JP2009133798A - Position detection method and position detection device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To solve the problems that are generated in various detections at a specific position that exists on a spherical surface, such as, inside/outside determination. <P>SOLUTION: Closed domain setting reference points a-f are set on the surface of a spherical body 300, and a determination position 100 is also set. These points are stereographically projected onto a complex plane, by using a pole 400 as a projection reference point. Since the closed domain setting reference points a-f on the spherical surface and projection points A-F on the complex plane have the same phase relation respectively, inside/outside determination of the determination position 100 on the spherical surface is replaced with the inside/outside determination of a projection point 101 on the complex plane. The projection point 101 is translated to the origin on the complex plane, and a negative value half-line 110 is set in the negative direction of the real number axis, by using the moved projection point 101' as a starting point. The inside/outside determination is performed, based on a crossing state between each arc vector set by the moved projection points A'-F' and the negative value half-line 110. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention provides an internal / external determination for determining whether or not a specific position such as the current position of a ship exists within a predetermined region, and an azimuth misalignment for detecting how much the navigation direction of the ship deviates from the direction indicating the target position. The present invention relates to a position detection method for detecting information related to a position such as detection.

Currently, there is a communication system using Inmarsat satellite as a communication system for ships. In the Inmarsat communication system, there is a service that broadcasts a transmission parameter to be followed for each preset area, and it is necessary to detect whether or not the ship is located in the area. A method for determining whether or not the own ship (specific position) exists in such a specific region is referred to as internal / external determination, and various internal / external determination methods are disclosed (for example, refer to Patent Documents 1 to 3). ). It is also important to detect that the current direction of the ship is deviated from the direction in which the ship should be directed, and various methods for detecting azimuth misalignment information that indicates how much is deviated are disclosed. (For example, see Patent Document 4).
JP 2005-227992 A JP-A-8-320938 JP 2001-84384 A Japanese Patent Laid-Open No. 6-26878

When detecting the position of a ship as in the above-mentioned inside / outside determination and azimuth deviation detection, it is necessary to set the boundary line of the region in the inside / outside determination and the course in the azimuth deviation detection. These settings are hardly a problem if the area is sufficiently small with respect to the size of the earth, that is, the sphere, or a short course. However, if the radius of curvature of the sphere is so large that the radius of curvature cannot be ignored, as shown in FIG. I can't get results.
FIG. 19A is a conceptual diagram showing a setting state of the boundary line for inside / outside determination in the conventional great circle type processing.
In the great circle type processing, as shown in FIG. 19A, the boundary setting points a to f are set with respect to the spherical surface of the earth, and the boundary setting points a to f are connected by geodesic lines. 200 is set. And inside / outside determination is performed based on the geodesic curve which is this curve. In this case, the relationship between the boundary line by the geodesic line and the specific position which is the ship position is calculated centering on the spherical trigonometric calculation. Even if this calculation process is analytically valid, there is a possibility that the calculation result may be lost due to the reason that an inverse trigonometric function is used in an intermediate calculation. There is also a problem that the setting is complicated and the amount of calculation increases.

For this reason, there is a stepwise linear process in which a spherical surface as shown in FIG. 19B is calculated by projecting a spherical surface onto a plane by the Mercator projection or the like. FIG. 19B is a conceptual diagram showing a setting state of the boundary line for internal / external determination in the conventional incremental linear processing.
In the case of such a stepwise linear process, as in the problem that occurs in the general Mercator projection, by replacing the spherical surface with a rectangular plane, defining the boundary line in the high latitude zone of the earth in the sphere, Defines a different boundary. In addition, since a part of the sphere is cut by making the sphere flat, it is not possible to define a single closed area when setting a closed area that crosses the cut part. For this reason, a plurality of closed regions 201A and 201B must be set as shown in FIG. 19B, and a complicated inside / outside determination algorithm including this case must be created.

  Such a problem occurs not only in the inside / outside determination but also in the above-described azimuth deviation detection.

  Further, each of the above-described methods includes a potential front / back problem in the case of internal / external determination. That is, when the sphere is divided into two regions by the boundary line, it is not generally known which region is the designated closed region. This is called the front and back problem, and it becomes more difficult to understand if the specified closed area is large.

  Accordingly, an object of the present invention is to realize a position detection method capable of solving problems that occur during various types of detection relating to a specific position existing on a spherical surface, such as the above-described inside / outside determination and azimuth deviation detection.

  The present invention relates to a position detection method for detecting what position a specific position on a spherical surface is. In this position detection method, a plurality of boundary lines for forming a closed region on the spherical surface are set. A projection reference point is set on the spherical surface, and a plane perpendicular to an axis passing through the projection reference point and the center of the sphere forming the spherical surface and including the center of the sphere is set as a complex plane. A specific position and a plurality of boundary lines are projected on a complex plane with reference to the projection reference point. On the complex plane, the inside / outside determination of the specific position with respect to the closed region is performed based on the intersection of the half line starting from the projected specific position and the plurality of projected boundary lines.

  In this method, a closed region set on a spherical surface is projected onto a complex plane by a stereoscopic projection that becomes an equiangular map. By performing such projection, the closed region on the spherical surface and the closed region projected onto the complex plane have the same phase. For this reason, the relationship between the plurality of boundary lines forming the closed region on the spherical surface is the same as the relationship between the plurality of boundary lines forming the projected closed region. Similarly, a specific position on the spherical surface is projected on the same basis as the closed region. Thereby, the relationship between the specific position on the spherical surface and the closed region also has the same phase, and the inside / outside determination on the spherical surface is replaced with the inside / outside determination on the complex plane. When a half line starting from a specific position is formed on this complex plane, the cross relationship between the half line and each boundary line is clearly classified according to whether the specific position is inside or outside the closed area. it can. Therefore, the inside / outside determination is performed by calculating the intersection relation between the half line starting from the specific position and each boundary line. Here, since the half line and each boundary line are lines on the complex plane, the crossing relationship, that is, the presence or absence of the intersection, etc., is the solution of the simultaneous equations of the equation representing the half line and the respective equations representing each boundary line. Replaced by judgment. At this time, the determination of the solution is completed by four arithmetic operations in the complex operation, so that a simple operation is sufficient.

  In the position detection method of the present invention, the inside / outside determination is performed after the projected specific position and the plurality of projected boundary lines are translated so that the projected specific position is the origin of the complex plane on the complex plane.

  In this method, the half line used for the inside / outside determination becomes a half line starting from the origin, and the inside / outside determination can be performed with a simpler calculation.

  In the position detection method of the present invention, an intersection possibility determination reference element including a plurality of straight line segments is set for each of a plurality of projected boundary lines. And the boundary line from which the intersection of a half straight line and a crossing possibility determination criterion element is not detected does not detect the intersection with the half straight line.

  In this method, a plurality of straight line segments are set for each boundary line, and for each boundary line, firstly, a crossing state between the half line and each straight line segment is detected. At this point, if no intersection with the half line is detected, it is determined that there is no possibility of an intersection with the corresponding boundary line, and the detection of the intersection relationship between the boundary line and the half line is not performed. Thus, by first detecting an intersection with a straight line segment, there is no need to detect an intersection with a curved boundary line with no possibility of an intersection. At this time, since the straight line segment is a linear function, the calculation for detecting the intersection is easier than detecting the intersection for all of the boundary lines that are the quadratic function.

  Further, in the position detection method of the present invention, the closed region is defined as the one that does not include the projection reference point among the two regions on the spherical surface divided by the closed curve formed by a plurality of boundary lines.

  In this method, one of the two regions divided by the boundary line can be reliably defined as a closed region.

  In the position detection method of the present invention, the inside / outside determination is performed after one of the two areas on the spherical surface divided by the plurality of boundary lines is designated as the closed area.

  In this method, the setting of the closed region is easily realized by the user's designation.

  In the position detection method of the present invention, when the projection reference point is included in the closed region, the projection and the inside / outside determination are performed after setting the projection reference point outside the designated closed region.

  In this method, considering that the projection reference point itself is an infinite point on the complex plane, when a projection reference point is set within the closed region, a new projection reference point is changed outside the closed region. Thereby, even if the projection reference point of the book and the immediate vicinity of the projection reference point are set to a specific position or a point on the boundary line, the projection is reliably performed by the new projection reference point.

  In the position detection method of the present invention, the boundary line is a spherical geodesic line.

  Further, in the position detection method of the present invention, the traveling direction specific point set ahead of the direction in which the mobile object existing at the specific position travels and the target direction specific point set ahead of the direction in which the mobile object should travel. And set. A projection reference point is set on the spherical surface, and a plane perpendicular to an axis passing through the projection reference point and the center of the sphere forming the spherical surface and including the center of the sphere is set as a complex plane. The specific position, the traveling direction specific point, and the target direction specific point are projected on the complex plane based on the projection reference point. On the complex plane, set a progress direction vector whose end point is the progress direction specific point projected from the projected specific position, and a target direction vector whose end point is the target direction specific point projected from the projected specific position To do. An angle formed by the traveling direction vector and the target direction vector is calculated.

  In this method, a traveling direction vector according to the traveling direction of the moving body set on the spherical surface and a target direction vector connecting the target direction specifying point from the current position of the moving body are projected onto the complex plane. Each projected vector has the same phase as each vector set on the spherical surface. That is, the cross relationship of the projected vectors has the cross relationship of the vectors set on the spherical surface. The intersection angle of each projected vector is stored as the intersection angle of each vector set on the spherical surface. Therefore, the azimuth difference on the spherical surface is calculated by calculating the angle formed by each vector projected onto the complex plane.

  Further, in the position detection method of the present invention, a point on the spherical surface that is perpendicular to the circular plane passing through the traveling direction specific point and the target direction specific point and is farthest from the circular plane is set as a virtual pole. A virtual pole point is projected onto the complex plane based on the projection reference point. A first azimuth vector whose end point is a traveling direction specific point projected from the projected virtual pole point as a starting point and a second azimuth vector whose end point is a target direction specific point projected from the projected virtual pole point as a starting point are set. An angle formed by the first azimuth vector and the second azimuth vector is calculated. The distance on the spherical surface between the traveling direction specific point and the target direction specific point is calculated from the formed angle and the radius of the sphere.

  In this method, the farthest point perpendicular to the circular plane having the outer diameter including the curved line segment connecting the traveling direction specific point and the target direction specific point is set as the virtual pole. By setting three points, a moving direction specific point on the sphere, a target direction specific point, and a virtual pole, a vector from the virtual pole to the traveling direction specific point and a vector from the virtual pole to the target direction specific point are formed. From the corner and the radius of the sphere, the length of the curved line segment connecting the traveling direction specific point and the target direction specific point is calculated by simple multiplication.

  According to the present invention, various detection operations related to points, line segments, and regions existing on a spherical surface such as inside / outside determination and azimuth misalignment detection are performed, and each element such as a point, line segment, or region is represented on a complex plane. Can be replaced with a problem. At this time, since the phase relationship between the elements is maintained, a highly accurate detection result can be obtained. Furthermore, since these various problems result in problems on the complex plane, the various problems can be accomplished with simple complex operations.

A first embodiment of the present invention will be described with reference to the drawings. In the present embodiment, a method for performing inside / outside determination will be described as a kind of position detection method.
FIG. 1 is a flowchart showing a main flow of inside / outside determination.
FIG. 2 is an explanatory diagram for explaining the inside / outside determination method, (A) is a diagram showing the concept of stereoscopic projection from the spherical surface to the complex plane, and (B) is the concept of parallel movement on the complex plane. FIG.
3A and 3B are diagrams showing a specific method of stereoscopic projection, in which FIG. 3A shows a state of projection from a spherical surface to a complex plane, and FIG. 3B shows a vector projected onto the complex plane.
FIG. 4 is a flowchart more specifically showing the processing flow of each main block of the inside / outside determination method shown in FIG. 1, (A) shows the closed region definition processing, and (B) shows the determination position input processing. (C) shows the inside / outside determination process.
FIG. 5 is a diagram showing a parameter configuration of a variable table used for inside / outside determination.

  The inside / outside determination of this embodiment is performed according to the flowchart shown in FIG. 1, and this processing is executed by, for example, an information processing apparatus. In the following description, an example in which the number of closed region setting reference points is set to 6 is shown, but the number of closed region setting reference points may be set as appropriate according to the shape of the closed region to be set.

  The information processing apparatus includes a storage medium that stores an internal / external determination program in which internal / external determination processing is written, a database described later, and the like, and an arithmetic processing device such as a CPU that executes the internal / external determination program. The information processing apparatus also inputs an operation input unit for inputting a closed region setting reference point (see a (G1) to f (G6) in FIG. 2A) for setting the region, and the operation content and operation instruction. A display unit for displaying the contents, the inside / outside determination result, and the like is provided. In addition, the information processing apparatus is connected to, for example, a positioning apparatus arranged at an adjacent position or the like, and acquires its own apparatus position (100 (H) in FIG. 2A) obtained from the positioning apparatus. The positioning device described above corresponds to “positioning means” of the present invention, and the information processing device described above corresponds to “boundary line setting means” and “inside / outside determination means” of the present invention.

With such a hardware configuration and software configuration, the following inside / outside determination method is executed.
First, when the operator performs an operation input for starting an inside / outside determination using the operation unit, an inside / outside determination start instruction is accepted, and an inside / outside determination process is started (S1). If the specification is such that the inside / outside determination is always performed, the inside / outside determination may be started with power-on as a trigger.

Next, closed region definition processing is performed (S2). A specific processing flow is shown in FIG.
The input of spherical coordinates G1 to G6 of the closed region setting reference points a to f for setting the closed region desired by the operator is received (S201). The spherical coordinates G1 to G6 are represented by latitude φ and longitude λ, respectively. Thereby, the spherical coordinates Gm (m = 1 to 6) are input as real longitude and latitude (φm, λm). The input spherical coordinates Gm are stored in the database in the form of longitude and latitude (φm, λm). The closed region on the spherical surface is set by connecting the closed region setting reference points a to f set in this way by the geodesic lines GL1 to GL6 in order. At this time, the operator designates which closed region setting reference points a to f are connected by geodesic lines (for example, the order of the closed region setting reference points a, b, c, d, e, and f).

  When the spherical coordinate Gm is input, a three-dimensional projection onto the complex plane is performed (S202). In the three-dimensional projection, as shown in FIG. 2, a pole 401 among two opposing poles 400 and 401 of a sphere 300 having a spherical surface including a spherical coordinate Gm is set as a projection reference point. A plane including a circle 301 that is orthogonal to the axis connecting the opposing bipolar points 400 and 401 and includes the center O of the sphere 300 is set as a complex plane. Taking the earth as an example, this corresponds to setting the plane including the equator plane as a complex plane with the S pole as the projection reference point out of the N and S poles. Thus, by setting the projection reference point and the complex plane, the closed region setting reference points a (G1) to f (G6) on the surface of the sphere 300 are three-dimensionally projected on the complex plane, and the projection point A (P1 ) To F (P6). The coordinates of the projection points A to F are converted from the spherical coordinates G1 to G6 of the closed region setting reference points a (G1) to f (G6) into complex coordinates P1 to P6. . Here, in Equation 1, R is the sphere radius of the sphere 300. The radius R of the sphere is not limited to the sphere 300, and may be set as appropriate.

This projection is an equiangular projection, and the arc vectors CL1 to CL6 formed by connecting the projection points A to F are geodesic lines GL1 to GL6 formed by connecting the closed region setting reference points a to f. It becomes the same phase. Further, the angle formed by the arc vectors CL1 to CL6 is the same as the angle formed by the geodesic lines GL1 to GL6. At this time, the vector obtained by projecting the geodesic line is always an arc or a straight line. That is, it is represented by a straight line that is an arc having a predetermined finite length radius or an arc having an infinite length radius.
When such coordinate conversion is performed, the parameters of the arc vectors CL1 to CL6 are calculated in which the geodesic lines GL1 to GL6 connecting the closed region setting reference points a to f described above are three-dimensionally projected on the complex plane. . The parameters of the arc vectors CL1 to CL6 include a center coordinate Ct that is a complex number, an arc path flag Rot represented by a binary value, an arc radius Rc that is a real number, and a radius vector Z that is complexly expressed.
The center coordinates Ct1 to Ct6 are calculated for each of the arc vectors CL1 to CL6, and the center coordinates on the complex plane of each arc vector CL1 to CL6 are given. The center coordinates Ctm (m = 1 to 6) are given by Equation 2. Here, <Pm, Pn> represents an inner product operation of Pm and Pn, and j represents an imaginary unit. Note that n is n = m + 1 if 1 <m <5, and n = 1 if m = 6.

  The arc path flag Rot is also set for each of the arc vectors CL1 to CL6, and indicates the rotation direction from the start point to the end point of each arc vector CL1 to CL6. This also indicates whether the arc vector is a short path side or a long path side of a circle including the arc vector. That is, the start point and the end point are points on a circle including the arc vector, and there are two paths that reach the end point from the start point via the circle. Therefore, it is determined which path the projected arc vector CLm belongs to, and the determination result is given as the arc path flag Rotm. For example, in FIG. 3, the arc vector connecting the projection point A and the projection point B includes a short path (thick solid line) that rotates clockwise on the complex plane and a long path (two-dot chain line) that rotates counterclockwise. Exists. In this case, since the arc vector CL1 onto which the geodesic line GL1 is projected becomes a short path (thick solid line), the arc path flag Rot1 is given “St” indicating a short path. In the case of a long route, “Lg” is given. Such a process is performed for all the circular arc vectors CL1 to CL6, which are given as circular path flags Rot1 to Rot6, respectively.

  The arc radius Rcm is also set for each of the arc vectors CL1 to CL6, and a radius of a circle including the arc vector is given. The arc radius Rcm is calculated from the distance between the projected point on the arc vector CLm and the center coordinate Ctm of the arc vector CLm. For example, in FIG. 3, the arc radius Rc1 is calculated from the distance between the complex coordinates P1 of the projection point A and the center coordinates Ct1. Such a process is performed for all the arc vectors CL1 to CL6, which are given as arc radii Rc1 to Rc6, respectively.

  Two radius vectors Z are set for each of the arc vectors CL1 to CL6, and are given by a complex representation of a vector from the center of the arc vector to the start point and a vector from the center of the arc vector to the end point. It is done. For example, in FIG. 3, with respect to the arc vector CL1, a radius vector Z11 from the center Ct1 to the start point (P1) that is the projection point A and a radius vector from the center Ct1 to the end point (P2) that is the projection point B. Z12 is given by a complex expression. Such processing is performed for all the arc vectors CL1 to CL6, radius vectors Z11 and Z12 are given to the arc vector CL1, radius vectors Z22 and Z23 are given to the arc vector CL2, and the arc vector is given. Radial vectors Z33 and Z34 are given to CL3. Further, radius vectors Z44 and Z45 are given to the arc vector CL4, radius vectors Z55 and Z56 are given to the arc vector CL5, and radius vectors Z66 and Z61 are given to the arc vector CL6.

  When such projection processing is completed, a closed region setting requirement is selected (S203). The closed region setting requirement specifies whether the closed region setting standard may be left as default, whether the selection of the arc vector is correct, or the like. For example, when a region that does not include a projection reference point is set as a designated closed region as a default, a region that does not include a default projection reference point is determined as a closed region unless a closed region designation operation is performed. If a closed region designation operation is performed, the designated region is determined as a closed region. Such area designation information is given as an area selection flag f. For example, if an area not including the projection reference point is designated, the area selection flag f is set to “1”, and if not, the area selection flag f is set to “0”.

  As described above, each parameter calculated and set is associated with each of the arc vectors CL1 to CL6 and stored as a database in the variable table (S204).

  When the closed region definition process S2 is completed, a determination position input process is performed (S3). In the determination position input process, as shown in FIG. 4B, first, spherical coordinates H of the determination position 100 (corresponding to the “specific position” of the present invention) are input. The determination position 100 is, for example, a position measured by the above-described positioning device, and the spherical coordinate H is input as a real longitude and latitude (φ0, λ0), like the spherical coordinate G of the closed region setting reference point. The Then, when the spherical coordinate H of the determination position 100 is input, a three-dimensional projection is performed on the complex plane on the same basis as the closed region setting reference points a to f (S302). Thereby, the complex coordinate S of the projection point 101 is obtained. These spherical coordinates H and complex coordinates S are stored in a variable table.

  As described above, when the closed region setting reference points a to f and the determination point 100 are input and the parameters regarding the projected closed region and the projected point 101 are input, the inside / outside determination processing is executed (S4). The inside / outside determination process ends when an inside / outside determination end instruction is accepted (S5: Y), and is continuously performed when it is not accepted (S5: N → S6). If there is no change in the setting of the closed region, the inside / outside determination is performed based on the newly acquired determination position (S6: N → S3), and if there is a setting change in the closed region, the inside / outside determination is performed from the closed region definition process. (S6: Y → S2).

Next, detailed processing of the inside / outside determination will be described with reference to FIG.
FIG. 6 is a flowchart showing a detailed flow of each block in the inside / outside determination process.
First, as shown in FIG. 4C, when the inside / outside determination process is started, the parallel movement process of the center coordinates Ct1 to Ct6 of the arc vectors CL1 to CL6 is performed (S401). This translation is to translate the complex coordinate S of the projection point 101, which is the projection of the determination position 100, to the origin of the complex plane. Relative centers Q1-Q6 are calculated and stored in the variable table. Due to this parallel movement, as shown in FIG. 2B, on the complex plane, the post-movement projection point 101 ′ is positioned at the origin of the complex plane, and the projection points A (P1) to F (P6) are post-movement projections. It is converted into points A ′ (P1 ′) to F ′ (P6 ′). As a result, the arc vectors CL1 to CL6 are also converted into arc vectors CL1 ′ to CL6 ′.

  Next, one of the arc vectors CL1 'to CL6' is selected (S402). Here, if all the arc vectors have been read out, the inside / outside determination based on the total score is performed (S403: N → S409). On the other hand, if the selected arc vector has not been read yet (S403: Y), clipping determination is executed (S404).

  In the clipping determination, as shown in FIG. 6A, first, a determination reference element set for each arc vector to be determined for clipping is acquired (S441).

FIG. 7 is a diagram showing the concept of a determination criterion element for clipping determination. (A) shows a determination criterion element based on a plurality of line segments, and (B) shows a determination criterion element based on a rectangle.
These determination reference elements are calculated when the arc vectors CL1 ′ to CL6 ′ are set. In the case of a plurality of line segments, arcs from the negative side of the arc vector CLm ′ on the complex plane. It is composed of two straight line segments LLm1 and LLm2 that are in contact with the vector CLm ′. These straight line segments LLm1 and LLm2 are set as line segments having a shape schematically showing the position and range of the arc vector CLm. In the case of a rectangle, the rectangle BTm is set as the minimum area including the arc vector CLm ′ on the complex plane.

  When the determination reference element is acquired, the intersection point between the determination reference element and the post-movement projection point 101 ′, that is, the negative half-line extending in the negative direction from the origin of the complex plane (corresponding to 110 in FIG. 2B) is calculated. For example, if the determination reference element is a straight line segment LLm1, LLm2, the intersection of these and the negative half-line 110 is calculated (S442). This intersection calculation process is performed by simultaneous equations of two linear functions indicating linear line segments LLm1 and LLm2 on the complex plane and a linear function indicating a negative half line. If even one solution exists in this simultaneous equation, a flag indicating that there is a possibility of crossing is set (S443: Y → S444). On the other hand, if there is no solution, a flag indicating that there is no possibility of intersection is set (S443: N → S445).

  Returning to the flow of FIG. 4C, if a flag indicating that there is a possibility of intersection is acquired after the clipping determination, intersection detection is performed (S405: Y → S406). On the other hand, if a flag indicating that there is no possibility of intersection is acquired, the next arc vector is selected (S405: N → S402).

  In the intersection detection (S406), the intersection between the arc vector CLm 'and the negative half-line 110 is calculated. At this time, an “internal determination break” occurs in a specific situation described later (S407: Y), the internal determination (S410) is determined, and the internal / external determination process ends. On the other hand, if the “inside determination break” does not occur (S407: N), the score integration process S408 is executed.

  In intersection detection and “inside determination break”, as shown in FIG. 6B, first, intersection candidates between the arc vector CLm ′ and the negative half-line 110 are calculated (S461). This intersection point candidate is calculated by a binary equation including an equation of a circle including the arc vector CLm ′, that is, an equation of a circle obtained from the relative center Qm and radius Rcm of the arc vector CLm ′ and an equation of the negative half-line 110. It is obtained by solving the solution of the following equation (determining the solution). Here, if there is no solution (S462: N), intersectionless data is output (S467).

  On the other hand, if there is a solution (S462: Y), the coordinates V of the intersection candidate (solution) are calculated, and it is determined whether the intersection candidate is within the line segment of the arc vector CLm '(S463).

As shown in FIG. 6C, the determination of being within the arc vector range first obtains the radius vectors Zmm ′ and Zmn ′ of the arc vector CLm ′ obtained by translating the radius vectors Zmm and Zmn of the arc vector CLm. To do. Further, an intersection vector vm starting from the coordinate V of the intersection candidate and having the relative center Qm as the starting point is acquired. Further, the complex conjugates Zmm ′ ^* , Zmn ′ ^* , vm ^* of the radius vectors Zmm ′, Zmn ′ and the intersection vector vm are calculated. Then, the imaginary part of the inner product calculation value of the radius vector Zmn ′ on the end point side and the complex conjugate Zmm ′ ^* of the radius vector on the start point side is calculated, and the sign is detected. Similarly, the imaginary part of the inner product calculation value of the intersection vector vm and the complex conjugate Zmm ′ ^* of the radius vector on the start point side is calculated, and the sign is detected. Further, the imaginary part of the inner product calculation value of the radius vector Zmn ′ on the end point side and the complex conjugate vm ^* of the intersection vector is calculated to detect the sign (S601). This process is performed according to the number of solutions. When there are two solutions (intersection candidates), the process is performed for each of the intersection coordinates Vm and Vm ′.

  Next, with respect to the intersection vector vm, it is confirmed whether or not all the codes detected by the calculation of S601 are the same sign. Here, all the symbols are the same, as shown in FIG. 8 (A), that the intersection Vm exists on the circumference of the short side of the circle including the projection point coordinates Pm ′ and Pn ′. In other words, it shows that the intersection vector vm exists in a narrow region with the radius vector Zmm ′ as the start point side end and the radius vector Zmn ′ as the end point side end. On the other hand, even if one symbol is not the same, as shown in FIG. 8B, the intersection Vm exists on the long circumference of the circle including the projection point coordinates Pm ′ and Pn ′, in other words, For example, it is indicated that the intersection vector vm exists in a wide area having the radius vector Zmm ′ as the end on the start point and the radius vector Zmn ′ as the end on the end. FIG. 8 is a diagram illustrating an example of a positional relationship on the complex plane between the radius vectors Zmm ′ and Zmn ′ and the intersection vector vm.

  In accordance with this, whether or not the arc vector CLm ′ is on the short side of the circle is acquired based on the arc path flag (S603, S606). When it is detected that all the codes are in the same state and the circular arc vector CLm ′ is the shorter one of the circles (S602: Y → S603 → S604: Y), it is determined that there is an intersection (S605). On the other hand, when it is detected that all the codes are in the same state and the arc vector CLm ′ is the longer circle (S602: Y → S603 → S604: N), it is determined that there is no intersection (S608). If it is detected that the arc vector CLm ′ is the shorter one of the circles even when one code is not the same (S602: N → S606 → S607: Y), it is determined that there is no intersection (S608). On the other hand, if it is detected that the arc vector CLm ′ is the longer circle (S602: N → S606 → S607: N) even if one code is not the same, it is determined that there is an intersection (S609). Such a determination is also performed for the intersection Vm ′ when the intersection Vm ′ exists.

  Returning to FIG. 6B, if the solution (intersection candidate) is within the range, that is, if there is an intersection determination (S464: Y), it is examined whether the solution is a complex origin. Here, if the solution is the complex origin (S465: Y), the inside determination is performed (S410), and the inside / outside determination is terminated. On the other hand, if the solution is not the complex origin (S465: N), the intersection existence data is output (S466). If the solution (intersection candidate) is not within the range, that is, if there is no intersection determination (S464: N), no intersection data is output (S467). By performing the processing as described above, intersection detection and “internal determination break” are performed.

  Next, returning to FIG. 4C, if there is no “internal determination break” (S407: N), score integration processing (S408) is performed.

FIG. 9 is a flowchart showing a schematic flow of the score integration processing flow.
FIG. 10 shows the main concept of the scoring method. FIG. 11 shows a state where the negative half-line 110 and the arc vector CLm ′ intersect at one point on the complex plane, and the score in that state.
FIG. 12 is a flowchart showing a score integration process flow when there is one intersection.
FIG. 13 is a flowchart showing a score integration process flow when there are two intersections.
As shown in FIG. 9, in the score integration process, if there are two intersections, score calculation for two intersections is performed (S801: Y → S802). Next, if there is only one intersection, a score calculation for one intersection is performed (S801: N → S803: Y → S804). If there is no intersection, the score is set to “0” (S803: N).

  Since there are a plurality of intersection states as shown in FIGS. 11A to 11P, the concept of the intersection state of the negative half-line 110 and the arc vector CLm ′ will be described first with reference to FIG. . As shown in FIG. 10, the intersecting state is classified according to the rotation direction of the arc vector CLm ′ and from which direction on the complex plane it intersects or touches the negative half-line 110. Here, positive rotation indicates rotation of the arc vector CLm ′ that is counterclockwise with respect to the complex plane, and negative rotation indicates rotation of the arc vector CLm ′ that is clockwise with respect to the complex plane.

  “Positive intersection” indicates that the arc vector CLm ′ intersects the negative half-line 110 from the positive region side in the imaginary axis (Im) direction. “Negative intersection” means that the arc vector CLm ′ intersects the negative half-line 110 from the negative region side in the imaginary axis (Im) direction. In the case of intersection, when the arc vector CLm ′ completely intersects the negative half-line 110 (see FIGS. 11A to 11D), the starting point or end point of the arc vector CLm ′ is the negative half-line. 110 (see FIGS. 11I to 11P).

  Further, “contact” indicates that the arc vector CLm ′ is in contact with the negative half-line 110, that is, the maximum or minimum of the function representing the arc vector CLm ′ exists on the negative half-line 110 (FIG. 11 ( E) to (H)).

  The distinction between the “intersecting” state and the “contacting” state is made by identifying the real part Re (Qm) of the center coordinate Q of the arc vector CLm ′ after translation and the real part Re (Vm) of the intersection point coordinate V. And using. Further, in the state of “intersecting”, whether or not the end point of the arc vector CLm ′ exists on the negative half-line 110 is identified by the imaginary part Im (Pm) of the start point side end point coordinate Pm ′ of the arc vector CLm ′. ') And the imaginary part Im (Pn') of the end point side end point coordinate Pn 'of the arc vector CLm'. Here, the start point side end point coordinate Pm ′ and end point side end point coordinate Pn ′ of the arc vector CLm ′ are the start point side end point coordinate Pm and end point side end point coordinate Pn of the arc vector CLm, and the complex coordinates of the projection point 101 of the determination position 100. Calculated by S and represented by Pm ′ = Pm−S and represented by Pn ′ = Pn−S.

Next, a scoring method when there is one intersection and two intersections will be described.
(I) When there is one intersection The score calculation method when there is one intersection will be described with reference to FIGS.

  In the score calculation process in the case where there is one intersection, first, the start point side end point coordinate Pm ′, end point side end point coordinate Pn ′, center coordinate Qm, arc of the arc vector CLm ′ described above based on the information stored in the database The route flag Rotm and the intersection coordinate Vm are acquired (S821). The product Im (Pm ′) * Im (Pn ′) of the imaginary part Im (Pm ′) of the start point side end point coordinate Pm ′ and the imaginary part Im (Pn ′) of the end point side end point coordinate Pn ′ is calculated (S822), It is detected whether the value of the product Im (Pm ′) * Im (Pn ′) is 0 (S823). Such processing of S822 and S823 is to determine whether or not the start point or end point of the circular arc vector CLm ′ is on the negative half-line 110, and Im (Pm ′) * Im (Pn ′) = 0. If there is (S823: Y), it indicates that the start point or end point is on the negative half-line 110, and if Im (Pm ′) * Im (Pn ′) ≠ 0 (S823: N), the start point or end point is It indicates that it is not on the negative half-line 110.

  Next, the real part Re (Qm) of the center coordinate Q and the real part Re (Vm) of the intersection coordinate V are acquired (S824, S824 ').

(I-1) When the start point or the end point is not on the negative half-line 110 (S823: N)
It is determined whether or not the real part Re (Qm) of the central coordinate Q and the real part Re (Vm) of the intersection coordinate V are the same, that is, Re (Qm) = Re (Vm). If Re (Qm) = Re (Vm) (S825: Y), it is determined that the arc vector CLm ′ is in contact with the negative half-line 110. In this case, the relationship between the arc vector CLm ′ and the negative half-line 110 is one of FIGS. 11E to 11H, and a score “0” is given.

  On the other hand, if Re (Qm) ≠ Re (Vm) (S825: N), it is determined that the arc vector CLm 'intersects the negative half-line 110. When the intersection is determined, the rotation direction based on the circular path flag Rotm and the magnitude relation between the real part Re (Qm) of the center coordinate Qm and the real part Re (Vm) of the intersection coordinate Vm are used, and the relationship shown in FIG. Based on the above, it is determined whether or not it is a positive intersection (S826). Then, if it is a positive intersection, that is, in any state of FIGS. 11A and 11C (S826: Y), a score “+1” is given (S827). On the other hand, if it is a negative intersection, that is, in any of the states of FIGS. 11B and 11D (S826: N), a score “−1” is given (S828).

(I-2) When the start point or end point is on the negative half-line 110 (S823: Y)
Using the rotation direction based on the arc path flag Rotm and the magnitude relationship between the real part Re (Qm) of the center coordinate Q and the real part Re (Vm) of the intersection coordinate V, a positive intersection is obtained based on the relationship of FIG. It is determined whether or not (S829). In this case, the crossing is not exactly performed, and the negative half line 110 is in contact with either the start point or the end point of the arc vector. Here, a state in which the start point is in contact with the negative half line 110 is referred to as end point firing, and a state in which the end point is in contact with the negative value half line 110 is referred to as end point landing. Then, if the positive end point firing or the positive end point landing corresponding to the positive intersection, that is, any of the states shown in FIGS. 11 (I) to (L) (S829: Y), the score “+0.5” is given. (S830). On the other hand, if the negative end point firing or negative end point landing corresponding to the negative crossing, that is, any of the states shown in FIGS. 11M to 11P (S829: N), the score “−0.5” is obtained. (S831).

(Ii) When there are two intersection points A score calculation method when there are two intersection points will be described with reference to FIGS.
FIG. 14 shows a state where the negative half-line 110 and the arc vector CLm ′ intersect at two points on the complex plane, and an example of the score in that state.

  When there are two intersections, the arc vector CLm ′ always intersects the negative half-line 110 at two points, so there is no need to consider the case where it touches the negative half-line 110. If the arc vector CLm ′ and the negative half-line 110 intersect at each of the two intersections, the score becomes “0”. However, when at least one of the two intersections is the start point or the end point of the arc vector CLm ′, it does not correspond to the above two cases, and a predetermined score must be given.

  In the score calculation process when there are two intersections, first, the start point side end point coordinates Pm 'and the end point side end point coordinates Pn' of the arc vector CLm 'are acquired based on the information stored in the database (S851). A product Im (Pm ′) * Im (Pn ′) of the imaginary part Im (Pm ′) of the start point side end point coordinate Pm ′ and the imaginary part Im (Pn ′) of the end point side end point coordinate Pn ′ is calculated (S852), It is detected whether the value of the product Im (Pm ′) * Im (Pn ′) is 0 (S853). Such processing of S8252 and S853 is to determine whether the starting point or the ending point of the circular arc vector CLm ′ is on the negative half-line 110, and Im (Pm ′) * Im (Pn ′) = 0. If there is (S853: Y), it indicates that at least one of the start point and the end point is on the negative half-line 110, and if Im (Pm ′) * Im (Pn ′) ≠ 0 (S823: N), the start point Alternatively, the end point is not on the negative half-line 110.

  When Im (Pm ′) * Im (Pn ′) ≠ 0 (S823: N), for example, the state of FIG. 14A is shown, and “0” is given as the score as described above.

  If Im (Pm ′) * Im (Pn ′) = 0 (S823: Y), it is determined whether Im (Pm ′) = 0. If Im (Pm ′) = 0, the variable y = Im (Pn ′) and if Im (Pm ′) ≠ 0, the variable y = Im (Pm ′) is set (S854). Thereby, it is distinguished whether the start point is on the negative half-line 110 or the end point is on the negative half-line 110. After such distinction, it is determined whether y = 0. In this process, it is determined whether or not the end point opposite to the end point determined to be on the negative value half line 110 is on the negative value half line 110. If y = 0 (S855: Y), it is determined that both the start point and the end point are on the negative half-line 110. This is a state as shown in FIG. 14B, for example, and a score “0” is given.

  When y ≠ 0 (S855: N), if y = Im (Pm ′), f = + 1 is set, and if y = (Pn ′), f = −1 is set (S856). Next, it is determined whether y> 0. Thereby, it is determined whether the end point opposite to the end point determined to be on the negative half-line 110 in the above process is on the positive side or the negative side in the imaginary axis direction with respect to the negative half-line 110. . If y> 0 is not satisfied (S855: N), it is determined that the opposite end point is on the negative side. This is, for example, a state as shown in FIGS. 14C and 14D, and “−0.5 * f” is given as a score. On the other hand, if y> 0 (S855: Y), it is determined that the opposite end point is on the positive side. This is, for example, a state as shown in FIGS. 14E and 14F, and “+ 0.5 * f” is given as a score.

  The score calculated in this way is stored in the database for each arc vector CLm.

  Returning to FIG. 4, when the above processing is performed for all the arc vectors CLm, the inside / outside determination based on the total score is performed (S409). The total score is obtained by adding the scores of all the arc vectors CLm. If the score result is “0”, an internal determination is made, and if it is not “0”, an external determination is made.

  As described above, by performing the processing of the present embodiment, the inside / outside determination can be performed by simple arithmetic processing without performing complicated arithmetic processing such as an inverse trigonometric function. At this time, no calculation error such as a digit loss occurs, so that the inside / outside determination can be performed with high accuracy and reliability.

Next, a second embodiment will be described with reference to the drawings. In the present embodiment, an azimuth deviation calculation method will be described as a kind of position detection method.
The calculation of the azimuth deviation shown below has the same hardware configuration as that of the first embodiment. In this embodiment, the positioning device corresponds to the “positioning means” of the present invention, and the information processing device of “ It corresponds to “specific point setting means” and “azimuth deviation detection means”.

FIG. 15 is a diagram for explaining the concept of azimuth misalignment.
When a moving body such as a ship is present at the current position 100, the traveling direction designation position 102 (corresponding to the “traveling direction specific point” of the present invention) and the target position 103 on the current navigation course on the sphere SP. (Corresponding to “target direction specific point” of the present invention). The angle between the geodesic line from the current position 100 toward the traveling direction designation position 102 and the geodesic line from the current position 100 toward the target position 103 is defined as a deviation azimuth angle θ. Further, the distance according to the geodesic line between the traveling direction designation position 102 and the target position 103 is defined as a cross track error XTE. The deviation azimuth angle θ and the cross track error XTE are azimuth deviations.

  FIG. 16 is a flowchart for calculating the azimuth deviation, (A) is a calculation flow of the deviation azimuth angle θ, and (B) is a calculation flow of the cross track error XTE.

(I) Calculation of deviation azimuth angle θ (see FIG. 16A)
When calculating the deviation azimuth angle θ, first, the current position 100, the traveling direction designation position 102 on the current navigation course, and the target position 103 are input in spherical coordinates (S911). Next, the current position 100, the traveling direction designation position 102, and the target position 103 are three-dimensionally projected from the spherical surface to the complex plane, using the same method as shown in the first embodiment (S912).
FIG. 17 is a diagram showing the relationship among the current projection position 101, the projection progress direction designation position 121, and the projection target position 131 on the complex plane.
As shown in FIG. 17, the deviation azimuth angle θ is an arc vector CL02 (corresponding to the “traveling direction vector” of the present invention) having the current projection position 101 as the start point and the projection progress direction designation position 121 as the end point, and the projection. It is replaced with an angle θ formed by an arc vector CL03 (corresponding to the “target direction vector” of the present invention) having the current position 101 as a start point and the projection target position 131 as an end point.

  Next, the center coordinate Ct02 of the circle Cir02 including the arc vector CL02 and the center coordinate Ct03 of the circle Cir03 including the arc vector CL03 are calculated (S913). Then, a radius vector CtL02 having the center coordinate Ct02 as the start point and the projection current position 101 as the end point, and a radius vector CtL03 having the center coordinate Ct03 as the start point and the projection current position 101 as the end point are calculated. From the tangent theorem, the angle θ formed above is replaced with the angle formed by the radius vector CtL02 and the radius vector CtL03, which becomes the deviation azimuth angle θ.

  Therefore, using the inner product of the radius vectors CtL02 and CtL03, the deviation azimuth angle θ is calculated by Equation 3 (S914).

  By such processing, the deviation azimuth angle θ can be easily calculated.

(Ii) Calculation of cross track error XTE (see FIG. 16B)
18A and 18B are diagrams for explaining a method of calculating the cross track error XTE. FIG. 18A shows a method of setting the virtual pole 140, and FIG. 18B shows a projected virtual pole position 141 on the complex plane after the three-dimensional projection, and the projection progress. It is a figure which shows the relationship between the direction designation | designated position 122 and the projection target position 132. FIG.

  Even when the cross track error XTE is calculated, first, the current position 100, the traveling direction designation position 102 on the current navigation course, and the target position 103 are input in spherical coordinates (S911). Next, as shown in FIG. 18A, a circle having the same diameter as the sphere SP and passing through the traveling direction designation position 102 and the target position 103 is set for the sphere SP. At this time, this circle is formed along the spherical surface of the sphere SP. Further, one of the two points on the spherical surface that is on the axis perpendicular to the circle and is farthest from the circle is set as the virtual pole 140 (S921).

  Next, with respect to a circle passing through the advancing direction designation position 102 and the target position 103, the pole on the side facing the virtual pole 140 is set as a projection reference point, and a plane including the circle is set as a complex plane. In the same manner as in the embodiment and the deviation azimuth angle θ calculation method, stereoscopic projection is performed (S922). The projection reference point is not limited to this pole and may be set as appropriate. Further, the projection progress direction designation position 122 and the projection target position 132 by such a three-dimensional projection are respectively complex planes with respect to the projection progress direction designation position 121 and the projection target position 131 when the above-described deviation azimuth angle θ is calculated. It can be easily calculated by performing Moebius transformation according to the relationship between the two.

  Next, an arc vector CL42 (corresponding to the “first azimuth vector” of the present invention) starting from the projected virtual pole position 141 and ending at the projected traveling direction designation position 122 is set, and the projected virtual pole position 141 is set as the projected virtual pole position 141. An arc vector CL43 (corresponding to the “second azimuth vector” of the present invention) having the start point and the projection target position 132 as the end point is set. Then, the center coordinate Ct42 of the circle Cir42 including the arc vector CL42 and the center coordinate Ct43 of the circle Cir43 including the arc vector CL43 are calculated (S923).

  Here, as shown in FIG. 18B, an arc vector CL42 starting from the projection virtual pole position 141 and ending at the projection progress direction designation position 122, and the projection target position 131 starting from the projection virtual pole position 141 and ending. An angle formed by the arc vector CL43 is defined as an opening angle ψ. From the tangent theorem, the opening angle ψ is a radius vector CtL42 starting from the center coordinate Ct42 and ending with the projected virtual pole position 141, and a radius vector CtL43 starting from the center coordinate Ct43 and starting from the projected virtual pole position 141. It becomes the same as the angle formed by. Therefore, the angle formed by the inner product calculation shown in Equation 4 of the radius vectors CtL42 and CtL43 is calculated (S924).

  When the opening angle ψ is calculated, the cross track error XTE is calculated from Equation 5 as the radius R of the sphere (S925).

XTE = R * ψ− (Formula 5)
As described above, the cross track error XTE can also be calculated by a simple calculation.

  As described above, by using the above-described method, the inside / outside determination and the azimuth deviation detection can be performed with a reliable and highly accurate calculation process. At this time, for example, in the case of inside / outside determination, the size of the designated closed region can be increased.

  Further, by using the above-described method, it is possible to eliminate singular points that are basically not settable except for the projection reference point. When the projection reference point is included in the arc vector, it is only necessary to change the projection reference point so that it is not included in the arc vector, which can ultimately result in a simple calculation that does not include the singular point.

  In the above-described method, only the so-called Jordan curve in which each arc vector does not intersect with itself is shown. However, in this method, the calculation can be performed even for an arbitrary curve without being limited to the Jordan curve. .

  In the above description, the case of a sphere has been described as an example, but the above configuration and processing can be applied to an ellipsoid. In this case, a point on the ellipsoid may be projected onto the spherical surface, and the above-described processing may be performed using the projected point and line. Thereby, it is possible to easily perform the inside / outside determination and the calculation of the azimuth deviation even for the elliptical surface.

It is a flowchart which shows the main flow of inside / outside determination. It is explanatory drawing for demonstrating the inside / outside determination method. It is a figure which shows the specific method of a three-dimensional projection. It is the flowchart which showed more concretely the processing flow of each main block of the inside / outside determination method shown in FIG. It is a figure which shows the parameter structure of the database used for inside / outside determination. It is a flowchart which shows the detailed flow of each block in an inside / outside determination process. It is a figure which shows the concept of the determination reference | standard element of clipping determination. It is a figure which shows the example of the positional relationship on the complex plane of radius vector Zmm ', Zmn' and intersection vector vm. It is a flowchart which shows the general | schematic flow of a score integrating | accumulating process flow. It is a figure which shows the main concept of a scoring method. FIG. 11 shows a state where the negative half-line 110 and the arc vector CLm ′ intersect at one point on the complex plane, and the score in that state. It is a flowchart which shows the score integration process flow in case there is one intersection. It is a flowchart which shows the score integration process flow in case there are two intersections. An example of a state in which the negative half-line 110 and the arc vector CLm ′ intersect at two points on the complex plane and points in that state are shown. It is a figure explaining the concept of direction shift. It is a calculation flowchart of an azimuth | direction deviation. It is a figure which shows the relationship between the projection present position 101 on a complex plane, the projection advancing direction designation | designated position 121, and the projection target position 131. FIG. It is a figure explaining the cross track error XTE calculation method. It is explanatory drawing for demonstrating the problem of a prior art.

Explanation of symbols

a to f-closed region setting reference point, A to F-projection point, 100-determination position, 102-traveling direction designation position, 103-target position, 101-current projection position, 110-negative half-line, 121, 122 -Projection advance direction designation position, 131, 132-Projection target position, 140-Virtual pole, 141-Projection virtual pole, 200, 201A, 201B-Closed region, 300, SP-Sphere, 400, 401-Pole

Claims (13)

A position detection method for detecting the position of a specific position on a spherical surface,
Setting a plurality of boundary lines forming a closed region on the spherical surface;
Set a projection reference point on the spherical surface,
A plane perpendicular to an axis passing through the projection reference point and the center of the sphere forming the spherical surface and including the center of the sphere is set as a complex plane;
Projecting the specific position and the plurality of boundary lines on the complex plane with respect to the projection reference point,
A position detection method for performing inside / outside determination of the specific position with respect to the closed region on the complex plane based on a crossing situation of a half line starting from the projected specific position and the plurality of projected boundary lines.   2. The inside / outside determination is performed after the projected specific position and the plurality of projected boundary lines are translated so that the projected specific position is the origin of the complex plane on the complex plane. The position detection method as described in. For each of the projected boundary lines, set a crossing possibility criterion element composed of a plurality of straight line segments,
The position detection method according to claim 1 or 2, wherein a boundary line where an intersection between the half line and the intersection possibility determination criterion element is not detected does not detect the intersection with the half line.   4. The closed region according to claim 1, wherein the closed region is set on a side not including the projection reference point among two regions on the spherical surface divided by the plurality of boundary lines. 5. Position detection method.   The position according to any one of claims 1 to 3, wherein the inside / outside determination is performed after designating one of two regions on the spherical surface divided by a closed curve formed by the plurality of boundary lines as the closed region. Detection method.   The position detection method according to claim 5, wherein, when the projection reference point is included in the closed region, the projection and the inside / outside determination are performed after the projection reference point is set outside the designated closed region.   The position detection method according to claim 1, wherein the boundary line is a geodesic line on the spherical surface. A position detection method for detecting the position of a specific position on a spherical surface,
A traveling direction specific point set ahead of the direction in which the mobile object existing at the specific position travels, and a target direction specific point set ahead of the direction in which the mobile body should travel,
Set a projection reference point on the spherical surface,
A plane perpendicular to an axis passing through the projection reference point and the center of the sphere forming the spherical surface and including the center of the sphere is set as a complex plane;
Projecting the specific position, the traveling direction specific point, and the target direction specific point on the complex plane with respect to the projection reference point,
On the complex plane, a travel direction vector starting from the projected specific position as a starting point and a traveling direction specific point projected as an end point, and a target whose end point is the projected target direction specific point starting from the projected specific position as a starting point Set the direction vector and
A position detection method for calculating an angle formed by the traveling direction vector and the target direction vector. A point on the spherical surface that is perpendicular to and farthest from the circular plane passing through the traveling direction specific point and the target direction specific point is set as a virtual pole;
Projecting the virtual pole on the complex plane with respect to the projection reference point;
A first azimuth vector having the projected virtual pole point as a starting point and the projected traveling direction specifying point as an end point, and a second azimuth vector having the projected virtual pole point as a starting point and the projected target direction specifying point as an end point Set,
Calculating an angle formed by the first orientation vector and the second orientation vector;
The position detection method according to claim 8, wherein a distance on the spherical surface between the traveling direction specific point and the target direction specific point is calculated from the formed angle and the radius of the sphere. A position detection device for detecting what position a specific position on a spherical surface is,
Positioning means for acquiring the specific position;
Boundary line setting means for setting a plurality of boundary lines forming a closed region on the spherical surface;
A projection reference point is set on the spherical surface, a plane perpendicular to an axis passing through the projection reference point and the center of the sphere forming the spherical surface and including the center of the sphere is set as a complex plane, and the projection reference point is set. The specific position and the plurality of boundary lines are projected on the complex plane with reference to the reference plane, and on the complex plane, a half line starting from the projected specific position and the projected plurality of boundary lines Inside / outside determination means for determining inside / outside of the specific position with respect to the closed region based on an intersection situation;
A position detection device comprising: A position detection device for detecting what position a specific position on a spherical surface is,
Positioning means for acquiring the specific position;
Specific point setting means for setting a traveling direction specific point set ahead of the direction in which the mobile object existing at the specific position travels and a target direction specific point set ahead of the direction in which the mobile object should travel When,
A projection reference point is set on the spherical surface, a plane perpendicular to an axis passing through the projection reference point and the center of the sphere forming the spherical surface and including the center of the sphere is set as a complex plane, and the projection reference point is set. The specific position, the traveling direction specific point, and the target direction specific point are projected onto the complex plane on the basis of, and the projected traveling direction specific point is projected from the projected specific position on the complex plane. And a target direction vector starting from the projected specific position and having the projected target direction specific point as an end point, and an angle formed by the traveling direction vector and the target direction vector. Azimuth misalignment detection means for calculating,
A position detection device comprising: The direction deviation detecting means is
A point on the spherical surface that is perpendicular to the circular plane passing through the traveling direction specific point and the target direction specific point and is farthest from the circular plane is set as a virtual pole, and the virtual pole is set as the reference with respect to the projection reference point. Projecting onto a complex plane, starting from the projected virtual pole point, the first direction vector starting from the projected traveling direction specifying point and the projected target direction specifying point starting from the projected virtual pole point as the end point A second azimuth vector is set, an angle formed by the first azimuth vector and the second azimuth vector is calculated, and the traveling direction specific point and the target direction specific point are determined from the formed angle and the radius of the sphere. Calculating the distance on the spherical surface of
The position detection device according to claim 11. The spherical surface is the surface of the earth assumed to be a sphere,
The position detection device according to claim 10, wherein the specific position is a position of the device itself.

Images