beneficial effects of the present invention are: (1) The elevation KDE uses the stable density peak of the water surface photons to determine the instantaneous water surface position and identify the candidate underwater photon set. This can reduce the influence of artificial threshold changes on the candidate underwater photon division and provide an accurate data basis for subsequent calculations. (2) The slope direction is estimated by PCA, the slope angle is calculated, and a slope alignment coordinate system is established. Then, the candidate underwater photons are uniformly converted to the slope alignment coordinate system, so that the photons of the inclined terrain are more concentrated in the vertical direction, which can improve the stability of KDE peak positioning. (3) Kernel density peak detection is performed using large-scale windows and small-scale windows respectively. The large-scale window provides macro-topographic reference, while the small-scale window reflects local undulations. Then, based on the signal saliency index (SSI), dual-scale peak soft decision fusion is performed to generate underwater topographic seed points, which can take into account both topographic continuity and local response. (4) An adaptive ellipse is constructed with the underwater topographic seed point as the center, and the major semi-axis is constrained by the local density and slope to achieve adaptive filtering. This can expand the search range along the slope in low-density areas and reduce vertical false detections at steep slopes. (5) After the coordinates of the underwater topographic photons identified by the filter are inversely transformed back to the original coordinate system, refraction correction is performed. The true water depth after refraction correction can be obtained from the apparent water depth. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the overall process of the method described in the embodiments of the present invention; Figure 2 This is a schematic diagram of the original water point cloud distribution of the photon counting lidar method described in this embodiment of the invention; Figure 3 This is a schematic diagram of underwater topographic photon extraction and water depth results according to the method described in this embodiment of the invention; Figure 4 This is a schematic diagram of the dual-scale KDE peak detection and SSI soft decision fusion method described in the embodiments of the present invention; Figure 5 This is a local topographic photon extraction result image of a complex shallow water topographic area using the method described in this embodiment of the invention; Figure 6 This is a schematic diagram illustrating the water depth accuracy verification of the method described in an embodiment of the present invention. Detailed Implementation

[0019] To make the technical means, creative features, objectives and effects of this invention easier to understand, the following embodiments, in conjunction with the accompanying drawings, specifically illustrate the photon counting lidar slope sensing adaptive filtering method for water depth of this invention. It should be noted that the description of these embodiments is for the purpose of helping to understand this invention, but does not constitute a limitation of this invention.

[0020] To address the issues of mixed surface and underwater photons, sparse photons in deep water topography, and easily broken topographic signals under complex slope conditions, such as... Figure 1As shown, this invention provides a slope-sensing adaptive filtering method for photon-counting lidar in water depth. The method sequentially performs water surface identification and candidate photon generation, local slope estimation, slope alignment coordinate system generation, dual-scale seed point generation based on signal saliency index fusion, seed point-guided adaptive ellipse filtering, and refraction correction. This acquires the original water point cloud data from the photon-counting lidar and determines the instantaneous water surface elevation based on elevation kernel density estimation to form a candidate underwater photon dataset. A local window is moved along the trajectory direction with a fixed step size, and principal component analysis (PCA) is applied within each local window. A method estimates the local slope direction and corresponding slope angle to construct a slope-aligned coordinate system consistent with the local slope, and then uniformly transforms candidate underwater photons to this coordinate system. Within the slope-aligned space, kernel density peak detection is performed for each local window using both large-scale and small-scale windows, and dual-scale soft decision fusion is performed based on the signal significance index to generate underwater terrain seed points. Centered on the underwater terrain seed points, an adaptive elliptical filtering neighborhood is constructed based on local photon density and slope geometric constraints to filter and extract candidate underwater photons, and continuous water depth results are obtained after refraction correction. Validation results using spaceborne photon counting lidar data as an example show that this method has good terrain tracking capabilities under complex slope conditions, high background photons, and weak deep-water signals. The R² values ​​for the five validation trajectories are 0.977–0.995, RMSE is 0.38–0.54 m, and MAE is 0.26–0.39 m.

[0021] Specifically as follows: S1: Surface Recognition and Candidate Underwater Photon Formation By acquiring the original water body photon point cloud, the instantaneous water surface elevation and the range of photons on the water surface are determined using KDE (Kinetic Geometry) to form a candidate underwater photon dataset. Then, coarse denoising is performed on the candidate underwater photon dataset. This step outputs the instantaneous water surface elevation to S2. and candidate underwater photon set . Figure 2 Composed of four original ICESAT-2 point cloud profiles: Figure 2 (a) Located in the upper left, this is track 20230722GT1L of Dongsha Atoll, showing the topography of the transition from reef flat to reef slope; Figure 2 (b) Located in the upper right, it is the Qilianyu 20240707GT2L track, showing the shallow water platform and local undulations; Figure 2 (c) Located in the lower left, it is the Bahamas 20240317GT1R orbit. The profile is relatively long, with a wide distribution of photons in the water column background and obvious local topographic changes. Figure 2(d) Located in the lower right, it represents the Oahu 20210103GT3L orbit, with a large water depth range and relatively sparse topographic echoes in the deep water section. The four sub-images together provide the original input under conditions of complex slopes, shallow water undulations, high background photons, and weak signals in deep water.

[0022] Photons returning from the water surface typically form the most prominent aggregation band along the elevation direction; therefore, a Gaussian kernel density estimate is used for the elevation of all photons. (1) In the formula, For elevation The KDE value at that location is the kernel density value; The number of photons used for water surface identification; For the first The elevation of a photon; The elevation KDE bandwidth is used to control the smoothness of the density curve; in this example, it is set to 0.01 m.

[0023] The elevation corresponding to the maximum value of the kernel density curve is defined as the instantaneous water surface elevation. : (2) To determine the range of photons on the water surface, from Searching for the KDE value in the direction of increasing elevation until it drops to its peak value, which represents the instantaneous water surface elevation. of The elevation corresponding to the time multiplication factor is recorded as the upper boundary. The lower boundary is determined symmetrically according to the water surface elevation, that is... . This is the water surface boundary ratio, used only in this step; in this example, it is 0.10.

[0024] (3) (4) In the formula, For the first A photon. A photon satisfying equation (3) is classified as a surface photon; a photon satisfying equation (4) is classified as an underwater photon. Let it be denoted as the candidate underwater photon set.

[0025] Candidate underwater photons may still contain discrete water column noise and background noise; therefore, DBSCAN is used for coarse denoising. The neighborhood radius of DBSCAN is used to limit the spatial distance between adjacent photons, and the minimum neighborhood photon count is used to determine whether a density-connected cluster can be formed; isolated photons that cannot be classified into valid clusters are deleted. To avoid introducing new set symbols, the following text will continue to use the symbols... This represents the candidate underwater photon set after coarse denoising, and it is used as candidate data for S2 to S4.

[0026] S2: Local slope estimation, generation of slope-aligned coordinate system S21: Move the local window along the trajectory direction with a fixed step size, and estimate the local slope orientation using PCA within each local window. This step receives the output of S1. Output the local center of each sliding position to S3 ( , and slope angle .

[0027] The sliding position is the coordinate along the track where the center of the local window is located after each movement. It is only a reference position that defines the local calculation range, not a specific photon, and is not required to coincide with the coordinates of any photon. For each sliding position, the local photon selection, coordinate centering, covariance matrix calculation, and principal direction solution are performed sequentially.

[0028] Let the starting coordinates along the track be... The distance between adjacent sliding positions is Then the first The sliding positions are ,in =1, 2, ..., J, where J is the total number of sliding positions, and the window moves forward each time... This forms the next sliding position. Establish a track width of [missing information] centered on [missing information] A local window, from Select from those that satisfy | - |≤ / 2 of the candidate photons. This embodiment takes =50 m =5 m.

[0029] Let the first There are a total of [number] local windows. The candidate photon, the first The two-dimensional profile coordinates of a photon are ( , First, calculate the average distance along the track within the local window. and the average elevation The two average values ​​are used to represent the local center of the local point cloud. Then, the coordinates of each photon are subtracted from these two average values ​​to obtain its position relative to the local center. - , - This process only translates the point cloud without changing the relative positions between photons or the actual slope, allowing PCA to analyze only the extension direction of the local point cloud itself; this local center also serves as a reference point for S3 coordinate rotation and seed point coordinate restoration.

[0030] Calculate the first based on the centered coordinates. The covariance matrix of each sliding position This matrix describes the joint discretization of the local point cloud along the track distance and elevation, and its calculation formula is: (5) The direct input to equation (5) is the first The covariance matrix of each sliding position ; It is an eigenvalue and their corresponding eigenvectors The number. Because... Given a two-dimensional matrix, solving it yields two sets of eigenvalues ​​and a unit eigenvector, i.e. Arrange the eigenvalues ​​according to arrangement.

[0031] Take the unit eigenvector corresponding to the largest eigenvalue The main direction is the direction of the local slope, among which and These are the components of the principal direction along the track distance and elevation directions, respectively. Since an eigenvector and its inverse vector represent the same principal axis, when... When <0, both components are multiplied by -1 to ensure the principal direction always points in the direction of increasing distance along the track; when When =0, take ≥0.

[0032] No. Slope angle at each sliding position Calculate using the following formula: (6) The slope angle in equation (6) This represents the angle between the local slope direction and the positive direction of the distance along the track; this angle is also used for the first... The large and small windows at the sliding positions allow candidate underwater photons within the two windows to be converted to the same slope-aligned coordinate system.

[0033] S22: Using the local center of the current local window as the origin of the coordinate system, and the local slope direction as the coordinate system... The axis, perpendicular to the local slope direction, is used as... Establish a coordinate system aligned with the slope axis.

[0034] During coordinate transformation, the local center coordinate is first subtracted from the original coordinates of each candidate underwater photon. , This makes the center of the current window the origin of the coordinate system aligned with the slope; then, according to the slope angle... Rotation. Subtracting the center coordinates will not change the slope; it only prevents irrelevant offsets in the absolute position along the track and absolute elevation after rotation. The axis is parallel to the local slope. The axis is perpendicular to the direction of the local slope.

[0035] (7) In the formula, For photons Slope-direction coordinates relative to the local center; Its vertical coordinate represents the distance the photon deviates from the local slope. Direction depends on slope angle The change is not equivalent to the original elevation direction. Subsequent KDE only applies to... Perform one-dimensional peak finding.

[0036] S3: Two-scale seed point generation based on signal saliency index fusion Within the slope-aligned coordinate system, kernel density peak detection is performed using both large-scale and small-scale windows. A dual-scale soft decision fusion based on the signal significance index is then performed to generate underwater topographic seed points. The dual-scale KDE peak detection and SSI soft decision fusion process is as follows: Figure 4 As shown, where, Figure 4 (a) Located on the left, showing the original candidate underwater photons of the complex reef slope section, which includes rapid topographic changes and residual background photons; Figure 4 (b) Located on the right, the green dots are seed points formed by the KDE peaks of the large window, which are used to reflect the relatively stable overall terrain trend; the orange dots are seed points formed by the KDE peaks of the small window, which are used to track local undulations; and the blue dots are seed points after SSI fusion, which are used to balance the overall continuity of the seed point sequence and the local tracking ability.

[0037] Although photons on the same inclined slope have different positions along their orbits and different original elevations, they have similar vertical coordinates after rotation. Therefore, in Directional KDE values ​​can reduce elevation broadening caused by slope, resulting in a more concentrated density peak for terrain-related photons.

[0038] This step continues to use the Gaussian KDE calculation method of Equation (1), but replaces the original photon elevation in Equation (1) with the rotated vertical slope coordinates.

[0039] At the same sliding position Establish a large window for the center and small window A large window covers a longer area along the track, providing a stable macroscopic topographic reference; a smaller window covers a shorter area near the current location, reflecting local undulations. Both windows use the same local center and slope angle. , Example =500 m =50 m.

[0040] The vertical slope coordinates of photons within the large and small windows are estimated using KDE according to equation (1), and the vertical slope coordinate corresponding to the maximum value of the kernel density curve is taken as the peak value of the large window. and small window peak In the calculation, the elevation in equation (1) is replaced with the vertical slope coordinate. .

[0041] The large window peak and small window peak here are statistical positions of the seabed on the vertical slope, not a photon directly selected from the candidate photons.

[0042] exist Set half a width on both sides Count the number of candidate photons in the small window within the vertical slope neighborhood. The signal significance index is obtained. : (8) in, The symbol # indicates the number of photons within the curly braces that simultaneously satisfy two conditions: the first condition indicates that the candidate underwater photon is located at the [missing information]. Within a small window, the second condition indicates that its vertical slope coordinates are located on either side of the KDE peak of the small window, with a half-width of... Within the neighborhood; The preset peak reliability reference photon count is used to determine whether the actual number of photons near the KDE peak in the small window is sufficient. In this example, it is set to... It is 10.

[0043] Small window peak reliability used to compare different sliding positions The larger the value, the more sufficient the actual photon support for the peak value, and the more reliable the peak value is, indicating that the actual photon support near the small window peak value is more sufficient. The smaller the value, the more likely the peak value of the small window is to be formed by a small amount of noise, and more should be relied upon for the peak value of the large window.

[0044] To avoid sudden switching between large and small windows, the Sigmoid function is used. Continuous conversion to small window weights : (9) In the formula, Located between 0 and 1, it represents the weight of the peak value in the small window; The weight of the peak value in the large window; The sigmoid slope controls the rate of change of the weights; the constant 0.5 indicates that when... When the value is 0.5, the two peak weights are equal.

[0045] The underwater topography seed point is not a raw photon directly selected from the candidate photons, but rather a local seabed statistical point generated at the center of each local window. The coordinates along the track corresponding to the sliding position of each local window are: The peak value of the vertical slope KDE after fusion is denoted as .

[0046] First, calculate the vertical slope coordinates of the underwater topographic seed point according to formula (10). ; (10) The output of equation (10) It belongs to the slope-aligned coordinate system.

[0047] Then take the coordinates along the track where the current local window's sliding position is located. And calculate its corresponding slope coordinates according to the coordinate transformation relationship of equation (7). ,in, For step two The local center of a local window. The slope angle of this local window is used to obtain the coordinates of the underwater topographic seed point in the slope-aligned coordinate system. The underwater terrain seed points of each local window are arranged according to the original track distance to form the seabed terrain seed skeleton.

[0048] S4: Adaptive elliptic filtering guided by underwater terrain seed points and outputting the water depth along the track after refraction correction. Centered on the underwater topography seed point, an adaptive elliptical filter neighborhood is constructed based on local photon density and slope geometric constraints. The underwater topography photons are filtered and extracted, and continuous water depth results are obtained after refraction correction.

[0049] When performing ellipse screening, the candidate underwater photons need to be converted from S2 to slope-aligned coordinates beforehand. The underwater terrain seed points generated by S3 also belong to the slope-aligned coordinate system. In this way, the ellipse center, candidate underwater photons, and ellipse discrimination distance are all represented in the slope-aligned coordinate system.

[0050] For the first A seed point for underwater terrain is used, and its coordinates are aligned with the transformed slope surface. As the center of the ellipse, with The axial direction is the direction of the major semi-axis, with The axial direction is the direction of the minor semi-axis. (Minor semi-axis) For a fixed value, the example uses 0.5m; the long half-shaft The seed point is determined by both the candidate photon density and the slope constraint, as follows: Centered on the orbital coordinates of the underwater topography seed point, within a width of Count the number of candidate photons within the window And calculate the local candidate photon density according to equation (11). and density-controlled long semi-axis : (11) In the formula, This represents the number of candidate photons within the window. The width of the window; For local candidate photon densities, the instance takes the photon density per square meter; For reference density, the example uses 25 photons / m; The semi-major axis is obtained based on the local density.

[0051] To limit the expansion of the ellipse in the elevation direction when the slope is large, the maximum allowable semi-major axis under the slope condition is calculated according to equation (12). : (12) In the formula, The maximum allowable half-span of the ellipse in the original elevation direction is 2.0 m in this example; It is the short half-axis; For the first The slope angle corresponding to each underwater terrain seed point; This represents the upper limit of the major semi-axis allowed by the slope conditions.

[0052] No. The actual semi-major axis of the ellipse is taken as and The smaller value in: (13) For the Alignment coordinates of the slope surface of any candidate underwater photon within a local window Align the slope of the seed point with coordinates Calculate the slope-direction distance and vertical distance of the candidate photon relative to the seed point: In the formula, and These represent the distances of the candidate photon relative to the seed point along the slope and perpendicular to the slope, respectively, in the slope-aligned coordinate system. The discrimination formula for elliptical denoising is: (14) When a candidate photon satisfies equation (14), it is located at the seed point. Photons located inside the ellipse centered at a seed point are identified and retained as underwater topographic signal photons; if equation (14) is not satisfied, the photons located outside the ellipse are not retained by the ellipse. Candidate photons are identified as underwater topographic signal photons as long as they are located inside the ellipse corresponding to any seed point.

[0053] Photons refract at the air-seawater interface; therefore, the difference between the water surface elevation and the original underwater photon elevation is the uncorrected apparent water depth. For each terrain photon obtained through elliptical filtering, the output of S1 is used... Perform vertical refractive index ratio correction.

[0054] Elliptical filtering yields the slope-aligned coordinates of underwater topographic signal photons. Before refraction correction, the inverse transformation of equation (7) is used to restore them to their original orbital distance-elevation coordinates; let the first... The original elevation of each terrain photon is ,but This indicates the apparent depth of the water relative to the instantaneous water surface.

[0055] (15) In the formula, For the first Water depth after refraction correction for topographic photons; and The refractive indices of air and seawater are respectively; the example uses... =1.00、 =1.34; From S1.

[0056] Overall underwater topography photon extraction and water depth results are as follows Figure 3 As shown, the local underwater topographic photon extraction results for complex shallow water terrain areas are as follows: Figure 5 As shown, where, Figure 3 and Figure 2 The four representative orbits in the text correspond one-to-one. Figure 3 (a) Top left Figure 3 (b) Top right Figure 3 (c) Bottom left and Figure 3(d) The bottom right figures show the processing results for Dongsha Atoll 20230722GT1L, Qilianyu Islands 20240707GT2L, Bahamas 20240317GT1R, and Oahu 20210103GT3L. In each sub-figure, gray dots represent the original photons, blue dots represent the identified surface photons, orange dots represent underwater topographic photons before refraction correction, and red dots represent underwater topographic photons after refraction correction. The red results are shifted towards deeper water relative to the orange results, indicating that the apparent depth deviation caused by surface refraction has been corrected.

[0057] Figure 5 This is used to illustrate the guiding role of underwater topographic seed points in local extraction, among which Figure 5 (a) Located at the top, a complete profile is given and complex slope sections are marked with red boxes; Figure 5 (b) Located in the lower left, magnified to show the continuous distribution of underwater topographic seed points along the main seabed photon band in this section; Figure 5 (c) Located in the lower right, it shows that after elliptical filtering guided by underwater topography seed points, the photons are concentrated in the seabed topography zone, and the background photons outside the zone are removed.

[0058] To verify the feasibility of this invention, in a specific embodiment, shallow water point cloud data from a spaceborne photon-counting lidar is used as test data. This data can record photon time, spatial location, and elevation information, and can be converted into a distance-elevation profile point cloud along the orbit. It should be noted that the use of spaceborne photon-counting lidar data in this embodiment is only for illustrating the implementation of the technical solution of this invention and does not constitute a limitation on the data source and application platform of this invention; this invention is also applicable to water point cloud data from airborne or other platforms acquired by photon-counting lidar.

[0059] In practice, ICESat-2ATL03 photon data from Dongsha Atoll, Qilianyu Islands, the Bahamas, and Oahu, Hawaii, were selected. Figure 2A representative track from each of the four regions is presented. First, the latitude, longitude, and elevation data of each track are converted into a track-distance-elevation profile. Then, in step S1, the water surface is identified using elevation KDE to generate candidate underwater photons, and isolated noise is removed using DBSCAN. Next, in step S2, the slope is estimated using a 50 m local window and a 5 m step size, and transformed to a slope-aligned coordinate system. In step S3, KDE peaks are detected within a 500 m large window and a 50 m small window, respectively, and SSI fusion is used to generate underwater topographic seed points with the sliding window center as the original track-distance coordinate system. In step S4, using the underwater topographic seed points as the center of an ellipse, the major semi-axis is determined based on local photon density and slope, and underwater topographic photons are filtered with a minor semi-axis of 0.5 m. Finally, the filtered results are inversely transformed back to the original track-distance-elevation coordinate system, and refraction correction is performed to obtain the true water depth. For the Oahu data, the refraction-corrected water depth is further spatially matched with the NOAA airborne lidar depth sounding DEM to verify accuracy.

[0060] The results demonstrate that in shallow sea areas with complex slopes, high background noise, and weak deep-water signals, this invention can extract topographic photons distributed along the main underwater topographic trend and form continuous water depth results through refraction correction. In the verification example based on an airborne lidar bathymetry DEM, the coefficient of determination (R²) for the five test profiles is 0.977–0.995, the RMSE is 0.38–0.54 m, and the MAE is 0.26–0.39 m. These results indicate that this invention can obtain relatively stable water depth extraction results while maintaining the continuity of underwater topographic photons. Water depth accuracy verification results are as follows: Figure 6 As shown, there are five precision verification subplots from left to right. The horizontal axis represents the DEM water depth, the vertical axis represents the ICESat-2 water depth extracted by this invention, the black dashed line is the 1:1 reference line, the red line is the fitting line, and the scatter color represents the sample density. Figure 6 (a) is 20190609GT1L, R²=0.995, RMSE=0.50 m, MAE=0.34 m, Bias=0.17 m; Figure 6 (b) is 20240627GT3L, R²=0.990, RMSE=0.38 m, MAE=0.26 m, Bias=0.13 m; Figure 6 (c) is 20210103GT3L, R²=0.987, RMSE=0.42 m, MAE=0.32 m, Bias=0.20 m; Figure 6 (d) is 20190613GT1L, R²=0.995, RMSE=0.54 m, MAE=0.39 m, Bias=0.29 m; Figure 6(e) is 20210411GT1R, R²=0.977, RMSE=0.49 m, MAE=0.35 m, Bias=0.06 m. The scatter points in the five subplots are generally close to the 1:1 reference line, indicating that the present invention has achieved sub-meter level water depth accuracy on different orbits.

[0061] In summary, based on the data characteristics of photon-counting lidar water point clouds, this invention proposes a water depth extraction method that integrates slope sensing, multi-scale seed point generation, and adaptive elliptic filtering. This method can adaptively extract effective photon signals from both the water surface and underwater topography, and acquire continuous water depth data, even in situations with high photon signal noise, uneven distribution of photon signals between the water surface and underwater, and complex underwater topographic variations.

[0062] It is important to note that the schemes and arrangements of this application shown in the exemplary embodiments are merely exemplary. Although only a few embodiments are described in detail in this disclosure, those who consult this disclosure will readily understand that many modifications are possible (e.g., variations in various parameter values ​​(temperature, power, humidity, etc.), installation arrangements, names, colors, logical orders, etc.) without substantially departing from the novel teachings and advantages of the subject matter described in this application. Therefore, all such modifications are also included within the scope of the invention, and the order or sequence of any process or method steps may be changed or rearranged according to alternative embodiments. In the claims, any "apparatus plus function" clause is intended to cover the structure described herein for performing the function, and not only structurally equivalent but also equivalent in structure. Other substitutions, modifications, alterations, and omissions may be made in the design, operation, and arrangement of the exemplary embodiments without departing from the scope of the invention. Therefore, the invention is not limited to the particular embodiments but extends to a variety of modifications that still fall within the scope of the appended claims.

[0063] Furthermore, in order to provide a concise description of exemplary embodiments, not all features of actual embodiments (i.e., those features that are not relevant to the best mode of carrying out the invention as currently considered, or those features that are not relevant to implementing the invention) may be omitted.

[0064] It should be understood that numerous specific implementation decisions can be made during the development of any practical implementation, such as in any engineering or design project. Such development efforts may be complex and time-consuming, but for those skilled in the art who benefit from this disclosure, the development effort will be a routine work of design, manufacturing, and production without requiring much experimentation.

[0065] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A slope-sensing adaptive filtering method for photon-counting lidar in water depth, characterized in that... Includes the following steps: Step 1: Acquire the raw water point cloud data of the photon counting lidar and determine the instantaneous water surface elevation based on the elevation kernel density estimation to form a candidate underwater photon dataset; Step 2: Move the local window along the trajectory direction with a fixed step size, and use the principal component analysis algorithm (PCA) to estimate the local slope direction and the corresponding slope angle in each local window. In this way, construct a slope alignment coordinate system consistent with the local slope, and uniformly transform the candidate underwater photons to the slope alignment coordinate system. Step 3: Within the slope alignment space, kernel density peak detection is performed for each local window using both large-scale and small-scale windows, and dual-scale soft decision fusion is performed based on the signal significance index to generate underwater terrain seed points. Step 4: Using the underwater topography seed point as the center, construct an adaptive elliptical filter neighborhood based on the local photon density and slope geometric constraints, filter and extract candidate underwater photons, and obtain continuous water depth results after refraction correction.

2. The photon counting lidar slope sensing adaptive filtering method for water depth as described in claim 1, characterized in that: Using the local center of the current local window as the origin of the coordinate system, and the local slope direction as the coordinate system... The axis is defined by a direction perpendicular to the local slope. Establish a coordinate system aligned with the slope axis. In step three, the current sliding position of the local window is first determined. Establish large windows for the center and small window Gaussian kernel density estimation was performed on all candidate underwater photon elevations within each window, and the vertical slope coordinates corresponding to the maximum value of the kernel density curve were taken as the peak values ​​of the large window. and small window peak , Then in the small window peak Set half a width on both sides The vertical slope to the neighborhood is used to count the number of candidate underwater photons in the small window. The signal significance index is obtained. : in, The symbol # indicates the number of photons within the curly braces that simultaneously satisfy both conditions. This represents the pre-set peak reliability reference photon count; Then the Sigmoid function is used to measure the signal significance index. Continuous conversion to small window weights : The vertical slope coordinates of the underwater topography seed point are then calculated using the following formula. , Finally, the sliding position of the current local window is... Transform to a slope-aligned coordinate system, using the slope-side coordinates of the underwater topography seed point. This forms the slope-aligned coordinates of the underwater topographic seed point. .

3. The photon counting lidar slope sensing adaptive filtering method for water depth as described in claim 2, characterized in that: In step four, first the first Align the slope surfaces of the underwater terrain seed points with coordinates. As the first The center of the ellipse, with The axial direction is the direction of the major semi-axis, with The axial direction is the direction of the minor semi-axis, and its minor semi-axis Set to a fixed value, major half-axis It is determined by the candidate photon density near the seed point and the slope constraint; For the Alignment coordinates of the slope surface of any candidate underwater photon within a local window Align the coordinates of the underwater terrain seed point with the slope surface. Calculate the distance along the slope and the distance perpendicular to the slope between the two objects in a coordinate system aligned on the same slope: If a candidate underwater photon satisfies the following formula, then the candidate underwater photon is determined to be located at the underwater terrain seed point. Within the central ellipse, photons are identified and preserved as underwater terrain signal photons; If a candidate underwater photon does not satisfy the following formula, it shall be eliminated; 。 4. The photon counting lidar slope sensing adaptive filtering method for water depth as described in claim 3, characterized in that: Determining the major semi-axis First, using the orbital coordinates of the underwater terrain seed point as the center, set a width of... The window is used to count the total number of candidate underwater photons within the window. The semi-major axis of density control is calculated using the following formula. : In the formula, For reference density, For local candidate photon density, The maximum allowable semi-major axis under slope conditions can be calculated using the following formula. : In the formula, This represents the maximum permissible half-span of the ellipse along the original elevation direction. It is the short half-axis; For the first The slope angle corresponding to each underwater terrain seed point; Then the first The actual semi-major axis of the ellipse Pick and The smaller value in: 。 5. The photon counting lidar slope sensing adaptive filtering method for water depth as described in claim 3, characterized in that: Using the inverse transformation of the coordinate transformation in step two, the slope-aligned coordinates of the underwater terrain signal photons after elliptical filtering are restored to the original track distance-elevation coordinates. Let the inverse transformation yield the first The original elevation of the underwater terrain signal photon is Then, the water depth information after refraction correction is calculated using the following formula. In the formula, For the first Water depth after refraction correction for underwater topographic signal photons and The refractive indices of air and seawater are respectively. This indicates the water surface elevation at the instant the underwater topographic signal photon is emitted.

6. The photon counting lidar slope sensing adaptive filtering method for water depth as described in claim 2, characterized in that: In step two, the covariance matrix of the current local window is first calculated. And for the covariance matrix Perform eigenvalue decomposition, take the unit eigenvector corresponding to the largest eigenvalue as the main direction, i.e. the local slope direction, and calculate the slope angle from the unit eigenvector corresponding to the main direction.

7. The photon counting lidar slope sensing adaptive filtering method for water depth as described in claim 6, characterized in that: Let the first There are a total of [number] local windows. The candidate underwater photon, the first The two-dimensional profile coordinates of the candidate underwater photons are ( The orbital distance of all candidate underwater photons within this local window is used as a reference. average and elevation average This indicates the local center of the local window. , ), First, use the following formula to calculate the covariance matrix of the current local window. , Then consider the covariance matrix Perform eigenvalue decomposition and solve ,get eigenvalues and its corresponding unit eigenvector Let the unit eigenvector corresponding to the largest eigenvalue be . ,in, and Let represent the components of the principal direction along the track distance and elevation directions, respectively. The slope angle is then calculated using the following formula. , Then, using the following formula, the candidate underwater photons are uniformly transformed to a slope-aligned coordinate system. In the formula, Candidate underwater photons Slope-direction coordinates relative to the local center; Candidate underwater photons Vertical coordinates.

8. The photon counting lidar slope sensing adaptive filtering method for water depth as described in claim 1, characterized in that: In step one, the Gaussian kernel density is estimated for the elevation of all photons using the following formula: In the formula, For elevation The KDE value at that location is the kernel density value. The number of photons used for water surface identification. For the first The elevation of a photon For elevation KDE bandwidth, The elevation corresponding to the maximum value of the kernel density curve is defined as the instantaneous water surface elevation. : Photons that satisfy the following formula are classified as underwater photons. Let it be denoted as the candidate underwater photon set. In the formula, For the first One photon, Indicates the lower boundary and upper boundary. From instantaneous water surface elevation Searching for the KDE value in the direction of increasing elevation until it decreases to the instantaneous water surface elevation. of The elevation corresponding to the time multiplier. This represents the proportion of the water surface boundary.

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