JP2006047700A - Three-dimensional bathymetric chart display device and method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide water depth data of a region over a wide range, at higher precision than before. <P>SOLUTION: Submarine tomography having high interpolation precision can be generated with small amount of calculation, as compared with the conventional Kriging method, by applying the Kriging method restricting data number used for interpolation with respect to an interpolating method of deficient mesh. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a method for generating data distributed in a two-dimensional space, and more particularly to a method for creating a seafloor topographic map by interpolating data deficient portions of mesh water depth data and an apparatus for implementing the method.

  Conventionally, with respect to a method for generating data distributed in a two-dimensional space, Lagrange interpolation is performed from depth data of four points adjacent to the mesh in two opposite directions out of the n directions based on the interpolation target mesh. The method of interpolating the depth by weighted averaging of the depths determined in the direction (Patent Document 1) and the technology of constructing the terrain using the Kriging method correct the terrain elevation data using ordinary Kriging interpolation. There is a method (Patent Document 2).

JP 2002-335431 A Japanese Patent Laying-Open No. 2003-5634 (Section 11, FIG. 4)

  Lagrangian interpolation is performed from the depth data of four points near the mesh in the two opposite directions out of the n directions based on the interpolation target mesh according to Patent Document 1, and the depths obtained in each direction are weighted averaged In the method of interpolating the depth by this, when the searched data is far from the interpolation target mesh, not only the interpolation accuracy is bad, but when searching for data in the n direction, there is no data in the data search direction, There was a problem that interpolation was not possible.

A kriging method is a highly accurate interpolation method. FIG. 2 (a) shows a flowchart of a conventional kriging method, and FIG. 2 (b) shows a distribution of depth data before interpolation in the display area. A black dot is a mesh in which i is a data-specific index, and a black dot holds depth data z _i , and the Kriging method obtains a depth interpolation value of an interpolation target mesh using all these depth data z _i and weight coefficient w _i (Equation 1 ).

In order to obtain the weighting coefficient w _i , the process of the flowchart shown in FIG. 2 (a) is required. First, semi-variogram function estimation S201 is performed using the total water depth data (n data) in the interpolation target region. Next, the left side of the simultaneous equations for obtaining the weighting coefficient corresponding to the total water depth data (n data) is set using the semivariogram function (S202). This simultaneous equation is in matrix form as shown in (Equation 2). Here, s _i represents the position vector of the water depth data holding mesh, s ₀ represents the position vector of the estimation target mesh, and γ represents the semivariogram function obtained in S201. Since the right side of the simultaneous equations contains the position vector of the interpolation target mesh, it is set in the mesh loop S204 to S208, and the weighting coefficient is obtained by multiplying by the inverse matrix of the coefficient matrix of the simultaneous equations calculated in S203 (S206) Then, the estimated value of the mesh is calculated (S208). According to this method, since the number of weighting factors to be obtained is proportional to the number of depth data, the amount of calculation increases as the number of depth data increases (Formula 2).

  In the embodiment of the method for correcting the topographic elevation data using ordinary kriging interpolation according to Patent Document 2, the maximum area is 81 × 81 6561 meshes, and the mesh interval is 5 m. Can only handle. If the number of meshes is increased, a wider area can be handled. However, since the survey value (data holding mesh) increases as the area expands, the calculation amount increases for the reason described above. By increasing the mesh interval, a wider area can be handled without changing the amount of calculation, but the resolution is lowered. In other words, there is a problem that it takes a calculation cost to generate high-resolution water depth data over a wide range with the conventional technology, and the water depth data around the ship is automatically generated and updated in conjunction with the movement of the ship. In order to do so, water depth data must be generated faster than the speed of the ship's movement.

  An object of the present invention is to solve the above-mentioned problems of the prior art and to obtain a water depth value in a display area over a wide range with high accuracy in a short time.

  By applying the Kriging method that limits the number of data used for interpolation to the missing mesh interpolation method, it is possible to generate submarine topography with high interpolation accuracy with a small amount of calculation compared to the conventional Kriging method. It becomes possible.

  The three-dimensional submarine topographic map display device of the present invention can provide highly accurate water depth data over a wide range while maintaining the same resolution as the conventional one. Furthermore, by reducing the calculation cost of the interpolation processing unit, the apparatus can be realized with a hardware configuration with a lower specification.

  Hereinafter, application examples of the present invention will be described in detail with reference to the drawings.

  FIG. 1 is an operational image diagram of a 3D submarine topographic map display device according to the present invention. In the situation where a ship is navigating, it is usually impossible to see the shape of the seabed. The 3D submarine topographic map display device is mounted on the ship, calculates the current position of the ship based on GPS and other position information, extracts the water depth data around the current ship position from the water depth DB, and interpolates all the data in the display area. This is a device that generates mesh water depth data and displays a 3D submarine topographic map around the ship on the display screen. The 3D seafloor topographic map display device automatically updates the area of the seafloor topographic map to be displayed by inputting position information from the GPS etc. as the ship moves.

  FIG. 3 is a diagram showing a configuration of a three-dimensional seafloor topographic map display device according to the present apparatus. This apparatus includes a CPU 301, a main memory 302, a hard disk 303, two I / Fs 304 and 305, a keyboard 306, and a CRT 307 via a system bus. Based on own ship position information input from GPS or the like, necessary water depth data is read from the hard disk 303, each process on the main memory 302 is executed by the CPU 301, and a three-dimensional seabed topographic map is displayed on the CRT 307. From the keyboard 306, it is possible to input parameters relating to water depth data generation processing. Further, when water depth data is input from an acoustic sounding instrument or the like, the mesh water depth database can be strengthened by accumulating in the hard disk 303 together with position information obtained from GPS or the like (mesh data water depth database).

  FIG. 4 is a processing block diagram of the submarine topographic map display device. This device assigns latitude / longitude mesh numbers to commercially available water depth data and water depth data acquired in past voyages and accumulates them in the mesh water depth database 401. In addition, the mesh water depth data is managed in an area where the ocean called tiles is divided into a certain size. The water depth data generation process 403 executes an interpolation process for each tile.

  Based on the current position of the ship that the position information input unit 402 outputs, the water depth data generation processing unit 403 acquires the water depth data of 5 × 5 tiles from the mesh water depth database 401 centering on the tile where the ship is present, and the water depth data generation processing The unit 403 generates water depth data of a 3 × 3 tile area and outputs it to the three-dimensional seabed topography display control unit 404.

  The three-dimensional submarine landform display control unit 404 outputs, as a bird's-eye view, water depth data of an area of the same size as the tile centered on the own ship from the water depth data of 3 × 3 tiles output from the water depth data generation processing unit 403. The depth measurement data (time, water depth) input from the depth measurement data input unit 405 for this apparatus is meshed with the position information (time, latitude, longitude) from the position information input unit 402 input at the same time. Processed by the water depth data storage processing unit 406 and accumulated in the mesh water depth database 401.

  FIG. 5 (a) shows a flowchart of the water depth data generation processing unit 403. FIG. 5 (b) is a diagram for explaining FIG. 5 (a). The explanatory diagram shown in Fig. 5 (b) is a diagram showing the area of 3x3 tiles. The mesh painted in black is the water depth data holding mesh, and the data group that appears to be linear is because the contour lines are mesh expanded. is there. The start trigger of the water depth data generation process is when the ship's position crosses the tile boundary, and by constantly generating the water depth data of 3x3 tiles, the ship's center 3D seafloor topographic map is displayed continuously. Is considered.

  A circle with a radius R centering on the interpolation target mesh is used as the interpolation use data selection range. An area obtained by equally dividing this into m sectors is called an area, and l (= interpolation use data number n / division area number m) data is selected for each area in the interpolation use data selection processing S502. In this embodiment, these parameters can be specified by the user, but the default values are optimum values obtained by simulation. Next, the selected water depth data is input to the semivariogram function estimation process S503 to estimate the semivariogram function (S503). Next, if the simultaneous equations of (Equation 2) are generated (S504), the weighting coefficient can be calculated by LU decomposition, Gaussian elimination, or the like (S505). Finally, an interpolation value is calculated using (Equation 1) (S507). If these processes are executed for all the meshes of the interpolation target tile (S501, S507), a three-dimensional seafloor topographic map can be generated.

  FIG. 6A is a flowchart of the interpolation use data selection process S502. FIG. 6B is a diagram showing the configuration of the interpolation use data table. First, for all meshes that hold depth data, the distance from the interpolation target mesh is calculated (S602), and it is determined whether the depth data is within the interpolation use data selection range (S603). If it is within the interpolation use data selection range, it is determined which of the divided areas the mesh position holding the depth data is divided (S604). Next, if the number of interpolation use data candidates in the area is less than l, the water depth data is set as an interpolation use data candidate, and if more than l, the maximum distance of the interpolation use data candidate is compared (S605), If the distance of the water depth data is smaller, it is replaced with water depth data having the maximum distance to make an interpolation use data candidate (S606). These processes are executed for all the meshes that hold the water depth data, and the mesh water depth data of n pieces of interpolation use data is selected.

  Three parameters used in the interpolation use data selection processing S502, that is, the radius R of the data selection range, the number n of interpolation use data, and the number m of divided areas will be described. These parameters can be specified by the user and accept input from the keyboard. Next, the concept of default values of these parameters will be described. By setting the radius R of the interpolation use data selection range to be large, the possibility that no data exists in the data selection range can be reduced, but the processing efficiency is poor because a search process is performed for a large area. Therefore, in this apparatus, a semivariogram function is obtained for each tile, and the range of the obtained function is set as the radius R of the data selection range. For the default values of the number n of interpolation use data and the number m of divided areas, the accuracy is verified and the optimum parameters are determined.

  FIG. 11 shows the result of accuracy verification performed on three terrains having different characteristics in order to determine the number n of interpolation use data and the number m of divided areas. FIG. 11 (a) is a graph showing the relationship between the number of interpolation use data n and the interpolation error. The number m of divided areas at this time is assumed to be eight. From FIG. 11 (a), it can be seen that the interpolation error for the observation data number n converges at 64 points. Also, looking at the relationship between the number n of interpolated data used and the processing time in FIG. 11 (b), the processing time when the number of interpolated data used is 64 is about 300 [s], and about 128 [128] for 128 points. . Based on this result, the number n of interpolated data used in this apparatus was 64 points.

  12 (a) and 12 (b) are graphs showing the relationship between the number m of divided areas and the interpolation error. From this figure, it can be seen that the accuracy is best when the division number m is four divisions. The processing time is proportional to the number m of divided areas, but since the slope is small, the number m of divided areas of this apparatus is set to four.

  FIGS. 7A to 7C show the concept of the semivariogram function estimation process S503. The semivariogram function estimation process S503 calculates the distance h between the data and the semivariogram γ using (Equation 3) based on the interpolation use data obtained in the interpolation use data selection process S502. Here, x, y, and z represent latitude, longitude, and depth, respectively, and the subscripts are data-specific indexes.

As shown in FIG. 7A, the relationship between the distance and the semivariogram obtained by (Expression 3) is plotted as a distance h between data on the horizontal axis and a semivariogram γ averaged by classifying the vertical axis. An approximate expression that matches the plot of this graph is created as a function γ (h) of distance. The shape of a typical semivariogram function has parameters such as nugget, range, and sill as shown in FIG. Here, the nugget can be interpreted as an error included in the data, and the range can be interpreted as a distance having a correlation between the data. Typical approximation equations using the parameters include a linear model (Equation 4) and a spherical model (Equation 5). Here, n, r, and s represent nugget, range, and sill, respectively.

  In order to create an approximate expression that matches the plot of FIG. 7A, it is necessary to determine the parameters n, r, and s. In order to solve this problem, the least squares method is often used. In this apparatus, as a simpler method, the nugget extrapolates the straight line 701 in FIG. For the range, the distance h between data in which the slope of the semivariogram between classes is negative is searched in order from class 1, and the class in which the slope of the semivariogram is negative for two consecutive times is defined as the range. That is, in the example of FIG. 7C, the determination is performed in order from the inclination of the straight line 701, and the determination process is continued because the inclination of the straight line 704 is positive even if the inclination of the straight line 703 is negative. Range 707 and sill 708 are determined when the slope of the straight line is continuously negative, such as straight lines 705 and 706. For the linear model or spherical model, select a model with a small residual sum of squares.

  An explanatory diagram of the accuracy verification method of the present invention is shown in FIG. 801 is a test terrain, which is a 9300 m square area divided into 155 x 155 (24025 mesh) meshes, and the mesh width is 60 m. Contour lines 802 every 300 m in this terrain and elevation points 803 corresponding to about 3% of all meshes are stored in the depth mesh database 804 of this apparatus, and an interpolation terrain 806 of 155 × 155 mesh is generated by interpolation processing 805. By comparing the generated interpolation terrain 806 with the test terrain 801 and calculating the error frequency distribution 807, the interpolation accuracy according to the present invention is evaluated.

  9 (a) to 9 (c) show error frequency distributions of interpolation results obtained by the prior art and this apparatus. FIG. 9 (a) applies the interpolation technique described in Patent Document 1 and FIG. 9 (b) applies the interpolation technique described in Patent Document 2 to FIG. 9 (c). The error frequency distribution of the interpolation result is shown. The horizontal axis is the altitude error, and the vertical axis is the total number of points. The higher the altitude error is 0 m, the sharper the distribution shape, the better the interpolation accuracy. Looking at the total number of points with an altitude error of 0 m, the interpolation technique described in Patent Document 1 (FIG. 9A) is about 7000 points, the interpolation technique described in Patent Document 1 (FIG. 9B) and the interpolation technique according to the present invention ( FIG. 9 (c)) shows about 11000 points, and it can be seen that the interpolation accuracy of the present invention is comparable to the interpolation accuracy of Non-Patent Document 1.

  FIG. 9D shows the average error, standard deviation of error, maximum error, and processing time of each interpolation technique. In the interpolation processing of this embodiment, calculation is performed on a workstation equipped with a 500 MHz MIPS R14000 (IP35) Processor with MIPS R14010 FPU in the CPU, and all processing times are measured under the same conditions. While the interpolation processing according to the present invention maintains the same accuracy as that of Non-Patent Document 1, the processing time is about 1/15, and the processing time is greatly reduced.

  FIG. 10 (a) shows the concept of the interpolation processing range for dynamically displaying a three-dimensional submarine topographic map in conjunction with the movement of the ship. Assume that 1001 is the ship's position and is moving in the 1002 direction. The feature of this device is that the submarine topographic map 1003 centered on the ship is continuously displayed and updated in conjunction with the movement of the ship 1001, and mesh water depth data outside the display area is also calculated in advance. As shown in FIG. 10 (b), when the own ship leaves the own ship presence tile 1004, 1006 becomes a new own ship existence tile, and the water depth data generation processing 403 of the hatched shaded tile 1007 is started. If the ship changes its position in the 1009 direction at the position 1008, it is necessary to finish the interpolation process for five tiles shaded by hatching while moving half a tile (position 1010). The relationship between the mesh step width [m], the tile length [m], and the water depth data generation time [s / tile] is (Expression 6).

  That is, when the CPU is used, since the water depth data generation time per tile by the water depth data generation processing 403 of the present invention is 305.6 seconds, the calculation time for generating the water depth data for 5 tiles is 1528 seconds. Become. If the ship's speed is assumed to be 10kt, it will travel a distance of about 7854m in 1528 seconds, so one tile should be 15708m or more, and it can generate a high resolution submarine topographic map with a mesh increment of about 101m. it can. On the other hand, in the method of Non-Patent Document 1, when the CPU is used, it is necessary to set the mesh step width to 1574 m or more, and it is possible to generate only a submarine topographic map with low resolution.

It is the figure showing the three-dimensional submarine topographic map display apparatus operation image by this invention. It is a flowchart of the conventional kriging method. It is a figure which shows distribution of the depth mesh data before interpolation in a display area. It is a block diagram which shows the structure of the three-dimensional submarine topographic map display apparatus by this invention. It is a block diagram which shows the process outline | summary of the three-dimensional submarine topographic map display apparatus by this invention. It is a flowchart which shows the process of the three-dimensional submarine topographic map display apparatus by this invention. It is a figure which shows the concept of interpolation use data selection. It is a flowchart which shows an interpolation use data selection process. It is a figure which shows the structure of an interpolation use data table. It is a figure which shows the estimation method of a semivariogram function. Similarly, it is a figure which shows the estimation method of a semivariogram function. Similarly, it is a figure which shows the estimation method of a semivariogram function. It is a figure explaining the accuracy verification method of an interpolation process. It is an error-frequency distribution diagram which shows the accuracy verification result of patent document 1. 6 is an error-frequency distribution diagram showing the accuracy verification result of Patent Document 2. FIG. It is an error-frequency distribution figure which shows the precision verification result of this invention. It is a figure which shows the average error of the patent documents 1, 2 and the interpolation technique by this invention, the standard deviation of an error, the maximum error, and processing time. It is a figure explaining the change of the interpolation range accompanying own ship movement. Similarly, it is a figure explaining the change of the interpolation range accompanying own ship movement. It is a figure showing the relationship between the number n of interpolation use data, an interpolation error, and processing time. Similarly, it is a diagram showing the relationship between the number of interpolation use data n and the interpolation error / processing time. It is a figure showing the relationship between the division area number m and an interpolation error. Similarly, it is a diagram showing the relationship between the number m of divided areas and the interpolation error.

Explanation of symbols

301 CPU
302 Main memory
303 hard disk
304 I / F
305 I / F
306 keyboard
307 CRT
401 mesh depth database
402 Location information input section
403 Water depth data generator
404 3D submarine topographic map display controller
405 Sounding data input section
406 Mesh depth data storage processing unit
801 test data
802 Contour map
803 Altitude map
807 Error frequency distribution
1001 Own ship
1003 Submarine topographic map display area
1004 Own ship presence tile
1005 Water depth data holding area
1007 Interpolated tile

Claims (3)

A method of generating seabed depth data for each mesh by interpolation processing,
Select the data to be used in the interpolation process from the seafloor depth data stored in advance,
A submarine water depth data generation method, wherein a predetermined interpolation process is performed using the selected interpolation use data to generate the submarine water depth data. A three-dimensional submarine topographic map display device that automatically generates seafloor depth data around the ship by interpolation processing in conjunction with the movement of the ship.
Storage means for storing the seabed depth data as a latitude / longitude mesh divided into a horizontal space;
Selecting means for selecting data to be used in the interpolation processing from the seabed depth data stored in the storage means;
Performing a predetermined interpolation process using the interpolation use data selected by the selection means, generating the seabed depth data,
A three-dimensional submarine topographic map display device. The generating means divides equally into m areas centering on the interpolation target mesh, and selects l interpolation use data for each area in order of distance from the interpolation target mesh, for a total of n (l × m) 3. The three-dimensional submarine topographic map display device according to claim 2, wherein interpolation processing is performed using submarine water depth data.

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