JP4088234B2 - How to assign world coordinates to a geodetic survey map - Google Patents

Description

  The present invention relates to a method for assigning world coordinates to a geodetic survey map.

  As is well known, the geodetic survey map uses the distance measurement unit, horizontal angle measurement unit, and altitude angle measurement unit of the total station (TS) to observe the distance, horizontal angle, and altitude angle from the reference point to the boundary point of the geodetic survey map. These observation data are sent to the data collector, the data collected by the data collector is sent to the personal computer, and the best linear calculation is performed on the personal computer. The created geodetic survey map describes the exact area. Are registered at the Legal Affairs Bureau in arbitrary coordinates.

  The real estate registration law is scheduled to be revised based on the government's e-Japan plan, and here, the geodetic survey map will be digitized.

  On the other hand, the revised surveying law has been implemented since 2002. Of the surveying standards that should be followed by basic surveying and public surveying, the measurement of longitude and latitude is a global geodetic system (surveying) instead of the traditional Japanese surveying system. For this reason, if you need to obtain a land survey map registered with the Legal Affairs Bureau at a land and house investigator office, etc. It is necessary to give the world geodetic coordinate (world coordinate) to.

  Therefore, for example, it is necessary to obtain the world coordinates of the reference point that is the reference point of the land survey map, and convert the land survey map from arbitrary coordinates to world coordinates based on the world coordinates of the reference point. Here, in order to obtain the world coordinates of the reference point, a GPS receiving antenna is installed at the reference point, the radio wave of the GPS satellite is received by the GPS receiving antenna, and the received GPS data is transmitted to the GPS data center by the mobile phone. Then, the world coordinates of the reference point processed in the GPS data center are received by the receiver through the mobile phone and accumulated in the data collector.

However, while total station (TS) surveying can accurately measure the relative position of a relatively narrow distance range as shown in a geodetic survey map, GPS surveying has a certain range (about 2 cm) regardless of the measurement distance. ) Always occurs, so the reference point cannot be shown in the correct world coordinates in the first place. Therefore, as shown in FIG. 4A, the positions in the arbitrary coordinate system (referred to as arbitrary coordinate positions) P ₁ , P ₂ , and each reference point of the area survey map in which the relative positional relationship by the total station (TS) survey is accurate. P ₃ , P _4, and positions of the respective reference points in the world coordinate system (referred to as observed world coordinate positions) p ₁ , p ₂ , p ₃ , p ₄ as shown in FIG. In the meantime, a gap occurs, and if you try to fit the ground survey map from arbitrary coordinates to world coordinates by a simple method for each reference point with world coordinates obtained by GPS survey, As shown in FIG. 5, there is a risk that the geodetic survey map having the exact shape and size obtained by the total station (TS) survey may be distorted.

  The present invention is not limited to the case where the reference point is obtained by GPS surveying as described above, but also when the world coordinates of the reference point set by the Geographical Survey Institute or the public reference point set by the local government are used. Applicable, but solves the above problems, and for each reference point with world coordinates obtained by GPS surveying etc., the geodetic survey map from any coordinates to the world without distorting its shape and size It is an object of the present invention to provide a world geodetic system coordinate assignment method for a geodetic survey map that can be converted into coordinates and adapted.

ここで、

である。なお、Tは転置を表す。また、vはベクトルを表す。
3)上記式(3)に示す最小バイアスの条件に基づいて解s（＝[x _0, y ₀ ,kcosθ,ksinθ] ^T ）を求める。解sは下記式(4)で示される。
s＝（A ^T A） ^-1 A ^T L (4)
ここで、

である。
4)解s（＝[x _0, y ₀ ,kcosθ,ksinθ] ^T ）と任意座標（X _i ,Y _i ）を上記式(1)、(2)に代入し、世界座標（X _i ^' ,Y _i ^' ）を求める。 The world coordinate assigning method of the geodetic survey map according to the present invention is obtained by the observation world coordinate (ξ _i , η _i ) of the observation world coordinate position p _i of each reference point obtained by GPS survey etc. and the total station (TS) survey. any coordinate (X _i, Y _i) of any coordinate position P _i of each引照points by performing a minimum bias calculations for bias to minimize relative and, optionally coordinates (X arbitrary coordinate position P _i of each引照point _i, Y _i) of the world coordinate position P _i 'world coordinates (X ^_i', Y _i ^'into a), the world coordinates of ground product survey plan that converts the acreage survey maps from any coordinate system to the world coordinate system A method of giving , characterized by performing the following information processing 1) to 4) .
1) A similarity transformation model represented by the following formulas (1) and (2) is defined (x ₀ , y ₀ : translation, θ: rotation, k: scale ratio).
X _i '= x ₀ + kcos θX _i + ksin θY _i (1)
Y _i '= y ₀ −ksinθX _i + kcosθY _i (2)
2) When i = 1 to n (n ≥ 3), the world coordinate positions P ₁ ', P ₂ ', ... P _n ^' are the best match to the observed world coordinate positions p ₁ , p ₂ , ... p _n Therefore, the following formula (3) indicating the minimum bias is satisfied.

here,

It is. T represents transposition. V represents a vector.
3) A solution s (= [x _0, y ₀ , kcos θ, ksin θ] ^T ) is obtained based on the minimum bias condition shown in the above equation (3) . The solution s is expressed by the following equation (4).
s = (A ^T A) ^-1 A ^T L (4)
here,

It is.
4) Substituting the solution s (= [x _0, y ₀ , kcosθ, ksinθ] ^T ) and arbitrary coordinates (X _i , Y _i ) into the above equations (1) and (2), the world coordinates (X _i ^′ , Y _i ^' ).

  According to the present invention, the geodetic survey map is converted from arbitrary coordinates to world coordinates without distorting the shape and size of each reference point having world coordinates obtained by GPS surveying or the like by the minimum bias calculation. Can be made.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

  FIG. 1 shows a part of a schematic flowchart of a system for carrying out this embodiment, and FIG. 2 shows the rest of the schematic flowchart of the system. 1 and 2 correspond to the case where the world coordinates of the reference point are obtained by GPS surveying, but as other embodiments, the reference point set by the Geospatial Information Authority of Japan or the public standard set by the local government The present invention is also applicable when the world coordinates of a point are used as the world coordinates of the reference point.

  In FIG. 1, Step 1 to Step 3 represent a processing procedure for obtaining arbitrary coordinates of the reference point and the land survey map. Specifically, first, a total station (TS) is installed at each of the plurality of reference points, and a ground survey map from the reference point by the distance measuring unit, horizontal angle measuring unit and altitude angle measuring unit of the total station (TS). The distance to the boundary point, the horizontal angle and the altitude angle are observed, these observation data are sent to the data collector, and the data collected by the data collector is sent to the personal computer (step 1). Next, the personal computer performs the best linear calculation on the sent data and creates arbitrary coordinates of the geodetic survey map (step 2). The created area survey map and the arbitrary coordinates of the reference point are subjected to a world coordinate assigning process to be described later (step 3).

  In FIG. 2, Steps 4 to 6 represent processing procedures for converting the geodetic survey map and the reference point from arbitrary coordinates to world coordinates. Specifically, first, a GPS receiving antenna is installed at each reference point, a radio wave transmitted from a GPS satellite is received by the GPS receiving antenna, and the received GPS data is transmitted to the GPS data center by a mobile phone. The world coordinates (GPS coordinates) of the reference point processed in step 1, that is, the observed world coordinates are received by the receiver through the mobile phone, accumulated in the data collector, and the data accumulated in the data collector is sent to the personal computer (step 4). Next, the personal computer calculates the minimum bias based on the observed world coordinates of each reference point, the ground survey map obtained in step 3 and the arbitrary coordinates of the reference point (step 5), and the ground survey map described in the world coordinates. Is obtained (step 6).

  The minimum bias calculation will be described below.

First, the arbitrary coordinate position of the reference point is P _i , the arbitrary coordinate is (X _i , Y _i ), the observation world coordinate position by the GPS survey of the reference point is p _i , the observation world coordinate is (ξ _i , η _i ), conversion The later world coordinate position is P _i ′ and the world coordinates are (X _i ′, Y _i ′), and a conversion model for converting from arbitrary coordinates to world coordinates is determined. The optimal model for giving accurate world coordinates without distorting the shape and size of the geodetic survey map described in arbitrary coordinates is the similarity transformation expressed by the following equations (1) and (2).

X _i ′ = x ₀ + k cos θX _i + k sin θY _i (1)
Y _i ′ = y ₀ −k sin θX _i + k cos θY _i (2)
Here, x ₀ and y ₀ are parallel movements, θ is rotation, and k is a scale factor.

Further, when i = 1 to 4, the world coordinate positions P ₁ ′, P ₂ ′, P ₃ ′, and P ₄ ′ are the most suitable for the observed world coordinate positions p ₁ , p ₂ , p ₃ , and p _4. Therefore, the following expression (3) indicating the minimum bias is satisfied.

x ₁ ² + x ₂ ² + x ₃ ² + x ₄ ² = minimum (3)
here,
x ₁ = p ₁ P ₁ ′ = [x ₁ , y ₁ ] ^T
x ₂ = p ₂ P ₂ '= [x ₂ , y ₂ ] ^T
x ₃ = p ₃ P ₃ '= [x ₃ , y ₃ ] ^T
x ₄ = p ₄ P ₄ '= [x ₄ , y ₄ ] ^T
It is. T represents transposition.

The relationship between the observed world coordinates (ξ _i , η _i ) and the world coordinates (X _i ′, Y _i ′) shown in the above equations (1) and (2) is expressed by the following equations (4) and (5). The

_{x i = X i '-ξ} i = x 0 + kcosθX i + ksinθY i -ξ i (4)
_{y i = Y i '-η} i = y 0 -ksinθX i + kcosθY i -η i (5)
Four parameters (x ₀ , y ₀ , kcosθ, ksinθ) are obtained based on the minimum bias condition shown in the above equation (2). The solution s (= [x ₀ , y ₀ , kcos θ, k sin θ] ^T ) is a value equivalent to the least square method and is represented by the following equation (6).

s = (A ^T A) ⁻¹ A ^T L (6)
here,

It is.

By substituting the four parameters (x ₀ , y ₀ , kcosθ, ksinθ) and arbitrary coordinates (X _i , Y _i ) thus obtained into the above equations (1) and (2), the world coordinates (X _i ′, Y _i ′) can be obtained, and a geodetic survey map described in world coordinates can be obtained. Note that the parameter (kcosθ, ksinθ) is related to the scale factor k. If the area (size) of the geodetic survey map is not changed, k = 1 and (cosθ, sinθ) instead of the parameters (kcosθ, ksinθ) ) Is used.

  The following equations (7), (8), and (9) are derived from the above equation (3).

x ₁ + x ₂ + x ₃ + x ₄ = 0 (7)
y ₁ + y ₂ + y ₃ + y ₄ = 0 (8)
(X ₁ Y ₁ + x ₂ Y ₂ + x ₃ Y ₃ + x ₄ Y ₄ ) −
(Y ₁ X ₁ + y ₂ X ₂ + y ₃ X ₃ + y ₄ X ₄ ) = 0 (9)
Of these three formulas, formulas (7) and (8) are the center of the coordinates of the arbitrary coordinate positions P ₁ , P ₂ , P ₃ and P ₄ by the total station (TS) survey, and the observed world coordinate position p ₁ by the GPS survey. , P ₂ , p ₃ , and p ₄ are coincident with the center of coordinates. In addition, the rotation of the figure at the arbitrary coordinate positions P ₁ , P ₂ , P ₃ , P _{4 and} the figure at the observed world coordinate positions p ₁ , p ₂ , p ₃ , p ₄ by the GPS survey is fixed in the equation (9). It shows that.

  FIG. 3 shows the results of six GPS surveys performed at the three reference points A, B, and C. The GPS coordinate variation at each of the three points is large as A = 10 mm, B = 20 mm, and C = 16 mm, but the variation in the center position of the three points A, B, and C is as small as 6 mm.

  As described above, the world coordinate assigning method of the geodetic survey map according to the present embodiment includes the world coordinates of each reference point obtained by GPS survey and the like, and the arbitrary coordinates of each reference point obtained by total station (TS) survey. By converting the arbitrary coordinates of each reference point to world coordinates and converting the geodetic survey map from arbitrary coordinates to world coordinates, it has the world coordinates obtained by GPS surveying etc. For each reference point, the geodetic survey map can be adapted by converting from arbitrary coordinates to world coordinates without distorting its shape and size.

2 is a part of a schematic flowchart of a system for carrying out the present embodiment. The rest of the schematic flow diagram of the system It is an effect explanatory view of this embodiment. It is explanatory drawing of the world coordinates by the arbitrary coordinates by a total station (TS) survey, and GPS survey. It is explanatory drawing of the problem of the conversion to the world coordinate by a simple method.

Explanation of symbols

(X _i , Y _i ) Arbitrary coordinates (ξ _i , η _i ) World coordinates by GPS survey etc. (X _i ′, Y _i ′) World coordinates after conversion

Claims (1)

Arbitrary coordinates of observation world coordinates (ξ _i , η _i ) of observation world coordinate position p _i of each reference point obtained by GPS survey etc. and arbitrary coordinate position P _i of each reference point obtained by total station (TS) survey (X _i, Y _i) by performing the minimum bias calculation to minimize the bias to the arbitrary coordinates (X _i, Y _i) of the world coordinate position P _i 'of any coordinate position P _i of each引照point world coordinates ^{_{(X i ', Y i'}} ) is converted into an acreage survey plan a world coordinate method of applying ground product survey plan that converts from any coordinate system to the world coordinate system, the following 1) to 4) of A method for assigning world coordinates characterized by performing information processing .
1) A similarity transformation model represented by the following formulas (1) and (2) is defined (x ₀ , y ₀ : translation, θ: rotation, k: scale ratio).
X _i '= x ₀ + kcos θX _i + ksin θY _i (1)
Y _i '= y ₀ −ksinθX _i + kcosθY _i (2)
2) When i = 1 to n (n ≥ 3), the world coordinate positions P ₁ ', P ₂ ', ... P _n ^' are the best match to the observed world coordinate positions p ₁ , p ₂ , ... p _n Therefore, the following formula (3) indicating the minimum bias is satisfied.

here,

It is. T represents transposition.
3) A solution s (= [x _0, y ₀ , kcos θ, ksin θ] ^T ) is obtained based on the minimum bias condition shown in the above equation (3) . The solution s is expressed by the following equation (4).
s = (A ^T A) ^-1 A ^T L (4)
here,

It is.
4) Substituting the solution s (= [x _0, y ₀ , kcosθ, ksinθ] ^T ) and arbitrary coordinates (X _i , Y _i ) into the above equations (1) and (2), the world coordinates (X _i ^′ , Y _i ^' ).

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