JP2009047538A

JP2009047538A - Device and program for detecting position

Info

Publication number: JP2009047538A
Application number: JP2007213586A
Authority: JP
Inventors: Takuya Horikawa; 拓也堀川; Mitsunori Kono; 実則河野
Original assignee: Mitsubishi Electric Information Network Corp; RCS Co Ltd
Current assignee: Mitsubishi Electric Information Network Corp; RCS Co Ltd
Priority date: 2007-08-20
Filing date: 2007-08-20
Publication date: 2009-03-05

Abstract

<P>PROBLEM TO BE SOLVED: To provide a device and a program for receiving high frequency signals transmitted from a plurality of antennas to be periodically switched at a base station with a mobile terminal and calculating relative phases, and detecting the position of the mobile terminal, or the distance between them, or their mutual direction with high accuracy. <P>SOLUTION: A calculation formula is disclosed which is used for detecting a relative positional relation of the mobile terminal 2 to the base station with high accuracy, by making the intervals between the plurality of directional antennas 11a-11d not wider than one wavelength and transmitting the high frequency signals while periodically switching the antennas at the base station 1, installing the directional antennas 11a-11d so that the directions of their directivities become obliquely downward and have angles, and measuring phase differences between the high frequency signals received by the mobile terminal 2. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

この発明は、基地局と携帯端末の間で超音波信号あるいは高周波信号あるいは光信号を送受信することによって、当該基地局と携帯端末間の相対的な位置関係を検知するための位置検知装置および位置検知プログラムに関するものである。
The present invention relates to a position detection device and a position for detecting a relative positional relationship between a base station and a mobile terminal by transmitting and receiving an ultrasonic signal, a high-frequency signal, or an optical signal between the base station and the mobile terminal. It relates to the detection program.

図１は、特許文献１に記載されている従来の無線マーカの実施例である。図１において、１は基地局、２は携帯端末、１１ａ〜１１ｄは指向性アンテナ、４１は基地局１の指向性アンテナ１１ａ〜１１ｄの真下からの角度、４２は携帯端末２が位置する方向、４３は基地局の指向性アンテナ１１ａ〜１１ｄの高さ、４４は携帯端末２のアンテナの高さ、４５は基地局１の指向性アンテナ１１ａ〜１１ｄの真下からの距離、４６は基地局１の真下の位置(X0)、(Y0)である。
前記基地局１の指向性アンテナ１１ａ〜１１ｄは、発信する高周波信号の１波長以下の間隔で設置され、周期的に切替えられながら高周波信号を発信しているものとする。
前記携帯端末２が前記指向性アンテナ１１ａ〜１１ｄの真下から角度４２の方向に存在するとすると、Δd(X)＝(H−h)×Tan{ΔΦ(X)}、Δd(Y)＝(H−h)×Tan{ΔΦ(Y)}となる。
ここで、Δd(X)、Δd(Y)は前記指向性アンテナ１１ａ〜１１ｄの真下からの距離４５、Ｈは前記指向性アンテナ１１ａ〜１１ｄの高さ４３、ｈは前記携帯端末２のアンテナの高さ４４、ΔΦ(X)、ΔΦ(Y)は前記携帯端末２が位置する方向４２である。
前記指向性アンテナ１１ａ〜１１ｄの真下の位置を（X0，Y0）とすると、前記携帯端末２の位置（Xx，Yy）は、Xx＝X0＋Δd(X)、Yy＝Y0＋Δd(Y)から計算できるとしている。
しかしながら、従来の位置検知の計算式では、前記携帯端末２の位置が正確に計算できない問題点があった。

特願２００５−３６３１７１号 FIG. 1 shows an example of a conventional wireless marker described in Patent Document 1. In FIG. In FIG. 1, 1 is a base station, 2 is a mobile terminal, 11a to 11d are directional antennas, 41 is an angle from directly below the directional antennas 11a to 11d of the base station 1, 42 is a direction in which the mobile terminal 2 is located, 43 is the height of the directional antennas 11a to 11d of the base station, 44 is the height of the antenna of the mobile terminal 2, 45 is the distance from directly below the directional antennas 11a to 11d of the base station 1, and 46 is the height of the base station 1 Directly below the positions (X0) and (Y0).
The directional antennas 11a to 11d of the base station 1 are installed at intervals of one wavelength or less of a high-frequency signal to be transmitted, and transmit high-frequency signals while being periodically switched.
If the portable terminal 2 is present in the direction of the angle 42 from directly below the directional antennas 11a to 11d, Δd (X) = (H−h) × Tan {ΔΦ (X)}, Δd (Y) = (H −h) × Tan {ΔΦ (Y)}.
Here, Δd (X) and Δd (Y) are distances 45 from directly below the directional antennas 11a to 11d, H is the height 43 of the directional antennas 11a to 11d, and h is the antenna of the portable terminal 2. Height 44, ΔΦ (X), ΔΦ (Y) are directions 42 in which the mobile terminal 2 is located.
If the position directly below the directional antennas 11a to 11d is (X0, Y0), the position (Xx, Yy) of the mobile terminal 2 can be calculated from Xx = X0 + Δd (X), Yy = Y0 + Δd (Y). Yes.
However, the conventional position detection calculation formula has a problem that the position of the portable terminal 2 cannot be calculated accurately.

Japanese Patent Application No. 2005-363171

この発明は、基地局と携帯端末の間の位置関係を高い精度で検知するための位置検知装置および位置検知プログラムを提供する。
The present invention provides a position detection device and a position detection program for detecting a positional relationship between a base station and a mobile terminal with high accuracy.

この発明に係わる位置検知装置および位置検知プログラムは、基地局に接続する複数のアンテナあるいは複数の送受波器の任意の組合わせの間隔を１波長以下とし周期的に切替えながら超音波信号あるいは高周波信号あるいは光信号を発信しおよび／あるいは受信することによって、携帯端末との間の位置関係を検知するための計算式に関するものである。
A position detection apparatus and a position detection program according to the present invention provide an ultrasonic signal or a high-frequency signal while periodically switching the interval of any combination of a plurality of antennas or a plurality of transducers connected to a base station to one wavelength or less. Alternatively, the present invention relates to a calculation formula for detecting a positional relationship with a portable terminal by transmitting and / or receiving an optical signal.

従来の位置検知装置あるいは位置検知プログラムで用いられる計算式では、基地局の複数のアンテナあるいは複数の送受波器が傾斜して設置される場合に誤差を生じる問題点がある。本発明の位置検知装置および位置検知プログラムで用いられる計算式では、基地局の複数のアンテナあるいは複数の送受波器が傾斜して設置される場合に位置検知誤差を縮減することが可能となる。
In the calculation formula used in the conventional position detection apparatus or position detection program, there is a problem that an error occurs when a plurality of antennas or a plurality of transducers of a base station are installed at an inclination. In the calculation formula used in the position detection apparatus and the position detection program of the present invention, it is possible to reduce the position detection error when a plurality of antennas or a plurality of transducers of the base station are installed at an inclination.

この発明に係わる位置検知装置および位置検知プログラムは、図１に示すように、基地局１と携帯端末２から構成され、基地局１には、複数のアンテナ１１ａ〜１１ｄの任意の組合わせが１波長以下の間隔で配置されており、当該複数のアンテナ１１ａ〜１１ｄが周期的に切替えられて高周波信号を発信しあるいは受信し、前記高周波信号の位相差を測定し、前記基地局１と携帯端末２相互間の方向を算出している。
ここで、携帯端末２には少なくとも１基のアンテナが接続されているものとする。 As shown in FIG. 1, the position detection device and the position detection program according to the present invention are composed of a base station 1 and a portable terminal 2, and the base station 1 has one arbitrary combination of a plurality of antennas 11 a to 11 d. The plurality of antennas 11a to 11d are periodically switched to transmit or receive a high-frequency signal, measure a phase difference of the high-frequency signal, and the base station 1 and the mobile terminal The direction between the two is calculated.
Here, it is assumed that at least one antenna is connected to the mobile terminal 2.

上記の図１に示すように、前記複数のアンテナ１１ａ〜１１ｄが前記基地局の真下方向あるいは真下方向から傾斜して設置された場合に、前記基地局１と前記携帯端末２の間の相対的な位置関係を求めるために、まず、前記高周波信号の伝搬路長を所与の計算式により求め、前記線路長と前記方向の算出結果とから、前記基地局１と携帯端末２の間の相対的な位置関係を求める。
前記基地局１と携帯端末２の間の伝搬路長を求める計算式を[(H−h)／Cos{α(Y)＋ΔΦ(Y)}]あるいは[(H−h)／Cos{α(X)＋ΔΦ(X)}]とし、前記基地局１と携帯端末２の間の相対的な位置関係を、
Δd(X)＝[(H−h)／Cos{α(Y)＋ΔΦ(Y)}]×Tan{α(X)＋ΔΦ(X)}
Δd(Y)＝(H−h)×Tan{α(Y)＋ΔΦ(Y)}
あるいは
Δd(X)＝(H−h)×Tan{α(X)＋ΔΦ(X)}
Δd(Y)＝[(H−h)／Cos{α(X)＋ΔΦ(X)}]×Tan{α(Y)＋ΔΦ(Y)}
により求める。
あるいは、前記基地局１と携帯端末２の間の伝搬路長を求める計算式を[(H−h)／√{1−sin2(α(X)＋ΔΦ(X))−sin2(α(Y)＋ΔΦ(Y))}]とし、前記基地局１と携帯端末２の間の相対的な位置関係を、
Δd(X)＝[(H−h)／√{1−sin2(α(X)＋ΔΦ(X))−sin2(α(Y)＋ΔΦ(Y))}]×sin(α(X)＋ΔΦ(X))
Δd(Y)＝[(H−h)／√{1−sin2(α(X)＋ΔΦ(X))−sin2(α(Y)＋ΔΦ(Y))}]×sin(α(Y)＋ΔΦ(Y))
により求める。
As shown in FIG. 1 above, when the plurality of antennas 11a to 11d are installed in a direction directly below or below the base station, the relative relationship between the base station 1 and the mobile terminal 2 is relatively large. In order to obtain a proper positional relationship, first, the propagation path length of the high-frequency signal is obtained by a given calculation formula, and the relative length between the base station 1 and the portable terminal 2 is calculated from the line length and the direction calculation result. To obtain a realistic positional relationship.
[(H−h) / Cos {α (Y) + ΔΦ (Y)}] or [(H−h) / Cos {α () is used to calculate the propagation path length between the base station 1 and the portable terminal 2. X) + ΔΦ (X)}], and the relative positional relationship between the base station 1 and the portable terminal 2 is
Δd (X) = [(H−h) / Cos {α (Y) + ΔΦ (Y)}] × Tan {α (X) + ΔΦ (X)}
Δd (Y) = (H−h) × Tan {α (Y) + ΔΦ (Y)}
Or Δd (X) = (H−h) × Tan {α (X) + ΔΦ (X)}
Δd (Y) = [(H−h) / Cos {α (X) + ΔΦ (X)}] × Tan {α (Y) + ΔΦ (Y)}
Ask for.
Alternatively, the calculation formula for obtaining the propagation path length between the base station 1 and the portable terminal 2 is [(H−h) / √ {1−sin2 (α (X) + ΔΦ (X)) − sin2 (α (Y)] + ΔΦ (Y))}], and the relative positional relationship between the base station 1 and the portable terminal 2 is
Δd (X) = [(H−h) / √ {1−sin2 (α (X) + ΔΦ (X)) − sin2 (α (Y) + ΔΦ (Y))}] × sin (α (X) + ΔΦ ( X))
Δd (Y) = [(H−h) / √ {1−sin2 (α (X) + ΔΦ (X)) − sin2 (α (Y) + ΔΦ (Y))}] × sin (α (Y) + ΔΦ ( Y))
Ask for.

図１は、本発明の一実施例を示す概念図である。図１において、１は基地局、２は携帯端末、１１ａ〜１１ｄは指向性アンテナ、４１は基地局１の指向性アンテナ１１ａ〜１１ｄの真下からの角度、４２は携帯端末２が位置する方向、４３は基地局１の指向性アンテナ１１ａ〜１１ｄの高さ、４４は携帯端末２のアンテナの高さ、４５は基地局１の指向性アンテナ１１ａ〜１１ｄの真下からの距離、４６は基地局１の真下の位置(X１)、(Y1)である。
前記基地局１の指向性アンテナ１１ａ〜１１ｄは、発信する高周波信号の１波長以下の間隔で設置され、周期的に切替えながら高周波信号を発信し、携帯端末２において前記複数の指向性アンテナに対応して受信した高周波信号の位相差を測定することによって、前記基地局１と携帯端末２の相対的な方向を算出しているものとする。 FIG. 1 is a conceptual diagram showing an embodiment of the present invention. In FIG. 1, 1 is a base station, 2 is a mobile terminal, 11a to 11d are directional antennas, 41 is an angle from directly below the directional antennas 11a to 11d of the base station 1, 42 is a direction in which the mobile terminal 2 is located, 43 is the height of the directional antennas 11a to 11d of the base station 1, 44 is the height of the antenna of the mobile terminal 2, 45 is the distance from directly below the directional antennas 11a to 11d of the base station 1, and 46 is the base station 1 The positions (X1) and (Y1) are directly below.
The directional antennas 11a to 11d of the base station 1 are installed at intervals of one wavelength or less of a high-frequency signal to be transmitted, transmit high-frequency signals while periodically switching, and correspond to the plurality of directional antennas in the mobile terminal 2 It is assumed that the relative direction between the base station 1 and the portable terminal 2 is calculated by measuring the phase difference of the received high-frequency signal.

前記携帯端末２が前記指向性アンテナ１１ａ〜１１ｄの真下から角度４２の方向に存在するとすると、前記基地局１と携帯端末２の間の伝搬路長は計算式[(H−h)／Cos{α(Y)＋ΔΦ(Y)}]あるいは[(H−h)／Cos{α(X)＋ΔΦ(X)}]によって求めると、前記基地局１と携帯端末２の間の相対的な位置関係は、
Δd(X)＝[(H−h)／Cos{α(Y)＋ΔΦ(Y)}]×Tan{α(X)＋ΔΦ(X)}
Δd(Y)＝(H−h)×Tan{α(Y)＋ΔΦ(Y)}
あるいは
Δd(X)＝(H−h)×Tan{α(X)＋ΔΦ(X)}
Δd(Y)＝[(H−h)／Cos{α(X)＋ΔΦ(X)}]×Tan{α(Y)＋ΔΦ(Y)}
となる。
なお、前記指向性アンテナ１１ａ〜１１ｄの真下の位置を（X0，Y0）とすると、前記携帯端末２の位置（Xx，Yy）は、Xx＝X0＋Δd(X)、Yy＝Y0＋Δd(Y)から求められる。 If the mobile terminal 2 exists in the direction of the angle 42 from directly below the directional antennas 11a to 11d, the propagation path length between the base station 1 and the mobile terminal 2 is calculated by the formula [(H−h) / Cos { [alpha] (Y) + [Delta] [Phi] (Y)}] or [(H-h) / Cos {[alpha] (X) + [Delta] [Phi] (X)}], the relative positional relationship between the base station 1 and the portable terminal 2 Is
Δd (X) = [(H−h) / Cos {α (Y) + ΔΦ (Y)}] × Tan {α (X) + ΔΦ (X)}
Δd (Y) = (H−h) × Tan {α (Y) + ΔΦ (Y)}
Or Δd (X) = (H−h) × Tan {α (X) + ΔΦ (X)}
Δd (Y) = [(H−h) / Cos {α (X) + ΔΦ (X)}] × Tan {α (Y) + ΔΦ (Y)}
It becomes.
When the position directly below the directional antennas 11a to 11d is (X0, Y0), the position (Xx, Yy) of the mobile terminal 2 is obtained from Xx = X0 + Δd (X), Yy = Y0 + Δd (Y). It is done.

ここで、Δd(X)、Δd(Y)は前記指向性アンテナ１１ａ〜１１ｄの真下からの距離４５、Ｈは前記指向性アンテナ１１ａ〜１１ｄの高さ４３、ｈは前記携帯端末２のアンテナの高さ４４、{α(X)＋ΔΦ(X)}と{α(Y)＋ΔΦ(Y)}は前記携帯端末が位置する方向４２、[(H−h)／Cos{α(Y)＋ΔΦ(Y)}]と[(H−h)／Cos{α(X)＋ΔΦ(X)}]は前記指向性アンテナ１１ａ〜１１ｄと携帯端末２を結ぶ高周波信号の伝搬路の長さである。 Here, Δd (X) and Δd (Y) are distances 45 from directly below the directional antennas 11a to 11d, H is the height 43 of the directional antennas 11a to 11d, and h is the antenna of the portable terminal 2. Height 44, {α (X) + ΔΦ (X)} and {α (Y) + ΔΦ (Y)} are directions 42, [(H−h) / Cos {α (Y) + ΔΦ ( Y)}] and [(H−h) / Cos {α (X) + ΔΦ (X)}] are the lengths of high-frequency signal propagation paths connecting the directional antennas 11 a to 11 d and the portable terminal 2.

あるいは、、前記基地局１と携帯端末２の間の伝搬路長は計算式[(H−h)／√{1−sin2(α(X)＋ΔΦ(X))−sin2(α(Y)＋ΔΦ(Y))}]によって求めると、前記基地局１と携帯端末２の間の相対的な位置関係は、
Δd(X)＝[(H−h)／√{1−sin2(α(X)＋ΔΦ(X))−sin2(α(Y)＋ΔΦ(Y))}]×sin(α(X)＋ΔΦ(X))
Δd(Y)＝[(H−h)／√{1−sin2(α(X)＋ΔΦ(X))−sin2(α(Y)＋ΔΦ(Y))}]×sin(α(Y)＋ΔΦ(Y))
となる。 Alternatively, the propagation path length between the base station 1 and the portable terminal 2 is calculated by the formula [(H−h) / √ {1−sin2 (α (X) + ΔΦ (X)) − sin2 (α (Y) + ΔΦ]. (Y))}], the relative positional relationship between the base station 1 and the portable terminal 2 is
Δd (X) = [(H−h) / √ {1−sin2 (α (X) + ΔΦ (X)) − sin2 (α (Y) + ΔΦ (Y))}] × sin (α (X) + ΔΦ ( X))
Δd (Y) = [(H−h) / √ {1−sin2 (α (X) + ΔΦ (X)) − sin2 (α (Y) + ΔΦ (Y))}] × sin (α (Y) + ΔΦ ( Y))
It becomes.

ここで、Δd(X)、Δd(Y)は前記指向性アンテナ１１ａ〜１１ｄの真下からの距離４５、Ｈは前記指向性アンテナ１１ａ〜１１ｄの高さ４３、ｈは前記携帯端末２のアンテナの高さ４４、{α(X)＋ΔΦ(X)}と{α(Y)＋ΔΦ(Y)}は前記携帯端末が位置する方向４２、[(H−h)／√{1−sin2(α(X)＋ΔΦ(X))−sin2(α(Y)＋ΔΦ(Y))}]は前記指向性アンテナ１１ａ〜１１ｄと携帯端末２を結ぶ高周波信号の伝搬路の長さである。
また、上記以外に、前記指向性アンテナ１１ａ〜１１ｄと携帯端末２を結ぶ高周波信号の伝搬路の長さを求めることが可能であり、求められた伝送路のｘ軸成分とｙ軸成分を計算することで、携帯端末の位置が高精度で検知できる。
Here, Δd (X) and Δd (Y) are distances 45 from directly below the directional antennas 11a to 11d, H is the height 43 of the directional antennas 11a to 11d, and h is the antenna of the portable terminal 2. Height 44, {α (X) + ΔΦ (X)} and {α (Y) + ΔΦ (Y)} are directions 42, [(H−h) / √ {1−sin2 (α ( X) + [Delta] [Phi] (X))-sin2 ([alpha] (Y) + [Delta] [Phi] (Y))}] is the length of the high-frequency signal propagation path connecting the directional antennas 11a to 11d and the portable terminal 2.
In addition to the above, it is possible to determine the length of the propagation path of the high-frequency signal connecting the directional antennas 11a to 11d and the portable terminal 2, and calculate the x-axis component and the y-axis component of the obtained transmission path. By doing so, the position of the mobile terminal can be detected with high accuracy.

以上の説明では、基地局からは高周波信号を発信しおよび／あるいは受信するとしているが、超音波トランスデューサーあるいは超音波送波器を用いて超音波信号を発信しおよび／あるいは受信し、携帯端末において超音波トランスデューサーあるいは超音波受波器を用いて超音波信号を受信しおよび／あるいは受信しても同様な効果が得られる。なお、本出願では、超音波トランスデューサーあるいは超音波送受波器と発光ダイオードあるいはレーザーダイオードあるいはホトダイオードを総称して送受波器と呼称するものとする。また、送受波器の送波器あるいは受波器のみを用いる場合でも送受波器として記載している。
また、基地局が別の基地局あるいは携帯端末からの信号を受信して再発信する中継局の役割を果たす場合にも本発明を適用することができる。
また、基地局から信号を発信し、携帯端末で受信する場合についても同様に本発明を適用することができる。
In the above description, a high-frequency signal is transmitted and / or received from a base station. However, an ultrasonic signal is transmitted and / or received using an ultrasonic transducer or an ultrasonic transmitter. A similar effect can be obtained by receiving and / or receiving an ultrasonic signal using an ultrasonic transducer or ultrasonic receiver. In the present application, the ultrasonic transducer or ultrasonic transducer and the light emitting diode, laser diode or photodiode are collectively referred to as a transducer. Even when only the transmitter or receiver of the transmitter / receiver is used, it is described as a transmitter / receiver.
The present invention can also be applied when the base station plays the role of a relay station that receives and retransmits a signal from another base station or a portable terminal.
Further, the present invention can be similarly applied to a case where a signal is transmitted from a base station and received by a mobile terminal.

本発明は、上記のように構成されているため、携帯端末の位置あるいは距離あるいは方向あるいはこれらの組合わせが高精度で検知できる。
Since the present invention is configured as described above, the position, distance, direction, or combination thereof of the mobile terminal can be detected with high accuracy.

従来の実施例および本発明の一実施例を示す概念図である。It is a conceptual diagram which shows the conventional Example and one Example of this invention.

Explanation of symbols

１基地局
２携帯端末
１１ａ、１１ｂ、１１ｃ、１１ｄ指向性アンテナ
４１基地局のアンテナの垂直面からの角度
４２携帯端末が位置する方向
４３基地局のアンテナの高さ
４４携帯端末のアンテナの高さ
４５基地局のアンテナの真下からの距離
４６基地局のアンテナの真下の位置 DESCRIPTION OF SYMBOLS 1 Base station 2 Mobile terminal 11a, 11b, 11c, 11d Directional antenna 41 Angle from the vertical plane of the base station antenna 42 Direction in which the mobile terminal is located 43 Base station antenna height 44 Mobile terminal antenna height 45 Distance from directly below base station antenna 46 Position directly below base station antenna

Claims

In position detection systems using ultrasonic signals, high-frequency signals, or optical signals,
Transmitting a carrier signal, a subcarrier signal, a modulation signal, a digital code, or an ultrasonic signal, a high-frequency signal, or an optical signal composed of a combination thereof, while periodically switching a plurality of antennas or a plurality of transducers; Alternatively, a base station for receiving and receiving an ultrasonic signal, a high-frequency signal, or an optical signal transmitted from the base station and / or transmitting an ultrasonic signal, a high-frequency signal, or an optical signal toward the base station Of mobile devices,
A plurality of antennas or a plurality of transducers of the base station are arranged at intervals of one wavelength or less of the ultrasonic signal, high-frequency signal, or optical signal, and tilted at an arbitrary angle from a direction directly below or directly below the base station Installed,
In the base station and / or the mobile terminal, the phase difference between the ultrasonic signal, the high frequency signal or the optical signal is measured between the base station and the mobile terminal in correspondence with the plurality of antennas or the plurality of transducers. Calculate the direction of
When calculating the positional relationship between the base station and the mobile terminal from the calculation result of the mutual direction, the propagation path length of the ultrasonic signal, the high frequency signal or the optical signal is obtained by a given calculation formula. A position detection device and a position detection program for obtaining a relative positional relationship between the base station and the portable terminal from the line length and the calculation result of the direction

A given formula for obtaining the line length is [(H−h) / Cos {α (Y) + ΔΦ (Y)}] or [(H−h) / Cos {α (X) + ΔΦ (X)}]. And
The relative positional relationship between the base station and the mobile terminal is
Δd (X) = [(H−h) / Cos {α (Y) + ΔΦ (Y)}] × Tan {α (X) + ΔΦ (X)}
Δd (Y) = (H−h) × Tan {α (Y) + ΔΦ (Y)}
Or Δd (X) = (H−h) × Tan {α (X) + ΔΦ (X)}
Δd (Y) = [(H−h) / Cos {α (X) + ΔΦ (X)}] × Tan {α (Y) + ΔΦ (Y)}
The position detection apparatus and the position detection program according to claim 1, wherein

A given calculation formula for obtaining the line length is [(H−h) / √ {1−sin2 (α (X) + ΔΦ (X)) − sin2 (α (Y) + ΔΦ (Y))}],
The relative positional relationship between the base station and the mobile terminal is
Δd (X) = [(H−h) / √ {1−sin2 (α (X) + ΔΦ (X)) − sin2 (α (Y) + ΔΦ (Y))}] × sin (α (X) + ΔΦ ( X))
Δd (Y) = [(H−h) / √ {1−sin2 (α (X) + ΔΦ (X)) − sin2 (α (Y) + ΔΦ (Y))}] × sin (α (Y) + ΔΦ ( Y))
The position detection apparatus and the position detection program according to claim 1, wherein