CN114510678A - China coastal sea area depth reference frame point layout method - Google Patents
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Abstract
The invention discloses a method for laying depth reference frame points in a Chinese coastal sea area, and belongs to the field of depth reference precision control research. The invention mainly researches the nonlinear change degree of the sea map depth reference surface in different directions by using a second derivative on the basis of a sea map depth reference surface model, and deduces the tolerance requirement of the sea map depth reference surface model error and a mathematical model of the maximum interpolation distance of the reference surface in different directions. The difference limiting index of the datum plane interpolation is given by combining the difference limiting index of the water depth measurement in the sea channel measurement specification (GB 12327-1998), the effective range of the datum plane linear interpolation is determined, the graphic expression of the effective range is realized, and the research result can provide a theoretical basis for the frame point arrangement of the coastal sea area in China and provide a means for the rationality evaluation of the frame point position on the one hand; on the other hand, the arrangement of the tide checking stations can be assisted, and the water level reduction precision is improved.
Description
Technical Field
The invention belongs to the field of depth reference precision control research, and particularly relates to graphic expression of a reference frame dotted linear interpolation effective range.
Background
The sea map depth reference surface is a calculation surface of map-carried water depth, is an ideal curved surface defined for ensuring the sailing safety of ships and warships, and the accuracy of the sea map depth reference surface directly influences the accuracy degree of the map-carried water depth. On one hand, 13 tide divisions adopted by depth datum plane calculation need to be obtained through long-term tide examination data, and China has the characteristics that tide examination sites of long-term observation data are distributed more discretely, and the determined depth datum plane also has the characteristic of discrete distribution; on the other hand, the depth datum plane is closely related to the tidal property, and the tidal wave change of China coastal is very complex due to the influence of sea-land distribution, submarine topography and coastal shape, so that the depth datum plane also presents a complex nonlinear distribution characteristic. In the actual operation process, the marine surveying and mapping worker often performs the interpolation of the depth reference plane by using a single-station, double-station or three-station correction method, and the correction method does not consider or only considers the linear change of the depth reference plane in one direction or two directions and ignores the spatial bending of the depth reference plane. In this case, the above two factors seriously affect the interpolation accuracy of the sea map depth reference plane, and further affect the accuracy of the water level correction and the map-carried water depth. With the increasing of the depth measurement and positioning accuracy, the influence of the interpolation accuracy of the sea map depth reference surface on the image-borne water depth is increasingly highlighted, a sea map depth reference system with higher accuracy and higher uniformity is established, and the influence of nonlinear change of the sea map depth reference surface on the image-borne water depth accuracy is effectively weakened. In recent years, the construction of a coastal high-precision tidal model in China provides a good data base for the construction of a sea chart depth reference model, however, in coastal sea areas, tidal waves are influenced by the shape of a coast and the topography of a sea bed more obviously, the model precision is generally reduced, and the precision control of the coastal sea area model is difficult to realize by a tide station with a limited number, so that a new station (called as a frame point) needs to be additionally established, and the tide station is assisted to realize the control of the depth reference plane model. On the basis of a sea map depth reference surface model, the invention tries to research the nonlinear change degree of the sea map depth reference surface in different directions and the limit precision requirement of linear interpolation, provides the maximum interpolation distance of the sea map depth reference surface in different directions, realizes the graphic expression of an effective range, and initially designs a frame point layout scheme by taking a Bohai sea coastal sea area as an example.
Disclosure of Invention
The invention mainly researches the nonlinear change degree of the sea map depth reference surface in different directions by using a second derivative on the basis of a sea map depth reference surface model, and deduces the tolerance requirement of the sea map depth reference surface model error and a mathematical model of the maximum interpolation distance of the reference surface in different directions. The difference limiting index of datum plane interpolation is given by combining the difference limiting index of water depth measurement in the sea channel measurement specification (GB 12327-1998) (hereinafter referred to as the specification), the effective range of datum plane linear interpolation is determined, the graphic expression of the effective range is realized, and on one hand, the research result can provide a theoretical basis for the arrangement of frame points of coastal sea areas in China and provide a means for the rationality evaluation of the positions of the frame points; on the other hand, the arrangement of the tide checking stations can be assisted, and the water level reduction precision is improved.
In order to achieve the purpose, the technical scheme of the invention is as follows:
the method for laying the depth reference frame points in the coastal waters of China specifically comprises the following steps:
first, a depth reference plane linear interpolation error model
When the water level is changed, the water level of the sounding point is usually obtained by interpolating the water level observation value at the tidal observation station, the process implies linear interpolation of the depth datum, but the actual depth datum is nonlinear change, so that the depth datum of the interpolation point has linear interpolation error. For convenience of expression, A, B, P three points are located on the same straight line, and as shown in fig. 1, the depth reference planes of the three points are respectively LA、LB、LPThe coordinates are respectively xA、xB、xP。
And performing Taylor series expansion on the depth reference plane at the point A, B at the point P, wherein the expressions are respectively:
of formula (II) to'PAnd L ″)PRespectively representing P point depthFirst and second derivatives of the reference plane; rn(xA) And Rn(xB) All are infinitesimal terms, with Rn(x) Instead.
The depth reference surface value at the P point obtained by the arrangement of the formula (1) and the formula (2) is as follows:
the depth reference surface value of the point P when the water level is changed is as follows:
in the formula, SAPIndicating A, P the distance between; sABIndicating A, B the distance between them.
As can be seen from the above equation, during the water level correction, the depth reference plane of the interpolated point is substantially obtained by linear interpolation from the depth reference plane of the known point. Comparing the formula (3) with the formula (4), wherein the first term on the right side of the equal sign in the formula (3) is a depth reference surface value obtained by A, B through dotted linear interpolation, and the second term is a depth reference surface value without considering LPAnd (3) model errors influenced by the nonlinear term when the middle n is more than 2.
The linear interpolation error is greatest when point P is at the midpoint A, B. At this time, SAP、SABD, carry formula (3) and ignore the influence of higher-order terms of 3 times and above, and arrange to obtain:
the second term on the right side of equation (5) is the model error, i.e., the extreme error caused by the second-order nonlinear term of the depth reference plane, which is the systematic error, and is expressed by epsilon, then:
second, depth reference plane interpolation limit accuracy estimation
Assuming that the accuracy of the depth reference plane at point A, B is the same, the accuracy of the depth reference plane at the interpolation point P can be obtained from equations (5) and (6):
in the formula (I), the compound is shown in the specification,
the precision of the depth reference plane obtained by P point interpolation is shown; sigmaLIndicating A, B the accuracy of the point depth reference plane.
If the P point precision is consistent with the A, B point precision, the P point precision and the A, B point precision are consistent
The model error epsilon should satisfy:
the accuracy of the water depth on the map is influenced by two parts, namely depth measuring accuracy and water level correction accuracy, and can be expressed as follows:
in the formula, σDA median error representing the depth of the map-borne water; sigmahRepresenting the mean error of the sounding value at a certain moment; sigmaTIndicating a median error in the water level correction value at the corresponding moment.
At present, the 'norm' in China only gives the limit error of water depth measurement, and as shown in table 1, the accuracy indexes of water level correction and map-mounted water depth are not explicitly given.
TABLE 1 Limit error of depth measurement
In principle, the error of water level correction must be smaller than the depth measurement error, and under ideal conditions, the influence of the water level correction error can be ignored, that is, the accuracy of the map-carried water depth is mainly determined by the depth measurement accuracy. In practical application, if σTIs σ h1/3 or less, σ may be calculatedTThe effect of (c) is negligible. Therefore, the accuracy requirement of the water level correction is set to 1/3 of the sounding accuracy, that is:
the method is characterized in that the allowable error for water level correction is mainly caused by three factors, namely a datum plane spatial form effect, a frequency spectrum matching effect and a spatial distribution effect, wherein the datum plane spatial form effect is an error caused by the difference between datum plane interpolation and actual datum plane distribution implicit in the water level correction process; the frequency spectrum matching effect is an error caused by different filtering capabilities of different methods and equipment on the instantaneous sea surface during sounding and water level observation; the spatial distribution effect is an error caused by describing the water level of a measuring area through several discretely distributed tide gauging stations when the water level is changed. Assuming that the errors caused by the three factors are the same, the median error of the depth reference plane is:
from equations (8), (10) and (11), the tolerance expression of the depth reference plane model error ∈ can be obtained as:
the model error limits at different depths are shown in table 2.
TABLE 2 depth reference plane model error tolerance
Third, the graphic representation of the effective range is linearly interpolated by the depth reference plane
By working up formula (6), the following can be obtained:
by combining the equation (13) and the model error tolerance shown in table 2, the interpolatable distance d of the depth reference plane can be obtained, and the effective range of the linear interpolation is determined by fitting, so that the graphic expression of the effective range is realized.
Selecting a certain grid point as a frame point, reading a depth reference plane model value of N multiplied by N grid points around the frame point, respectively calculating second derivatives in 2N directions by adopting a central difference method, wherein the 2N directions are symmetric in a uniform way, determining model error limit differences corresponding to different depths by adopting an equation (12), determining the maximum interpolatable distance of the depth reference plane in each direction by adopting an equation (13), and performing interpolation fitting on the maximum interpolatable distances in the 2N directions by adopting a piecewise cubic hermite function (a 'pchip' function in MATLAB 2017 a) to finally provide a graph of the linear interpolation effective range of the depth reference plane of the frame point.
Drawings
FIG. 1 is a schematic diagram of depth reference plane interpolation;
FIG. 2 is a schematic view of the location of points of the frame; wherein, (a) is the sea area A, (B) is the sea area B, and (C) is the sea area C.
FIG. 3 is a schematic view of an alternative 16-way view;
FIG. 4 is a schematic view of the effective range of frame points in the sea area A; wherein, (a) is the sea area A, (b) is the effective range of the point 1, (c) is the effective range of the point 2, and (d) is the effective range of the point 3.
FIG. 5 is a schematic view of the effective range of frame points in the sea area B; wherein, (a) is the sea area B, (B) is the effective range of the point 4, (c) is the effective range of the point 5, and (d) is the effective range of the point 6.
FIG. 6 is a schematic view of the effective range of the frame points in the C sea area; wherein, (a) is C sea area, (b) is point 7 effective range, (C) is point 8 effective range, and (d) is point 9 effective range.
FIG. 7 shows the effective range (32 directions) of the point 3 linear interpolation;
FIG. 8 is a graph of the effective range (32 directions) for linear interpolation at point 6;
FIG. 9 is a graph of the effective range (32 directions) for linear interpolation at point 9;
Detailed Description
In order to make the method scheme adopted by the invention and the obtained effect clearer, the invention is further described in detail by combining the attached drawings and experiments. It is to be understood that the specific experiments described herein are illustrative only and are not limiting upon the present invention. It should be further noted that, for the convenience of description, only some but not all of the relevant aspects of the present invention are shown in the drawings.
In order to study the effective range of the frame point depth datum plane linear interpolation, 9 frame points are selected in the sea area A, the sea area B and the sea area C on the basis of a high-precision depth datum plane model, and the point positions are shown in FIG. 2. In the figure, black points 1-9 represent 9 selected frame points, points 1-3 and points 4-6 are respectively located in the sea area A and the sea area B, are located inside a bay, are surrounded on three sides, are located in the sea area C, are located in a wider sea area, are different in tidal wave propagation characteristics of the three areas, are different in shape of a coastline, are particularly close to a plurality of main tide-separating no-tide points 7-9, and are greatly influenced by the no-tide points.
Firstly, calculating a 16-direction second derivative of points 1-9, and the specific process is as follows: reading the depth reference plane model values of 5 multiplied by 5 grid points around the frame point, and respectively calculating the second derivatives in 16 directions by adopting a central difference method, wherein the 16 directions are respectively as follows: 0 °, 27 °, 45 °, 63 °, 90 °, 117 °, 135 °, 153 °, and the remaining 8 directions are distributed with central symmetry, as shown in fig. 3. The maximum, minimum and average values of the second derivative at each point are shown in table 3.
TABLE 3 second derivative calculation of frame point depth reference plane
The water depth of the frame points selected in the experiment is basically within 30 meters, and for the sake of conservation, the model error limit of each point is the limit requirement corresponding to the water depth within 20 meters, namely epsilon is 0.04 meter. Calculating the interpolatable distances of the depth reference plane of each direction of the frame points according to the second derivative and the tolerance requirement, wherein the maximum value, the minimum value, the average value and the maximum mutual difference of the interpolatable distances of each point are shown in the table 4.
TABLE 4 frame Point depth reference plane interpolatable distance calculation results
It should be noted that the minimum value of the second derivative of the depth reference plane of each point in table 3 is 0, and if the interpolatable distance d is determined, the interpolatable distance of the reference plane should be infinite in the direction of the second derivative of the depth reference plane being 0, which obviously does not conform to the actual situation, and is not applicable to the actual operation. It is thus processed that, for a direction in which the interpolatable distance is infinity, the interpolatable distance in that direction is uniformly set to the maximum value of the interpolatable distance in the other directions than infinity for that point.
From tables 3 and 4, the following rules can be obtained:
(1) the maximum value of the second derivative of each point depth datum plane is centrally distributed in 0.1992cm (')-2And 0.0996cm (')-2The distribution difference of the average values of the two values and each point shows the difference of second-order derivatives between different frame points and the same frame point in different directions, and the nonlinear change degrees of the points 4-6, namely the depth reference plane of the sea area B are more consistent when the average values of the three areas are compared.
(2) Except for point 7, the maximum interpolatable distances for each point are 20.04 ', the minimum values are above 6 ', and the average values for each point are above 12 '. The average interpolatable distance of point 7 is the smallest because the maximum and maximum mutual differences of point 7 are both small, indicating that the non-linearity of the depth reference plane around point 7 is overall more severe, and as can be seen from fig. 2, the contour between point 7 and point 8 is curved, presumably to distort the tidal wave as it propagates from point 8 to point 7, which also affects the interpolatable distance of point 7.
The interpolatable distances in each direction are fitted with the frame points as the center of a circle according to the interpolatable distances in each direction to obtain the effective range of the linear interpolation of the depth reference lines of each point, and the results are shown in fig. 4 to 6. From fig. 4 to 6, the following law can be derived:
(1) the shapes of the linear interpolation effective ranges of the depth reference planes of each point are irregular, the shapes of the effective ranges corresponding to different points are different, and even the interpolatable distances of different points in different directions are different, which reflects the complexity of the spatial distribution of the depth reference planes.
(2) Theoretically, the maximum value of the interpolatable distance of the depth reference plane can appear in the direction parallel to the contour line, but the experimental result is not obvious, the directions of the maximum values of partial sites are not parallel to the contour line, and some points do not show the maximum value of the interpolatable distance in the direction parallel to the contour line. Analysis shows that the generation of the phenomenon is related to model precision on one hand, and as the model precision is improved, the estimation of the depth reference plane linear interpolation effective range is more accurate, and the situation is improved; on the other hand, this is related to the selected calculation direction, and the experiment only selects the effective range of the linear interpolation of the calculated depth reference plane in 16 directions, but actually, the direction of the contour line is likely to be different from the 16 directions, and when the direction of the contour line is located between the two selected directions and the interpolatable distances on both sides are slightly smaller, after the interpolation fitting, the interpolatable distance obtained by the fitting in the direction of the contour line is smaller than the original interpolatable distance, and at this time, the maximum value of the interpolatable distance does not appear in the direction parallel to the contour line.
To verify the above guess, points 3, 6, 9 were chosen for recalculating the fit. The depth reference surface values of 9 × 9 grid points around the frame point are used at this time, and the same method is adopted to calculate the interpolatable distances of the depth reference surfaces in 32 directions, wherein the 32 directions are respectively as follows: 0 °, 14 °, 27 °, 37 °, 45 °, 53 °, 63 °, 76 °, 90 °, 104 °, 117 °, 127 °, 135 °, 143 °, 153 °, 166 °, and the remaining 16 directions are centrosymmetric to each other, and interpolation fitting is performed on the interpolatable distances in the 32 directions in the same manner, so as to obtain effective ranges of linear interpolation of the depth reference plane at the point 3, the point 6, and the point 9, as shown in fig. 7 to 9. From fig. 7 to 9, the following law can be derived:
(1) the effective range of linear interpolation of the depth datum obtained by adopting 32 directions shows larger irregularity compared with 16 directions, because when 32 directions are adopted, the difference of multidirectional tidal wave propagation characteristics can be shown, and the more directions, the more details are carved.
(2) Comparing the effective range of linear interpolation calculated using 32 directions at point 9 with the direction of the contour of the depth reference surface of the chart at that point, it was found that the maximum value of the interpolatable distance was exhibited in the direction parallel to the contour (around 15 °), which corroborates the above guess, but the behavior at points 3 and 6 was not obvious and may still be related to the number of directions selected.
(3) When the effective range of the linear interpolation of the depth reference plane is calculated in 32 directions, the interpolatable distances in different directions are generally larger than the interpolatable distances in 16 directions, which is because model values of surrounding 9 × 9 grid points are required to be adopted in the calculation of 32 directions, and as the area of the region is increased, the nonlinear change of the depth reference plane is relatively smooth, so that the interpolatable distances in many directions are increased, and because of the factor, although the effective range of the linear interpolation of the depth reference plane is more finely described in 32 directions, the effective range of the linear interpolation of the depth reference plane is still calculated in 16 directions in subsequent experiments.
As can be seen from fig. 4 to 9, the direction of the maximum value of the interpolatable distance is not limited to the direction parallel to the contour line, but the maximum value of the interpolatable distance is exhibited in other directions because the magnitude of the interpolatable distance is related to the degree of the non-linear variation of the depth reference plane, and when the degree of the non-linear variation is large, the interpolatable distance is small, and when the degree of the non-linear variation is small, the interpolatable distance is large. Therefore, in view of the complexity of the tidal wave, the direction of the maximum value of the interpolatable distance is not limited to the direction of the parallel contour, and the maximum value of the interpolatable distance is reached when a certain direction changes linearly.
According to the graphical effective range, by taking the Bohai coastal sea area as an example, the preliminary design of the frame point layout scheme is realized. The frame point arrangement should fully consider the tidal wave propagation characteristics, reduce the arrangement number of frame points in the direction of gentle tidal wave change, increase the arrangement number of frame points in the direction of severe tidal wave change, and strive for the maximum range controlled by the minimum point positions. The frame point selection standard is to ensure that the effective range of the depth reference surface can realize the coverage of the whole coastal area, and on the basis, the overlapping area between the effective ranges of the adjacent frame points is reduced as much as possible so as to reduce the arrangement number of the frame points. The specific implementation process is as follows: selecting a certain grid point as a frame point, calculating the effective range of linear interpolation, plotting in the graph, calculating the effective range of linear interpolation for the grid points of adjacent areas, and plotting in the graph to compare with the effective range of the previous frame point, when the effective ranges of two frame points can realize the coverage along the bank and the overlapping area is minimum, the grid point is determined as the frame point. Therefore, the layout scheme of the frame points is preliminarily designed.
The effective range of the linear interpolation of the frame points in different areas is different, and the arrangement number of the frame points required by different areas is also different. When the coastline is smooth and straight, the effective range of the frame point linear interpolation is often more regular, and the benefit of the frame point layout is larger, so that the optimization of the frame point layout scheme is easier to realize, and the frame point layout density is relatively smaller, such as the southwest coast of the Liaodong bay and the eastern coast of the Laizhou bay; however, when the coastline meanders, the effective range of the frame points is often irregular, and the effective range of the frame points is difficult to be fully utilized, and in order to realize coverage of the coastline, the overlapping area of the effective ranges of the adjacent frame points is often large, and in this case, the arrangement density of the frame points is also correspondingly large, for example, on the west coast of lazhou bay, on the coast of bohai bay. The layout scheme shares 38 frame points, and the boundaries of the effective ranges of all the frame points are connected to form a control area of the whole layout scheme.
Finally, it should be noted that: the above experiments are only intended to illustrate the process scheme of the present invention, and not to limit it; although the present invention has been described in detail, those of ordinary skill in the art will understand that: modifications of the above-described process variant or equivalent substitution of some or all of its process features may be made without departing from the scope of the process variant of the invention.
Claims (1)
1. The method for laying the depth reference frame points in the coastal waters of China is characterized by comprising the following steps of:
first, depth reference plane linear interpolation error model
Let A, B, P three points on the same straight line, the depth reference planes of the three points are LA、LB、LPThe coordinates are respectively xA、xB、xP；
And performing Taylor series expansion on the depth reference plane at the point A, B at the point P, wherein the expressions are respectively:
of formula (II) to'PAnd L ″)PRespectively representing the first derivative and the second derivative of the depth reference plane of the point P; rn(xA) And Rn(xB) Are all made ofFor infinity terms, with Rn(x) Replacing;
the depth reference surface value at the P point obtained by the arrangement of the formula (1) and the formula (2) is as follows:
the depth reference surface value of the point P when the water level is changed is as follows:
in the formula, SAPIndicating A, P the distance between; s. theABIndicating A, B distance;
as can be seen from the above equation, during the water level correction, the depth reference plane of the interpolated point is substantially obtained by linear interpolation from the depth reference plane of the known point; comparing the formula (3) with the formula (4), wherein the first term on the right side of the equal sign in the formula (3) is a depth reference surface value obtained by A, B through dotted linear interpolation, and the second term is a depth reference surface value without considering LPModel error influenced by nonlinear terms when the middle n is more than 2;
when point P is at the midpoint A, B, the linear interpolation error is maximum; at this time, SAP、SABD, carry formula (3) and ignore the influence of higher-order terms of 3 times and above, and arrange to obtain:
the second term on the right side of equation (5) is the model error, i.e., the extreme error caused by the second-order nonlinear term of the depth reference plane, which is the systematic error, and is expressed by epsilon, then:
second, depth reference plane interpolation limit accuracy estimation
Assuming that the accuracy of the depth reference plane at point A, B is the same, the accuracy of the depth reference plane at the interpolation point P can be obtained from equations (5) and (6):
in the formula (I), the compound is shown in the specification,
the precision of the depth reference plane obtained by P point interpolation is shown; sigmaLRepresenting the accuracy of the A, B point depth reference plane;
if the P point precision is consistent with the A, B point precision, the P point precision and the A, B point precision are consistent
The model error epsilon should satisfy:
the accuracy of the water depth on the graph is influenced by the depth measurement accuracy and the water level correction accuracy, and can be expressed as follows:
in the formula, σDA median error representing the depth of the map-borne water; sigmahRepresenting the mean error of the sounding value at a certain moment; sigmaTA median error representing the water level correction value at the corresponding moment;
at present, the 'sea-road survey standard' (GB 12327-1998) in China only gives a limit error of water depth measurement, and the accuracy indexes of water level correction and map-carried water depth are not explicitly given;
in principle, the error of water level correction must be smaller than the depth measurement error, and under ideal conditions, the influence of the water level correction error is ignored, that is, the accuracy of the map-carried water depth is determined byDetermining the sounding precision; in practical application, if σTIs σh1/3 or less, then σ will beTThe influence of (2) is ignored; therefore, the accuracy requirement of the water level correction is set to 1/3 of the sounding accuracy, that is:
the error of water level correction is caused by three factors of a reference surface space form effect, a frequency spectrum matching effect and a space distribution effect, wherein the reference surface space form effect is an error caused by the difference between reference surface interpolation and actual reference surface distribution hidden in the water level correction process; the frequency spectrum matching effect is an error caused by different filtering capabilities of different methods and equipment on the instantaneous sea surface during sounding and water level observation; the spatial distribution effect is an error caused by describing the water level of a measuring area through a plurality of discretely distributed tide gauging stations when the water level is changed; if the errors caused by the three factors are the same, the median error of the depth reference plane is:
from equations (8), (10) and (11), the tolerance expression of the depth reference plane model error ∈ can be obtained as:
the model error tolerance at different depths is:
when the depth measurement ranges are respectively 0-20, 20-30, 30-50, 50-100, 100-200 and >200h/m, the depth measurement limit errors are respectively +/-0.3, +/-0.4, +/-0.5, +/-1.0, +/-Z multiplied by 2% and +/-Z multiplied by 2%, the model error limit differences are respectively +/-0.04, +/-0.05, +/-0.07, +/-0.14 and +/-Z multiplied by 0.3%, and the water level correction is not carried out, without considering epsilon;
third, the graphic representation of the effective range is linearly interpolated by the depth reference plane
By working up formula (6), the following can be obtained:
by combining the formula (13) and model error tolerance at different depths, the interpolatable distance d of the depth reference plane can be obtained, and then the linear interpolation effective range of the depth reference plane is determined in a fitting manner, so that the graphic expression of the effective range is realized;
selecting a certain grid point as a frame point, reading a depth reference plane model value of N multiplied by N grid points around the frame point, respectively calculating second derivatives in 2N directions by adopting a central difference method, wherein the 2N directions are symmetric in a uniform way, determining model error limit differences corresponding to different depths by adopting a formula (12), determining the maximum interpolatable distance of the depth reference plane in each direction by adopting a formula (13), carrying out interpolation fitting on the maximum interpolatable distances in the 2N directions by adopting a piecewise cubic hermite function, and finally providing a graph of the linear interpolation effective range of the depth reference plane of the frame point.
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