JP5132731B2 - Position calculation apparatus, position calculation method, position calculation program, and storage medium for position calculation program - Google Patents

Description

  The present invention relates to a position calculation device, a position calculation method, a position calculation program, and a storage medium for the position calculation program.

The earth is an ellipsoid (earth ellipsoid), and a position on the earth can be specified by geographical longitude and latitude. However, because of the convenience of handling, plane rectangular coordinates are used in general surveys, etc., and the position is specified by the coordinates (Survey Method Article 11). For this coordinate plane, Gauss-Krugel isometric projection (transverse Mercator projection) projected directly from the spheroid (Earth ellipsoid) onto the plane is adopted, and the scale factor at the origin is set to 0.99990.
In order to use the earth ellipsoid as the survey reference, it is necessary to determine where the center of the ellipsoid is on the actual earth and where the coordinate axis of the ellipsoid passes on the actual earth. Yes, the earth ellipsoid whose position and direction are determined is the reference ellipsoid.

Strictly speaking, the horizontal position of the point on the earth should be represented by the geographical longitude and latitude on the reference ellipsoid, but the position, direction, distance, etc. are projected onto the plane as described above, and the survey calculation is performed. Doing is much easier and more convenient than on a curved surface. In addition, when the surveying range is narrow as in public surveying, it can be expressed sufficiently accurately.
Planar Cartesian coordinates used in Japan are based on the Gauss-Krugel conformal projection method. The meridian passing through the origin of the coordinate system is projected to be of equal length, and the figure is projected to a similar equiangular shape. However, for the distance, as the plane distance increases from the reference meridian to the east and west, the above scale factor (0.9999) is given to the coordinate origin so that the error of the projection distance is relatively within 1 / 10,000, In addition, a coordinate system (planar rectangular coordinate system divides the whole country of Japan into 19 coordinate systems) is set within 130 km from east to west from the reference meridian (Non-Patent Document 1).
Note that the X axis of the coordinate system is the axis that coincides with the meridian at the origin, and the value from the origin toward true north is positive. The Y axis is an axis orthogonal to the X axis at the origin, and a value toward the east is positive. In this respect, the definition is different from the three-dimensional orthogonal coordinates (X, Y, Z). The value of the origin of each coordinate system is X = Y = 0.000 meters.

  In the result table of survey results, the distance on the ellipsoidal surface is described as the distance, and the plane rectangular coordinate (x, y) is described in addition to the latitude and longitude as the coordinate. Regarding the relationship between the ellipsoidal surface and the plane, the ellipsoidal cylinder (virtual cylinder) covered with the reference ellipsoid is expanded to obtain the plane coordinates (x, y). In this case, the plane distance on the reference meridian is shorter than the distance on the ellipsoid by 1 / 10,000, and the scale factor is 0.9999. In a place about 90 km away from the reference meridian east and west, the distance between the plane and the ellipsoidal plane is equal, and the scale factor is 1.0000. When 130 km away from the reference meridian from east to west, the plane distance becomes 1 / 10,000 longer than the ellipsoidal plane distance, and the scale factor is 1.0001.

As a means of calculating the latitude and longitude of coordinated coordinates x and y on the plane Cartesian coordinates X and Y for Japan, “Conversion to latitude and longitude” on the GSI website (Non-patent Document 3) Programs are available.
By using this program, the latitude and longitude can be easily calculated on the web by inputting the coordinate values x and y.
However, in this program, the error increases with increasing distance from the reference meridian of the coordinate system to which the coordinate values x and y belong.
This error is the same as the latitude and longitude obtained by the “Conversion to Latitude / Longitude” program on the Geographical Survey Institute website. It can be easily confirmed.

For example, in the GSI website “Conversion to Latitude / Longitude” (Non-Patent Document 3), the geodetic system is the world geodetic system, the plane rectangular coordinate system is 3, and the above-mentioned “Conversion from planar rectangular coordinates to latitude / longitude” The coordinate values X and Y of arbitrary five points on the plane rectangular coordinates were given to the program, and the results (latitude and longitude) shown in a-1) to a-5) were obtained.
a-1) is a point on the meridian passing through the coordinate origin (0, 0) of the coordinate system 3, and in a-2) to a-5), the value of the input coordinate value Y is moved westward from the reference meridian. Gradually move away.
Then, in the “conversion to plane rectangular coordinates” program, the north latitude and the east longitude are input by trial and error so that the coordinate values input in the above a-1) to a-5) match the conversion results (north latitude and Various changes were made to the east longitude values, and the output values were found to match the input values in the “Conversion to plane rectangular coordinates” program). And the result (coordinate value on a plane rectangular coordinate) shown in b-1) to b-5) was obtained.

a-1)
Input value X coordinate -207504.143 m Y coordinate
0 m
Results Latitude 34 ° 07'45.93167 "Longitude 132 ° 10'00.00000"
True north direction angle + 0 ° 00'00.00 "Scale factor 0.99990000
a-2)
Input value X coordinate -207494.938 m Y coordinate -59997.338 m
Results Latitude 34 ° 07'40.02853 "Longitude 131 ° 30'58.32911"
True north direction angle + 0 ° 21'53.81 "Scale factor 0.99994436
a-3)
Input value X coordinate -207483.393 m Y coordinate -90082.603 m
Results Latitude 34 ° 07'32.62476 "Longitude 131 ° 11'24.23439"
True north direction angle + 0 ° 32'52.52 "Scale factor 1.00000000
a-4)
Input value X coordinate -207467.727 m Y coordinate
-119340.074 m
Results Latitude 34 ° 07'22.57910 "Longitude 130 ° 52'22.58340"
True north direction angle + 0 ° 43'32.98 "Scale factor 1.00007551
a-5)
Input value X coordinate -207462.646 m Y coordinate
-127394.933 m
Results Latitude 34 ° 07'19.32100 "Longitude 130 ° 47'08.30605"
True north direction angle + 0 ° 46'29.28 "Scale factor 1.00010000

b-1)
Input value North latitude 34 ° 07'45.93167 "East longitude 132 ° 10'00.00000"
Conversion result X coordinate -207504.143 m Y coordinate
0.0000 m
True north direction angle + 0 ° 00'00.00 "Scale factor 0.99990000
b-2)
Input value North latitude 34 ° 07'40.02854 "East longitude 131 ° 30'58.32910"
Conversion result X coordinate -207494.938 m Y coordinate
-59997.338m
True north direction angle + 0 ° 21'53.81 "Scale factor 0.99994436
b-3)
Input North latitude 34 ° 07'32.62478 "East longitude 131 ° 11'24.23440"
Conversion result X coordinate -207483.393 m Y coordinate
-90082.603m
True north direction angle + 0 ° 32'52.52 "Scale factor 1.00000000
b-4)
Input value North latitude 34 ° 07'22.57909 "East longitude 130 ° 52'22.58341"
Conversion result X coordinate -207467.727 m Y coordinate
-119340.074 m
True north direction angle + 0 ° 43'32.98 "Scale factor 1.00007551
b-5)
Input value North latitude 34 ° 07'19.32099 "East longitude 130 ° 47'08.30603"
Conversion result X coordinate -207462.646 m Y coordinate
-127394.933 m
True north direction angle + 0 ° 46'29.28 "Scale factor 1.00010000

Looking at the above results, the input value obtained in b-1) so as to obtain an output value that matches the input value in a-1) matches the conversion result in a-1). (Latitude 34 ° 07'45.93167 "and longitude 132 ° 10'00.00000" in the conversion result in the above a-1) coincide with the north latitude and east longitude of the input value in b-1). That is, on the reference meridian passing through the origin, it can be said that the “convert to plane rectangular coordinate” program does not cause an error at least within the number of digits that can be calculated.
However, with regard to a-2), looking at b-2) in which the same operation as described above is performed, the conversion result in a-2) and the input value in b-2) do not match. That is, the former a-2) has a latitude of 34 ° 07'40.02853 "and a longitude of 131 ° 30'58.32911", whereas the latter b-2) has a north latitude of 34 ° 07'40.02854 "and an east longitude of 131 It is assumed that the angle is 30'58.32910 ", and there is a discrepancy between the latitude and longitude at the fifth decimal place (lowest).
Regarding the occurrence of such an error, when looking at b-3) to b-5) corresponding to a-3 to a-5), as the distance from the reference meridian goes west, the error particularly with respect to longitude increases. I understand that
For example, a conversion result (latitude 34 ° 07'19.32100 ", longitude 130 ° 47'08.30605") at a point about 127 km away from the reference meridian to the west, and an input value corresponding to b-5) ( With latitude 34 ° 07'19.32099 "north latitude 130 ° 47'08.30603"), there is already a discrepancy already in the third decimal place in latitude.

Geographical Survey Institute website http://vldb.gsi.go.jp/sokuchi/datum/tokyodatum.html Geospatial Information Authority of Japan “Calculation of latitude by giving meridian arc length from the equator” http://vldb.gsi.go.jp/sokuchi/surveycalc/algorithm/s2b/s2b.htm Geospatial Information Authority of Japan “Conversion to latitude and longitude” http://vldb.gsi.go.jp/sokuchi/surveycalc/xy2blf.html Geospatial Information Authority of Japan homepage "Conversion to planar rectangular coordinates" http://vldb.gsi.go.jp/sokuchi/surveycalc/bl2xyf.html

Therefore, in this program, there is no problem in the vicinity of the reference meridian of the coordinate system origin to which the input coordinate values X and Y belong, but as the distance from the reference meridian to the east and west, the accuracy of latitude and longitude as the conversion result decreases significantly. It becomes impossible to handle as strict data.
In the above, the cause of such an error is not disclosed to the present inventor because the contents of the program are not disclosed.
Further, as far as possible by the inventor, patent gazettes were examined as prior art documents, but no gazette in which the same kind of invention was described has been found.
Therefore, the inventor pondered and inferred this point, for example, in the above program of the Geospatial Information Authority of Japan, for the latitude, for example, the GSI website “Calculation to find latitude by giving meridian arc length from the equator” The convergence calculation for latitude will be performed using the formula shown in the literature 2), etc., but the change of the scale factor when it is away from the reference meridian is not sufficiently reflected. As a result, it is considered that the accuracy of the latitude that has become stable due to convergence (repetitive calculation) is not sufficient (has converged at a shifted position).
Specifically, the above program of the Geospatial Information Authority of Japan is the φ _{n + 1} shown in “6. Calculation to obtain latitude by giving meridian arc length from the equator” on the Geographical Survey Institute website shown in Non-Patent Document 2. It is considered that iterative calculation is performed using an expression for obtaining (the result using this expression agrees with the above). When iterative calculation is performed using this equation, as described above, the numerical value is stabilized (converged) with a value having a large error. Considering the reason, in the calculation of this formula, the scale factor is fixed to the scale factor m ₀ (= 0.9999) at the origin, and the scale factor at the coordinate position to be obtained other than the reference meridian is The fact that it is different from the scale factor m ₀ (= 0.9999) has been ignored (note that M used in the Geographical Survey Institute equation represents the meridian arc length from the equator to the origin of the coordinate system, Different from M, which indicates the meridian radius of curvature used in this specification).
At present, it is not out of speculation, but the results of using the program are obvious.
Therefore, the program is extremely unreliable and difficult to use in situations where strictness is required.

  The present invention flexibly handles the scale factor for a position calculation device capable of obtaining at least the latitude on the earth ellipsoid from the coordinate values on the plane rectangular coordinates X and Y for projecting the earth ellipsoid by the isometric projection method. In order to solve the above problems, a new apparatus with low error is provided.

According to the first invention of the present application, by inputting coordinate values x and y on the plane rectangular coordinates X and Y for projecting the earth ellipsoid by the isometric projection method, at least the latitude on the earth ellipsoid corresponding to the coordinate values. A position calculation device capable of outputting φ _n is provided with the following configuration.
That is, the position calculation device includes a coordinate input unit, an output unit, a constant setting unit, a condition setting unit, a first temporary latitude storage unit, a second temporary latitude storage unit, and a first temporary scale coefficient storage unit. And a second temporary scale coefficient storage unit, at least five first to fifth calculation units, a calculation control unit, a determination unit, and a regression control unit. The constant setting unit includes at least a latitude φ ₀ of the origin of the coordinate system, a major radius a and a minor radius b of the earth ellipsoid, a first eccentricity e of the earth ellipsoid, and a second eccentricity e ′ of the earth ellipsoid, The radius of curvature c of the ellipsoid of the earth ellipsoid and the values of the following constants A to F necessary for calculating the meridian arc length W on the reference meridian from the equator to the coordinate value x are previously stored. It is.
A = 1 + (3/4) e ² + (45/64) e ⁴ + (175/256 ) e ⁶ + (11025/16384) e ⁸ + (43659/65536) e ^{10
B = (3/4) e 2 +} (15/16) e 4 + (525/512) e 6 + (2205/2048) e 8 + (72765/65536) e 10
^{C = (15/64) e 4 +} (105/256) e 6 + (2205/4096) e 8 + (10395/16384) e 10
D = (35/512) e ⁶ + (315/2048) e ⁸ + (31185/131072) e ¹⁰
E = (315/16384) e 8 + (3465/65536) e 10
F = (693/131072) e ¹⁰
The latitude of the perpendicular line drawn from the input coordinate to the reference meridian passing through the origin of the coordinate system to which the input coordinate belongs is defined as the perpendicular latitude, and a threshold value that is a convergence condition IPS of the perpendicular latitude is preset in the condition setting unit. The first temporary latitude accommodating portion is capable of accommodating the initial value φ _j of the normal latitude , and the first temporary scale factor accommodating portion accepts any real number other than 0 as the temporary scale factor m. It can be accommodated as _t .
The first calculation unit has a function of executing at least the calculations of the following formulas 7, 8, and 9.
V _{k + 1} = (1 + e ′ ² cos ² φ _{k + 1} ) ^1/2 .
R _k2 = c / V _{k + 1} ²
... Formula 8
^{_{m t2 = (1 + y 2}} / 2m t 2 R k2 2 + y 4 / 24m t 4 R k2 4) × 0.9999 ... Equation 9
The second calculation unit has a function of executing at least the calculation of Expression 10 below.
W = a (1-e ² ) · {A · φ ₀ − (B / 2) · (sin 2φ ₀ ) + (C / 4) · (sin 4φ ₀ ) − (D / 6) · (sin 6φ ₀ ) + (E / 8) · (sin 8φ ₀ ) − (F / 10) · (sin 10φ ₀ )} + x / m _t Equation 10
The third calculation unit has a function of executing at least the calculation of Expression 11 below.
S (φ _j
) = A (1-e ² ) · {A · φ _j − (B / 2) · (sin 2φ _j ) + (C / 4) · (sin 4φ _j ) − (D / 6) · (sin 6φ _j ) + (E / 8) · (sin 8φ _j ) − (F / 10) · (sin 10φ _j )}
The fourth arithmetic unit is at least W in Equation 10 and S (φ _{j in} Equation 11).
) And a function for executing a calculation for calculating the normal latitude φ _{j + 1} by the convergence calculation of the normal latitude .
The fifth calculation unit has a function of executing at least the calculation of Expression 3 below.
φ _{k + 1} = φ _k −t _k (y / m _t ) ² / 2M _k N _k + t _k (y / m _t ) ⁴ (5 + 3 t _k ² + η _{k
^{2 -9t k 2 η k 2 -4η}} k 4) / 24M k N k 3 -t k (y / m t) 6 (61 + 90t k 2 + 45t k 4) / 720M k N k 5
... Formula 3
The coordinate input unit accepts input of the coordinate values x and y. The calculation control unit causes the second calculation unit to refer to the constant setting unit, the coordinate input unit, and the first temporary scale coefficient storage unit, and the major radius a of the earth ellipsoid and the first eccentricity of the earth ellipsoid. and rate e, the origin latitude phi _0, and input coordinate values x, standards of the temporary scale factor m _t, and a said constant to F, by calculating the above equation 10, from the equator to the coordinate values x The meridian arc length W on the meridian is calculated, and the second calculation unit stores the calculated meridian arc length W in the constant setting unit. The calculation control unit causes the third calculation unit to refer to the constant setting unit and the first temporary latitude storage unit, the major radius a of the earth ellipsoid, the first eccentricity e of the earth ellipsoid, and the normal latitude. an initial value phi _j of the from constant to F, by calculating the above equation 11, meridian arc length S from the equator to the initial value phi _j of a perpendicular latitude (phi _j
) And the third calculation unit stores the calculated meridian arc length S (φ _j ) in the constant setting unit. The calculation control unit causes the fourth calculation unit to refer to the constant setting unit and the first temporary latitude accommodation unit, the initial value φ _j of the normal latitude, the major radius a of the earth ellipsoid, and the first value of the earth ellipsoid. 1 eccentricity e and the meridian arc length W on the reference meridian from the equator to the coordinates x, meridian arc length from the equator to the initial value phi _j of a perpendicular latitude S (phi _j
) To calculate the latitude φ _{j + 1} , and the fourth calculation unit stores the calculated latitude φ _{j + 1} in the first temporary latitude storage unit. The first temporary latitude housing portion which receives the latitude phi _{j + 1} of the fourth arithmetic unit is accommodated to have latitude phi _j
Passes into the second temporary latitude accommodating portion, for accommodating the value of the latitude phi _{j + 1} instead of the latitude phi _j. The determination unit refers to the first temporary latitude storage unit, the second temporary latitude storage unit, and the condition setting unit, and uses the absolute value of the difference between the latitude φ _{j + 1} and the latitude φ _j and the convergence condition IPS of the normal latitude. When the absolute value of the difference between latitude φ _{j + 1} and latitude φ _j is determined to be greater than the threshold value by comparing with a certain threshold value, the result is notified to the regression control unit and the notification is received. regression control unit, the value of the latitude phi _{j + 1} of the first temporary latitude housing portion, as the latitude phi _j, the third arithmetic unit again to perform the calculation of equation 11, the calculated meridian arc length S (phi _j
) Is stored in the constant setting unit, and the fourth arithmetic unit is again referred to the constant setting unit and the meridian arc length S (φ _j
From), to calculate the latitude phi _{j + 1,} the first temporary latitude accommodating portion, thereby passed the latitude phi _j that held until then to the second temporary latitude accommodating portion, first to the latitude phi _j that held 4 The latitude φ _{j + 1} calculated again by the calculation unit is replaced. The determination unit performs the above determination again with reference to the first temporary latitude storage unit, the second temporary latitude storage unit, and the condition setting unit, and calculates the absolute value of the difference between the latitude φ _{j + 1} and the latitude φ _j Until it is determined that the value is equal to or lower than the threshold value, the regression control unit repeatedly causes the third calculation unit to perform the calculation of Expression 11 and causes the fourth calculation unit to repeatedly perform the convergence calculation of the latitude. When the determination unit determines that the absolute value of the difference between the latitude φ _{j + 1} and the latitude φ _j is equal to or less than the threshold value, the asymptotic latitude φ _{j + 1} is set as the perpendicular latitude φ _k and the regression control is performed. The unit refers to the coordinate input unit, the first temporary latitude accommodating unit, the constant setting unit, and the first temporary scale factor accommodating unit, and the provisional scale factor m _t , and the perpendicular latitude phi _k, the radius M _k and prime vertical radius of curvature N _k meridian curvature at the perpendicular latitude phi _k, a first value eta _k determined by e'cos φ _k, tan
By calculating the above equation 3 from the second value t _k determined by φ _k and the input coordinate value y, the latitude φ _{k + 1} is calculated, and the fifth calculation unit calculates The latitude φ _{k + 1} is stored as a latitude φ _n of the input coordinate point in the first temporary latitude storage unit, replacing the value previously stored in the first temporary latitude storage unit. The latitude accommodating unit passes the value of the latitude φ _k that has been held so far to the second temporary latitude accommodating unit. Further, in the calculation control unit, the first calculation unit is referred to the constant setting unit and the first temporary latitude accommodation unit, the second eccentricity e ′ of the earth ellipsoid, the latitude φ _{k + 1,} and Therefore, the average curvature radius R _k2 at the latitude φ _{k + 1} is calculated by _{performing the} calculation of Expression 7 and Expression 8 . Arithmetic control unit, the first operation unit, a coordinate input unit, by referring to the first temporary scale factor accommodating portion, and the value of the coordinate value y input, a temporary scale factor m _t, the mean curvature The scale factor _mt2 is calculated from the radius _Rk2 by calculating the above formula 9 , and the first calculation unit stores the calculated scale factor _mt2 in the first temporary scale factor storage unit. 1 temporary scale factor accommodating portion passes the housing to have a scale factor m _t to the second temporary scale factor accommodating portion, for accommodating the scale factor m _t2 instead as the scale factor m _t above. Regression control unit, through the operation control unit, the scale factor m _t2 that the calculated instead of the temporary scale factor m _t so far as scale factor m _t of the next temporary, at least once, the second, fourth and 5. Recalculate Equation 10, Convergence of Latitude, Equation 3 in the 5 arithmetic unit, and Equations 7, 8, and 9 in the first arithmetic unit. The regression control unit causes the output unit to output at least the value of the latitude φ _{k + 1} stored in the first temporary latitude storage unit after the recalculation .
The earth ellipsoid here includes various reference ellipsoids.
The reference meridian means a meridian passing through the origin of the coordinate system to which the coordinates belong.
The perpendicular latitude is the latitude at the intersection of the perpendicular drawn from the input coordinates to the reference meridian and the reference meridian.
In the above, the regression control unit is not limited to a unit that directly issues a calculation command to the calculation unit, but includes a unit that causes the calculation unit to perform calculation indirectly.

According to the second invention of the present application , by inputting coordinate values x and y on plane rectangular coordinates X and Y for projecting the earth ellipsoid by an isometric projection method, at least the latitude on the earth ellipsoid corresponding to the coordinate values. A position calculation device capable of outputting φ _n is provided with the following configuration.
That is, the position calculation device includes a coordinate input unit, an output unit, a constant setting unit, a condition setting unit, a first temporary latitude storage unit, a second temporary latitude storage unit, and a first temporary scale coefficient storage unit. And a second temporary scale coefficient storage unit, at least five first to fifth calculation units, a calculation control unit, a determination unit, and a regression control unit. The constant setting unit includes at least the latitude φ _{0 of} the origin of the coordinate system, the value of the scale factor m _{0 at} the origin , the major radius a and minor radius b of the earth ellipsoid, the first eccentricity e of the earth ellipsoid, and the earth ellipse The following constants A to F necessary to calculate the second eccentricity e ′ of the body, the radius of curvature c of the pole of the earth ellipsoid, and the meridian arc length W on the reference meridian from the equator to the coordinate value x, respectively. Is stored in advance.
A = 1 + (3/4) e ² + (45/64) e ⁴ + (175/256 ) e ⁶ + (11025/16384) e ⁸ + (43659/65536) e ^{10
B = (3/4) e 2 +} (15/16) e 4 + (525/512) e 6 + (2205/2048) e 8 + (72765/65536) e 10
^{C = (15/64) e 4 +} (105/256) e 6 + (2205/4096) e 8 + (10395/16384) e 10
D = (35/512) e ⁶ + (315/2048) e ⁸ + (31185/131072) e ¹⁰
E = (315/16384) e 8 + (3465/65536) e 10
F = (693/131072) e ¹⁰
The latitude of the perpendicular line drawn from the input coordinate to the reference meridian passing through the origin of the coordinate system to which the input coordinate belongs is defined as the perpendicular latitude, and a threshold value that is a convergence condition IPS of the perpendicular latitude is preset in the condition setting unit. The first temporary latitude accommodating portion is capable of accommodating the initial value φ _j of the normal latitude , and the first temporary scale factor accommodating portion accepts any real number other than 0 as the temporary scale factor m. It can be accommodated as _t .
The first calculation unit has a function of executing at least the calculations of the following formulas 7, 8, and 9.
V _{k + 1} = (1 + e ′ ² cos ² φ _{k + 1} ) ^1/2 .
R _k2 = c / V _{k + 1} ²
... Formula 8
^{_{m t2 = (1 + y 2}} / 2m t 2 R k2 2 + y 4 / 24m t 4 R k2 4) × 0.9999 ... Equation 9
The second calculation unit has a function of executing at least the calculation of Expression 10 below.
W = a (1-e ² ) · {A · φ ₀ − (B / 2) · (sin 2φ ₀ ) + (C / 4) · (sin 4φ ₀ ) − (D / 6) · (sin 6φ ₀ ) + (E / 8) · (sin 8φ ₀ ) − (F / 10) · (sin 10φ ₀ )} + x / m _t Equation 10
The third calculation unit has a function of executing at least the calculation of Expression 11 below.
S (φ _j
) = A (1-e ² ) · {A · φ _j − (B / 2) · (sin 2φ _j ) + (C / 4) · (sin 4φ _j ) − (D / 6) · (sin 6φ _j ) + (E / 8) · (sin 8φ _j ) − (F / 10) · (sin 10φ _j )}
The fourth arithmetic unit is at least W in Equation 10 and S (φ _{j in} Equation 11).
) And a function for executing a calculation for calculating the normal latitude φ _{j + 1} by the convergence calculation of the normal latitude .
The fifth calculation unit has a function of executing at least the calculation of Expression 3 below.
φ _{k + 1} = φ _k −t _k (y / m _t ) ² / 2M _k N _k + t _k (y / m _t ) ⁴ (5 + 3 t _k ² + η _{k
^{2 -9t k 2 η k 2 -4η}} k 4) / 24M k N k 3 -t k (y / m t) 6 (61 + 90t k 2 + 45t k 4) / 720M k N k 5
... Formula 3
The coordinate input unit accepts input of the coordinate values x and y. The calculation control unit causes the first calculation unit to refer to the constant setting unit, the latitude φ ₀ of the origin of the coordinate system , the second eccentricity e ′ of the earth ellipsoid, and the radius of curvature of the pole of the earth ellipsoid From c, in the calculation function of Equation 7 and Equation 8 above,
V ₀ = (1 + e ′ ² cos ² φ ₀ ) ^1/2
R ₀ = c / V ₀ ²

To calculate the average radius of curvature R ₀ at the origin .
The average curvature radius R ₀ at the origin is calculated by the first calculation unit and stored in the constant setting unit. The arithmetic control unit stores the scale factor m ₀ at the origin of the constant setting unit in the first temporary scale factor storage unit. Said 1st calculating part can perform the calculation of following Formula 2 with the calculation function of said Formula 9. FIG.
m _t = {1+ (y ² / 2m ₀ ² R ₀ ² ) + (y ⁴ / 24m ₀ ⁴ R ₀ ⁴ )} × 0.9999 Equation 2
The calculation control unit causes the first calculation unit to refer to the constant setting unit or the first temporary scale factor storage unit and the coordinate input unit, and inputs the value of the coordinate value y, the origin scale factor m ₀ , the average radius of curvature R ₀ Prefecture, by causing the calculation of equation 2 to calculate the temporary scale factor m _t, a first arithmetic unit, a scale factor m _t calculated tentative as scale factor of the provisional Then, instead of the origin scale factor m _0, it is accommodated in the first temporary scale factor accommodating part. The calculation control unit causes the second calculation unit to refer to the constant setting unit, the coordinate input unit, and the first temporary scale coefficient storage unit, and the major radius a of the earth ellipsoid and the first eccentricity of the earth ellipsoid. and rate e, the origin latitude phi _0, and input coordinate values x, standards of the temporary scale factor m _t, and a said constant to F, by calculating the above equation 10, from the equator to the coordinate values x The meridian arc length W on the meridian is calculated, and the second calculation unit stores the calculated meridian arc length W in the constant setting unit. The calculation control unit causes the third calculation unit to refer to the constant setting unit and the first temporary latitude storage unit, the major radius a of the earth ellipsoid, the first eccentricity e of the earth ellipsoid, and the normal latitude. an initial value phi _j of the from constant to F, by calculating the above equation 11, meridian arc length S from the equator to the initial value phi _j of a perpendicular latitude (phi _j
) And the third calculation unit stores the calculated meridian arc length S (φ _j ) in the constant setting unit. The calculation control unit causes the fourth calculation unit to refer to the constant setting unit and the first temporary latitude accommodation unit, the initial value φ _j of the normal latitude, the major radius a of the earth ellipsoid, and the first value of the earth ellipsoid. 1 eccentricity e and the meridian arc length W on the reference meridian from the equator to the coordinates x, meridian arc length from the equator to the initial value phi _j of a perpendicular latitude S (phi _j
) To calculate the latitude φ _{j + 1} , and the fourth calculation unit stores the calculated latitude φ _{j + 1} in the first temporary latitude storage unit. The first temporary latitude housing portion which receives the latitude phi _{j + 1} of the fourth arithmetic unit is accommodated to have latitude phi _j
Passes into the second temporary latitude accommodating portion, for accommodating the value of the latitude phi _{j + 1} instead of the latitude phi _j. The determination unit refers to the first temporary latitude storage unit, the second temporary latitude storage unit, and the condition setting unit, and uses the absolute value of the difference between the latitude φ _{j + 1} and the latitude φ _j and the convergence condition IPS of the normal latitude. When the absolute value of the difference between latitude φ _{j + 1} and latitude φ _j is determined to be greater than the threshold value by comparing with a certain threshold value, the result is notified to the regression control unit and the notification is received. regression control unit, the value of the latitude phi _{j + 1} of the first temporary latitude housing portion, as the latitude phi _j, the third arithmetic unit again to perform the calculation of equation 11, the calculated meridian arc length S (phi _j
) Is stored in the constant setting unit, and the fourth arithmetic unit is again referred to the constant setting unit and the meridian arc length S (φ _j
From), to calculate the latitude phi _{j + 1,} the first temporary latitude accommodating portion, thereby passed the latitude phi _j that held until then to the second temporary latitude accommodating portion, first to the latitude phi _j that held 4 The latitude φ _{j + 1} calculated again by the calculation unit is replaced. The determination unit performs the above determination again with reference to the first temporary latitude storage unit, the second temporary latitude storage unit, and the condition setting unit, and calculates the absolute value of the difference between the latitude φ _{j + 1} and the latitude φ _j Until it is determined that the value is equal to or lower than the threshold value, the regression control unit repeatedly causes the third calculation unit to perform the calculation of Expression 11 and causes the fourth calculation unit to repeatedly perform the convergence calculation of the latitude. When the determination unit determines that the absolute value of the difference between the latitude φ _{j + 1} and the latitude φ _j is equal to or less than the threshold value, the asymptotic latitude φ _{j + 1} is set as the perpendicular latitude φ _k and the regression control is performed. The unit refers to the coordinate input unit, the first temporary latitude accommodating unit, the constant setting unit, and the first temporary scale factor accommodating unit, and the provisional scale factor m _t , and the perpendicular latitude phi _k, the radius M _k and prime vertical radius of curvature N _k meridian curvature at the perpendicular latitude phi _k, a first value eta _k determined by e'cos φ _k, tan
By calculating the above equation 3 from the second value t _k determined by φ _k and the input coordinate value y, the latitude φ _{k + 1} is calculated, and the fifth calculation unit calculates The latitude φ _{k + 1} is stored as a latitude φ _n of the input coordinate point in the first temporary latitude storage unit, replacing the value previously stored in the first temporary latitude storage unit. The latitude accommodating unit passes the value of the latitude φ _k that has been held so far to the second temporary latitude accommodating unit. Further, in the calculation control unit, the first calculation unit is referred to the constant setting unit and the first temporary latitude accommodation unit, the second eccentricity e ′ of the earth ellipsoid, the latitude φ _{k + 1,} and Therefore, the average curvature radius R _k2 at the latitude φ _{k + 1} is calculated by _{performing the} calculation of Expression 7 and Expression 8 . Arithmetic control unit, the first operation unit, a coordinate input unit, by referring to the first temporary scale factor accommodating portion, and the value of the coordinate value y input, a temporary scale factor m _t, the mean curvature The scale factor _mt2 is calculated from the radius _Rk2 by calculating the above formula 9 , and the first calculation unit stores the calculated scale factor _mt2 in the first temporary scale factor storage unit. 1 temporary scale factor accommodating portion passes the housing to have a scale factor m _t to the second temporary scale factor accommodating portion, for accommodating the scale factor m _t2 instead as the scale factor m _t above. Regression control unit, through the operation control unit, the scale factor m _t2 that the calculated instead of the temporary scale factor m _t so far as scale factor m _t of the next temporary, at least once, the second, fourth and 5. Recalculate Equation 10, Convergence of Latitude, Equation 3 in the 5 arithmetic unit, and Equations 7, 8, and 9 in the first arithmetic unit. The regression control unit causes the output unit to output at least the value of the latitude φ _{k + 1} stored in the first temporary latitude storage unit after the recalculation .

According to the third invention of the present application , by inputting coordinate values x and y on the plane rectangular coordinates X and Y for projecting the earth ellipsoid by the isometric projection method, at least the latitude on the earth ellipsoid corresponding to the coordinate values. A position calculation device capable of outputting φ _n is provided with the following configuration.
That is, the position calculation device includes a coordinate input unit, an output unit, a constant setting unit, a condition setting unit, a first temporary latitude storage unit, a second temporary latitude storage unit, and a first temporary scale coefficient storage unit. And a second temporary scale coefficient storage unit, at least five first to fifth calculation units, a calculation control unit, a main determination unit, a sub determination unit, and a regression control unit. The constant setting unit includes at least a latitude φ ₀ of the origin of the coordinate system, a major radius a and a minor radius b of the earth ellipsoid, a first eccentricity e of the earth ellipsoid, and a second eccentricity e ′ of the earth ellipsoid, The radius of curvature c of the ellipsoid of the earth ellipsoid and the values of the following constants A to F necessary for calculating the meridian arc length W on the reference meridian from the equator to the coordinate value x are previously stored. It is.
A = 1 + (3/4) e ² + (45/64) e ⁴ + (175/256 ) e ⁶ + (11025/16384) e ⁸ + (43659/65536) e ^{10
B = (3/4) e 2 +} (15/16) e 4 + (525/512) e 6 + (2205/2048) e 8 + (72765/65536) e 10
^{C = (15/64) e 4 +} (105/256) e 6 + (2205/4096) e 8 + (10395/16384) e 10
D = (35/512) e ⁶ + (315/2048) e ⁸ + (31185/131072) e ¹⁰
E = (315/16384) e 8 + (3465/65536) e 10
F = (693/131072) e ¹⁰
The normal latitude drawn from the input coordinate to the reference meridian passing through the origin of the coordinate system to which the input coordinate belongs is defined as the normal latitude, and the condition setting unit includes a threshold value that is a convergence condition IPS of the normal latitude, A threshold value that is a coefficient convergence condition IPS2 is set in advance, and the first temporary latitude accommodating portion can accommodate an initial value φ _j of a normal latitude , and the first temporary scale factor accommodating portion is one that can accommodate an arbitrary real number other than 0 as the temporary scale factor m _t.
The first calculation unit has a function of executing at least the calculations of the following formulas 7, 8, and 9.
V _{k + 1} = (1 + e ′ ² cos ² φ _{k + 1} ) ^1/2 .
R _k2 = c / V _{k + 1} ²
... Formula 8
^{_{m t2 = (1 + y 2}} / 2m t 2 R k2 2 + y 4 / 24m t 4 R k2 4) × 0.9999 ... Equation 9
The second calculation unit has a function of executing at least the calculation of Expression 10 below.
W = a (1-e ² ) · {A · φ ₀ − (B / 2) · (sin 2φ ₀ ) + (C / 4) · (sin 4φ ₀ ) − (D / 6) · (sin 6φ ₀ ) + (E / 8) · (sin 8φ ₀ ) − (F / 10) · (sin 10φ ₀ )} + x / m _t Equation 10
The third calculation unit has a function of executing at least the calculation of Expression 11 below.
S (φ _j
) = A (1-e ² ) · {A · φ _j − (B / 2) · (sin 2φ _j ) + (C / 4) · (sin 4φ _j ) − (D / 6) · (sin 6φ _j ) + (E / 8) · (sin 8φ _j ) − (F / 10) · (sin 10φ _j )}
The fourth arithmetic unit is at least W in Equation 10 and S (φ _{j in} Equation 11).
) And a function for executing a calculation for calculating the normal latitude φ _{j + 1} by the convergence calculation of the normal latitude .
The fifth calculation unit has a function of executing at least the calculation of Expression 3 below.
φ _{k + 1} = φ _k −t _k (y / m _t ) ² / 2M _k N _k + t _k (y / m _t ) ⁴ (5 + 3 t _k ² + η _{k
^{2 -9t k 2 η k 2 -4η}} k 4) / 24M k N k 3 -t k (y / m t) 6 (61 + 90t k 2 + 45t k 4) / 720M k N k 5
... Formula 3
The coordinate input unit accepts input of the coordinate values x and y. The calculation control unit causes the second calculation unit to refer to the constant setting unit, the coordinate input unit, and the first temporary scale coefficient storage unit, and the major radius a of the earth ellipsoid and the first eccentricity of the earth ellipsoid. and rate e, the origin latitude phi _0, and input coordinate values x, standards of the temporary scale factor m _t, and a said constant to F, by calculating the above equation 10, from the equator to the coordinate values x The meridian arc length W on the meridian is calculated, and the second calculation unit stores the calculated meridian arc length W in the constant setting unit. The calculation control unit causes the third calculation unit to refer to the constant setting unit and the first temporary latitude storage unit, the major radius a of the earth ellipsoid, the first eccentricity e of the earth ellipsoid, and the normal latitude. an initial value phi _j of the from constant to F, by calculating the above equation 11, meridian arc length S from the equator to the initial value phi _j of a perpendicular latitude (phi _j
) And the third calculation unit stores the calculated meridian arc length S (φ _j ) in the constant setting unit. The calculation control unit causes the fourth calculation unit to refer to the constant setting unit and the first temporary latitude accommodation unit, the initial value φ _j of the normal latitude, the major radius a of the earth ellipsoid, and the first value of the earth ellipsoid. 1 eccentricity e and the meridian arc length W on the reference meridian from the equator to the coordinates x, meridian arc length from the equator to the initial value phi _j of a perpendicular latitude S (phi _j
) To calculate the latitude φ _{j + 1} , and the fourth calculation unit stores the calculated latitude φ _{j + 1} in the first temporary latitude storage unit. The first temporary latitude housing portion which receives the latitude phi _{j + 1} of the fourth arithmetic unit is accommodated to have latitude phi _j
Passes into the second temporary latitude accommodating portion, for accommodating the value of the latitude phi _{j + 1} instead of the latitude phi _j. The main determination unit refers to the first temporary latitude accommodation unit, the second temporary latitude accommodation unit, and the condition setting unit, and the absolute value of the difference between the latitudes φ _{j + 1} and the latitude φ _j and the normal latitude convergence condition IPS If the absolute value of the difference between latitude φ _{j + 1} and latitude φ _j is determined to be greater than the threshold, the result is notified to the regression control unit and the notification receives regression controller, the value of the latitude phi _{j + 1} of the first temporary latitude accommodating portion, the latitude phi as _j, the third arithmetic unit again to perform the calculation of equation 11, the calculated meridian arc length S ( φ _j
) Is stored in the constant setting unit, and the fourth arithmetic unit is again referred to the constant setting unit and the meridian arc length S (φ _j
From), to calculate the latitude phi _{j + 1,} the first temporary latitude accommodating portion, thereby passed the latitude phi _j that held until then to the second temporary latitude accommodating portion, first to the latitude phi _j that held 4 The latitude φ _{j + 1} calculated again by the calculation unit is replaced. The main determination unit performs the above determination again with reference to the first temporary latitude storage unit, the second temporary latitude storage unit, and the condition setting unit, and calculates the absolute value of the difference between the latitude φ _{j + 1} and the latitude φ _j , Until it is determined that the value is equal to or less than the threshold, the regression control unit repeatedly causes the third calculation unit to perform the calculation of Expression 11 and causes the fourth calculation unit to repeatedly perform the convergence calculation of the latitude. When the main determination unit determines that the absolute value of the difference between latitude φ _{j + 1} and latitude φ _j is equal to or less than the threshold, the asymptotic latitude φ _{j + 1} is set as the normal latitude φ _k and the regression is performed. The control unit causes the fifth calculation unit to refer to the coordinate input unit, the first temporary latitude accommodating unit, the constant setting unit, and the first temporary scale factor accommodating unit, and the temporary scale factor m _t , and the perpendicular line latitude phi _k, the radius M _k and prime vertical radius of curvature N _k meridian curvature at the perpendicular latitude phi _k, a first value eta _k determined by e'cos φ _k, tan
By calculating the above equation 3 from the second value t _k determined by φ _k and the input coordinate value y, the latitude φ _{k + 1} is calculated, and the fifth calculation unit calculates The latitude φ _{k + 1} is stored as a latitude φ _n of the input coordinate point in the first temporary latitude storage unit, replacing the value previously stored in the first temporary latitude storage unit. The latitude accommodating unit passes the value of the latitude φ _k that has been held so far to the second temporary latitude accommodating unit. Further, in the calculation control unit, the first calculation unit is referred to the constant setting unit and the first temporary latitude accommodation unit, the second eccentricity e ′ of the earth ellipsoid, the latitude φ _{k + 1,} and Therefore, the average curvature radius R _k2 at the latitude φ _{k + 1} is calculated by _{performing the} calculation of Expression 7 and Expression 8 . Arithmetic control unit, the first operation unit, a coordinate input unit, by referring to the first temporary scale factor accommodating portion, and the value of the coordinate value y input, a temporary scale factor m _t, the mean curvature The scale factor _mt2 is calculated from the radius _Rk2 by calculating the above formula 9 , and the first calculation unit stores the calculated scale factor _mt2 in the first temporary scale factor storage unit. 1 temporary scale factor accommodating portion passes the housing to have a scale factor m _t to the second temporary scale factor accommodating portion, for accommodating the scale factor m _t2 instead as the scale factor m _t above. The sub-determination unit refers to the first temporary scale factor storage unit, the second temporary scale factor storage unit, and the condition setting unit, and calculates the absolute difference between the calculated scale factor m _t2 and the provisional scale factor m _t until then. and a value, the absolute value of the difference between a convergence condition IPS2 scale factor compared with the threshold value, the calculated scale factor m _t2 as the temporary scale factor m _t of far greater than the threshold value Is determined, the result is notified to the regression control unit. Regression controller which has received the notification, through the operation control unit, the scale factor m _t2 as scale factor m _t of the next tentative the calculated instead of the temporary scale factor m _t so far, at least, second, fourth And the fifth arithmetic unit again calculates Equation 10, latitude convergence calculation, Equation 3, and the first arithmetic unit again calculates Equation 7, Equation 8, and Equation 9. Secondary determination unit, compares the absolute value of the difference of the temporary scale factor m _t so far the scale factor m _t2 calculated again, the threshold and the convergence condition IPS2 the scale factor, the calculated scale factor m the absolute value of the difference between the temporary scaling factor m _{t t2} and until then, until it is determined to be equal to or less than the threshold value, the regression controller, via the operation control unit, at least, second, fourth and 5. The calculation unit 5 repeats the calculation of Equation 10, the convergence calculation of latitude, and the calculation of Equation 3, and the first calculation unit repeats the calculation of Equations 7, 8, and 9. Secondary determination unit, the absolute value of the difference between the calculated scale factor m _t2 as the temporary scale factor m _t In the meantime, when it is determined that less the threshold value, and notifies the result to the regression controller The regression control unit that has received the notification causes the output unit to output at least the value of the latitude φ _{k + 1} stored in the first temporary latitude storage unit .

Each invention of the present application calculates at least the latitude automatically by inputting coordinate points on a rectangular coordinate, and during the calculation of the latitude, An apparatus, method, program and recording medium capable of reflecting the convergence of the scale factor corresponding to the latitude can be provided. As a result, it is possible to perform latitude calculation with extremely high accuracy.
That is, according to the present invention, in calculating the latitude of a perpendicular line (vertical latitude) drawn on the reference meridian from the input coordinates, the convergence of the latitude is calculated , and the point (input coordinate value) is calculated from the obtained perpendicular latitude using Equation 3. By recalculating the latitude (corresponding to), a more accurate latitude can be obtained. Further, by calculating the scale factor from the latitude thus obtained and performing post-processing taking into account the convergence of the scale factor, the latitude of the point can be calculated with extremely high accuracy .

  Hereinafter, preferred embodiments of the present invention will be described.

1. Outline of Calculation Method According to the Present Invention The present invention provides a position calculation method for accurately calculating latitude, longitude, and meridian aberration on the corresponding earth ellipsoid from the coordinates x, y on the plane rectangular coordinates. Is. That is, the latitude, longitude, and meridian aberration of the corresponding point on the earth ellipse are calculated with high accuracy from the coordinate values of the plane rectangular coordinates that project the earth ellipsoid using the Gauss-Krugel isometric projection method. A method is provided.
This method improves the accuracy of the calculation result in consideration of the convergence of the scale factor in the convergence calculation for calculating the normal latitude.

That is, in this method, in the main process, the perpendicular latitude is repeatedly calculated by the following formula 1, and the latitude is calculated by calculating the following formula 3 from the value after the repeated calculation. Then, the scale factor is calculated by the following formula 2 using the value obtained through formula 3, and the normal latitude is repeated again by formula 1 using the meridian arc length on the reference meridian derived from the calculated scale factor. The calculation is further performed as a post-processing step by calculating the expression 3 with the value after the repeated calculation according to the expression 1 again.
Prior to the post-processing step, it is checked whether the calculated scale factor has converged. As a result, if the scale factor has converged, the calculation can be terminated without performing the post-processing step.
Therefore, it is possible to obtain a result obtained by performing the post-processing step subsequent to the main step processing and taking the scale factor calculated above into consideration, and determining the convergence of the calculated scale factor with respect to the result of the main step. The post-processing step may be performed only when the scale factor has not converged.
As described above, both in the case where the post-processing step is always performed after the main step and the case where the post-processing step is performed based on the determination of the convergence of the scale factor after the main step, the convergence of the scale factor is performed in the convergence calculation of the normal latitude. It takes into account, and the necessary accuracy can be ensured for the calculation result of latitude. Note that when it is determined whether or not the post-processing step is performed by checking the convergence of the scale factor, it is not necessary to perform useless iterative calculation (post-processing step). For example, in the vicinity of the reference meridian, sufficient accuracy of latitude and longitude may be ensured only by the main process. This is because it is not necessary to perform a post-processing step in such a case.
However, even if the post-processing step is always performed after the main step due to the recent improvement in computer performance, there is no practical problem of increase in calculation time or hardware load.
Further, the post-processing process is not limited to once. Further, similar to the above, it is possible to determine whether or not the scale factor is converged every time the post-processing step is performed, and to determine whether or not the post-processing step is further performed based on the result.

In the following, an outline of the post-processing step performed by determining the convergence of the scale factor after the main step will be described.
This position calculation method accepts input of the coordinate values x and y. Given the coordinate value x, the coordinate value x is set to a temporary scale factor m _t other than 0 for the meridian arc length from the equator of the earth ellipsoid to the origin of the coordinate system to which the coordinate values x and y belong. The values divided by are added to obtain the meridian arc length W on the reference meridian from the equator to the coordinate value x. For the meridian curvature radius determined from the major radius of the earth ellipsoid, the first eccentricity, and the latitude, an arbitrary value (latitude φ _j ) is given as an initial value together with the major radius a of the earth ellipsoid and the first eccentricity e. Separately, the meridian arc length S (φ _j ) on the reference meridian from the equator is calculated by integrating (approximate calculation) from the equator to the latitude φ _j with a meridian radius of curvature. Then, Equation 1 is calculated from the asymptotic latitude φ _j on the reference meridian to calculate the latitude φ _{j + 1} on the reference meridian as an asymptotic value (asymptotic latitude φ _{j + 1} ).
φ _{j + 1} = φ <sub>j
+ (W-S (φ j</sub> )) (1-e 2 sin 2 φ j) 3/2 / a (1-e 2) ... formula 1
It performs the absolute value of the difference between the latitude phi _j on latitude phi _{j + 1} and the reference meridian on the reference meridian is calculated by the above equation 1, the comparison with the reference value, on the reference meridian, asymptotic latitude phi _{j When} it is determined that the absolute value of the difference between ₊₁ and the latitude φ _j exceeds the reference value, that is, to make the asymptotic latitude φ _{j + 1} a latitude of a perpendicular line that is lowered from the input coordinates above the reference meridian If it is determined that it has not converged sufficiently, the asymptotic latitude φ _{j + 1} is set as the latitude φ _j on the reference meridian, the meridian arc length S (φ _j ) from the equator on the reference meridian is calculated, and the meridian arc The asymptotic latitude φ _{j + 1} is calculated again from the length S (φ _j ) by the calculation of the above equation 1, and the comparison is performed again. As a result, when it is determined that the absolute value of the difference between the asymptotic latitude φ _{j + 1} and the latitude φ _j on the reference meridian is within the reference value, that is, this asymptotic latitude φ _{j + 1} (hereinafter approximated as necessary) Is called the perpendicular latitude), and the asymptotic latitude φ _{j + 1} is perpendicular to the reference meridian from the input coordinates. as the latitude phi _k, and tentative scale factor m _t, and the vertical line latitude phi _k, and the vertical line latitude meridian radius of curvature phi _k M _k and prime vertical radius of curvature N _k, the determined at E'cosfai _k a value of 1 eta _k, calculates a second value t _k determined by tan [phi _k, from the above coordinate values y, the latitude phi _{k + 1} by calculating the equation 3.
φ _{k + 1} = φ _{k
-T k (y / m t)} 2 / 2M k N k + t k (y / m t) 4 (5 + 3t k 2 + η k
^{_{2 -9t k 2 η k 2 -4η}} k 4) / 24M k N k 3 -t k (y / m t) 6 (61 + 90t k 2 + 45t k 4) / 720M k N k 5
... Formula 3
The scale factor m _{t + 1} is calculated using the latitude φ _{k + 1} obtained above as the latitude φ _n (corresponding to the input coordinate value), and the scale factor m _{t + 1} and the temporary scale factor m _t the absolute value of the difference between, and compares with the predetermined value (or main process), if the absolute value of the difference between the scaling factor m _{t + 1} and the temporary scale factor m _t is determined to exceed the predetermined value Then, the calculation of Equation 1 above is performed again with the meridian arc length W on the reference meridian obtained using the scale factor m _{t + 1} (post-processing step).
The resulting latitude is output as the calculation result. Also, longitude and meridian aberrations are calculated in the process of calculating latitude.
The iterative calculation in which the above Equation 1 is used as an iteration equation (iteration equation) is as follows. In the plane coordinates shown in FIG. 3, the asymptotic latitude φ _{j + 1} on the reference meridian (X axis) This is a calculation for approximating (approaching) an intersection G between a perpendicular h drawn down to the reference meridian (X axis) and the reference meridian (X axis). The scale factor is 0.9999 on the reference meridian. The iteration according to Equation 1, if the asymptotic latitude phi _{j + 1} is sufficiently close to the handle and the intersection point G, and the asymptotic latitude phi _{j + 1} the nearest perpendicular latitude, the calculation of equation 3, the coordinate values (x, The latitude φ _{k + 1} corresponding to y) is calculated.
The provisional scale factor is calculated from the coordinate value y of the rectangular coordinate, the scale factor m _{0 at the} origin or an alternative value thereof, and the average curvature radius R _{0 at} the origin of the coordinate system to which the coordinate belongs. the second calculation is calculated scale factor m _t.
m _t = {1+ (y ² / 2m ₀ ² R ₀ ² ) + (y ⁴ / 24m ₀ ⁴ R ₀ ⁴ )} × 0.9999 Equation 2
The average radius of curvature R _{0 at} the origin is derived from the major radius a and minor radius b of the earth ellipsoid, or the radii a and b, together with the latitude φ ₀ of the origin of the coordinate system to which the coordinate belongs, or an alternative value thereof. This is determined using the first eccentricity e and the second eccentricity e ′.
The provisional scale factor is not limited to that calculated by Equation 2, and any numerical value other than 0 can be adopted. However, from the viewpoint of reducing useless post-processing steps, it is preferable to adopt the one calculated using the above formula 2.
Also, in the above, even when Expression 2 is used, any numerical value other than 0 can be used as an alternative value for the scale factor m _{0 at} the origin. However, from the same viewpoint as the above, such an alternative value is not used. The calculation is preferably performed using the scale factor m ₀ at the origin.
The scale factor m _{t + 1} is the latitude φ _n calculated by using the scale factor m _t instead of the origin scale factor m ₀ and the equation 3 instead of the average radius of curvature R ₀ at the origin.
Using the average radius of curvature R [phi] _n (described later R _k2) in, and calculates the above equation 2 (in other words, in Equation 2, by substituting m _t to m _0, by substituting R [phi] _n to R ₀ To calculate).

As described above, the main process is to repeatedly calculate the normal latitude in Equation 1 and then go through Equation 3, Equation 4 (Equation 19), Equation 5, and Equation 2 to obtain the latitude, longitude, meridian aberration angle, and This is a step of calculating a scale factor. Repetitive convergence calculation of perpendicular latitude is calculated by changing the asymptotic latitude φ _{j + 1} to latitude φ _j in Equation 1 above without changing other values, and newly calculating asymptotic latitude φ _{j + 1} Until | φ _{j + 1} −φ _j | converges. ). When | φ _{j + 1} −φ _j | converges in the main process, that is, when the asymptotic latitude φ _{j + 1} becomes the most approximate normal latitude, the asymptotic latitude φ _{j + 1} is used as the normal latitude φ _k. Equation 3 is calculated. Assuming that the value obtained by the calculation of Equation 3 is the latitude φ _{k + 1} as φ _n , the scale factor m _{t + 1} is obtained from the average radius of curvature at the latitude φ _n as described above.
Determines whether converges | a scaling factor m _{t + 1} calculated in the above, for a scale factor m _t used for calculating the values until then, | m t _{+ 1} -m _t. As a result, if converged, the calculation is terminated, and the latitude φ _n , longitude λ, meridian aberration angle γ, and scale factor obtained through Equation 3, Equation 4 (Equation 19), Equation 5 and Equation 2 are obtained. m _{t + 1} is output as a target numerical value.
If it is determined that | m _{t + 1} −m _t | has not converged, a post-processing step is performed. In the post-processing process, the scale factor m _{t + 1} obtained in the main process is used, and other values are the same as those in the main process without being changed (the same as that used in the main process). In the post-processing step | m _{t + 1} −m _t
If | has not converged, a further post-processing step is performed using the scale factor m _{t + 1} obtained in the post-processing step.
In short, in Formula 2, by using the scale factor m _t instead of the origin scale factor m _0, the average curvature at the latitude phi _n calculated by Equation 3 radius R [phi] _n average radius of curvature at the origin of the (R _k2 below) By using it instead of R ₀ , the scale factor of the point is calculated.
When this is repeated, the scale factor of the point has the property of convergence, and the scale factor when completely converged is the scale factor at the point (input coordinates).

2. Outline of Device According to the Present Invention and its Configuration FIG. 1 is an explanatory diagram of this device. FIG. 2 is an explanatory diagram showing the flow of the processing.
2-1) Outline of position calculation device This device accepts input of coordinate values x and y on a plane rectangular coordinate from an operator, and performs calculation automatically (only with the device without manpower until output). , The latitude and longitude on the corresponding earth ellipsoid (referring to the reference ellipsoid. Here, the WGS84 ellipsoid is adopted. Output.

2-2) Hardware configuration This position calculation device is constructed by introducing a position calculation program into a computer. This computer employs a general PC (personal computer) or WS (workstation) equipped with an input device, an arithmetic device, a control device, and a storage device (internal storage device and external storage device). can do. That is, an input device represented by a keyboard and a mouse, an output device represented by a display and a printer, an arithmetic device and control device (arithmetic control device) represented by a CPU (central upper processing device), and a RAM (random access) The present invention can be implemented by employing a general computer having an internal storage device represented by a memory) and an external storage device represented by a hard disk, a flexible disk, other magnetic disks, or an optical disk.

2-3) Software The above position calculation program can be implemented even with dedicated software that occupies all the resources of the computer. However, MS-DOS (registered trademark), Windows (registered trademark), UNIX ( The present invention can also be implemented by operating on a well-known OS (operating system) represented by a registered trademark.
Further, the position calculation program may be an interpreter type, or may be generated using an assembler or a compiler.
In this embodiment, the position calculation program is installed on a computer in which an OS is installed to realize a position calculation apparatus. Hereinafter, the OS and the position calculation program are referred to as position calculation software (simply referred to as software as necessary).

2-4) Configuration of Calculation Device The position calculation device shown in this embodiment inputs coordinate values x and y on plane rectangular coordinates X and Y for projecting an earth ellipsoid (reference ellipsoid) by an isometric projection method. By doing so, at least the latitude φ _n , longitude λ, and meridian aberration γ on the earth ellipsoid corresponding to the coordinate value are output.
As shown in FIG. 1, this apparatus includes a coordinate input unit 1 having a data placement unit 10, an output unit 2, a constant setting unit 31, an initial value setting unit 32, a condition setting unit 33, and a first temporary latitude. The accommodating part 41, the second temporary latitude accommodating part 42, the first temporary scale coefficient accommodating part 51, the second temporary scale coefficient accommodating part 52, and the first to seventh arithmetic units 61, 62, 63, The calculation part 6 which has 64, 65, 66, 67, the calculation control part 7, the determination part 8 which has the main determination part 81 and the sub determination part 82, and the regression control part 9 are provided.
In this embodiment, the coordinate input unit 1 includes a data placement unit 10 that temporarily holds input data. The constant setting unit 31 includes a calculated value setting unit 30.
The coordinate input unit 1 is constructed by the software, the input device, and the arithmetic control device that the computer has. The output unit 2 is constructed by the software, the output device included in the computer, and an arithmetic control device.
Each of the constant setting unit 31, the initial value setting unit 32, and the condition setting unit 33 is constructed by the software and the arithmetic control device, internal storage device, and external storage device that the computer has.
The first temporary latitude accommodating portion 41, the second temporary latitude accommodating portion 42, the first temporary scale factor accommodating portion 51, and the second temporary scale factor accommodating portion 52 are respectively the above-described arithmetic and control devices included in the software and the computer. And an internal storage device.
The first to seventh arithmetic units 61, 62, 63, 64, 65, 66, 67, the arithmetic control unit 7, the main determination unit 81, the sub determination unit 82, and the regression control unit 9 are: Each of them is constructed by the software, the arithmetic and control unit of the computer, and an internal storage device.

2-5) Details of Configuration of Computing Device The coordinate input unit 1 receives the input of the coordinate values x and y from the operator and stores them in the data placement unit 10.
The constant setting unit 31 is configured so that the major radius a, the minor radius b, the first eccentricity e, the second eccentricity e ′ of the earth ellipsoid, or values corresponding to these, and the coordinates x and y are The latitude φ ₀ or its substitute value, longitude λ ₀ of the origin of the coordinate system to which it belongs, the scale factor m ₀ or its substitute value at the origin, and constants A to F described later are set as known numerical values. ing.
Here, “setting” means that the operator inputs these values (constants) through the input device every time the position is calculated using this device, and the operator stores these values (constants) in the external storage device in advance. And any of those stored in the external storage device by introducing the program as part of the position calculation program.
Here, the necessary constants are introduced into the external storage device as being included in the program, and can be rewritten by the operator through the input device included in the computer after the introduction (rewriting is mainly performed at the origin point described above. Latitude φ ₀ or its substitute value, longitude λ ₀ , and origin scale factor m ₀ or its substitute value).
The constant setting unit 31 includes a calculated value placing unit 30. The calculated value placement unit 30 stores the value calculated by the calculation unit 6.

The calculation unit 6 will be described. Here (in the description of 2-5), the first to seventh calculation units 61 to 67 constituting the calculation unit 6 are ignored in relation to other calculation units (the calculation units 61 to 61). The data flow between 67 is ignored), and the content of each calculation unit will be mainly described. Therefore, in this 2-5), symbols used for explanation of each computation unit are independent from those used in other computation units unless otherwise specified (other computation units are represented by the same symbols). Even if it uses constants or parameters, the numerical value indicated by the symbol is different unless otherwise noted).
The addition, subtraction, multiplication, division, and sine, cosine, and tangent processed in each calculation are performed by information processing (numerical calculation) by software using a computer (including approximate calculation) by a known method.

The first calculation unit 61 can perform at least the following four calculations 1) to 4).
Calculation 1)
^{c = a 2 / b = a} / (1-e 2) 1/2 = a (1 + e '2) 1/2 ... Equation 6
Is calculated from the values of the major radius a of the earth ellipsoid, the minor radius b of the earth ellipsoid, the first eccentricity e of the earth ellipsoid, and the second eccentricity e ′ of the earth ellipsoid. To obtain the radius of curvature c. The first and second eccentricities can be calculated from the major radius a and the minor radius b of the earth ellipsoid. The curvature radius c of the pole of the earth ellipsoid may be held by the constant setting unit 31 without being calculated as a constant.
Calculation 2)
V = (1 + e ′ ² cos ² φ) ^1/2 .
Calculate the above equation 7 from each value of latitude φ and second eccentricity e ′ to obtain V.
Calculation 3)
R = c / V ² Formula 8
Equation 8 is calculated from the radius of curvature c of the pole of the earth ellipsoid and the value of V, and the average radius of curvature at latitude φ is obtained.
Calculation 4)
_{m n + 1 = (1 +} y 2 / 2m n 2 R 2 + y 4 / 24m n 4 R 4) × 0.9999
... Formula 9
The above equation 9 is calculated from the y values of the coordinate values x, y on the plane rectangular coordinates and the temporary scale factor _mn to obtain the scale factor _{mn + 1} .
This calculation 4) is a function for processing the equation 2 shown in the claims (the scale factor _mn in equation 9 is the origin scale factor m ₀ , and the average curvature radius R is the average curvature radius R ₀ at the origin). (Equation 2 shown in claim 2).

The second calculation unit 62 can perform the following calculation 5).
Calculation 5)
W = a (1-e ² ) · {A · φ− (B / 2) · (sin 2φ)
+ (C / 4) · (sin 4φ)-(D / 6) · (sin 6φ)
+ (E / 8) · (sin 8φ) − (F / 10) · (sin 10φ)}
+ X / m
... Formula 10
From the above equation 10, the second calculator 62 calculates the value of the major radius a of the earth ellipsoid, the values of the constants A to F, the value of the latitude φ, and the x and y of the coordinate values x and y on the plane rectangular coordinates. And a meridian arc length W on the reference meridian from the equator to the coordinate value x is calculated from the value of and any real number m other than 0. Each of the constants A to F is determined by the first eccentricity e (see step 107 described later).

The third calculation unit 63 can perform the following calculation 6).
Calculation 6)
S (φ) = a (1-e ² ) · {A · φ− (B / 2) · (sin 2φ)
+ (C / 4) · (sin 4φ)-(D / 6) · (sin 6φ)
+ (E / 8) · (sin 8φ) − (F / 10) · (sin10 φ)}
... Formula 11
The above equation 11 is calculated from the major radius a of the earth ellipsoid, the first eccentricity e, the above constants A to F, and the latitude φ, and the meridian arc length S (φ from the equator to the latitude φ )

The fourth calculation unit 64 can perform the following calculation 7).
Calculation 7)
φ _{n + 1} = φ _n
+ (WS (φ _n )) (1-e ² sin ² φ _n ) ^3/2 / a (1-e ² )
... Formula 12
The above equation 12 is obtained by substituting the temporary normal latitude φ _n , the meridian arc length W on the reference meridian from the equator to the coordinate value x, and the meridian arc length S (φ _n from the equator at the temporary normal latitude φ _n .
), The major radius a of the earth ellipsoid, and the first eccentricity e to calculate the normal latitude φ _{n + 1} .
This expression 12 corresponds to the expression 1 shown in the claims.

The fifth calculation unit 65 can perform the following five calculations 8) to 12).
Calculation 8)
t = tan φ ... Formula 13
Calculate the above equation 13 from the given latitude φ value to obtain t.
Calculation 9)
η = e'cos
φ ... Formula 14
The above equation 14 is calculated from the values of the second eccentricity e ′ of the earth ellipsoid and the latitude φ to obtain η.
Calculation 10)
M = c / _V ³ Formula 15
The above equation 15 is calculated from the value of the curvature radius c of the pole of the earth ellipsoid and the value of V determined by the latitude φ to obtain the meridian curvature radius M for the latitude φ.
Calculation 11)
N = c / V Equation 16
The above equation 16 is calculated from the value of the curvature radius c of the pole of the earth ellipsoid and the value of V determined by the latitude φ to obtain the shoreline curvature radius N for the latitude φ.
Calculation 12)
φ _{n + 1} = φ _n −t _n (y / m _t ) ² / 2M _n N _n + t _n (y / m _t ) ⁴ (5 + 3 t _n ² + η _n ² −9t _n ² η _n ² −4η _n ⁴ ) / 24M _n N _n ³ −t _n (y / m _t ) ⁶ (61 + 90 t _n ² +45 t _n ⁴ ) / 720M _n N _n ⁵ Equation 17
The above equation 17, the coordinate values x, y values of y in the plane rectangular coordinates, nearest perpendicular latitude phi _n, scale factor m _t, t _n for nearest perpendicular latitude phi _n, the nearest perpendicular latitude phi _n of eta _n, meridian radius of curvature M _n of nearest perpendicular latitude phi _n, and, of U Tri line curvature radius n _n of nearest perpendicular latitude phi _n, calculated from the values of respective the latitude phi _{n + 1} To seek.
This Expression 17 corresponds to Expression 3 shown in the claims.

The sixth calculation unit 66 can perform the following two calculations 13) and 14).
Calculation 13)
Δλ = (y / m _t ) / N _n cos φ _{n
^{- (y / m t) 3}} (1 + 2t n 2 + η n 2) / 6N n 3 cosφ n
+ (Y / m _t ) ⁵ (5 + 28t _n ² + 24t _n ⁴ ) / 120N _n ⁵ cosφ _n
... Formula 18
The above equation 18, the coordinate values x, y values of y in the plane rectangular coordinates, nearest perpendicular latitude phi _n, scale factor m _t, t _n for nearest perpendicular latitude phi _n, the nearest perpendicular latitude phi _n To calculate the longitude difference Δλ from the respective values of the η _{n of} the curve and the radius of curvature N _n of the most approximate perpendicular latitude φ _n .
Calculation 14)
λ = λ ₀
+ Δλ Equation 19
The above equation 19 is expressed by the longitude λ _{0 of the} origin to which the coordinate values x, y on the plane rectangular coordinates belong.
And calculate the longitude λ from each value of the longitude difference.

The seventh calculation unit 67 can perform the following calculation 15).
Calculation 15)
γ = (y / m _t ) / N _{n
^{- (y / m t) 3}} t n (1 + t n 2 -η n 2) / 3N n 3
+ (Y / m _t ) ⁵ t _n (2 + 5 t _n ² + 3t _n ⁴ ) / 15N _n ⁵
... Formula 20
The above equation 20 can be expressed by y-values of coordinate values x and y on a plane rectangular coordinate, a scale factor m _t , and the most approximate perpendicular latitude φ _n.
T _n, eta _n of a perpendicular latitude phi _n most approximate of, and, of U Tri line curvature radius N _n of nearest perpendicular latitude phi _n, calculated from the values of respective determining the meridian aberration gamma.

The calculation control unit 7 instructs the calculation units 61 to 67 of the calculation unit 6 to perform calculation. In response to the calculation and the location (placement) of numerical values necessary for the calculation from the calculation units 61 to 67, the calculation units 61 to 67 perform the commanded calculation in the order of the commands of the calculation control unit 7.
In addition, the calculation control unit 7 causes the determination unit 8 to determine the latitude and the scale factor convergence status obtained as a result of the calculation of the calculation units 61 to 67.
The determination unit 8 includes a main determination unit 81 that determines the convergence state of the normal latitude and a sub determination unit 82 that determines the determination state of the scale factor.
The regression control unit 9 receives the determination of the determination unit 8 and gives an instruction corresponding to the determination to the arithmetic control unit 7. In accordance with the instruction, the arithmetic control unit 7 issues a command to each of the arithmetic units 61 to 67. That is, the regression calculation unit 9 controls the calculation units 61 to 67 through the calculation control unit 7 according to the determination result by the determination unit 8.

The initial value setting unit 32 is set with a numerical value (hereinafter referred to as an initial value determining assistant if necessary) for determining an initial value of perpendicular latitude calculation (performed by the arithmetic unit 6). Hold.
The condition setting unit 33 is set with a reference value necessary for determination (comparison) by the determination unit 8, and holds the set reference value.

The first temporary latitude storage unit 41 stores the latitude value calculated by the calculation unit 6. The first temporary latitude accommodation unit 41 receives the latitude value newly calculated by the calculation unit 6, and passes the latitude value that has been accommodated until then to the second temporary latitude accommodation unit 42. The latitude value is rewritten to the newly received latitude value to accommodate the new latitude value.
The second temporary latitude accommodating unit 42 receives the value of the latitude accommodated by the first temporary latitude accommodating unit 41 from the first temporary latitude accommodating unit 41, and accommodates the value of the latitude. The second temporary latitude accommodating unit 42 further receives the latitude value from the first temporary latitude accommodating unit 41, and rewrites the latitude value that has been accommodated up to the latitude value after that, Contains the latitude value.

The first temporary scale factor storage unit 51 stores the value of the scale factor calculated by the calculation unit 6. The first temporary scale factor storage unit 51 receives the value of the scale factor newly calculated by the calculation unit 6, thereby passing the value of the scale factor stored so far to the second temporary scale factor storage unit 52. The scale factor value accommodated so far is rewritten to the newly received scale factor value to accommodate the new scale factor value.
The second temporary scale factor storage unit 52 receives the value of the scale factor stored in the first temporary scale factor storage unit 51 from the first temporary scale factor storage unit 51 and stores the value of the scale factor. The second temporary latitude accommodating portion 42 further receives the scale factor value from the first temporary scale factor accommodating portion 51 and rewrites the scale factor value that has been accommodated up to the scale factor value that has been received so far. The subsequent scale factor value is stored.
The output unit 2 receives the commands of the calculation control unit 7 and the regression calculation unit 9 and outputs the calculation result of the calculation unit 6.

3. Calculation Procedure The flow of calculating latitude, longitude, and meridian aberration using this apparatus will be described below with reference to FIG.
In this calculation method, the main process 100 is performed, and the post-processing process is further performed based on the determination result of the scale factor convergence state.
Prior to the execution of the main process 100, a pretreatment process is performed in advance.

3-0) Pre-processing process The pre-processing process is various setting processes performed before position calculation by an operator.
Specifically, in the pre-processing step, the operator sets a numerical value (initial value determining assistant) for determining the initial value of the latitude calculation by the initial value setting unit 32. As such an auxiliary number, 1/206265, which is a value obtained by converting 1 ″ (1 second) into rad (radian), is set in the condition setting unit 33. However, such a numerical value can be changed.
In the preprocessing step, the operator sets a normal latitude convergence condition IPS (threshold value) in the condition setting unit 33.
This convergence condition IPS is important for ensuring the accuracy of calculation. That is, even if accurate calculation is performed by each expression in the calculation unit, it is difficult to ensure sufficient accuracy if the convergence condition IPS is wide.
Here, the convergence condition IPS is set to 2 ″ × 10 ⁻⁵ / 206265 rad.
Further, in the preprocessing step, the operator sets the scale factor convergence condition IPS 2 in the initial value setting unit 32. Here, IPS2 is set to 4 × 10 ^{−12 in} consideration of significant digits (up to 9 digits) of coordinate values.
However, the numerical values of the convergence conditions IPS and IPS2 are not limited to the above values and can be changed.
The processes after the main process 100 are processes in which the position calculation device that receives the coordinate values x and y from the operator actually performs the position calculation.
In the main process, the following steps 101 to 125 are sequentially performed.

3-1) Step 101 (Coordinate value reception process)
The operator inputs the coordinate values x and y of the rectangular coordinates and the coordinate system Z to which the coordinate values belong by using the coordinate input unit 1. The input of the coordinate system Z specifies which of the 19 coordinate systems set in Japan belong to.
The above input operation is performed by an operator (other operations thereafter are performed by the position calculation device. In this embodiment, the initial value setting unit 32 and the constant setting unit 31 to be described later are set. The substitute value is set by the operator before the position is calculated).
The coordinate input unit 1 stores the input coordinate values x and y in the data storage unit 10 and notifies the calculation control unit 7 that the coordinate value has been input.
In response to the notification, the calculation control unit 7 causes the first calculation unit 61 to refer to the constant setting unit 31. That is, the constant setting unit 31 holds the numerical values of the latitude and longitude of the origin of each coordinate system, and the first calculation unit 61 is the origin of the input coordinate system Z (to which the coordinate values x and y belong). The latitude φ ₀ and longitude λ ₀ are specified. Accordingly, the latitude φ ₀ and longitude λ ₀ of the origin that each calculation unit refers to in the constant setting unit 31 are determined.

3-2) Step 102 (Pole curvature radius calculation step)
In this step 102, the calculation control unit 7 makes the first calculation unit 61 refer to the constant setting unit 31, and determines from the major radius a and minor radius b of the earth ellipsoid held by the constant setting unit 31. Alternatively, from the major radius a of the earth ellipsoid and the first eccentricity e, or from the major radius a of the earth ellipsoid and the second eccentricity e ′, the following calculation 1 is performed to calculate the curvature of the pole of the earth ellipsoid. The radius c is calculated. The first calculator 61 stores the calculated curvature radius c of the pole in the calculated value placement unit 30.
c = a ² / b = a / (1-e ² ) ^1/2 = a (1 + e ′ ² ) ^1/2 ... Calculation 1
Calculation 1 is executed by the calculation function of Expression 6 of calculation 1) of the first calculation unit 61.

3-3) Step 103 (V ₀ calculation process)
In step 103, the calculation control unit 7 causes the first calculation unit 61 to refer to the constant setting unit 31, and the second eccentricity e ′ and the origin latitude φ ₀ (hereinafter simply referred to as the origin latitude φ _{0) to} which the coordinates belong. Then, calculation 2 is performed, and V ₀ is calculated. The first calculation unit 61 stores the calculated Vφ ₀ in the calculated value storage unit 30.
V ₀ = (1 + e ′ ² cos ² φ ₀
^1/2 ... Calculation 2
Calculation 2 is executed by the calculation function of Expression 7 in Calculation 2) of the first calculation unit 61.

3-4) Step 104 (Calculation process of average radius of curvature of origin)
In step 104, the calculation control unit 7 causes the first calculation unit 61 to refer to the constant setting unit 31 (the calculated value setting unit 30), and performs calculation 3 from the curvature radius c of the pole and the value of V _0. The average radius of curvature R ₀ at the origin of the coordinate system is calculated. The first calculation unit 61 stores the calculated average curvature radius R ₀ in the calculated value storage unit 30.
R ₀ = c / V ₀ ² ... Calculation 3
Calculation 3 is executed by the calculation function of Expression 8 of calculation 3) of the first calculation unit 61.

3-5) Step 105 (Scale factor calculation process)
In step 105, the arithmetic control unit 7 stores the scale factor m _{0 at} the origin of the constant setting unit 31 (hereinafter referred to as the origin scale factor m ₀ ) in the first temporary scale factor storage unit 51 (constant setting unit 31). The original scale factor m ₀ is copied to the first temporary scale factor container 51). This origin scale factor m ₀ takes a numerical value of 0.9999.
Then, the calculation control unit 7 causes the first calculation unit 61 to refer to the data placement unit 10 and the constant setting unit 31 (or the first temporary scale coefficient storage unit 51) of the coordinate input unit 1 and input coordinate values. the value of y, the origin scale factor m _0, from the average radius of curvature R ₀ Prefecture, calculated 4 to perform the, to calculate the scale factor m _t.
m _t = (1 + y ² / 2m ₀ ² R ₀ ² + y ⁴ / 24m ₀ ⁴ R ₀ ⁴ ) × 0.9999
(The value 0.9999 on the right side is the same as the origin scale factor m ₀ as a numerical value, but this is a constant scale factor for setting the scale factor on the reference meridian to 0.9999.)
The calculation 4 is executed by the calculation function of Expression 9 of the calculation 4) of the first calculation unit 61.
First arithmetic unit 61 accommodates the calculated scale factor m _t in the first tentative scale factor housing portion 51. The first temporary scale factor accommodating portion 51 passes the origin scale factor m ₀ which has been accommodated into the second temporary scale factor accommodating portion 52 accommodates as the scale factor m _t of the place of origin scale factor m _0.

3-6) Step 106 (initial value setting process of perpendicular latitude)
In step 106, the calculation control unit 7 causes the first calculation unit 61 to refer to the constant setting unit 31 and the initial value setting unit 32 to obtain a value obtained by subtracting the assistant from the origin latitude φ ₀ , that is, the origin latitude. φ ₀
-Let 1/2206265 be calculated. The first calculation unit 61 stores the calculated value as the latitude φ _j in the first temporary latitude storage unit 41.

3-7) Step 107 (Meridian arc length calculation process on the reference meridian from the equator to the coordinate value x)
In this step 107, the calculation control unit 7 causes the second calculation unit 62 to refer to the constant setting unit 31, the data setting unit 10 of the coordinate input unit 1, and the first temporary scale coefficient storage unit 51, and and radius a, a first eccentricity e, the origin latitude and phi _0, the coordinate values x and, from the scaling factor m _t, is calculated 5, meridian arc length W on the reference meridian from the equator to the coordinate values x Calculate as
W = a (1-e ² ) · {A · φ ₀ − (B / 2) · (sin 2φ ₀ )
+ (C / 4) · (sin 4φ ₀ ) − (D / 6) · (sin 6φ ₀ )
+ (E / 8) · (sin 8φ ₀ ) − (F / 10) · (sin10 φ ₀ )}
+ X / m _t Calculation 5
A to F in the calculation 5 are as follows.
A = 1 + (3/4) e ² + (45/64) e ⁴ + (175/256) e ⁶
+ (11025/16384) e ⁸
+ (43659/65536) e ¹⁰
B = (3/4) e ² + (15/16) e ⁴ + (525/512) e ⁶
+ (2205/2048) e ⁸ + (72765/65536) e ¹⁰
C = (15/64) e ⁴ + (105/256) e ⁶
+ (2205/4096) e ⁸ + (10395/16384) e ¹⁰
D = (35/512) e ⁶
+ (315/2048) e ⁸ + (31185/131072) e ¹⁰
E = (315/16384) e 8
+ (3465/65536) e ¹⁰
F = (693/131072) e ¹⁰
The calculation 5 is executed by the calculation function of Expression 10 of the calculation 5) of the second calculation unit 62.
As described above, the constants A to F are stored in the constant setting unit 31 in advance, and are used by the second calculation unit 62 and other calculation units with reference to them.
Here, portions other than the x / m _t on the right side of the calculation 5 shows a meridian arc length from the equator of the ellipsoid to the coordinate system origin coordinates x, y belongs. Also, the scale factor m _t is referred to in the claims, is a scale factor of the temporary.
The second calculation unit 62 stores the calculated meridian arc length W on the reference meridian from the equator to the coordinate value x in the calculated value setting unit 30 of the constant setting unit 31.

3-8) Step 108 (Meridian arc length calculation process from the equator with respect to latitude)
In step 108, the calculation control unit 7 causes the third calculation unit 63 to refer to the constant setting unit 31 and the first temporary latitude accommodating unit 41, and the major radius a, the first eccentricity e, and the constants A to F. Then, the calculation 6 is performed from the latitude φ _j and the meridian arc length S (φ _j ) from the equator for the latitude φ _j is calculated.
S (φ _j ) = a (1-e ² ) · {A · φ _j
-(B / 2) ・ (sin 2φ _j )
+ (C / 4) · (sin 4φ _j ) − (D / 6) · (sin 6φ _j )
+ (E / 8) · (sin 8φ _j ) − (F / 10) · (sin10 φ _j )}
... Calculation 6
That is, this step 108 is a step of integrating from the equator to the perpendicular latitude φ _j with the meridian radius of curvature M, and the calculation 6 is an approximate calculation of the integration by the third calculation unit 63 as described above ( The integral here refers to the approximate calculation).
The calculation 6 is executed by the calculation function of Expression 11 of the calculation 6) of the third calculation unit 63.
The third computing unit 63 calculates the meridian arc length S (φ _j
Is stored in the calculated value placement unit 30.

3-9) Step 109 (initial perpendicular latitude convergence calculation step)
In step 109, the calculation control unit 7 causes the fourth calculation unit 64 to refer to the constant setting unit 31 and the first temporary latitude accommodating unit 41, the latitude φ _j , the major radius a, the first eccentricity e, the equator. From the meridian arc length W and meridian arc length S (φ _j ) on the reference meridian from to the coordinate value x, calculation 7 is performed, and the perpendicular latitude φ _{j + 1}
Is calculated.
φ _{j + 1} = φ _j + (W−S (φ _j )) (1-e ² sin ² φ _j ) ^3/2 / a (1-e ² )
The calculation 7 is executed by the calculation function of Expression 12 of the calculation 7) of the fourth calculation unit 64.
The fourth calculation unit 64 stores the calculated latitude φ _{j + 1} in the first temporary latitude storage unit 41. The first temporary latitude housing portion 41 from the fourth arithmetic unit 64 receives the latitude phi _{j + 1} The above housing to have latitude phi _j
Passes into the second temporary latitude accommodating portion 42 accommodates a value of the latitude phi _{j + 1} instead of the latitude phi _j.

3-10) Step 110 (Vertical latitude convergence determination step)
In step 110, the main determination unit 81 of the determination unit 8 refers to the first temporary latitude storage unit 41, the second temporary latitude storage unit 42, and the condition setting unit 33, and the difference between the latitude φ _{j + 1} and the latitude φ _j the absolute value of the _{words, | φ j + 1 -φ j} | a, comparing the convergence condition of latitude IPS (threshold). If it is determined that | φ _{j + 1} −φ _j |> IPS, the determination unit 8 (main determination unit 81) notifies the regression control unit 9 of the result.
Upon receipt of this notification, the regression control unit 9 receives the latitude φ _{j + 1 of} the first temporary latitude accommodating unit 41.
Of the value as the value of the latitude phi _j (the latitude phi _{j + 1} of the first temporary latitude housing portion 41 rewrites the latitude phi _j), again transferred to step 108 to process equipment. Then, the regression control unit 9 repeats steps 108 to 110 until the determination unit 8 (main determination unit 81) determines that | φ _{j + 1} −φ _j | ≦ IPS (repetitive calculation of perpendicular latitude is performed). ). In this iterative calculation, the normal latitude φ _{j + 1} is only replaced (rewritten) with the normal latitude φ _j , and other numerical values referred to by the calculation unit 6 (each calculation unit thereof) are not changed (for the other numerical values). , Calculated from the beginning using the original value).
As described above, when the determination unit 8 (the main determination unit 81) determines that | φ _{j + 1} −φ _j | ≦ IPS in step 110, the determination unit 8 notifies the regression control unit 9 of the result.
Regression control unit 9 receives the notice of convergence and shifts the processing to the next step 111. That is, the regression control unit 9 causes the calculation control unit 7 to perform the next step 111.

3-11) Step 111 ( _Vk calculation process)
In step 111, the calculation control unit 7 causes the first calculation unit 61 to refer to the constant setting unit 31 and the first temporary latitude accommodating unit 41, and determines the second eccentricity e ′ and the normal latitude φ _{j + 1} . Then, calculation 8 is performed to calculate V _k . For convenience of explanation, the perpendicular latitude φ _{j + 1} will be described as latitude φ _k .
V _k = (1 + e ′ ² cos ² φ _k
^1/2 ... Calculation 8
The calculation 8 is executed by the calculation function of Expression 7 of the calculation 2) of the first calculation unit 61.
The first calculation unit 61 stores the calculated V _k in the calculated value storage unit 30.

3-12) Step 112 (second value calculation step)
In step 112, the calculation control unit 7 causes the fifth calculation unit 65 to refer to the first temporary latitude accommodating unit 41 and uses the value of latitude φ _k (that is, the value of latitude φ _{j + 1} is calculated as latitude φ _k And use calculation 9 to calculate t _k (referred to as a second value t _k for convenience of explanation).
t _k = tan φ _k ... calculation 9
The calculation 9 is executed by the calculation function of Expression 13 of the calculation 8) of the fifth calculation unit 65.
Fifth arithmetic unit 65, a second value t _k, which is calculated to accommodate the calculated value portion 30.

3-13) Step 113 (first value calculation step)
In step 113, the calculation control unit 7 causes the fifth calculation unit 65 to refer to the constant setting unit 31 and the first temporary latitude accommodating unit 41, and uses the value of the latitude φ _k together with the second eccentricity e ′. Calculation 10 is performed, and η _k (referred to as a first value η _k for convenience of description) is calculated.
η _k = e'cos φ _k ... calculation 10
The calculation 10 is executed by the calculation function of Expression 14 of the calculation 9) of the fifth calculation unit 65.
The fifth calculation unit 65 stores the calculated first value η _k in the calculated value storage unit 30.

3-14) Step 114 (Meridian curvature radius calculation process)
In step 114, the operation control unit 7, the fifth arithmetic unit 65, and refers to the constant setting unit 31, and a radius of curvature c and V _k poles at calculation 11, the latitude φ meridian curvature at _k radius M _k Is calculated.
M _k = c / V _k ³
... Calculation 11
The calculation 11 is executed by the calculation function of Expression 15 of the calculation 10) of the fifth calculation unit 65.
The fifth arithmetic unit 65 stores the calculated meridian curvature radius M _k in the calculated value storage unit 30.

3-15) Step 115 (Calculation process of radiant curvature radius)
In step 115, the calculation control unit 7 causes the fifth calculation unit 65 to refer to the constant setting unit 31, and uses the curvature radius c and V _{k of} the pole to calculate the shoreline curvature radius at the latitude φ _k in the calculation 12. N _k is calculated.
N _k = c / V _k ... calculation 12
The calculation 12 is executed by the calculation function of Expression 16 of the calculation 11) of the fifth calculation unit 65.
The fifth arithmetic unit 65 stores the calculated value of the shoreline curvature radius N _k in the calculated value storage unit 30.

3-16) Step 116 (Latitude calculation process corresponding to input coordinates)
In step 116, the regression control unit 9 gives the latitude φ _k to the fifth calculation unit 65 through the calculation unit control unit 7 and causes the calculation 13 to be performed. Specifically, upon receiving a command from the regression control unit 9, the calculation control unit 7 sends the data calculation unit 10 of the coordinate input unit 1, the first temporary latitude storage unit 41, the first temporary calculation to the fifth calculation unit 65. by reference to the scale housing portion 51 and a constant setting unit 31, in the above, and the perpendicular latitude phi _k similar recently was calculated in the fourth calculation portion 64, and the scale factor of the point m _t, nearest perpendicular latitude phi _k Meridian curvature radius M _k and tangential curvature radius N _k , and e′cos φ _k
The first value η _k determined by, and tan φ _k
The latitude φ _{k + 1} is calculated by calculation 13 from the second value t _k determined by _## EQU2 _## and the coordinate value y.
φ _{k + 1} = φ _{k
-T k (y / m t)} 2 / 2M k N k + t k (y / m t) 4 (5 + 3t k 2 + η k
^{_{2 -9t k 2 η k 2 -4η}} k 4) / 24M k N k 3 -t k (y / m t) 6 (61 + 90t k 2 + 45t k 4) / 720M k N k 5
... Calculation 13
The calculation 13 is executed by the calculation function of Expression 17 of the calculation 12) of the fifth calculation unit 65.
The fifth arithmetic unit 65 stores the calculated latitude φ _{k + 1} as the latitude φ _n of the point (input coordinate point) to the first temporary latitude storage unit 41, and until then, is stored in the first temporary latitude storage unit 41. Replace with the stored value. At this time, the first temporary latitude accommodating unit 41 passes the value of the latitude φ _k held so far to the second temporary latitude accommodating unit 42.

3-17) Step 117 (Longitude Difference Calculation Step)
This step 117 is performed in parallel with step 116 described above. That is, step 117 is executed using the data used in the process of step 116, not the result (latitude φ _{k + 1} ) obtained in step 116.
In step 117, the calculation control unit 7 causes the sixth calculation unit 66 to refer to the data placement unit 10, the first temporary scale coefficient storage unit 51, and the calculated value placement unit 30 of the coordinate input unit 1, and the closest approximate perpendicular latitude phi _k (latitude obtained in a series of processes up to the step 111, i.e., the latitude phi _k using for the processing of steps 111 to 116), a scale factor m _t of the point, nearest perpendicular latitude phi meridian curvature at _k radius M _k (the result of step 114) and prime vertical radius of curvature N _k and (result of step 115), a first value determined by e'cos φ _k η _k and (result of step 113) , a tan phi is determined by _k second value t _k (the result of step 112), from the above coordinate values y, the calculation 14 was performed, to calculate the longitude difference [Delta] [lambda].
Δλ = (y / m _t ) / N _k cos
φ _{k
^{- (y / m t) 3}} (1 + 2t k 2 + η k 2) / 6N k 3 cosφ k

+ (Y / m _t ) ⁵ (5 + 28 t _k ² +24 t _k ⁴ ) / 120 N _k ⁵ cosφ _k .
The sixth arithmetic unit 66 stores the calculated longitude difference Δλ in the calculated value setting unit 30 of the constant setting unit 31.

3-18) Step 118 (longitude calculation process)
The step 118 and the step 119 following the step 118 are performed in parallel with the step 116 as in the case of the step 117.
In step 118, the calculation control unit 7 causes the sixth calculation unit 66 to refer to the constant setting unit 31 to calculate the sum of the origin longitude λ ₀ and the longitude difference Δλ, that is, the calculation 15 to calculate the longitude λ. Let it be calculated.
The sixth calculation unit 66 stores the calculated value of longitude λ in the calculated value storage unit 30.
λ = λ ₀
+ Δλ ... Calculation 15
The calculation 15 is executed by the calculation function of Expression 19 of the calculation 14) of the sixth calculation unit 66.

3-19) Step 119 (Meridian aberration calculation process)
This step 119 is a process following step 118 as described above, and is performed in parallel with step 116. That is, instead of using the result (latitude φ _{k + 1} ) obtained in step 116, the processing is executed using the data used in the processing in step 116.
In step 119, the calculation control unit 7 causes the seventh calculation unit 67 to refer to the data placement unit 10, the first temporary scale coefficient storage unit 51, and the calculated value placement unit 30 of the coordinate input unit 1, and the closest approximate perpendicular latitude phi _k (latitude obtained in a series of processes up to the step 111, i.e., the latitude phi _k using for the processing of steps 111 to 116), a scale factor m _t of the point, nearest perpendicular latitude phi a U Tri line curvature radius N _k in _k (the result of step 115), a first value determined by e'cos φ _k η _k and (result of step 113), tan determined by phi _k second value t Calculation 16 is performed from _k (result of step 112) and the coordinate value y, and meridian aberration γ is calculated.
γ = (y / m _t ) t _k / N _k
-(Y / m _t ) ³ t _k (1 + t _k ² -η _k ² ) / 3N _k ³
+ (Y / m _t ) ⁵ t _k (2 + 5 t _k ² +3 t _k ⁴ ) / 15 N _k ⁵ .
The calculation 16 is executed by the calculation function of Expression 20 of the calculation 15) of the seventh calculation unit 67.
The seventh arithmetic unit 67 stores the calculated meridian aberration γ in the calculated value storage unit 30.

3-20) Step 120 (V _k2 calculation step)
Step 120 is a process following step 116.
In step 120, the calculation control unit 7 causes the first calculation unit 61 to refer to the constant setting unit 31 and the first temporary latitude storage unit 41, and the second eccentricity e ′ and the point obtained in step 116. Then, the calculation 17 is performed from the latitude φ _{k + 1 of the current} and V _k2 is calculated. For convenience of explanation, this latitude φ _{k + 1} will be described as latitude φ _k2 .
V _k2 = (1 + e ′ ² cos ² φ _k2 ) ^1/2 ... Calculation 17
The calculation 17 is executed by the calculation function of Equation 7 in the calculation 2) of the first calculation unit 61.
The first calculation unit 61 stores the calculated V _k2 in the calculated value storage unit 30.

3-21) Step 121 (Meridian curvature radius calculation process)
In step 121, the calculation control unit 7 causes the fifth calculation unit 65 to refer to the constant setting unit 31, and calculates the meridian curvature radius M _k2 at the latitude φ _k2 from the curvature radius c and V _{k2 of} the pole. Is calculated.
M _k2 = c / V _k2 ³
... Calculation 18
The calculation 18 is executed by the calculation function of Expression 15 of the calculation 10) of the fifth calculation unit 65.
The fifth calculation unit 65 stores the calculated value of the meridian curvature radius M _k2 in the calculated value setting unit 30.

3-22) Step 122 (Calculation process of radiant curvature radius)
In step 122, the calculation control unit 7 causes the fifth calculation unit 65 to refer to the constant setting unit 31, and from the curvature radius c and V _{k2 of} the pole, in calculation 19, the _shore curvature radius at latitude φ _k2 N _k2 is calculated.
N _k2 = c / V _k2 ... Calculation 19
The calculation 19 is executed by the calculation function of Expression 16 of the calculation 11) of the fifth calculation unit 65.
The fifth arithmetic unit 65 stores the calculated value of the shoreline curvature radius N _k2 in the calculated value storage unit 30.

3-23) Step 123 (Calculation process of average radius of curvature)
In step 123, the calculation control unit 7 causes the first calculation unit 61 to refer to the constant setting unit 31 to perform calculation 20 from the value of the curvature radius c of the pole and the value of V _k2 , and the coordinates (input coordinates). ) Average curvature radius R _k2 is calculated. The first calculation unit 61 stores the calculated average radius of curvature R _k2 in the calculated value placement unit 30.
R _k2 = c / V _k2 ²
... calculation 20
The calculation 20 is executed by the calculation function of Expression 8 of the calculation 3) of the first calculation unit 61.

3-24) Step 124 (Scale factor calculation process)
In step 124, the calculation control unit 7 causes the first calculation unit 61 to refer to the data placement unit 10 and the first temporary scale coefficient storage unit 51 of the coordinate input unit 1, and the input coordinate value y, scale factor m _t1 (describing the scale factor m _t accommodated in the first tentative scale factor accommodating portion 51 as a scale factor m _t1. hereinafter the same.) and, from the average radius of curvature R _k2 Prefecture, the calculation 21 And let the scale factor m _t2 be calculated.
^{_{m t2 = (1 + y 2}} / 2m t1 2 R k2 2 + y 4 / 24m t1 4 R k2 4) × 0.9999
... Calculation 21
The calculation 21 is executed by the calculation function of Expression 9 of the calculation 4) of the first calculation unit 61.
The first calculation unit 61 stores the calculated scale factor m _t2 in the first temporary scale factor storage unit 51. The first temporary scale factor housing 51, passes a reduced scale factor m _t which has been accommodated into the second temporary scale factor housing portion 52, for accommodating the scale factor m _t2 instead as the scale factor m _t above.

3-25) Step 125 (Scale Factor Convergence Determination Step)
In step 125, the sub-determination unit 82 of the determination unit 8 refers to the first temporary scale factor storage unit 51, the second temporary scale factor storage unit 52, and the condition setting unit 33 and refers to the scale factor m _t1 and the scale factor. The absolute value of the difference of m _t2 , that is, | m _t2 −m _t1 | is compared with the convergence condition IPS2 of the scale factor. When it is determined that the scale factor m _t2 (and the absolute value of the difference between the scale factors m _t1 ) has converged, that is, when the sub-determination unit 82 determines | m _t2 −m _t1 | ≦ IPS2, the determination unit 8 notifies the regression control unit 9 of the result.

3-26) Step 126 (output process)
In step 125, the regression control unit 9 that has received the notification of the convergence of the scale factor uses the output unit 2 to at least the value of the latitude φ _{k + 1} of the point stored in the first temporary latitude storage unit 41. (Φ _n ) and the value of the longitude λ and the value of the meridian aberration γ stored in the calculated value placement unit 30 are output. At this time, if necessary, the input coordinate values x and y of the data placement unit 10 of the coordinate input unit 1 and the input coordinates held by the constant setting unit 31 and stored in the calculated value placement unit 30 belong. Even if the numerical value of the latitude and longitude of the origin, constants such as the major and minor radii of the earth ellipsoid, or intermediate values calculated during the calculation process are output to the output unit 2 together, the above result is This is convenient because it allows the operator to check what coordinate value corresponds to, and how the coordinate value is calculated.

On the other hand, when the determination unit 8 (sub-determination unit 82) determines | m _t2 −m _t1 |> IPS2 in step 125, the above-described post-processing process is performed without proceeding to step 126.
In other words, when it is determined that | m _t2 −m _t1 |> IPS2, the determination unit 8 notifies the regression control unit 9 of the result. The regression control unit 9 that has received this notification causes the operation control unit 7 to repeat the steps of the main process 100 . In other words, the post-processing step is a step of redoing the main step 100 using the scale factor _mt2 . Use in a later process step, being taken into account as a result of the main process 100 is only the scale factors calculated in the main step 100, the value of latitude, which is calculated by the main process 100 is not used, again with the main step 100 Calculate using the same values as those used for the calculation (even if the calculation does not use the scale factor or the calculation using the scale factor, the values other than the scale factor are the same as those used in the main process 100. To calculate).
When it is determined that | m _t2 −m _t1 |> IPS2 in step 125 in the post-processing process, the determination unit 8 notifies the regression control unit 9 of the result. Then, in scale factor m _t2 obtained through the post-treatment step, the higher the post-processing factory again. As described above, if it is not determined that the scale factor m _t2 (and the absolute value of the difference between the scale factors m _t1 ) has converged even after one post-processing step, the sub-determination unit 82 | The post-processing steps described above are repeated until m _t2 −m _t1 | ≦ IPS2.
In step 125 in the post-processing step, when the scaling factor m _t2 has converged, that is, when it is determined by | m _t2 −m _t1 | ≦ IPS2 and the sub-determination unit 82, as described above, the regression control unit 9 7 causes step 126 to be performed.

As described above, the post-treatment step (main process 100 of redo steps) is repeated, calculated 5 x / m _t is changed at step 107, the value of the meridian arc length W on the zero meridian to coordinate values x As a result, the calculation result of calculation 7 becomes more accurate.
In the above-described embodiment, the post-processing step is performed by the determination unit 8 (sub-determination unit 82) having insufficient scale factor convergence, that is, by determining | m _t2 −m _t1 |> IPS2.
In addition, as described above, the post-processing step can be performed without failing to determine the convergence of such a scale factor without fail. For example, it is possible to carry out the post-processing step as always being performed once (or twice or more).
Further, in the above embodiment, as the temporary numbers used in step 107, is used to scale factor m _t calculated in step 105, the initial step 107 (step 107 in post-treatment step is excluded.) The It can also be implemented as performing a calculation using an arbitrary real number other than 0 as a substitute value of the scale factor m _t.
However, as the scale factor of the temporary used in step 107, by using the scale factor m _t calculated in step 105, the convergence is efficiently performed, for example, repetition of the results the step 108 of the judgment in the step 110 (small loop ) Can be suppressed to about three times, and the repetition (large loop) of the post-processing step in Step 125 can be suppressed to within two times. Therefore, in this case, even if the post-processing process is fixed twice without determining in step 125, a practically good result can be obtained.

When it is assumed that the post-processing step is necessarily performed without determining the scale factor in step 125, the scale obtained by performing calculation 4 using the origin scale factor m ₀ as a temporary numerical value in step 105 of the main step 100 is usually used. when employing the coefficients m _t, the coordinate value x entered, even y is in any position of the coordinate system, in the main process 100 repeats the iterative calculation by the determination of step 110 (step 108 to 110), the post-processing If the process is performed once (iterative calculation based on the determination of step 110 (steps 108 to 110) is repeated even during the post-processing process), a sufficiently accurate result can be obtained.
In step 106, the origin latitude φ ₀
In contrast, it was shifted by 1 second (−1/206265 radians). This shift value is preferably in a range not exceeding ± 5 seconds with respect to the origin latitude phi _0. Within this range, as described above, the inventor is able to obtain sufficient accuracy with a maximum of three iterations (steps 108 to 110) based on the determination in step 110 of the main process 100 and one post-processing process. It has been confirmed. Therefore, it is preferable to perform the iterative calculation of steps 108 to 110 up to three times. However, the iterative calculation depends on the convergence condition IPS and is not limited to such a number.

In order to make the point on the plane correspond to the point on the ellipsoid, calculation for obtaining an approximate value (iterative calculation, that is, convergence calculation) is required, and in order to make it correspond with high accuracy, a device like the present invention is required. However, conversely, if the points on the ellipsoid are accurately associated with the points on the plane, the corresponding points can be easily calculated (iterative calculation is not required). That is, with a known calculation method or apparatus, an accurate value can be calculated by back calculating a coordinate value on a plane rectangular coordinate from latitude and longitude.
Therefore, the accuracy of the calculation result obtained by the method according to the present invention can be verified by such back calculation.

An example of the verification method will be briefly described.
The following calculation is performed with the result (output value) obtained by the above method according to the present invention as latitude φ (latitude φ _n ) and longitude λ.
In calculation 22, the longitude difference Δλ is calculated backward.
Δλ = λ−λ ₀ Calculation 22
The first value η is obtained by calculation 23 from the latitude φ of the result.
η = e'cos
φ ... Calculation 23
Further, the second value t is obtained by calculation 24 from the latitude φ of the above result.
t = tan φ ... calculation 24
Furthermore, the value of V is obtained by calculation 25 from the latitude φ of the above result.
V = (1 + e ′ ² cos ² φ) ^1/2 ... calculation 25
From the calculated value of V, the meridian curvature radius M is calculated by calculation 26, the shore curvature radius N is calculated by calculation 27, and the average curvature radius R is further calculated by calculation 28.
M = c / V ³ ... Calculation 26
N = c / V ... Calculation 27
R = c / V ² ... Calculation 28
From the latitude φ and longitude λ of the above result, and the first value η and second value t obtained above, the scale factor m at the latitude φ and longitude λ is obtained by calculation 29.
m = {(1 + Δλ ² cos ²
φ (1 + η ² ) / 2 + Δλ ⁴ cos ⁴ φ (5-4t ² ) / 24)} × 0.9999
And the latitude φ of the above result, the meridian curvature radius M, the shore curvature radius N, the average curvature radius R, the longitude difference Δλ, the first value η, the second value t for the φ, From the scale factor m, the coordinate value y on the plane Cartesian coordinates corresponding to the latitude φ and longitude λ can be obtained by the calculation 30 (0.9999 on the right side of the calculation 29 is expressed as the origin scale factor m ₀ as a numerical value). The same, but as mentioned above, this is a constant scale factor to make the scale factor on the reference meridian 0.999).
y = {ΔλNcos
φ + Δλ ³ Ncos ³
φ (1-t ² + η ² ) / 6
+ Δλ ⁵ Ncos ⁵ φ (5-18t ² + t ⁴ + 14η ² −58η ² t ² ) / 120} × m.

From the major radius a of the earth ellipsoid, the first eccentricity e, the latitude φ of the result, the coordinate value x, and the constants A to F described above, the calculation 31 calculates the latitude φ of the result. The meridian arc length S (φ) from the equator is obtained.
S (φ) = a (1-e ² ) · {A · φ− (B / 2) · (sin 2φ)
+ (C / 4) · (sin 4φ)-(D / 6) · (sin 6φ)
+ (E / 8) · (sin 8φ) − (F / 10) · (sin10 φ)}
... Calculation 31
Based on the meridian arc length S (φ) from the equator with respect to the latitude φ obtained above and the meridian arc length S (φ ₀ ) from the equator with respect to the origin latitude φ ₀ , the difference B is obtained in the calculation 32.
B = S (φ) −S (φ ₀ )... Calculation 32
Further, the difference B, the latitude φ of the result, the meridian curvature radius M, the shore curvature radius N, the average curvature radius R, the longitude difference Δλ, the first value η, the first 2 value t, and a scaling factor m, by calculation 33, it is possible to determine the coordinate values x in a plane perpendicular coordinates corresponding to those weft degree φ and the longitude lambda.
x = {B + Δλ ² sin φcos φ / 2 + Δλ ⁴ N sin φcos ³ φ (5-t ² + 9η ²
+ 4η ⁴ ) / 24 + Δλ ⁶ N sin φcos ⁵ φ (61−58 t ² + t ⁴ + 270η ² −330 η ² t ² ) / 720} × m.
Further, the meridian aberration γ at the latitude φ and the longitude λ can be obtained by the calculation 34 from the latitude φ as the result and the longitude difference Δλ, the first value η, and the second value t. .
γ = Δλsin
φ + Δλ ³ sin φcos ² φ (1 + 3η ² + 2η ⁴ ) / 3
+ Δλ ⁵ sin φcos ⁴ φ (2-t ² ) / 15 ... Calculation 34

In the background art section of this specification, the value used for calculation by the program of the Geospatial Information Authority of Japan was input to the calculation device according to the present invention and calculated, and the result value was verified by the above verification method, Within the range of significant figures set by the Geographical Survey Institute's program (within the number of digits of the calculated value), the value (x, y) input to the calculation device according to the present invention and the value (x, It was found that y) was completely in agreement.
Furthermore, specific examples are listed below.

Using the apparatus according to the present invention, the latitude φ and longitude λ were calculated (output) from the five coordinate values x and y (input) belonging to the coordinate system 3 (result data 1 to 5). Here, the coordinate value x is fixed, and the point where the coordinate value y moves away from the origin from the result data 1 to the result data 5 was examined. Result data 5 is that the scale factor is 1.0001.
From the latitude / longitude obtained in the result data 1-5, the verification data 1-5 for the coordinate values were obtained by the above-described verification method (verification program) (the number of the verification data is the number of the verified result data) Yes)
In the calculation of each data, the major radius a of the WGS84 earth ellipsoid, the curvature radius c (= a ² / b) of the pole of the earth ellipsoid, the square of the eccentricity (first eccentricity) e, the second eccentricity e Regarding the square of ', the coordinate system Z, the origin latitude φ _{0 of} the coordinate system Z, the origin longitude λ ₀ of the coordinate system Z, and the origin scale factor m ₀ , the following numerical values were used as constants.
a = 6378137.000
c = 6399593.62576
e ² = 0.006694379990141
e ' ² = 0.006739496742276
Z = 3
φ ₀ = 36-0-0.000
λ ₀ = 132-10- 0.000
m ₀ = 0.9999
In the following,
ZAHYOCHI X (1) indicates the input coordinate value x, and its unit is meter.
ZAHYOCHI Y (1) indicates the input coordinate value y, and its unit is meter.
PHAI indicates the closest perpendicular latitude φ _{j + 1} .
LATITUDE indicates the latitude φ _n (north latitude) of the point. For example, 34-7-45.93167 indicates 34 degrees 7 minutes 45.93167 seconds (34 ° 7'45 ".93167).
LONGITUDE indicates the longitude λ (east longitude) of the point.
GAMMA ANGLE shows meridian yield difference γ of the point.
MERIDIAN RADIUS indicates the meridian radius of curvature M of the point.
ORTHOG. MERIDIAN RADIUS indicates the radius of curvature N of the point.
MEAN RADIUS indicates the average radius of curvature R of the point.
SCALE FACTOR
Indicates the scale factor of the point.

(Result data 1)
1 ZAHYOCHI X (1) =
-207504.143
ZAHYOCHI Y (1) = 0.000
PHAI = 34- 7-45.93167
LATITUDE = 34- 7-45.93167
LONGITUDE = 132-10- 0.00000
GAMMA ANGLE = 0- 0-
0.00000
MERIDIAN RADIUS =
6355518.63673
ORTHOG. MERIDIAN RADIUS
= 6384868.10519
MEAN RADIUS = 6370176.46816
SCALE FACTOR = 0.9999000000

(Result data 2)
2 ZAHYOCHI X (2) = -207504.143
ZAHYOCHI Y (2) = -60000.000
PHAI = 34- 7-46.23045
LATITUDE = 34- 7-40.02854
LONGITUDE = 131-30-58.32910
GAMMA ANGLE =-
0-21-53.81142
MERIDIAN RADIUS =
6355516.93662
ORTHOG. MERIDIAN RADIUS
= 6384867.53587
MEAN RADIUS = 6370175.33215
SCALE FACTOR = 0.9999443586

(Result data 3)
3 ZAHYOCHI X (3) = -207504.143
ZAHYOCHI Y (3) = -90091.612
PHAI = 34- 7-46.60518
LATITUDE = 34-7-32.62478
LONGITUDE = 131-11-24.23440
GAMMA ANGLE = -0-32-52.51513
MERIDIAN RADIUS =
6355514.80440
ORTHODG. MERIDIAN RADIUS =
6384866.82185
MEAN RADIUS = 6370173.90739
SCALE FACTOR =
1.0000000000

(Result data 4)
4 ZAHYOCHI X (4) = -207504.143
ZAHYOCHI Y (4) = -119361.021
PHAI = 34-7-47.111365
LATITUDE = 34-7-22.57909
LONGITUDE = 130-52-22.58341
GAMMA ANGLE = -0-43-32.98171
MERIDIAN RADIUS = 6355511.91142
ORTHOG. MERIDIAN RADIUS = 6384865.85306
MEAN RADIUS = 6370171.97429
SCALE FACTOR = 1.0000755078

(Result data 5)
5 ZAHYOCHI X (5) = -207504.143
ZAHYOCHI Y (5) = -127420.415
PHAI = 34-7-47.27856
LATITUDE = 34-7-19.32099
LONGITUDE = 130-47-8.30603
GAMMA ANGLE =
-0-46-29.28380
MERIDIAN RADIUS =
6355510.97317
ORTHOG. MERIDIAN RADIUS = 6384865.53887
MEAN RADIUS = 6370171.34734
SCALE FACTOR =
1.0001000000

(Verification data 1)
1 ZAHYOCHI X (1) = -207504.143
ZAHYOCHI Y (1) = 0.000
LATITUDE = 34-7-45.93167
LONGITUDE = 132-10-0.00000
GAMMA ANGLE =
0-0-0.00000
MERIDIAN RADIUS =
6355518.63672
ORTHODG. MERIDIAN RADIUS
= 6384868.10519
MEAN RADIUS = 6370176.46816
SCALE FACTOR = 0.9999000000

(Verification data 2)
2 ZAHYOCHI X (2) = -207504.143
ZAHYOCHI Y (2) = -60000.000
LATITUDE = 34-7-40.02854
LONGITUDE = 131-30-58.32910
GAMMA ANGLE = -0-21-53.81142
MERIDIAN RADIUS = 6355516.93662
ORTHODG. MERIDIAN RADIUS
= 6384867.53587
MEAN RADIUS = 6370175.33215
SCALE FACTOR = 0.9999443586

(Verification data 3)
3 ZAHYOCHI X (3) = -207504.143
ZAHYOCHI Y (3) = -90091.612
LATITUDE = 34-7-32.62478
LONGITUDE = 131-11-24.23440
GAMMA ANGLE = -0-32-52.51514
MERIDIAN RADIUS = 6355514.80440
ORTHODG. MERIDIAN RADIUS = 6384866.82185
MEAN RADIUS = 6370173.90739
SCALE FACTOR = 0.9999999999

(Verification data 4)
4 ZAHYOCHI X (4) = -207504.143
ZAHYOCHI Y (4) = -119361.021
LATITUDE = 34-7-22.57909
LONGITUDE = 130-52-22.58341
GAMMA ANGLE =
-0-43-32.98172
MERIDIAN RADIUS =
6355511.91142
ORTHOG. MERIDIAN RADIUS = 6384865.85306
MEAN RADIUS = 6370171.97429
SCALE FACTOR = 1.0000755076

(Verification data 5)
5 ZAHYOCHI X (5) = -207504.143
ZAHYOCHI Y (5) = -127420.415
LATITUDE = 34-7-19.32099
LONGITUDE = 130-47-8.30603
GAMMA ANGLE =
-0-46-29.28381
MERIDIAN RADIUS = 6355510.97317
ORTHOG. MERIDIAN RADIUS = 6384865.53887
MEAN RADIUS = 6370171.34734
SCALE FACTOR = 1.0000999998

As described above, in each case, the input value of the result data and the output value of the verification data completely match. The latitude / longitude obtained here is the fifth place after the decimal point, and the difference in accuracy is clear with the program of the Geospatial Information Authority of Japan that has an error in this range.
Also, from the result data 5, it can be seen that the SCALE FACTOR indicating the scale factor also converges to 1.001 with high accuracy.

It is explanatory drawing of one Embodiment of the position calculation apparatus which concerns on this invention. It is explanatory drawing which shows the flow of the position calculation method which concerns on this invention. It is explanatory drawing about calculation of a perpendicular latitude of the position calculation method which concerns on this invention.

DESCRIPTION OF SYMBOLS 1 Coordinate input part 2 Main part 6 Calculation part 7 Calculation control part 8 Judgment part 9 Regression control part

Claims (3)

By inputting coordinate values x and y on the plane rectangular coordinates X and Y for projecting the earth ellipsoid by the conformal projection method, at least the latitude φ _n on the earth ellipsoid corresponding to the coordinate values can be output. In a possible position calculator,
Coordinate input unit, output unit, constant setting unit, condition setting unit, first temporary latitude storage unit, second temporary latitude storage unit, first temporary scale factor storage unit, and second temporary scale factor storage Unit, at least five first to fifth calculation units, a calculation control unit, a determination unit, and a regression control unit,
The constant setting unit includes at least a latitude φ ₀ of the origin of the coordinate system, a major radius a and a minor radius b of the earth ellipsoid, a first eccentricity e of the earth ellipsoid, and a second eccentricity e ′ of the earth ellipsoid, The radius of curvature c of the ellipsoid of the earth ellipsoid and the values of the following constants A to F necessary for calculating the meridian arc length W on the reference meridian from the equator to the coordinate value x are previously stored. And
A = 1 + (3/4) e ² + (45/64) e ⁴ + (175/256 ) e ⁶ + (11025/16384) e ⁸ + (43659/65536) e ^{10
B = (3/4) e 2 +} (15/16) e 4 + (525/512) e 6 + (2205/2048) e 8 + (72765/65536) e 10
^{C = (15/64) e 4 +} (105/256) e 6 + (2205/4096) e 8 + (10395/16384) e 10
D = (35/512) e ⁶ + (315/2048) e ⁸ + (31185/131072) e ¹⁰
E = (315/16384) e 8 + (3465/65536) e 10
F = (693/131072) e ¹⁰
The latitude of the perpendicular drawn from the input coordinate to the reference meridian passing through the origin of the coordinate system to which the input coordinate belongs is defined as the perpendicular latitude,
In the condition setting unit, a threshold value that is a convergence condition IPS of the normal latitude is preset,
The first temporary latitude accommodating portion is capable of accommodating the initial value φ _j of the normal latitude ,
The first temporary scale factor housing part, which can accommodate any real number other than 0 as the temporary scale factor m _t,
The first calculation unit has a function of executing at least the following expressions 7, 8, and 9.
V _{k + 1} = (1 + e ′ ² cos ² φ _{k + 1} ) ^1/2 .
R _k2 = c / V _{k + 1} ²
... Formula 8
^{_{m t2 = (1 + y 2}} / 2m t 2 R k2 2 + y 4 / 24m t 4 R k2 4) × 0.9999 ... Equation 9
The second calculation unit has a function of executing at least the calculation of Expression 10 below.
W = a (1-e ² ) · {A · φ ₀ − (B / 2) · (sin 2φ ₀ ) + (C / 4) · (sin 4φ ₀ ) − (D / 6) · (sin 6φ ₀ ) + (E / 8) · (sin 8φ ₀ ) − (F / 10) · (sin 10φ ₀ )} + x / m _t Equation 10
The third calculation unit has a function of executing at least the calculation of the following expression 11;
S (φ _j
) = A (1-e ² ) · {A · φ _j − (B / 2) · (sin 2φ _j ) + (C / 4) · (sin 4φ _j ) − (D / 6) · (sin 6φ _j ) + (E / 8) · (sin 8φ _j ) − (F / 10) · (sin 10φ _j )}
The fourth arithmetic unit is at least W in Equation 10 and S (φ _{j in} Equation 11).
) And a function to execute an operation for calculating a normal latitude φ _{j + 1} by a normal latitude convergence calculation ,
The fifth calculation unit has a function of executing at least the calculation of Expression 3 below.
φ _{k + 1} = φ _k −t _k (y / m _t ) ² / 2M _k N _k + t _k (y / m _t ) ⁴ (5 + 3 t _k ² + η _{k
^{2 -9t k 2 η k 2 -4η}} k 4) / 24M k N k 3 -t k (y / m t) 6 (61 + 90t k 2 + 45t k 4) / 720M k N k 5
... Formula 3
The coordinate input unit accepts input of the coordinate values x and y,
The calculation control unit causes the second calculation unit to refer to the constant setting unit, the coordinate input unit, and the first temporary scale coefficient storage unit, and the major radius a of the earth ellipsoid and the first eccentricity of the earth ellipsoid. and rate e, the origin latitude phi _0, and input coordinate values x, standards of the temporary scale factor m _t, and a said constant to F, by calculating the above equation 10, from the equator to the coordinate values x The meridian arc length W on the meridian is calculated, and the second calculation unit stores the calculated meridian arc length W in the constant setting unit,
The calculation control unit causes the third calculation unit to refer to the constant setting unit and the first temporary latitude storage unit, the major radius a of the earth ellipsoid, the first eccentricity e of the earth ellipsoid, and the normal latitude. an initial value phi _j of the from constant to F, by calculating the above equation 11, meridian arc length S from the equator to the initial value phi _j of a perpendicular latitude (phi _j
), And the third calculation unit stores the calculated meridian arc length S (φ _j ) in the constant setting unit,
The calculation control unit causes the fourth calculation unit to refer to the constant setting unit and the first temporary latitude accommodation unit, the initial value φ _j of the normal latitude, the major radius a of the earth ellipsoid, and the first value of the earth ellipsoid. 1 eccentricity e and the meridian arc length W on the reference meridian from the equator to the coordinates x, meridian arc length from the equator to the initial value phi _j of a perpendicular latitude S (phi _j
) To calculate the latitude φ _{j + 1} , and the fourth calculation unit stores the calculated latitude φ _{j + 1} in the first temporary latitude storage unit, and the latitude φ _{j + 1} from the fourth calculation unit Received the first provisional latitude accommodating part, the latitude φ _j that was accommodated
The pass to the second temporary latitude accommodating unit accommodates a value of the latitude phi _{j + 1} instead of the latitude phi _j,
The determination unit refers to the first temporary latitude storage unit, the second temporary latitude storage unit, and the condition setting unit, and uses the absolute value of the difference between the latitude φ _{j + 1} and the latitude φ _j and the convergence condition IPS of the normal latitude. When the absolute value of the difference between latitude φ _{j + 1} and latitude φ _j is determined to be greater than the threshold value by comparing with a certain threshold value, the result is notified to the regression control unit and the notification is received. regression control unit, the value of the latitude phi _{j + 1} of the first temporary latitude housing portion, as the latitude phi _j, the third arithmetic unit again to perform the calculation of equation 11, the calculated meridian arc length S (phi _j
) Is stored in the constant setting unit, and the fourth arithmetic unit is again referred to the constant setting unit and the meridian arc length S (φ _j
From), to calculate the latitude phi _{j + 1,} the first temporary latitude accommodating portion, thereby passed the latitude phi _j that held until then to the second temporary latitude accommodating portion, first to the latitude phi _j that held 4 The calculation unit replaces the latitude φ _{j + 1} calculated again ,
The determination unit performs the above determination again with reference to the first temporary latitude storage unit, the second temporary latitude storage unit, and the condition setting unit, and the absolute value of the difference between the latitude φ _{j + 1} and the latitude φ _j is Until it is determined that the value is equal to or less than the threshold value, the regression control unit repeatedly causes the third calculation unit to perform the calculation of Equation 11 and causes the fourth calculation unit to perform the convergence calculation of latitude.
When the determination unit determines that the absolute value of the difference between the latitude φ _{j + 1} and the latitude φ _j is equal to or less than the threshold value, the asymptotic latitude φ _{j + 1} is set as the perpendicular latitude φ _k and the regression control is performed. The unit refers to the coordinate input unit, the first temporary latitude accommodating unit, the constant setting unit, and the first temporary scale factor accommodating unit, and the provisional scale factor m _t , and the perpendicular latitude phi _k, the radius M _k and prime vertical radius of curvature N _k meridian curvature at the perpendicular latitude phi _k, a first value eta _k determined by e'cos φ _k, tan
By calculating the above equation 3 from the second value t _k determined by φ _k and the input coordinate value y, the latitude φ _{k + 1} is calculated, and the fifth calculation unit calculates The latitude φ _{k + 1} is stored as a latitude φ _n of the input coordinate point in the first temporary latitude storage unit, replacing the value previously stored in the first temporary latitude storage unit. The latitude accommodating part passes the value of the latitude φ _k that has been held so far to the second temporary latitude accommodating part,
Further, in the calculation control unit, the first calculation unit is referred to the constant setting unit and the first temporary latitude accommodation unit, the second eccentricity e ′ of the earth ellipsoid, the latitude φ _{k + 1,} and Then, by calculating Equation 7 and Equation 8, the average curvature radius R _k2 at the latitude φ _{k + 1} is calculated,
Arithmetic control unit, the first operation unit, a coordinate input unit, by referring to the first temporary scale factor accommodating portion, and the value of the coordinate value y input, a temporary scale factor m _t, the mean curvature The scale factor _mt2 is calculated from the radius _Rk2 by calculating the above formula 9 , and the first calculation unit stores the calculated scale factor _mt2 in the first temporary scale factor storage unit. 1 temporary scale factor accommodating portion passes the housing to have a scale factor m _t to the second temporary scale factor accommodating portion accommodates the scale factor m _t2 instead as the scale factor m _t above,
Regression control unit, through the operation control unit, the scale factor m _t2 that the calculated instead of the temporary scale factor m _t so far as scale factor m _t of the next temporary, at least once, the second, fourth and 5 calculation unit, equation 10, latitude convergence calculation, equation 3, and the first calculation unit recalculate equation 7, equation 8, and equation 9,
The regression control unit causes the output unit to output at least the value of latitude φ _{k + 1} stored in the first temporary latitude storage unit after the recalculation. By inputting coordinate values x and y on the plane rectangular coordinates X and Y for projecting the earth ellipsoid by the conformal projection method, at least the latitude φ _n on the earth ellipsoid corresponding to the coordinate values can be output. In a possible position calculator,
Coordinate input unit, output unit, constant setting unit, condition setting unit, first temporary latitude storage unit, second temporary latitude storage unit, first temporary scale factor storage unit, and second temporary scale factor storage Unit, at least five first to fifth calculation units, a calculation control unit, a determination unit, and a regression control unit,
The constant setting unit includes at least the latitude φ _{0 of} the origin of the coordinate system, the value of the scale factor m _{0 at} the origin , the major radius a and minor radius b of the earth ellipsoid, the first eccentricity e of the earth ellipsoid, and the earth ellipse Each of the following constants A to F necessary for calculating the second eccentricity e ′ of the body, the radius of curvature c of the pole of the earth ellipsoid, and the meridian arc length W on the reference meridian from the equator to the coordinate value x, respectively. The value of is stored in advance,
A = 1 + (3/4) e ² + (45/64) e ⁴ + (175/256 ) e ⁶ + (11025/16384) e ⁸ + (43659/65536) e ^{10
B = (3/4) e 2 +} (15/16) e 4 + (525/512) e 6 + (2205/2048) e 8 + (72765/65536) e 10
^{C = (15/64) e 4 +} (105/256) e 6 + (2205/4096) e 8 + (10395/16384) e 10
D = (35/512) e ⁶ + (315/2048) e ⁸ + (31185/131072) e ¹⁰
E = (315/16384) e 8 + (3465/65536) e 10
F = (693/131072) e ¹⁰
The latitude of the perpendicular drawn from the input coordinate to the reference meridian passing through the origin of the coordinate system to which the input coordinate belongs is defined as the perpendicular latitude,
In the condition setting unit, a threshold value that is a convergence condition IPS of the normal latitude is preset,
The first temporary latitude accommodating portion is capable of accommodating the initial value φ _j of the normal latitude ,
The first temporary scale factor housing part, which can accommodate any real number other than 0 as the temporary scale factor m _t,
The first calculation unit has a function of executing at least the following expressions 7, 8, and 9.
V _{k + 1} = (1 + e ′ ² cos ² φ _{k + 1} ) ^1/2 .
R _k2 = c / V _{k + 1} ²
... Formula 8
^{_{m t2 = (1 + y 2}} / 2m t 2 R k2 2 + y 4 / 24m t 4 R k2 4) × 0.9999 ... Equation 9
The second calculation unit has a function of executing at least the calculation of Expression 10 below.
W = a (1-e ² ) · {A · φ ₀ − (B / 2) · (sin 2φ ₀ ) + (C / 4) · (sin 4φ ₀ ) − (D / 6) · (sin 6φ ₀ ) + (E / 8) · (sin 8φ ₀ ) − (F / 10) · (sin 10φ ₀ )} + x / m _t Equation 10
The third calculation unit has a function of executing at least the calculation of the following expression 11;
S (φ _j
) = A (1-e ² ) · {A · φ _j − (B / 2) · (sin 2φ _j ) + (C / 4) · (sin 4φ _j ) − (D / 6) · (sin 6φ _j ) + (E / 8) · (sin 8φ _j ) − (F / 10) · (sin 10φ _j )}
The fourth arithmetic unit is at least W in Equation 10 and S (φ _{j in} Equation 11).
) And a function to execute an operation for calculating a normal latitude φ _{j + 1} by a normal latitude convergence calculation ,
The fifth calculation unit has a function of executing at least the calculation of Expression 3 below.
φ _{k + 1} = φ _k −t _k (y / m _t ) ² / 2M _k N _k + t _k (y / m _t ) ⁴ (5 + 3 t _k ² + η _{k
^{2 -9t k 2 η k 2 -4η}} k 4) / 24M k N k 3 -t k (y / m t) 6 (61 + 90t k 2 + 45t k 4) / 720M k N k 5
... Formula 3
The coordinate input unit accepts input of the coordinate values x and y,
The calculation control unit causes the first calculation unit to refer to the constant setting unit, the latitude φ ₀ of the origin of the coordinate system , the second eccentricity e ′ of the earth ellipsoid, and the radius of curvature of the pole of the earth ellipsoid From c, in the calculation function of Equation 7 and Equation 8 above,
V ₀ = (1 + e ′ ² cos ² φ ₀ ) ^1/2
R ₀ = c / V ₀ ²

To calculate the average radius of curvature R ₀ at the origin ,
The average radius of curvature R ₀ at the origin is calculated by the first calculation unit and stored in the constant setting unit.
The arithmetic control unit stores the scale factor m ₀ at the origin of the constant setting unit in the first temporary scale factor storage unit,
Said 1st calculating part can perform the calculation of following Formula 2 with the calculation function of said Formula 9,
m _t = {1+ (y ² / 2m ₀ ² R ₀ ² ) + (y ⁴ / 24m ₀ ⁴ R ₀ ⁴ )} × 0.9999 Equation 2
The calculation control unit causes the first calculation unit to refer to the constant setting unit or the first temporary scale factor storage unit and the coordinate input unit, and inputs the value of the coordinate value y, the origin scale factor m ₀ , the average radius of curvature R ₀ Prefecture, by causing the calculation of equation 2 to calculate the temporary scale factor m _t, a first arithmetic unit, a scale factor m _t calculated tentative as scale factor of the provisional , Instead of the original scale factor m ₀ , the first temporary scale factor accommodating part is accommodated,
The calculation control unit causes the second calculation unit to refer to the constant setting unit, the coordinate input unit, and the first temporary scale coefficient storage unit, and the major radius a of the earth ellipsoid and the first eccentricity of the earth ellipsoid. and rate e, the origin latitude phi _0, and input coordinate values x, standards of the temporary scale factor m _t, and a said constant to F, by calculating the above equation 10, from the equator to the coordinate values x The meridian arc length W on the meridian is calculated, and the second calculation unit stores the calculated meridian arc length W in the constant setting unit,
The calculation control unit causes the third calculation unit to refer to the constant setting unit and the first temporary latitude storage unit, the major radius a of the earth ellipsoid, the first eccentricity e of the earth ellipsoid, and the normal latitude. an initial value phi _j of the from constant to F, by calculating the above equation 11, meridian arc length S from the equator to the initial value phi _j of a perpendicular latitude (phi _j
), And the third calculation unit stores the calculated meridian arc length S (φ _j ) in the constant setting unit,
The calculation control unit causes the fourth calculation unit to refer to the constant setting unit and the first temporary latitude accommodation unit, the initial value φ _j of the normal latitude, the major radius a of the earth ellipsoid, and the first value of the earth ellipsoid. 1 eccentricity e and the meridian arc length W on the reference meridian from the equator to the coordinates x, meridian arc length from the equator to the initial value phi _j of a perpendicular latitude S (phi _j
) To calculate the latitude φ _{j + 1} , and the fourth calculation unit stores the calculated latitude φ _{j + 1} in the first temporary latitude storage unit, and the latitude φ _{j + 1} from the fourth calculation unit Received the first provisional latitude accommodating part, the latitude φ _j that was accommodated
The pass to the second temporary latitude accommodating unit accommodates a value of the latitude phi _{j + 1} instead of the latitude phi _j,
The determination unit refers to the first temporary latitude storage unit, the second temporary latitude storage unit, and the condition setting unit, and uses the absolute value of the difference between the latitude φ _{j + 1} and the latitude φ _j and the convergence condition IPS of the normal latitude. When the absolute value of the difference between latitude φ _{j + 1} and latitude φ _j is determined to be greater than the threshold value by comparing with a certain threshold value, the result is notified to the regression control unit and the notification is received. regression control unit, the value of the latitude phi _{j + 1} of the first temporary latitude housing portion, as the latitude phi _j, the third arithmetic unit again to perform the calculation of equation 11, the calculated meridian arc length S (phi _j
) Is stored in the constant setting unit, and the fourth arithmetic unit is again referred to the constant setting unit and the meridian arc length S (φ _j
From), to calculate the latitude phi _{j + 1,} the first temporary latitude accommodating portion, thereby passed the latitude phi _j that held until then to the second temporary latitude accommodating portion, first to the latitude phi _j that held 4 The calculation unit replaces the latitude φ _{j + 1} calculated again ,
The determination unit performs the above determination again with reference to the first temporary latitude storage unit, the second temporary latitude storage unit, and the condition setting unit, and the absolute value of the difference between the latitude φ _{j + 1} and the latitude φ _j is Until it is determined that the value is equal to or less than the threshold value, the regression control unit repeatedly causes the third calculation unit to perform the calculation of Equation 11 and causes the fourth calculation unit to perform the convergence calculation of latitude.
When the determination unit determines that the absolute value of the difference between the latitude φ _{j + 1} and the latitude φ _j is equal to or less than the threshold value, the asymptotic latitude φ _{j + 1} is set as the perpendicular latitude φ _k and the regression control is performed. The unit refers to the coordinate input unit, the first temporary latitude accommodating unit, the constant setting unit, and the first temporary scale factor accommodating unit, and the provisional scale factor m _t , and the perpendicular latitude phi _k, the radius M _k and prime vertical radius of curvature N _k meridian curvature at the perpendicular latitude phi _k, a first value eta _k determined by e'cos φ _k, tan
By calculating the above equation 3 from the second value t _k determined by φ _k and the input coordinate value y, the latitude φ _{k + 1} is calculated, and the fifth calculation unit calculates The latitude φ _{k + 1} is stored as a latitude φ _n of the input coordinate point in the first temporary latitude storage unit, replacing the value previously stored in the first temporary latitude storage unit. The latitude accommodating part passes the value of the latitude φ _k that has been held so far to the second temporary latitude accommodating part,
Further, in the calculation control unit, the first calculation unit is referred to the constant setting unit and the first temporary latitude accommodation unit, the second eccentricity e ′ of the earth ellipsoid, the latitude φ _{k + 1,} and Then, by calculating Equation 7 and Equation 8, the average curvature radius R _k2 at the latitude φ _{k + 1} is calculated,
Arithmetic control unit, the first operation unit, a coordinate input unit, by referring to the first temporary scale factor accommodating portion, and the value of the coordinate value y input, a temporary scale factor m _t, the mean curvature The scale factor _mt2 is calculated from the radius _Rk2 by calculating the above formula 9 , and the first calculation unit stores the calculated scale factor _mt2 in the first temporary scale factor storage unit. 1 temporary scale factor accommodating portion passes the housing to have a scale factor m _t to the second temporary scale factor accommodating portion accommodates the scale factor m _t2 instead as the scale factor m _t above,
Regression control unit, through the operation control unit, the scale factor m _t2 that the calculated instead of the temporary scale factor m _t so far as scale factor m _t of the next temporary, at least once, the second, fourth and 5 calculation unit, equation 10, latitude convergence calculation, equation 3, the first calculation unit recalculate equation 7, equation 8, and equation 9,
The regression control unit causes the output unit to output at least the value of latitude φ _{k + 1} stored in the first temporary latitude storage unit after the recalculation. By inputting coordinate values x and y on the plane rectangular coordinates X and Y for projecting the earth ellipsoid by the conformal projection method, at least the latitude φ _n on the earth ellipsoid corresponding to the coordinate values can be output. In a possible position calculator,
Coordinate input unit, output unit, constant setting unit, condition setting unit, first temporary latitude storage unit, second temporary latitude storage unit, first temporary scale factor storage unit, and second temporary scale factor storage Unit, at least five first to fifth calculation units, a calculation control unit, a main determination unit, a sub-determination unit, and a regression control unit,
The constant setting unit includes at least a latitude φ ₀ of the origin of the coordinate system, a major radius a and a minor radius b of the earth ellipsoid, a first eccentricity e of the earth ellipsoid, and a second eccentricity e ′ of the earth ellipsoid, The radius of curvature c of the ellipsoid of the earth ellipsoid and the values of the following constants A to F necessary for calculating the meridian arc length W on the reference meridian from the equator to the coordinate value x are previously stored. And
A = 1 + (3/4) e ² + (45/64) e ⁴ + (175/256 ) e ⁶ + (11025/16384) e ⁸ + (43659/65536) e ^{10
B = (3/4) e 2 +} (15/16) e 4 + (525/512) e 6 + (2205/2048) e 8 + (72765/65536) e 10
^{C = (15/64) e 4 +} (105/256) e 6 + (2205/4096) e 8 + (10395/16384) e 10
D = (35/512) e ⁶ + (315/2048) e ⁸ + (31185/131072) e ¹⁰
E = (315/16384) e 8 + (3465/65536) e 10
F = (693/131072) e ¹⁰
The latitude of the perpendicular drawn from the input coordinate to the reference meridian passing through the origin of the coordinate system to which the input coordinate belongs is defined as the perpendicular latitude,
In the condition setting unit, a threshold value that is a convergence condition IPS of a normal latitude and a threshold value that is a convergence condition IPS2 of a scale factor are set in advance.
The first temporary latitude accommodating portion is capable of accommodating the initial value φ _j of the normal latitude ,
The first temporary scale factor housing part, which can accommodate any real number other than 0 as the temporary scale factor m _t,
The first calculation unit has a function of executing at least the following expressions 7, 8, and 9.
V _{k + 1} = (1 + e ′ ² cos ² φ _{k + 1} ) ^1/2 .
R _k2 = c / V _{k + 1} ²
... Formula 8
^{_{m t2 = (1 + y 2}} / 2m t 2 R k2 2 + y 4 / 24m t 4 R k2 4) × 0.9999 ... Equation 9
The second calculation unit has a function of executing at least the calculation of Expression 10 below.
W = a (1-e ² ) · {A · φ ₀ − (B / 2) · (sin 2φ ₀ ) + (C / 4) · (sin 4φ ₀ ) − (D / 6) · (sin 6φ ₀ ) + (E / 8) · (sin 8φ ₀ ) − (F / 10) · (sin 10φ ₀ )} + x / m _t Equation 10
The third calculation unit has a function of executing at least the calculation of the following expression 11;
S (φ _j
) = A (1-e ² ) · {A · φ _j − (B / 2) · (sin 2φ _j ) + (C / 4) · (sin 4φ _j ) − (D / 6) · (sin 6φ _j ) + (E / 8) · (sin 8φ _j ) − (F / 10) · (sin 10φ _j )}
The fourth arithmetic unit is at least W in Equation 10 and S (φ _{j in} Equation 11).
) And a function to execute an operation for calculating a normal latitude φ _{j + 1} by a normal latitude convergence calculation ,
The fifth calculation unit has a function of executing at least the calculation of Expression 3 below.
φ _{k + 1} = φ _k −t _k (y / m _t ) ² / 2M _k N _k + t _k (y / m _t ) ⁴ (5 + 3 t _k ² + η _{k
^{2 -9t k 2 η k 2 -4η}} k 4) / 24M k N k 3 -t k (y / m t) 6 (61 + 90t k 2 + 45t k 4) / 720M k N k 5
... Formula 3
The coordinate input unit accepts input of the coordinate values x and y,
The calculation control unit causes the second calculation unit to refer to the constant setting unit, the coordinate input unit, and the first temporary scale coefficient storage unit, and the major radius a of the earth ellipsoid and the first eccentricity of the earth ellipsoid. and rate e, the origin latitude phi _0, and input coordinate values x, standards of the temporary scale factor m _t, and a said constant to F, by calculating the above equation 10, from the equator to the coordinate values x The meridian arc length W on the meridian is calculated, and the second calculation unit stores the calculated meridian arc length W in the constant setting unit,
The calculation control unit causes the third calculation unit to refer to the constant setting unit and the first temporary latitude storage unit, the major radius a of the earth ellipsoid, the first eccentricity e of the earth ellipsoid, and the normal latitude. an initial value phi _j of the from constant to F, by calculating the above equation 11, meridian arc length S from the equator to the initial value phi _j of a perpendicular latitude (phi _j
), And the third calculation unit stores the calculated meridian arc length S (φ _j ) in the constant setting unit,
The calculation control unit causes the fourth calculation unit to refer to the constant setting unit and the first temporary latitude accommodation unit, the initial value φ _j of the normal latitude, the major radius a of the earth ellipsoid, and the first value of the earth ellipsoid. 1 eccentricity e and the meridian arc length W on the reference meridian from the equator to the coordinates x, meridian arc length from the equator to the initial value phi _j of a perpendicular latitude S (phi _j
) To calculate the latitude φ _{j + 1} , and the fourth calculation unit stores the calculated latitude φ _{j + 1} in the first temporary latitude storage unit, and the latitude φ _{j + 1} from the fourth calculation unit Received the first provisional latitude accommodating part, the latitude φ _j that was accommodated
The pass to the second temporary latitude accommodating unit accommodates a value of the latitude phi _{j + 1} instead of the latitude phi _j,
The main determination unit refers to the first temporary latitude accommodation unit, the second temporary latitude accommodation unit, and the condition setting unit, and the absolute value of the difference between the latitudes φ _{j + 1} and the latitude φ _j and the normal latitude convergence condition IPS If the absolute value of the difference between latitude φ _{j + 1} and latitude φ _j is determined to be greater than the threshold, the result is notified to the regression control unit and the notification receives regression controller, the value of the latitude phi _{j + 1} of the first temporary latitude accommodating portion, the latitude phi as _j, the third arithmetic unit again to perform the calculation of equation 11, the calculated meridian arc length S ( φ _j
) Is stored in the constant setting unit, and the fourth arithmetic unit is again referred to the constant setting unit and the meridian arc length S (φ _j
From), to calculate the latitude phi _{j + 1,} the first temporary latitude accommodating portion, thereby passed the latitude phi _j that held until then to the second temporary latitude accommodating portion, first to the latitude phi _j that held 4 The calculation unit replaces the latitude φ _{j + 1} calculated again ,
The main determination unit performs the above determination again with reference to the first temporary latitude storage unit, the second temporary latitude storage unit, and the condition setting unit, and the absolute value of the difference between the latitude φ _{j + 1} and the latitude φ _j is Until it is determined that the value is equal to or lower than the threshold value, the regression control unit repeatedly causes the third calculation unit to perform the calculation of Expression 11 and causes the fourth calculation unit to perform the convergence calculation of latitude.
When the main determination unit determines that the absolute value of the difference between latitude φ _{j + 1} and latitude φ _j is equal to or less than the threshold, the asymptotic latitude φ _{j + 1} is set as the normal latitude φ _k and the regression is performed. The control unit causes the fifth calculation unit to refer to the coordinate input unit, the first temporary latitude accommodating unit, the constant setting unit, and the first temporary scale factor accommodating unit, and the temporary scale factor m _t , and the perpendicular line latitude phi _k, the radius M _k and prime vertical radius of curvature N _k meridian curvature at the perpendicular latitude phi _k, a first value eta _k determined by e'cos φ _k, tan
By calculating the above equation 3 from the second value t _k determined by φ _k and the input coordinate value y, the latitude φ _{k + 1} is calculated, and the fifth calculation unit calculates The latitude φ _{k + 1} is stored as a latitude φ _n of the input coordinate point in the first temporary latitude storage unit, replacing the value previously stored in the first temporary latitude storage unit. The latitude accommodating part passes the value of the latitude φ _k that has been held so far to the second temporary latitude accommodating part,
Further, in the calculation control unit, the first calculation unit is referred to the constant setting unit and the first temporary latitude accommodation unit, the second eccentricity e ′ of the earth ellipsoid, the latitude φ _{k + 1,} and Then, by calculating Equation 7 and Equation 8, the average curvature radius R _k2 at the latitude φ _{k + 1} is calculated,
Arithmetic control unit, the first operation unit, a coordinate input unit, by referring to the first temporary scale factor accommodating portion, and the value of the coordinate value y input, a temporary scale factor m _t, the mean curvature The scale factor _mt2 is calculated from the radius _Rk2 by calculating the above formula 9 , and the first calculation unit stores the calculated scale factor _mt2 in the first temporary scale factor storage unit. 1 temporary scale factor accommodating portion passes the housing to have a scale factor m _t to the second temporary scale factor accommodating portion accommodates the scale factor m _t2 instead as the scale factor m _t above,
The sub-determination unit refers to the first temporary scale factor storage unit, the second temporary scale factor storage unit, and the condition setting unit, and calculates the absolute difference between the calculated scale factor m _t2 and the provisional scale factor m _t until then. and a value, the absolute value of the difference between a convergence condition IPS2 scale factor compared with the threshold value, the calculated scale factor m _t2 as the temporary scale factor m _t of far greater than the threshold value when it is determined that notifies the result to the regression controller, regression controller which has received the notification, through the calculation control unit, scaling the coefficients m _t2 follows that the calculated instead of the temporary scale factor m _t so far As a temporary scale factor m _t , at least Equation 10, Latitude convergence calculation, Equation 3 is calculated for the second, fourth, and fifth arithmetic units, and Equations 7, 8, and 9 are calculated again for the first arithmetic unit. is, the sub-determination unit, and the absolute value of the difference of the temporary scale factor m _t so far the scale factor m _t2 calculated again, scale factor Comparing the a convergence condition IPS2 threshold, the absolute value of the difference between the calculated scale factor m _t2 as the temporary scale factor m _t so far, until it is determined to be equal to or less than the threshold value, The regression control unit, through the calculation control unit, at least the second, fourth, and fifth calculation units, Equation 10, the convergence calculation of latitude, and the calculation of Equation 3, and the first calculation unit, Equations 7, 8, and 9 of the calculation is repeated Kaee, secondary determination unit, when the absolute value of the difference between the calculated scale factor m _t2 as the temporary scale factor m _t so far, was determined to be less relevant threshold The result is notified to the regression control unit, and the regression control unit that receives the notification causes the output unit to output at least the value of the latitude φ _{k + 1} stored in the first temporary latitude storage unit. position calculating device, characterized in that there.

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