Aircraft position estimation method and position estimation program

Abstract

To improve the accuracy of aircraft position estimation and to streamline the aircraft position estimation process. [Solution] The present invention relates to a method for estimating the position of an aircraft 1. The position estimation method includes information acquisition steps S11, S21, S31, S41, S51, S61, S71, S81, which involve acquiring first to nth intercepted information obtained by intercepting a group of radio waves, including a second radio wave transmitted from the aircraft 1 based on a first radio wave transmitted from the radar 2, using first to nth receiving devices 11; and position calculation steps S12, S22, S32, S42, S52, S62, S72, S82, which involve calculating the position information of the aircraft 1 based on measurement information obtained based on the first to nth intercepted information and predetermined information determined based on the radar 2 and the first to nth receiving devices 11. n is an integer from 2 to 4.

Description

[Technical Field]

[0001] The present invention relates to an aircraft position estimation method, which estimates the position of an aircraft by intercepting radio waves transmitted from the aircraft based on radio waves emitted from radar. The present invention also relates to an aircraft position estimation program that causes a computer to execute this position estimation method. [Background technology]

[0002] In air traffic control and related fields, a device called ASR (Airport Surveillance Radar) is used. The ASR has two radars, called PSR (Primary Surveillance Radar) and SSR (Secondary Surveillance Radar).

[0003] Each of the PSR and SSR has a rotatable directional antenna, and the ASR uses the rotating directional antennas of the PSR and SSR to detect aircraft located within a 360-degree range around it.

[0004] PSR emits radio waves from its directional antenna and receives and processes the reflected waves (echoes) from aircraft, thereby obtaining information about the aircraft's distance and direction. PSR can detect aircraft even if the target aircraft is not equipped with special devices such as transponders, but the information obtained by PSR is limited.

[0005] Next, the SSR emits radio waves (including interrogation signals) from its directional antenna, and based on these interrogation signals, it receives and processes radio waves (including response signals) sent back by a transponder, a special device mounted on the aircraft, thereby obtaining information about the aircraft's distance, bearing, identification code, and altitude.

[0006] In some cases, local governments and other organizations monitor the position, altitude, and flight paths of aircraft flying to and from airports in order to understand the noise levels generated at and around airports. For example, in this monitoring, a passive SSR is used to estimate the position, altitude, and flight path of aircraft. A passive SSR obtains information on the distance, direction, identification code, and altitude of aircraft without emitting radio waves itself by receiving and processing radio waves emitted from the SSR simultaneously with the radio waves from the transponder. A passive SSR is also called a PSSR (Passive Secondary Surveillance Radar).

[0007] Therefore, receiving equipment capable of intercepting interrogation and response signals is installed around airfields, and in particular, the technology of estimating the position of an aircraft by intercepting interrogation and response signals using multiple receiving devices (aircraft position estimation technology) is widely employed.

[0008] One example of such aircraft position estimation technology involves acquiring multiple pieces of information based on interrogation and response signals intercepted by each receiving device, including the position of the receiving device, the position of the radar, the time difference between the transmission time of the interrogation signal and the reception time of the response signal, the direction of the main lobe of the radio waves transmitted from the SSR, and the aircraft's barometric altitude. Based on this information, an ellipse is created with the positions of each receiving device and the radar as two foci, passing through a trajectory that goes through the aircraft's position. The intersection point of these multiple ellipses, each created based on the positions of multiple receiving devices, is then used to estimate the aircraft's position. Each ellipse used for estimating the aircraft's position is detected as a collection of elliptical arcs extending in accordance with the (directly facing) beamwidth of the radio waves containing the interrogation signal, and the central position of this elliptical arc in the beamwidth direction is used to estimate the aircraft's position. (See, for example, Patent Documents 1-3.) [Prior art documents] [Patent Documents]

[0009] [Patent Document 1] Japanese Patent Publication No. 63-266381 [Patent Document 2] International Publication No. 2005 / 017555 [Patent Document 3] Japanese Patent Publication No. 2021-060429 [Overview of the Initiative] [Problems that the invention aims to solve]

[0010] However, as in the example of aircraft position estimation technology described above, when the central position of an elliptical arc extending in accordance with the beamwidth of radio waves is used to estimate the aircraft's position, the beamwidth of the radio waves widens as the distance from the radar to the aircraft increases, resulting in a decrease in the accuracy of the aircraft's position estimation. Therefore, it is desirable to improve the accuracy of aircraft position estimation while avoiding the effects associated with the increase in the beamwidth of radio waves.

[0011] Furthermore, as exemplified by the aircraft position estimation technology described above, the barometric altitude of an aircraft obtained by intercepting response signals is subject to confidentiality obligations under Article 59 of the Radio Law. Therefore, there is a significant burden on managing information regarding aircraft barometric altitude. There is also a demand to reduce the computational load on computers when estimating aircraft positions. For these reasons, it is desirable to improve the efficiency of aircraft position estimation, taking these problems and demands into consideration.

[0012] In light of these circumstances, there is a need to improve the accuracy of aircraft position estimation and to streamline the aircraft position estimation process in aircraft position estimation methods and programs. [Means for solving the problem]

[0013] In order to solve the above problems, the aircraft position estimation method according to the first aspect includes an information acquisition step of acquiring first and second eavesdropping information respectively obtained by eavesdropping a radio wave group including a second radio wave transmitted from an aircraft based on a first radio wave transmitted from a radar using first and second receiving devices, a position calculation step of calculating the position information of the aircraft based on measurement information obtained based on the first and second eavesdropping information and predetermined information determined based on the radar and the first and second receiving devices. In the position calculation step, the measurement information includes an angle φ in the horizontal direction of the main lobe in the first radio wave with respect to a specific azimuth, s a distance L from the radar to the i-th (i is an integer from 1 to 2) receiving device via the aircraft, i and an altitude h of the aircraft with respect to the radar. The predetermined information includes an angle φ of the i-th receiving device as seen from the radar with respect to the specific azimuth, i a horizontal distance D from the radar to the i-th receiving device, i and a height H of the i-th receiving device with respect to the radar. i The position information of the aircraft is calculated based on a horizontal angle difference Δφ between the direction of the main lobe in the first radio wave and the direction of the aircraft with respect to the radar, a horizontal distance d from the radar to the aircraft, the angle φ, s and the altitude h, where the angle difference Δφ and the horizontal distance d are P i =L i 2 -D i 2 -H i 2 +2H i h Q i =D i cos(φ s -φ i ) R i =D i sin(φ s -φ i ) α = L1P2 - L2P1 β = L1Q2 - L2Q1 γ = L1R2 - L2R1 t = tan(Δφ / 2) cosΔφ=(1-t 2 ) / (1+t 2 ) sinΔφ=2t / (1+t 2 ) a=(Q1α-P1β) 2 -(L1α) 2 -(2L1hβ) 2 b=4{(Q1α-P1β)(R1α-P1γ)-(2L1h) 2 βγ} c=2{(Q1α-P1β) 2 -2(R1α-P1γ) 2 +(L1α) 2 -(2L1h) 2 (β 2 -2γ 2 )} If defined as follows, at 4 +bt 3 -ct 2 -bt+a=0 d = -α / 2(βcosΔφ - γsinΔφ) It is calculated based on the following.

[0014] A method for estimating the position of an aircraft according to a second embodiment includes an information acquisition step of acquiring first, second, and third interception information obtained by intercepting a group of radio waves, including a second radio wave transmitted from an aircraft based on a first radio wave transmitted from a radar, using first, second, and third receiving devices; and a position calculation step of calculating the position information of the aircraft based on measurement information obtained based on the first, second, and third interception information and predetermined information determined based on the radar and the first, second, and third receiving devices, wherein in the position calculation step, the measurement information is the horizontal angle φ of the main lobe in the first radio wave with respect to a specific direction. s The distance L from the radar to the receiving device i (an integer from 1 to 3) via the aircraft. iThe predetermined information includes the angle φ of the i receiving device as seen from the radar, with respect to the specific direction. i The horizontal distance D from the radar to the i-th receiving device is... i And the height H of the i-th receiving device relative to the radar. i The aircraft's position information comprises the horizontal angular difference Δφ between the orientation of the main lobe in the first radio wave and the orientation of the aircraft, relative to the radar; the horizontal distance d from the radar to the aircraft; the altitude h of the aircraft relative to the radar; and the angle φ. s It is calculated based on the following: The angle difference Δφ, the horizontal distance d, and the altitude h are, P i =L i 2 -D i 2 -H i 2 Q i =D i cos(φ s -φ i ) R i =D i sin(φ s -φ i ) α=Q1(L2H3-L3H2)+Q2(L3H1-L1H3)+Q3(L1H2-L2H1) β=R1(L2H3-L3H2)+R2(L3H1-L1H3)+R3(L1H2-L2H1) γ=Q1(L2P3-L3P2)+Q2(L3P1-L1P3)+Q3(L1P2-L2P1) δ=R1(L2P3-L3P2)+R2(L3P1-L1P3)+R3(L1P2-L2P1) ε=H1(L2P3-L3P2)+H2(L3P1-L1P3)+H3(L1P2-L2P1) t = tan(Δφ / 2) cosΔφ=(1-t 2 ) / (1+t 2 ) sinΔφ=2t / (1+t 2 ) a=(P1α-H1γ+Q1ε) 2 -L1 2 (γ 2 +ε 2 ) b=4{(P1α-H1γ+Q1ε)(P1β-H1δ+R1ε)-L1 2 γδ} c = 2{(P1α - H1γ + Q1ε)} 2 -2(P1β-H1δ+R1ε) 2 -L1 2 (γ 2 -2δ 2 -ε 2 )} If defined as follows, at 4 +bt 3 -ct 2 -bt+a=0 d = ε / 2(αcosΔφ - βsinΔφ) h=-(γcosΔφ-δsinΔφ) / 2(αcosΔφ-βsinΔφ) It is calculated based on the following.

[0015] An aircraft position estimation method according to a third embodiment includes an information acquisition step of acquiring first, second and third interception information obtained by intercepting a group of radio waves, including a second radio wave transmitted from an aircraft based on a first radio wave transmitted from a radar, using first, second and third receiving devices, respectively; and a position calculation step of calculating the aircraft position information based on measurement information obtained based on the first, second and third interception information and predetermined information determined based on the radar and the first, second and third receiving devices, wherein in the position calculation step, the measurement information is the horizontal angle φ of the main lobe in the first radio wave with respect to a specific direction. s The distance L from the radar to the receiving device i (where i is an integer from 1 to 3) via the aircraft. i The predetermined information includes the altitude h of the aircraft relative to the radar, and the predetermined information includes the angle φ of the i receiving device as seen from the radar, relative to the specific bearing. i and, The horizontal distance D from the radar to the i-th receiving device i and the height H of the i-th receiving device with respect to the radar i and the position information of the aircraft is based on the horizontal angular difference Δφ between the direction of the main lobe in the first radio wave and the direction of the aircraft with respect to the radar, the horizontal distance d from the radar to the aircraft, the angle φ s and the altitude h, and is calculated when the angular difference Δφ and the horizontal distance d are P i =L i 2 -D i 2 -H i 2 +2H i h Q i =D i cos(φ s -φ i ) R i =D i sin(φ s -φ i ) α = Q1(L2P3 - L3P2) + Q2(L3P1 - L1P3) + Q3(L1P2 - L2P1) β = R1(L2P3 - L3P2) + R2(L3P1 - L1P3) + R3(L1P2 - L2P1) t = tan(Δφ / 2) cosΔφ = (1 - t 2 ) / (1 + t 2 ) sinΔφ = 2t / (1 + t 2 ) When defined as αt 2 + 2βt - α = 0 d = -(L1P2 - L2P1) / 2{(L1Q2 - L2Q1)cosΔφ - (L1R2 - L2R1)sinΔφ or d = -(L2P3 - L3P2) / 2{(L2Q3 - L3Q2)cosΔφ - (L2R3 - L3R2)sinΔφ is calculated based on

[0016] A method for estimating the position of an aircraft according to a fourth embodiment includes an information acquisition step of acquiring first, second, third, and fourth interception information obtained by intercepting a group of radio waves, including a second radio wave transmitted from an aircraft based on a first radio wave transmitted from a radar, using first, second, third, and fourth receiving devices, respectively; and a position calculation step of calculating the position information of the aircraft based on measurement information obtained based on the first, second, third, and fourth interception information and predetermined information determined based on the radar and the first, second, third, and fourth receiving devices, wherein in the position calculation step, the measurement information is the horizontal angle φ of the main lobe in the first radio wave with respect to a specific direction. s The distance L from the radar to the receiving device i (where i is an integer from 1 to 4) via the aircraft. i The predetermined information includes the angle φ of the i receiving device as seen from the radar, with respect to the specific direction. i The horizontal distance D from the radar to the i-th receiving device is... i And the height H of the i-th receiving device relative to the radar. i The aircraft's position information is defined as the horizontal angular difference Δφ between the orientation of the main lobe in the first radio wave and the orientation of the aircraft, with respect to the radar. The horizontal distance d from the radar to the aircraft, the altitude h of the aircraft relative to the radar, and the angle φ s It is calculated based on the following: The angle difference Δφ, the horizontal distance d, and the altitude h are, P i =L i 2 -D i 2 -H i 2 Q i =D i cos(φ s -φ i ) R i =D i sin(φ s -φi ) α = Q1(L2H3 - L3H2) + Q2(L3H1 - L1H3) + Q3(L1H2 - L2H1) β = R1(L2H3 - L3H2) + R2(L3H1 - L1H3) + R3(L1H2 - L2H1) γ = Q1(L2P3 - L3P2) + Q2(L3P1 - L1P3) + Q3(L1P2 - L2P1) δ = R1(L2P3 - L3P2) + R2(L3P1 - L1P3) + R3(L1P2 - L2P1) ε = H1(L2P3 - L3P2) + H2(L3P1 - L1P3) + H3(L1P2 - L2P1) t = tan(Δφ / 2) cosΔφ = (1 - t 2 ) / (1 + t 2 ) sinΔφ = 2t / (1 + t 2 ) a = (L1P4 - L4P1)α - (L1H4 - L4H1)γ + (L1Q4 - L4Q1)ε b = (L1P4 - L4P1)β - (L1H4 - L4H1)δ + (L1R4 - L4R1)ε When defined as at 2 + 2bt - a = 0 d = ε / 2(αcosΔφ - βsinΔφ) h = -(γcosΔφ - δsinΔφ) / 2(αcosΔφ - βsinΔφ) are calculated based on

[0017] A fifth aspect of an aircraft position estimation method includes an information acquisition step of acquiring first and second interception information obtained by intercepting a group of radio waves, including a second radio wave transmitted from an aircraft based on a first radio wave transmitted from a radar, using first and second receiving devices; and a position calculation step of calculating the aircraft position information based on measurement information obtained based on the first and second interception information and predetermined information determined based on the radar and the first and second receiving devices, wherein in the position calculation step, the measurement information is the horizontal angle φ of the main lobe in the first radio wave with respect to a specific direction. s The distance L from the radar to the receiving device i (where i is an integer between 1 and 2) via the aircraft. i The predetermined information includes the altitude k of the aircraft above sea level, and the predetermined information is the angle φ of the i receiving device as seen from the radar, with respect to the specific direction. i The horizontal distance D from the radar to the i-th receiving device is... i And the altitude K of the receiving device i. i And the radar's altitude K S The aircraft's position information comprises the horizontal angular difference Δφ between the orientation of the main lobe in the first radio wave and the orientation of the aircraft, with respect to the radar, the horizontal distance d from the radar to the aircraft, and the angle φ s And, calculated based on the aforementioned altitude k, The angle difference Δφ and the horizontal distance d are, P i =L i 2 -D i 2 -K i 2 +K S 2 +2(K i -K s )k Q i =D i cos(φ s -φ i ) R i =D i sin(φ s-φ i ) α = L1P2 - L2P1 β = L1Q2 - L2Q1 γ = L1R2 - L2R1 t = tan(Δφ / 2) cosΔφ = (1 - t 2 ) / (1 + t 2 ) sinΔφ = 2t / (1 + t 2 ) a = (Q1α - P1β) 2 -(L1α) 2 -{2L1(k - K S )β} 2 b = 4[(Q1α - P1β)(R1α - P1γ) - {2L1(k - K S )} 2 βγ] c = 2[(Q1α - P1β) 2 -2(R1α - P1γ) 2 +(L1α) 2 -{2L1(k - K S )} 2 (β 2 -2γ 2 )] When defined as at 4 +bt 3 -ct 2 -bt + a = 0 d = -α / 2(βcosΔφ - γsinΔφ) is calculated based on

[0018] An aircraft position estimation method according to the sixth embodiment includes an information acquisition step of acquiring first, second and third interception information obtained by intercepting a group of radio waves, including a second radio wave transmitted from an aircraft based on a first radio wave transmitted from a radar, using first, second and third receiving devices, respectively; and a position calculation step of calculating the aircraft position information based on measurement information obtained based on the first, second and third interception information and predetermined information determined based on the radar and the first, second and third receiving devices, wherein in the position calculation step, the measurement information is the horizontal angle φ of the main lobe in the first radio wave with respect to a specific direction s The distance L from the radar to the receiving device i (where i is an integer from 1 to 3) via the aircraft. i The predetermined information includes the angle φ of the i receiving device as seen from the radar, with respect to the specific direction. i The horizontal distance D from the radar to the i-th receiving device is... i And the altitude K of the receiving device i. i And the radar's altitude K S The aircraft's position information comprises the horizontal angular difference Δφ between the orientation of the main lobe in the first radio wave and the orientation of the aircraft, relative to the radar, the horizontal distance d from the radar to the aircraft, the altitude k of the aircraft above sea level, and the angle φ. s It is calculated based on the following: The angle difference Δφ, the horizontal distance d, and the altitude k above sea level are, P i =L i 2 -D i 2 -K i 2 +K S 2 Q i =D i cos(φ s -φ i ) R i =D i sin(φ s -φ i ) H i =K i -K S α = Q1(L2H3 - L3H2) + Q2(L3H1 - L1H3) + Q3(L1H2 - L2H1) β = R1(L2H3 - L3H2) + R2(L3H1 - L1H3) + R3(L1H2 - L2H1) γ = Q1(L2P3 - L3P2) + Q2(L3P1 - L1P3) + Q3(L1P2 - L2P1) δ = R1(L2P3 - L3P2) + R2(L3P1 - L1P3) + R3(L1P2 - L2P1) ε = H1(L2P3 - L3P2) + H2(L3P1 - L1P3) + H3(L1P2 - L2P1) ζ = P1α - H1γ + Q1ε η = P1β - H1δ + R1ε ξ = γ + 2K S α υ = δ + 2K S β t = tan(Δφ / 2) cosΔφ = (1 - t 2 ) / (1 + t 2 ) sinΔφ = 2t / (1 + t 2 ) a = ζ 2 -L1 2 (ε 2 +ξ 2 ) b = 4(ζη - L1 2 ξυ) c = 2{ζ 2 -2η 2 +L1 2 (ε 2 -ξ 2 +2υ 2 )} When defined as at 4 +bt 3 -ct 2 -bt + a = 0 d = ε / 2(αcosΔφ - βsinΔφ) k = -(γcosΔφ - δsinΔφ) / 2(αcosΔφ - βsinΔφ) It is calculated based on

[0019] An aircraft position estimation method according to the seventh embodiment includes an information acquisition step of acquiring first, second and third interception information obtained by intercepting a group of radio waves, including a second radio wave transmitted from an aircraft based on a first radio wave transmitted from a radar, using first, second and third receiving devices, respectively; and a position calculation step of calculating the aircraft position information based on measurement information obtained based on the first, second and third interception information and predetermined information determined based on the radar and the first, second and third receiving devices, wherein in the position calculation step, the measurement information is the horizontal angle φ of the main lobe in the first radio wave with respect to a specific direction. s The distance L from the radar to the receiving device i (where i is an integer from 1 to 3) via the aircraft. i The predetermined information includes the altitude k of the aircraft above sea level, and the predetermined information is the angle φ of the i receiving device as seen from the radar, with respect to the specific direction. i The horizontal distance D from the radar to the i-th receiving device is... i And the altitude K of the receiving device i. i , the altitude of the radar above sea level K S The aircraft's position information comprises the horizontal angular difference Δφ between the orientation of the main lobe in the first radio wave and the orientation of the aircraft, with respect to the radar, the horizontal distance d from the radar to the aircraft, and the angle φ s And, calculated based on the aforementioned altitude k, The angle difference Δφ and the horizontal distance d are, P i =L i 2 -D i 2 -K i 2 +K S 2 +2(K i -K s )k Q i =D i cos(φ s -φ i ) R i =D i sin(φ s -φ i ) α=Q1(L2P3-L3P2)+Q2(L3P1-L1P3)+Q3(L1P2-L2P1) β=R1(L2P3-L3P2)+R2(L3P1-L1P3)+R3(L1P2-L2P1) t = tan(Δφ / 2) cosΔφ=(1-t 2 ) / (1+t 2 ) sinΔφ=2t / (1+t 2 ) If defined as follows, αt 2 +2βt-α=0 d=-(L1P2-L2P1) / 2{(L1Q2-L2Q1)cosΔφ-(L1R2-L2R1)sinΔφ or d=-(L2P3-L3P2) / 2{(L2Q3-L3Q2)cosΔφ-(L2R3-L3R2)sinΔφ It is calculated based on the following.

[0020] An aircraft position estimation method according to the eighth aspect includes an information acquisition step of acquiring first, second, third, and fourth interception information obtained by intercepting a group of radio waves, including a second radio wave transmitted from an aircraft based on a first radio wave transmitted from a radar, using first, second, third, and fourth receiving devices, respectively; and a position calculation step of calculating the aircraft position information based on measurement information obtained based on the first, second, third, and fourth interception information and predetermined information determined based on the radar and the first, second, third, and fourth receiving devices, wherein in the position calculation step, the measurement information is the horizontal angle φ of the main lobe in the first radio wave with respect to a specific direction. s The distance L from the radar to the receiving device i (where i is an integer from 1 to 4) via the aircraft. i The predetermined information includes the angle φ of the i receiving device as seen from the radar, with respect to the specific direction.i The horizontal distance D from the radar to the i-th receiving device is... i And the altitude K of the receiving device i. i And the radar's altitude K S The aircraft's position information comprises the horizontal angular difference Δφ between the orientation of the main lobe in the first radio wave and the orientation of the aircraft, relative to the radar, the horizontal distance d from the radar to the aircraft, the altitude k of the aircraft above sea level, and the angle φ. s It is calculated based on the following: The angle difference Δφ, the horizontal distance d, and the altitude k above sea level are, P i =L i 2 -D i 2 -K i 2 +K S 2 Q i =D i cos(φ s -φ i ) R i =D i sin(φ s -φ i ) H i =K i -K S α=Q1(L2H3-L3H2)+Q2(L3H1-L1H3)+Q3(L1H2-L2H1) β=R1(L2H3-L3H2)+R2(L3H1-L1H3)+R3(L1H2-L2H1) γ=Q1(L2P3-L3P2)+Q2(L3P1-L1P3)+Q3(L1P2-L2P1) δ=R1(L2P3-L3P2)+R2(L3P1-L1P3)+R3(L1P2-L2P1) ε=H1(L2P3-L3P2)+H2(L3P1-L1P3)+H3(L1P2-L2P1) t = tan(Δφ / 2) cosΔφ=(1-t 2 ) / (1+t 2 ) sinΔφ=2t / (1+t 2 ) a=(L1P4-L4P1)α-(L1H4-L4H1)γ+(L1Q4-L4Q1)ε b=(L1P4-L4P1)β-(L1H4-L4H1)δ+(L1R4-L4R1)ε If defined as follows, at 2 +2bt-a=0 d = ε / 2(αcosΔφ - βsinΔφ) k=-(γcosΔφ-δsinΔφ) / 2(αcosΔφ-βsinΔφ) It is calculated based on the following.

[0021] The aircraft position estimation methods according to the first to eighth embodiments involve having a computer execute the first to eighth aircraft position estimation methods, respectively. [Effects of the Invention]

[0022] In the aircraft position estimation method and position estimation program according to each of the first to eighth embodiments, the accuracy of aircraft position estimation can be improved, and the aircraft position estimation can be made more efficient. [Brief explanation of the drawing]

[0023] [Figure 1] Figure 1 is a conceptual diagram of the aircraft position estimation method according to the first embodiment. [Figure 2] Figure 2 is a flowchart illustrating the aircraft position estimation method according to the first embodiment. [Figure 3] Figure 3 is a block diagram of the aircraft position estimation system, aircraft, and radar according to the first embodiment. [Figure 4] Figure 4 is a block diagram of the computer in the aircraft position estimation system according to the first embodiment. [Figure 5] Figure 5 is a flowchart illustrating the aircraft position estimation method according to the second embodiment. [Figure 6]Figure 6 is a flowchart illustrating the aircraft position estimation method according to the third embodiment. [Figure 7] Figure 7 is a flowchart illustrating the aircraft position estimation method according to the fourth embodiment. [Figure 8] Figure 8 is a conceptual diagram of the aircraft position estimation method according to the fifth embodiment. [Figure 9] Figure 9 is a flowchart illustrating the aircraft position estimation method according to the fifth embodiment. [Figure 10] Figure 10 is a flowchart illustrating the aircraft position estimation method according to the sixth embodiment. [Figure 11] Figure 11 is a flowchart illustrating the aircraft position estimation method according to the seventh embodiment. [Figure 12] Figure 12 is a flowchart illustrating the aircraft position estimation method according to the eighth embodiment. [Figure 13A] Figure 13A is a plan view of Example 1. [Figure 13B] Figure 13B is a time-based altitude change diagram for Example 1. [Figure 14A] Figure 14A is a plan view of Example 2. [Figure 14B] Figure 14B is a time-based altitude change diagram for Example 2. [Figure 15A] Figure 15A is a plan view of Example 3. [Figure 15B] Figure 15B is a time-based altitude change diagram for Example 3. [Figure 16A] Figure 16A is a plan view of Example 4. [Figure 16B] Figure 16B is a diagram showing the change in altitude over time in Example 4. [Figure 17A] Figure 17A is a plan view of Example 5. [Figure 17B] Figure 17B is a diagram showing the change in altitude over time in Example 5. [Figure 18A] Figure 18A is a plan view of Comparative Example 1. [Figure 18B] Figure 18B is a time-based altitude change diagram for Comparative Example 1. [Modes for carrying out the invention]

[0024] The aircraft position estimation method, position estimation program, and position estimation system according to the first to eighth embodiments will be described below.

[0025] "First Embodiment" Referring to Figures 1 to 4, the position estimation method, position estimation program, and position estimation system according to the first embodiment of the aircraft 1 will be described.

[0026] "Position estimation method" The method for estimating the position of the aircraft 1 according to this embodiment will be described with reference to Figures 1 and 2. As shown in Figure 1, in the position estimation method, the aircraft 1 is the target of position estimation, and the radar 2, n receiving devices 11, and position estimation device 12 are used to estimate the position of the aircraft 1. In this embodiment, n is 2. However, n can be an integer from 2 to 4.

[0027] The n receivers 11 are preferably arranged to straddle the flight path of the aircraft 1, particularly the runway. The n receivers 11 are also preferably arranged to be spaced apart from each other or distributed along the longitudinal direction of the flight path of the aircraft 1, particularly the runway. Figure 1 shows the relationship between the aircraft 1, radar 2, and i receivers 11 using altitude relative to radar 2, where i is an integer from 1 to n.

[0028] The parameters based on the relationship between the aircraft 1, radar 2, and n receiving devices 11 considered in the position estimation method are as follows: - The horizontal angle φ of the principal lobe in the first radio wave relative to a specific direction. s - The angle φ of the i-th receiver 11 as seen from radar 2, relative to a specific direction. i - The horizontal angular difference Δφ between the orientation of the main lobe in the first radio wave and the orientation of aircraft 1, with reference to radar 2. - Distance L from radar 2 via aircraft 1 to the i-th receiving device 11 i - Horizontal distance D from radar 2 to the i-th receiver 11 i - Height H of the i-th receiver 11 relative to radar 2 i - Distance e from aircraft 1 to the i-th receiver 11 i - Distance x from radar 2 to aircraft 1 - Altitude h of aircraft 1 relative to radar 2 - Horizontal distance d from radar 2 to aircraft 1

[0029] In Figure 1, a specific direction is indicated by arrow F, and the direction of the main lobe in the first radio wave is indicated by arrow B. The parameters for radar 2 are determined based on its antenna 2a. The parameters for the i-th receiving device 11 are determined based on its antenna 11a.

[0030] Next, as shown in Figure 2, the position estimation method according to this embodiment includes an information acquisition step S11 and a position calculation step S12. In the information acquisition step S11, intercepted information is obtained by intercepting a group of radio waves, including a second radio wave transmitted from the aircraft 1 based on a first radio wave transmitted from the radar 2, using the first to nth receiving devices 11. In the position calculation step S12, the position information of the aircraft 1 is calculated based on measurement information obtained based on the first to nth intercepted information and predetermined information determined based on the radar 2 and the first to nth receiving devices 11.

[0031] Measurement information: angle φ s , distance L i and altitude h. Default information is angle φ i , horizontal distance D i and height H i The position information of aircraft 1 includes the angle difference Δφ, horizontal distance d, and angle φ.s It can be calculated based on the altitude h. The angular difference Δφ and horizontal distance d are unknown information and variables, and the distance e i And the distance x is a parameter.

[0032] In estimating the position of aircraft 1, the angular difference Δφ and horizontal distance d can be calculated as follows. First, the following relation 1 is derived from the Pythagorean theorem. x 2 =h 2 +d 2 (L i -x) 2 =e i 2 +( hH i ) 2

[0033] Furthermore, the following relation 2 can be derived from the Law of Cosines. e i 2 =D i 2 +d 2 -2D i dcos(φ S -φ i +Δφ) =(L i -x) 2 -(hH i ) 2 D i 2 +x 2 -h 2 -2D i dcos(φ S -φ i +Δφ) =L i 2 -2L i x+x 2 -h 2 +2H i hH i 2 D i 2 -2D i dcos(φ S -φ i +Δφ) =L i 2 -2L i x+2H i hH i 2

[0034] Therefore, the distance x is defined as shown in the following relation 3. x={ L i 2 -D i 2 -H i 2 +2H i h+2D i dcos(φ S -φ i (+Δφ)} / 2L i =[L i 2 -D i 2 -H i 2 +2H i h+2D i dcos{cos(φ S -φ i )cosΔφ-sin(φ S -φ i )sinΔφ)}] / 2L i

[0035] As shown in the following relation 4, the constant P i , constant Q i and the constant R i Define. P i =L i 2 -D i 2 -H i 2 +2H i h Q i =D i cos(φ s -φ i ) R i =D i sin(φ s -φ i )

[0036] When i is 1, applying relation 4 to relation 3 yields the following relation 5. x={P1+2(Q1cosΔφ-R1sinΔφ)d} / 2L1

[0037] When i is 2, applying relation 4 to relation 3 yields the following relation 6. x={P2+2(Q2cosΔφ-R2sinΔφ)d} / 2L2

[0038] According to relations 5 and 6, the horizontal distance d is defined as shown in relation 7 below. d=-(L1P2-L2P1) / 2{(L1Q2-L2Q1)cosΔφ-(L1R2-L2R1)sinΔφ}

[0039] The constants α, β, and γ are defined as shown in relation 8 below. α = L1P2 - L2P1 β = L1Q2 - L2Q1 γ = L1R2 - L2R1

[0040] Applying relation 8 to relation 5, the distance x is defined as shown in relation 9. x=[P1-α{(Q1cosΔφ-R1sinΔφ) / (βcosΔφ-γsinΔφ)}] / 2L1

[0041] Applying relation 8 to relation 7, the horizontal distance d is derived as shown in relation 10. d = -α / 2(βcosΔφ - γsinΔφ)

[0042] Applying relations 9 and 10 to the Pythagorean theorem yields the following relation 11. x 2 =h 2 +d 2 ([P1-α{(Q1cosΔφ-R1sinΔφ) / (βcosΔφ-γsinΔφ)}] / 2L1) 2 =h 2 +{-α / 2(βcosΔφ-γsinΔφ)}2 {P1(βcosΔφ-γsinΔφ)-α(Q1cosΔφ-R1sinΔφ)} 2 ={2L1h(βcosΔφ-γsinΔφ)} 2 +(-L1α) 2

[0043] By substituting the angle Δφ with the variable t using Weierstrass substitution, the following relation 12 is derived. t = tan(Δφ / 2) cosΔφ=(1-t 2 ) / (1+t 2 ) sinΔφ=2t / (1+t 2 )

[0044] Applying relation 12 to relation 11 yields relation 13. {P1β(1-t 2 )-2P1γt-Q1α(1-t 2 )+2R1αt} 2 ={2L1hβ(1-t 2 )-2L1hγt} 2 +{-L1α(1+t 2 )} 2 {(Q1α-P1β)}t 2 +2(R1α-P1γ)t-(Q1α-P1β) 2 )} 2 =(2L1h) 2 (βt 2 +2γt-β) 2 +(L1αt 2 +L1α) 2 {(Q1α-P1β) 2 -(L1α) 2 -(2L1hβ) 2}t 4 +4{(Q1α-P1β)(R1α-P1γ)-(2L1h) 2 βγ}t 3 -2{(Q1α-P1β) 2-2(R1α-P1γ) 2 +(L1α) 2 -(2L1h) 2 (β 2 -2γ 2 )}t 2 -4{(Q1α-P1β)(R1α-P1γ)-(2L1h) 2 βγ}t +{(Q1α-P1β) 2 -(L1α) 2 -(2L1hβ) 2} =0

[0045] The constants a, b, and c are defined as shown in the following relational equation 14. a=(Q1α-P1β) 2 -(L1α) 2 -(2L1hβ) 2 b=4{(Q1α-P1β)(R1α-P1γ)-(2L1h) 2 βγ} c=2{(Q1α-P1β) 2 -2(R1α-P1γ) 2 +(L1α) 2 -(2L1h) 2 (β 2 -2γ 2 )}

[0046] Applying relation 14 to relation 13 yields relation 15. at 4 +bt 3 -ct 2 -bt+a=0

[0047] The angular difference Δφ can be calculated using relational equations 12 and 15. As mentioned above, the horizontal distance d can be calculated using relational equation 10.

[0048] Furthermore, the method for estimating the position of the aircraft 1 according to this embodiment can be described in detail as follows: The radar 2 is an SSR (Secondary Surveillance Radar). The radar 2 has a horizontally rotatable antenna 2a. The radar 2, in particular, the first radio wave transmitted from its antenna 2a, includes an interrogation signal. The first radio wave can be approximately 1030 MHz.

[0049] A second radio wave transmitted from aircraft 1 based on a first radio wave includes a response signal corresponding to the interrogation signal of the first radio wave. Aircraft 1 has a transponder 1a. The transponder 1a of aircraft 1 transmits a second radio wave that includes a response signal corresponding to the interrogation signal of the first radio wave. The second radio wave can be approximately 1090 MHz.

[0050] The response signal includes information about the altitude (barometric altitude) h of aircraft 1, i.e., altitude information. The response signal may also include identification information of aircraft 1, etc. The i-th receiving device 11 or position estimating device 12 can create a profile including information such as the interrogation period and interrogation pattern of radar 2 by receiving the interrogation signal in the first radio wave, and further, the position estimating device 12 can acquire such a profile. However, the profile is not limited to this. The profile may be one that has been created in advance based on previously acquired information such as the radar's interrogation period and interrogation pattern.

[0051] The horizontal angle φ of the principal lobe in the first radio wave relative to a specific direction. s This can be calculated based on the profile of radar 2. The distance L from radar 2 to the i-th receiver 11 via aircraft 1. i This can be calculated based on the profile of radar 2 and the reception time of the second radio wave, in particular the response signal by the i-th receiver 11. The group of radio waves received by the i-th receiver 11 may include the first group of radio waves in addition to the second group of radio waves.

[0052] However, radar is not limited to SSR. For example, radar can be PSR (Primary Surveillance Radar). In this case, the first radio wave is a direct wave from the PSR, and the second radio wave is a reflected wave of the first radio wave reflected by aircraft 1.

[0053] "Location Estimation Program" Referring to Figure 2, the position estimation program for the aircraft 1 according to this embodiment will be described. The position estimation program according to this embodiment causes a computer to execute multiple steps, each corresponding to one of the multiple steps of the position estimation method according to this embodiment.

[0054] The multiple steps include an information acquisition procedure corresponding to the information acquisition step S11 and a position estimation procedure corresponding to the position calculation step S12. The position estimation program can be stored in a computer-readable storage medium.

[0055] "Location estimation system" The position estimation system of the aircraft 1 according to this embodiment will be described with reference to Figures 3 and 4. As shown in Figure 3, the position estimation system has n receiving devices 11, i.e., the first to the nth receiving devices 11, and a position estimation device 12. In this embodiment, n is 2. That is, the position estimation system has two receiving devices 11, i.e., the first and second receiving devices 11.

[0056] The i-th receiving device 11 has an antenna 11a capable of receiving radio wave clusters. The i-th receiving device 11 has a communication unit 11b capable of communicating with the position estimation device 12. The position estimation device 12 is wirelessly or wiredly connected to the communication units 11b of n receiving devices 11. The i-th interception information obtained based on the radio wave cluster intercepted by the antenna 11a of the i-th receiving device 11 is sent from the communication unit 11b of the i-th receiving device 11 to the position estimation device 12. The position estimation device 12 estimates the position of the aircraft 1 using measurement information based on the i-th interception information and predetermined information acquired in advance.

[0057] The position estimation device 12 has a computer 13 capable of executing the position estimation program according to this embodiment. The computer 13 has a storage medium that the computer 13 can read and which stores the position estimation program according to this embodiment. Although not specifically shown, the computer 13 includes an information acquisition unit capable of executing an information acquisition procedure and a position estimation unit capable of executing a position estimation procedure. However, the position estimation device may also have a storage medium separate from the computer.

[0058] As shown in Figure 4, the computer 13 has a processing unit 13a capable of performing calculations to execute multiple steps of the position estimation program. The processing unit 13a can be a CPU (Central Processing Unit) 13a.

[0059] Computer 13 has an SSD (Solid State Drive) 13b configured as the storage medium described above. However, the storage medium can be something other than an SSD. For example, the storage medium can be an HDD (Hard Disk Drive), a semiconductor memory such as flash memory other than an SSD, etc. Also, if the position estimation device has a storage medium separate from the computer, the storage medium can be an external storage medium such as a semiconductor memory such as a USB flash memory drive, or an optical disc such as a DVD-ROM or Blu-ray (registered trademark). In this case, the computer has a device that can read the external storage medium.

[0060] Furthermore, the computer 13 includes RAM 13c, ROM 13d, input / output interface 13e, and communication interface 13f. The CPU 13a, SSD 13b, RAM 13c, ROM 13d, input / output interface 13e, and communication interface 13f are connected directly or indirectly. The input / output interface 13e can be connected to input devices, output devices, etc. The communication interface 13f can communicate wirelessly or wired with the communication unit 11b of the i-th receiving device 11.

[0061] Such a computer 13 can be on-premises. However, computers are not limited to on-premises configurations. For example, computers can also be cloud-based, etc.

[0062] As described above, according to the position estimation method of this embodiment, the horizontal angular difference Δφ between the orientation of the main lobe in the first radio wave and the orientation of the aircraft 1 can be calculated using the above measurement information and predetermined information, and the position of the aircraft 1 can be estimated by taking this angular difference Δφ into consideration. Therefore, even if the distance x from the radar 2 to the aircraft 1 increases, the accuracy of estimating the position of the aircraft 1 can be prevented from decreasing without being affected by the increase in the beam width of the direct-facing beam as in the conventional method, and the accuracy of estimating the position of the aircraft 1 can be improved. In turn, the estimation of the position of the aircraft 1 can be made more efficient.

[0063] The position estimation program and position estimation system according to this embodiment can also obtain the same effects and benefits as the position estimation method according to this embodiment.

[0064] "Second Embodiment" Referring to Figures 1 and 3-5, the position estimation method, position estimation program, and position estimation system according to the second embodiment of the aircraft 1 will be described.

[0065] "Position estimation method" Referring to Figures 1 and 5, the method for estimating the position of the aircraft 1 according to this embodiment will be described. The relationship between the aircraft 1, the radar 2, and the n receiving devices 11, and the parameters based on that relationship, according to this embodiment are the same as in the first embodiment, except that n is 3.

[0066] As shown in Figure 5, the position estimation method according to this embodiment includes an information acquisition step S21 and a position calculation step S22. The information acquisition step S21 is the same as the information acquisition step S11 of the first embodiment, except that n is 3. The position calculation step S22 is the same as the position calculation step S12 of the first embodiment, except that n is 3 and that the measurement information, default information, variables and parameter variables are defined as follows.

[0067] Measurement information: angle φ s and distance L i Includes. Default information is angle φ i , horizontal distance D i and height H i The position information of aircraft 1 includes the angle difference Δφ, horizontal distance d, and angle φ. s It can be calculated based on the angle difference Δφ, horizontal distance d, and altitude h, and distance e i And the distance x is a parameter.

[0068] In estimating the position of aircraft 1, the angular difference Δφ, horizontal distance d, and altitude h are calculated as follows. First, the distance x is defined as shown in relational equation 3 above. x=[L i 2 -D i 2 -H i 2 +2H i h+2D i d{cos(φ S -φ i )cosΔφ-sin(φ S -φ i )sinΔφ)}] / 2L i

[0069] As shown in the following relation 21, the constant P i , constant Q i and the constant R i Define. P i =L i 2 -D i 2 -H i2 Q i =D i cos(φ s -φ i ) R i =D i sin(φ s -φ i )

[0070] When i is 1, applying relation 21 to relation 3 yields the following relation 22. x={P1+2H1h+2(Q1cosΔφ-R1sinΔφ)d} / 2L1

[0071] When i is 2, applying relation 21 to relation 3 yields the following relation 23. x={P2+2H2h+2(Q2cosΔφ-R2sinΔφ)d} / 2L2

[0072] When i is 3, applying relation 21 to relation 3 yields the following relation 24. x={P3+2H3h+2(Q3cosΔφ-R3sinΔφ)d} / 2L3

[0073] Based on relations 22 and 23, the following relation 25 is derived. (L1P2-L2P1)+2(L1H2-L2H1)h+2{(L1Q2-L2Q1)cosΔφ-(L1R2-L2R1)sinΔφ}d=0

[0074] Based on relations 23 and 24, the following relation 26 is derived. (L2P3-L3P2)+2(L2H3-L3H2)h+2{(L2Q3-L3Q2)cosΔφ-(L2R3-L3R2)sinΔφ}d=0

[0075] Eliminating altitude h from relations 25 and 26 yields the following relation 27. 2[{(L1H2-L2H1)(L2Q3-L3Q2)-(L2H3-L3H2)(L1Q2-L2Q1)}cosΔφ-{(L1H2-L2H1)(L2R3-L3R2)-(L2H3-L3H2)(L1R2-L2R1)}sinΔφ]d =(L2H3-L3H2)(L1P2-L2P1)-(L1H2-L2H1)(L2P3-L3P2)

[0076] Eliminating the horizontal distance d from relations 25 and 26 yields the following relation 28. 2[{(L1H2-L2H1)(L2Q3-L3Q2)-(L2H3-L3H2)(L1Q2-L2Q1)}cosΔφ-{(L1H2-L2H1)(L2R3-L3R2)-(L2H3-L3H2)(L1R2-L2R1)}sinΔφ]h =-[{(L1P2-L2P1)(L2Q3-L3Q2)-(L2P3-L3P2)(L1Q2-L2Q1)}cosΔφ-{(L1P2-L2P1)(L2R3-L3R2)-(L2P3-L3P2)(L1R2-L2R1)}sinΔφ]

[0077] The constants α, β, γ, δ, and ε are defined as shown in the following relation 29. α=Q1(L2H3-L3H2)+Q2(L3H1-L1H3)+Q3(L1H2-L2H1) β=R1(L2H3-L3H2)+R2(L3H1-L1H3)+R3(L1H2-L2H1) γ=Q1(L2P3-L3P2)+Q2(L3P1-L1P3)+Q3(L1P2-L2P1) δ=R1(L2P3-L3P2)+R2(L3P1-L1P3)+R3(L1P2-L2P1) ε=H1(L2P3-L3P2)+H2(L3P1-L1P3)+H3(L1P2-L2P1)

[0078] Applying relation 29 to relation 27, the horizontal distance d is calculated as shown in relation 30. d = ε / 2(αcosΔφ - βsinΔφ)

[0079] Applying relation 29 to relation 28, the altitude h is calculated as shown in relation 31. h=-(γcosΔφ-δsinΔφ) / 2(αcosΔφ-βsinΔφ)

[0080] Applying relations 30 and 31 to relation 22, we derive the following relation 32. x=[P1-H1{(γcosΔφ-δsinΔφ) / (αcosΔφ-βsinΔφ)}+ε{(Q1cosΔφ-R1sinΔφ) / (αcosΔφ-βsinΔφ)}] / 2L1

[0081] Applying relations 30-32 to the Pythagorean theorem yields the following relation 33. x 2 =h 2 +d 2 ([P1-H1{(γcosΔφ-δsinΔφ) / (αcosΔφ-βsinΔφ)}+ε{(Q1cosΔφ-R1sinΔφ) / (αcosΔφ-βsinΔφ)}] / 2L1) 2 ={-(γcosΔφ-δsinΔφ) / 2(αcosΔφ-βsinΔφ)} 2 +{ε / 2(αcosΔφ-βsinΔφ)} 2 {P1(αcosΔφ-βsinΔφ)-H1(γcosΔφ-δsinΔφ)+ε(Q1cosΔφ-R1sinΔφ)} 2 ={L1(γcosΔφ-δsinΔφ)} 2 +(L1ε) 2

[0082] By substituting the angle Δφ with the variable t using Weierstrass substitution, we obtain the following relation 34. t = tan(Δφ / 2) cosΔφ=(1-t 2 ) / (1+t 2 ) sinΔφ=2t / (1+t 2 )

[0083] Range of 29 to 28 to 28 and 35 to 35 respectively. {P1α(1-t 2 )-2P1βt-H1γ(1-t). 2 )+2H1δt+Q1ε(1-t 2 )-2R1et} 2 ={L1γ(1-t 2 )-2L1δt} 2 +{L1ε(1+t 2 )} 2 {-(P1α-H1γ+Q1ε)t 2 -2(P1β-H1δ+R1ε)t+(P1α-H1γ+Q1ε)} 2 ={-L1γt 2 -2L1δt+L1γ} 2 +(L1yet 2 +L1ε) 2 {(P1α-H1γ+Q1ε) 2 -L1 2 (γ 2 +ε 2 )}t 4 +4{(P1α-H1γ+Q1ε)(P1β-H1δ+R1ε)-L1 2 γδ}t 3 -2{(P1α-H1γ+Q1ε) 2 -2(P1β-H1δ+R1ε) 2 -L1 2 (γ 2 -2δ 2 -ε 2 )}t 2 +{(P1α-H1γ+Q1ε) 2 -L1 2 (γ 2 +ε 2 )} =0

[0084] In the 36th range of the range, the range b is 3 minutes c. a=(P1α-H1γ+Q1ε) 2 -L1 2 (γ 2 +ε 2) b=4{(P1α-H1γ+Q1ε)(P1β-H1δ+R1ε)-L1 2 γδ} c = 2{(P1α - H1γ + Q1ε)} 2 -2(P1β-H1δ+R1ε) 2 -L1 2 (γ 2 -2δ 2 -ε 2 )}

[0085] Applying relation 36 to relation 35 yields relation 37. at 4 +bt 3 -ct 2 -bt+a=0

[0086] The angular difference Δφ can be calculated using relational equations 34 and 37. As mentioned above, the horizontal distance d can be calculated using relational equation 30. The altitude h can be calculated using relational equation 31.

[0087] "Location estimation program and location estimation system" Referring to Figures 3 to 5, the position estimation program and position estimation system of the aircraft 1 according to this embodiment will be described. Referring to Figure 5, the position estimation program according to this embodiment causes the computer to execute multiple procedures corresponding to multiple steps of the position estimation method according to this embodiment.

[0088] The multiple steps include an information acquisition procedure corresponding to the information acquisition step S21 and a position estimation procedure corresponding to the position calculation step S22. The position estimation program can be stored in a computer-readable storage medium.

[0089] Referring to Figures 3 and 4, the position estimation system according to this embodiment is the same as the first embodiment, except that n is 3 and that it enables the execution of the information acquisition procedure and position estimation procedure of the position estimation program according to this embodiment.

[0090] As described above, according to the position estimation method of this embodiment, the horizontal angular difference Δφ between the orientation of the main lobe in the first radio wave and the orientation of the aircraft 1 can be calculated using the above measurement information and predetermined information, and the position of the aircraft 1 can be estimated by taking this angular difference Δφ into consideration. Therefore, even if the distance x from the radar 2 to the aircraft 1 increases, it is possible to prevent a decrease in the accuracy of estimating the position of the aircraft 1 without being affected by the increase in the beam width of the direct-facing beam as in the conventional method, and the accuracy of estimating the position of the aircraft 1 can be improved.

[0091] Furthermore, the altitude h of aircraft 1 can be calculated using the above measurement information and default information. Since the altitude h calculated in this way is not subject to the confidentiality obligations stipulated in Article 59 of the Radio Law, the burden of information management regarding altitude h can be reduced. Therefore, the estimation of the position of aircraft 1 can be made more efficient.

[0092] The position estimation program and position estimation system according to this embodiment can also obtain the same effects and benefits as the position estimation method according to this embodiment.

[0093] "Third Embodiment" Referring to Figures 1, 3, 4, and 6, a position estimation method, position estimation program, and position estimation system according to the third embodiment of the aircraft 1 will be described.

[0094] "Position estimation method" The method for estimating the position of the aircraft 1 according to this embodiment will be described with reference to Figures 1 and 6. The relationship between the aircraft 1, the radar 2, and the n receiving devices 11, as well as the parameters based on that relationship, according to this embodiment are the same as in the second embodiment. That is, in this embodiment, n is 3.

[0095] As shown in Figure 6, the position estimation method according to this embodiment includes an information acquisition step S31 and a position calculation step S32. The information acquisition step S31 is the same as the information acquisition step S21 of the second embodiment. The position calculation step S32 is the same as the position calculation step S22 of the second embodiment, except that the measurement information, default information, variables and parameter variables are defined as follows.

[0096] Measurement information: angle φ s , distance L i and altitude h. Default information is angle φ i , horizontal distance D i and height H i The position information of aircraft 1 includes the angle difference Δφ, horizontal distance d, and angle φ. s It can be calculated based on the altitude h. The angular difference Δφ and horizontal distance d are unknown information and variables, and the distance e i And the distance x is a parameter.

[0097] When estimating the position of aircraft 1, the angular difference Δφ and the horizontal distance d can be calculated as follows. First, the distance x can be defined as shown in relational equation 3 above. x=[L i 2 -D i 2 -H i 2 +2H i h+2D i d{cos(φ S -φ i )cosΔφ-sin(φ S -φ i )sinΔφ)}] / 2L i

[0098] As shown in the following relation 41, the constant P i , constant Q i and the constant R i Define. P i =L i 2 -D i 2 -H i 2 +2H ih Q i =D i cos(φ s -φ i ) R i =D i sin(φ s -φ i )

[0099] When i is 1, applying relation 41 to relation 3 yields the following relation 42. x={P1+2(Q1cosΔφ-R1sinΔφ)d} / 2L1

[0100] When i is 2, applying relation 41 to relation 3 yields the following relation 43. x={P2+2(Q2cosΔφ-R2sinΔφ)d} / 2L2

[0101] When i is 3, applying relation 41 to relation 3 yields the following relation 44. x={P3+2(Q3cosΔφ-R3sinΔφ)d} / 2L3

[0102] Based on relations 42 and 43, the horizontal distance d is derived as shown in relation 45. d=-(L1P2-L2P1) / 2{(L1Q2-L2Q1)cosΔφ-(L1R2-L2R1)sinΔφ}

[0103] Based on relations 43 and 44, the horizontal distance d is derived as shown in relation 46. d=-(L2P3-L3P2) / 2{(L2Q3-L3Q2)cosΔφ-(L2R3-L3R2)sinΔφ}

[0104] Based on relations 45 and 46, the following relation 47 is derived. (L1P2-L2P1){(L2Q3-L3Q2)cosΔφ-(L2R3-L3R2)sinΔφ} =(L2P3-L3P2){(L1Q2-L2Q1)cosΔφ-(L1R2-L2R1)sinΔφ}

[0105] The constants α and β are defined as shown in the following relation 48. α=Q1(L2P3-L3P2)+Q2(L3P1-L1P3)+Q3(L1P2-L2P1) β=R1(L2P3-L3P2)+R2(L3P1-L1P3)+R3(L1P2-L2P1)

[0106] Applying relation 48 to relation 47 yields relation 49. αcosΔφ-βsinΔφ=0

[0107] By substituting the angle Δφ with the variable t using Weierstrass substitution, we obtain the following relation 50. t = tan(Δφ / 2) cosΔφ=(1-t 2 ) / (1+t 2 ) sinΔφ=2t / (1+t 2 )

[0108] Applying relation 50 to relation 49 yields relation 51. α(1-t 2 )-2βt=0 αt 2 -2βt-α=0

[0109] The angular difference Δφ can be calculated using relational equations 50 and 51. As mentioned above, the horizontal distance d can be calculated using relational equation 45 or 46.

[0110] "Location estimation program and location estimation system" Referring to Figures 3, 4, and 6, the position estimation program and position estimation system of the aircraft 1 according to this embodiment will be described. Referring to Figure 6, the position estimation program according to this embodiment causes a computer to execute multiple steps, each corresponding to a multiple step of the position estimation method according to this embodiment.

[0111] The multiple steps include an information acquisition procedure corresponding to the information acquisition step S31 and a position estimation procedure corresponding to the position calculation step S32. The position estimation program can be stored in a computer-readable storage medium.

[0112] Referring to Figures 3 and 4, the position estimation system according to this embodiment is the same as the first embodiment, except that n is 3 and that it enables the execution of the information acquisition procedure and position estimation procedure of the position estimation program according to this embodiment.

[0113] As described above, the position estimation method according to this embodiment can be used to obtain the same functions and effects as in the first embodiment. The position estimation program and position estimation system according to this embodiment can also be used to obtain the same functions and effects as in the position estimation method according to this embodiment.

[0114] "Fourth Embodiment" Referring to Figures 1, 3, 4, and 7, a position estimation method, position estimation program, and position estimation system according to the fourth embodiment of the aircraft 1 will be described.

[0115] "Position estimation method" Referring to Figures 1 and 7, the method for estimating the position of the aircraft 1 according to this embodiment will be described. The relationship between the aircraft 1, the radar 2, and the n receiving devices 11, and the parameters based on that relationship, according to this embodiment are the same as in the second embodiment, except that n is 4.

[0116] As shown in Figure 7, the position estimation method according to this embodiment includes an information acquisition step S41 and a position calculation step S42. The information acquisition step 41 is the same as the information acquisition step S11 of the first embodiment, except that n is 4. The position calculation step S42 is the same as the position calculation step S12 of the second embodiment, except that n is 4 and that the measurement information, default information, variables and parameter variables are defined as follows.

[0117] Measurement information: angle φ s and distance L i Includes. Default information is angle φi , horizontal distance D i and height H i The position information of aircraft 1 includes the angle difference Δφ, horizontal distance d, and angle φ. s It can be calculated based on the angle difference Δφ, horizontal distance d, and altitude h, and distance e i And the distance x is a parameter.

[0118] When estimating the position of aircraft 1, the angular difference Δφ, horizontal distance d, and altitude h can be calculated as follows. First, the distance x can be defined as shown in relational equation 3 above. x=[L i 2 -D i 2 -H i 2 +2H i h+2D i d{cos(φ S -φ i )cosΔφ-sin(φ S -φ i )sinΔφ)}] / 2L i

[0119] As shown in the following relation 61, the constant P i , constant Q i and the constant R i Define. P i =L i 2 -D i 2 -H i 2 Q i =D i cos(φ s -φ i ) R i =D i sin(φ s -φ i )

[0120] When i is 1, applying relation 61 to relation 3 yields relation 62. x={P1+2H1h+2(Q1cosΔφ-R1sinΔφ)d} / 2L1

[0121] When i is 2, applying relation 61 to relation 3 yields the following relation 63. x={P2+2H2h+2(Q2cosΔφ-R2sinΔφ)d} / 2L2

[0122] When i is 3, applying relation 61 to relation 3 yields the following relation 64. x={P3+2H3h+2(Q3cosΔφ-R3sinΔφ)d} / 2L3

[0123] When i is 4, applying relation 61 to relation 3 yields the following relation 65. x={P4+2H4h+2(Q4cosΔφ-R4sinΔφ)d} / 2L4

[0124] Based on relations 62 and 63, the following relation 66 is derived. (L1P2-L2P1)+2(L1H2-L2H1)h+2{(L1Q2-L2Q1)cosΔφ-(L1R2-L2R1)sinΔφ}d=0

[0125] Based on relations 63 and 64, the following relation 67 is derived. (L2P3-L3P2)+2(L2H3-L3H2)h+2{(L2Q3-L3Q2)cosΔφ-(L2R3-L3R2)sinΔφ}d=0

[0126] Eliminating altitude h from relations 66 and 67 yields the following relation 68. 2[{(L1H2-L2H1)(L2Q3-L3Q2)-(L2H3-L3H2)(L1Q2-L2Q1)}cosΔφ-{(L1H2-L2H1)(L2R3-L3R2)-(L2H3-L3H2)(L1R2-L2R1)}sinΔφ]d =(L2H3-L3H2)(L1P2-L2P1)-(L1H2-L2H1)(L2P3-L3P2)

[0127] Eliminating the horizontal distance d in relational equations 66 and 67 yields relational equation 69. 2[{(L1H2-L2H1)(L2Q3-L3Q2)-(L2H3-L3H2)(L1Q2-L2Q1)}cosΔφ-{(L1H2-L2H1)(L2R3-L3R2)-(L2H3-L3H2)(L1R2-L2R1)}sinΔφ]h =-[{(L1P2-L2P1)(L2Q3-L3Q2)-(L2P3-L3P2)(L1Q2-L2Q1)}cosΔφ-{(L1P2-L2P1)(L2R3-L3R2)-(L2P3-L3P2)(L1R2-L2R1)}sinΔφ]

[0128] The constants α, β, γ, δ, and ε are defined as shown in the following relation 70. α=Q1(L2H3-L3H2)+Q2(L3H1-L1H3)+Q3(L1H2-L2H1) β=R1(L2H3-L3H2)+R2(L3H1-L1H3)+R3(L1H2-L2H1) γ=Q1(L2P3-L3P2)+Q2(L3P1-L1P3)+Q3(L1P2-L2P1) δ=R1(L2P3-L3P2)+R2(L3P1-L1P3)+R3(L1P2-L2P1) ε=H1(L2P3-L3P2)+H2(L3P1-L1P3)+H3(L1P2-L2P1)

[0129] Applying relation 70 to relation 68, the horizontal distance d is calculated as shown in relation 71. d = ε / 2(αcosΔφ - βsinΔφ)

[0130] Applying relation 70 to relation 69, the altitude h is calculated as shown in relation 72. h=-(γcosΔφ-δsinΔφ) / 2(αcosΔφ-βsinΔφ)

[0131] Applying relations 71 and 72 to relation 62 yields the following relation 73. x=[P1-H1{(γcosΔφ-δsinΔφ) / (αcosΔφ-βsinΔφ)}+ε{(Q1cosΔφ-R1sinΔφ) / (αcosΔφ-βsinΔφ)}] / 2L1

[0132] Applying relations 71 and 72 to relation 65 yields the following relation 74. x=[P4-H4{(γcosΔφ-δsinΔφ) / (αcosΔφ-βsinΔφ)}+ε{(Q4cosΔφ-R4sinΔφ) / (αcosΔφ-βsinΔφ)}] / 2L4

[0133] Based on relations 73 and 74, the following relation 75 is derived. L4{P1(αcosΔφ-βsinΔφ)-H1(γcosΔφ-δsinΔφ)+ε(Q1cosΔφ-R1sinΔφ)} =L1{P4(αcosΔφ-βsinΔφ)-H4(γcosΔφ-δsinΔφ)+ε(Q4cosΔφ-R4sinΔφ)}

[0134] By substituting the angle Δφ with the variable t using Weierstrass substitution, we obtain the following relation 76. t = tan(Δφ / 2) cosΔφ=(1-t 2 ) / (1+t 2 ) sinΔφ=2t / (1+t 2 )

[0135] Applying relation 76 to relation 75 yields relation 77. L4[P1{α(1-t 2 )-2βt}-H1{γ(1-t 2 )-2δt}+ε{Q1(1-t 2 )-2R1t}] =L1[P4{α(1-t 2 )-2βt}-H4{γ(1-t 2 )-2δt}+ε{Q4(1-t 2 )-2R4t}] {(L1P4-L4P1)α-(L1H4-L4H1)γ+(L1Q4-L4Q1)ε}t2 +2{(L1P4-L4P1)β-(L1H4-L4H1)δ+(L1R4-L4R1)ε}t -{(L1P4-L4P1)α-(L1H4-L4H1)γ+(L1Q4-L4Q1)ε} =0

[0136] Here, the constants a and b are defined as shown in the following relational equation 78. a=(L1P4-L4P1)α-(L1H4-L4H1)γ+(L1Q4-L4Q1)ε b=(L1P4-L4P1)β-(L1H4-L4H1)δ+(L1R4-L4R1)ε

[0137] Applying relation 78 to relation 77 yields relation 79. at 2 +2bt-a=0

[0138] The angular difference Δφ can be calculated using equations 75 and 79. As mentioned above, the horizontal distance d can be calculated using equation 61. The altitude h can be calculated using equation 62.

[0139] "Location estimation program and location estimation system" Referring to Figures 3, 4, and 7, the position estimation program and position estimation system of the aircraft 1 according to this embodiment will be described. Referring to Figure 7, the position estimation program according to this embodiment causes a computer to execute multiple steps, each corresponding to a multiple step of the position estimation method according to this embodiment.

[0140] The multiple steps include an information acquisition procedure corresponding to the information acquisition step S41 and a position estimation procedure corresponding to the position calculation step S42. The position estimation program can be stored in a computer-readable storage medium.

[0141] Referring to Figures 3 and 4, the position estimation system according to this embodiment is the same as that of the second embodiment, except that n is 4 and that it is capable of executing the information acquisition procedure and position estimation procedure of the position estimation program according to this embodiment.

[0142] As described above, the position estimation method according to this embodiment can be obtained to achieve the same effects and benefits as in the second embodiment. The position estimation program and position estimation system according to this embodiment can also achieve the same effects and benefits as in the position estimation method according to this embodiment.

[0143] "Fifth Embodiment" Referring to Figures 3, 4, 8, and 9, a position estimation method, position estimation program, and position estimation system according to the fifth embodiment of the aircraft 1 will be described.

[0144] "Position estimation method" The method for estimating the position of the aircraft 1 according to this embodiment will be described with reference to Figures 8 and 9. As shown in Figure 8, in the position estimation method, the aircraft 1 is the target of position estimation, and the radar 2, n receiving devices 11, and position estimation device 12 are used to estimate the position of the aircraft 1. In this embodiment, n is 2. Figure 8 shows the relationship between the aircraft 1, the radar 2, and i receiving devices 11 using altitude above sea level. i is an integer from 1 to n.

[0145] The parameters based on the relationship between the aircraft 1, radar 2, and n receiving devices 11 considered in the position estimation method are as follows: - The horizontal angle φ of the principal lobe in the first radio wave relative to a specific direction. s - The angle φ of the i-th receiver 11 as seen from radar 2, relative to a specific direction. i - The horizontal angular difference Δφ between the orientation of the main lobe in the first radio wave and the orientation of aircraft 1, with reference to radar 2. - Distance L from radar 2 via aircraft 1 to the i-th receiving device 11 i - Horizontal distance D from radar 2 to the i-th receiver 11 i - The altitude K of the i-th receiving device 11 i - Radar 2's altitude K S - Distance e from aircraft 1 to the i-th receiver 11 i - Distance x from radar 2 to aircraft 1 - Altitude k of aircraft 1 - Horizontal distance d from radar 2 to aircraft 1

[0146] In Figure 8, a specific direction is indicated by arrow F, and the direction of the main lobe in the first radio wave is indicated by arrow B. The altitude parameter for radar 2 is determined relative to sea level, and parameters other than altitude are determined relative to its antenna 2a. The altitude parameter for the i-th receiving device 11 is determined relative to sea level, and parameters other than altitude are determined relative to its antenna 11a.

[0147] Next, as shown in Figure 9, the position estimation method according to this embodiment includes an information acquisition step S51 and a position calculation step S52. The information acquisition step 51 is the same as the information acquisition step S11 of the first embodiment, except that it acquires intercepted information regarding parameters using altitude above sea level. The position calculation step S52 is the same as the position calculation step S12 of the first embodiment, except that it defines the measurement information, default information, variables and parameter variables as follows.

[0148] Measurement information: angle φ s , distance L i and altitude k. Default information includes angle φ. i , horizontal distance D i , sea level K i and altitude K S The position information of aircraft 1 includes the angle difference Δφ, horizontal distance d, and angle φ. s It can be calculated based on the altitude k above sea level. The angular difference Δφ and horizontal distance d are unknown information and variables, and the distance e i And the distance x is a parameter.

[0149] In estimating the position of aircraft 1, the angular difference Δφ and the horizontal distance d can be calculated as follows. First, the following relation 81 is derived from the Pythagorean theorem. x 2 =(kK S ) 2 +d 2 (L i -x) 2 =e i 2 +(kK i ) 2

[0150] Furthermore, the following relation 82 can be derived from the Law of Cosines. e i 2 =D i 2 +d 2 -2D i dcos(φ S -φ i +Δφ) =(L i -x) 2 -(kK i ) 2 D i 2 +x 2 -(kK i ) 2 -2D i dcos(φ S -φ i +Δφ) =L i 2 -2L i x+x 2 -k 2 +2K i kK i 2 D i 2 +x 2 -k 2 +2K S kK S 2 -2D i dcos(φ S -φi +Δφ) =L i 2 -2L i x+x 2 -k 2 +2K i KK i 2 D i 2 -2D i dcos ( φ ) S -φ i +Δφ) =L i 2 -2L i x+2(K i -K S )kK i 2 +K S 2

[0151] It also has a 83-year-old license plate. x={L i 2 -D i 2 -K i 2 +K S 2 +2(K i -K S )k+2D i dcos ( φ ) S -φ i +Δϕ)} / 2L i =[L i 2 -D i 2 -K i 2 +K S 2 +2(K i -K S )k+2D i d{cos(φ). S -φ i )cosΔφ-sin(ϕ S -φ i )sinΔϕ)}] / 2L i

[0152] Here, the constant P i , constant Q i and the constant R i We define it as shown in the following relation 84. P i =L i 2 -D i 2 -K i 2 +K S 2 +2(K i -K s )k Q i =D i cos(φ s -φ i ) R i =D i sin(φ s -φ i )

[0153] When i is 1, applying relation 84 to relation 83 yields the following relation 85. x={P1+2(Q1cosΔφ-R1sinΔφ)d} / 2L1

[0154] When i is 2, applying relation 84 to relation 83 yields the following relation 86. x={P2+2(Q2cosΔφ-R2sinΔφ)d} / 2L2

[0155] According to relations 85 and 86, the horizontal distance d is defined as shown in relation 87. d=-(L1P2-L2P1) / 2{(L1Q2-L2Q1)cosΔφ-(L1R2-L2R1)sinΔφ}

[0156] The constants α, β, and γ are defined as shown in the following relation 88. α = L1P2 - L2P1 β = L1Q2 - L2Q1 γ = L1R2 - L2R1

[0157] Applying relation 88 to relation 84, the distance x is defined as shown in relation 89. x=[P1-α{(Q1cosΔφ-R1sinΔφ) / (βcosΔφ-γsinΔφ)}] / 2L1

[0158] Applying relation 88 to relation 87, the horizontal distance d is derived as shown in relation 90. d = -α / 2(βcosΔφ - γsinΔφ)

[0159] Applying relations 89 and 90 to the Pythagorean theorem yields the following relation 91. x 2 =(kK S ) 2 +d 2 ([P1-α{(Q1cosΔφ-R1sinΔφ) / (βcosΔφ-γsinΔφ)}] / 2L1) 2 =(kK S ) 2 +{-α / 2(βcosΔφ-γsinΔφ)} 2 {P1(βcosΔφ-γsinΔφ)-α(Q1cosΔφ-R1sinΔφ)} 2 ={2L1(kK S )(βcosΔφ-γsinΔφ)} 2 +(-L1α) 2

[0160] By substituting the angle Δφ with the variable t using Weierstrass substitution, we obtain the following relation 92. t = tan(Δφ / 2) cosΔφ=(1-t 2 ) / (1+t 2 ) sinΔφ=2t / (1+t 2 )

[0161] Applying relation 92 to relation 91 yields relation 93, which is as follows: {P1β(1-t 2 )-2P1γt-Q1α(1-t2 )+2R1αt} 2 ={2L1(kK S )β(1-t 2 )-2L1(kK S )γt} 2 +{-L1α(1+t 2 )} 2 {(Q1α-P1β)t 2 +2(R1α-P1γ)t-(Q1α-P1β)} 2 ={2L1(kK S )} 2 (βt 2 +2γt-β) 2 +(L1αt 2 +L1α) 2 [(Q1α-P1β) 2 -(L1α) 2 -{2L1(kK S )β} 2 ]t 4 +4[(Q1α-P1β)(R1α-P1γ)-{2L1(kK S ) 2 βγ}]t 3 -2[(Q1α-P1β) 2 -2(R1α-P1γ) 2 +(L1α) 2 -{2L1(kK S )} 2 (β 2 -2γ 2 )]t 2 -4[(Q1α-P1β)(R1α-P1γ)-{2L1(kK). S )} 2 βγ]t +[(Q1α-P1β) 2 -(L1α) 2 -{2L1(kK S )β} 2 ] =0

[0162] In the 94th century of the rest of the range, the range b is the 3rd c. a=(Q1α-P1β)2 -(L1α) 2 -{2L1(kK S )β} 2 b=4[(Q1α-P1β)(R1α-P1γ)-{2L1(kK S )} 2 βγ] c=2[(Q1α-P1β)] 2 -2(R1α-P1γ) 2 +(L1α) 2 -{2L1(kK S )} 2 (β 2 -2γ 2 )]

[0163] Applying relation 94 to relation 93, we can derive relation 95. at 4 +bt 3 -ct 2 -bt+a=0

[0164] The angular difference Δφ can be calculated using relational equations 92 and 95. As mentioned above, the horizontal distance d can be calculated using relational equation 90.

[0165] "Location estimation program and location estimation system" Referring to Figures 3, 4, and 9, the position estimation program and position estimation system of the aircraft 1 according to this embodiment will be described. Referring to Figure 9, the position estimation program according to this embodiment causes a computer to execute multiple steps, each corresponding to one of the multiple steps of the position estimation method according to this embodiment.

[0166] The multiple steps include an information acquisition procedure corresponding to the information acquisition step S51 and a position estimation procedure corresponding to the position calculation step S52. The position estimation program can be stored in a computer-readable storage medium.

[0167] Referring to Figures 3 and 4, the position estimation system according to this embodiment is the same as that of the first embodiment, except that it enables the execution of the information acquisition procedure and the position estimation procedure of the position estimation program according to this embodiment.

[0168] As described above, the position estimation method according to this embodiment can be used to obtain the same functions and effects as in the first embodiment. The position estimation program and position estimation system according to this embodiment can also be used to obtain the same functions and effects as in the position estimation method according to this embodiment.

[0169] "Sixth Embodiment" Referring to Figures 3, 4, 8, and 10, a position estimation method, position estimation program, and position estimation system according to the sixth embodiment of the aircraft 1 will be described.

[0170] "Position estimation method" Referring to Figures 8 and 10, the method for estimating the position of the aircraft 1 according to this embodiment will be described. The relationship between the aircraft 1, the radar 2, and the n receiving devices 11, and the parameters based on that relationship, according to this embodiment are the same as in the fifth embodiment, except that n is 3.

[0171] As shown in Figure 10, the position estimation method according to this embodiment includes an information acquisition step S61 and a position calculation step S62. The information acquisition step S61 is the same as the information acquisition step S21 of the second embodiment, except that it acquires intercepted information regarding parameters using altitude above sea level. The position calculation step S62 is the same as the position calculation step S22 of the second embodiment, except that it defines the measurement information, default information, variables and parameter variables as follows.

[0172] Measurement information: angle φ s and distance L i Includes. Default information is angle φ i , horizontal distance D i , sea level K i and altitude K S The position information of aircraft 1 includes the angle difference Δφ, horizontal distance d, and angle φ. sIt can be calculated based on the altitude k above sea level. The angle difference Δφ, horizontal distance d, and altitude k above sea level are unknown information and variables, and the distance e i And the distance x is a parameter.

[0173] In estimating the position of aircraft 1, the angular difference Δφ, horizontal distance d, and altitude k above sea level can be calculated as follows. First, the distance x can be defined as shown in relational equation 83 above. x=[L i 2 -D i 2 -K i 2 +K S 2 +2(K i -K S )k+2D i d{cos(φ S -φ i )cosΔφ-sin(φ S -φ i )sinΔφ)}] / 2L i

[0174] As shown in the following relation 101, the constant P i , constant Q i and the constant R i Define. P i =L i 2 -D i 2 -K i 2 +K S 2 Q i =D i cos(φ s -φ i ) R i =D i sin(φ s -φ i ) H i =K i -K S

[0175] When i is 1, applying relation 101 to relation 83 yields the following relation 102. x={P1+2H1k+2(Q1cosΔφ-R1sinΔφ)d} / 2L1

[0176] When i is 2, applying relation 101 to relation 83 yields the following relation 103. x={P2+2H2k+2(Q2cosΔφ-R2sinΔφ)d} / 2L2

[0177] When i is 3, applying relation 101 to relation 83 yields the following relation 104. x={P3+2H3k+2(Q3cosΔφ-R3sinΔφ)d} / 2L3

[0178] Based on relations 102 and 103, the following relation 105 is derived. (L1P2-L2P1)+2(L1H2-L2H1)k+2{(L1Q2-L2Q1)cosΔφ-(L1R2-L2R1)sinΔφ}d=0

[0179] Based on relations 103 and 104, the following relation 106 is derived. (L2P3-L3P2)+2(L2H3-L3H2)k+2{(L2Q3-L3Q2)cosΔφ-(L2R3-L3R2)sinΔφ}d=0

[0180] Eliminating the altitude k from equations 105 and 106 yields equation 107. 2[{(L1H2-L2H1)(L2Q3-L3Q2)-(L2H3-L3H2)(L1Q2-L2Q1)}cosΔφ-{(L1H2-L2H1)(L2R3-L3R2)-(L2H3-L3H2)(L1R2-L2R1)}sinΔφ]d =(L2H3-L3H2)(L1P2-L2P1)-(L1H2-L2H1)(L2P3-L3P2)

[0181] Eliminating the horizontal distance d in relational equations 105 and 106 yields relational equation 108. 2[{(L1H2-L2H1)(L2Q3-L3Q2)-(L2H3-L3H2)(L1Q2-L2Q1)}cosΔφ-{(L1H2-L2H1)(L2R3-L3R2)-(L2H3-L3H2)(L1R2-L2R1)}sinΔφ]k =-[{(L1P2-L2P1)(L2Q3-L3Q2)-(L2P3-L3P2)(L1Q2-L2Q1)}cosΔφ-{(L1P2-L2P1)(L2R3-L3R2)-(L2P3-L3P2)(L1R2-L2R1)}sinΔφ]

[0182] The constants α, β, γ, δ, and ε are defined as shown in the following relation 109. α=Q1(L2H3-L3H2)+Q2(L3H1-L1H3)+Q3(L1H2-L2H1) β=R1(L2H3-L3H2)+R2(L3H1-L1H3)+R3(L1H2-L2H1) γ=Q1(L2P3-L3P2)+Q2(L3P1-L1P3)+Q3(L1P2-L2P1) δ=R1(L2P3-L3P2)+R2(L3P1-L1P3)+R3(L1P2-L2P1) ε=H1(L2P3-L3P2)+H2(L3P1-L1P3)+H3(L1P2-L2P1)

[0183] Applying relation 109 to relation 107, the horizontal distance d can be calculated as shown in relation 110. d = ε / 2(αcosΔφ - βsinΔφ)

[0184] Applying relation 109 to relation 108, the altitude k above sea level can be calculated as shown in relation 111. k=-(γcosΔφ-δsinΔφ) / 2(αcosΔφ-βsinΔφ)

[0185] Applying relations 110 and 111 to relation 102 yields the following relation 112. x = [P1 - H1{(γcosΔφ - δsinΔφ) / (αcosΔφ - βsinΔφ)} + ε{(Q1cosΔφ - R1sinΔφ) / (αcosΔφ - βsinΔφ)}] / 2L1

[0186] Applying relational expressions 110 to 112 to the Pythagorean theorem, the following relational expression 113 is derived. x 2 = (k - K S ) 2 + d 2 ([P1 - H1{(γcosΔφ - δsinΔφ) / (αcosΔφ - βsinΔφ)} + ε{(Q1cosΔφ - R1sinΔφ) / (αcosΔφ - βsinΔφ)}] / 2L1) 2 = {-(γcosΔφ - δsinΔφ) / 2(αcosΔφ - βsinΔφ) - K S} 2 + {ε / 2(αcosΔφ - βsinΔφ)} 2 {P1(αcosΔφ - βsinΔφ) - H1(γcosΔφ - δsinΔφ) + ε(Q1cosΔφ - R1sinΔφ)} 2 = {L1(γcosΔφ - δsinΔφ) + 2L1K S (αcosΔφ - βsinΔφ)} 2 + (L1ε) 2

[0187] By substituting the angle Δφ with the variable t according to the Weierstrass substitution, the following relational expression 114 is obtained. t = tan(Δφ / 2) cosΔφ = (1 - t 2 ) / (1 + t 2 ) sinΔφ = 2t / (1 + t 2 )

[0188] Applying relational expression 114 to relational expression 113, the following relational expression 115 is derived. {P1α(1 - t 2 ) - 2P1βt - H1γ(1 - t 2 ) + 2H1δt + Q1ε(1 - t2 )-2R1et} 2 ={L1γ(1-t 2 )-2L1δt+2L1K S α(1-t 2 )-4L1K S βt} 2 +{L1ε(1+t 2 )} 2 {-(P1α-H1γ+Q1ε)t 2 -2(P1β-H1δ+R1ε)t+(P1α-H1γ+Q1ε)} 2 ={-L1(γ+2K S α)t 2 -2L1(δ+2K S β)t+L1(γ+2K S α)} 2 +(L1yet 2 +L1ε) 2

[0189] In the case of 116 of the rest of the range, the range of the ζ and the ξ ξ is strong. ζ=P1α-H1γ+Q1ε η=P1β-H1δ+R1ε ξ=γ+2K S α υ=δ+2K S β

[0190] The range 116 is the same as the range 115 and the rest of the range is (-ζt 2 -2ηt+ζ) 2 =L1 2 {(-ξt 2 -2υt+ξ) 2 +(etc 2 +ε) 2}} {ζ 2 -L1 2 (ε 2 +ξ 2 )}t 4 +4(ζη-L1 2 ξυ)t 3 -2{ζ2 -2η 2 +L1 2 (ε 2 -ξ 2 +2υ 2 )}t 2 -4(ζη-L1 2 ξυ)t +{ζ 2 -L1 2 (ε 2 +ξ 2 )} =0

[0191] The constants a, b, and c are defined as shown in the following relation 118. a=ζ 2 -L1 2 (ε 2 +ξ 2 ) b=4(ζη-L1 2 ξυ) c=2{ζ 2 -2η 2 +L1 2 (ε 2 -ξ 2 +2υ 2 )}

[0192] Applying relation 118 to relation 117, we can derive the following relation 119. at 4 +bt 3 -ct 2 -bt+a=0

[0193] The angular difference Δφ can be calculated using relational equations 114 and 119. As mentioned above, the horizontal distance d can be calculated using relational equation 110. The altitude k above sea level can be calculated using relational equation 111.

[0194] "Location estimation program and location estimation system" Referring to Figures 3, 4, and 10, the position estimation program and position estimation system of the aircraft 1 according to this embodiment will be described. Referring to Figure 10, the position estimation program according to this embodiment causes a computer to execute multiple steps, each corresponding to one of the multiple steps of the position estimation method according to this embodiment.

[0195] The multiple steps include an information acquisition procedure corresponding to the information acquisition step S61 and a position estimation procedure corresponding to the position calculation step S62. The position estimation program can be stored in a computer-readable storage medium.

[0196] Referring to Figures 3 and 4, the position estimation system according to this embodiment is the same as that of the second embodiment, except that it enables the execution of the information acquisition procedure and the position estimation procedure of the position estimation program according to this embodiment.

[0197] As described above, the position estimation method according to this embodiment can be obtained to achieve the same effects and benefits as in the second embodiment. The position estimation program and position estimation system according to this embodiment can also achieve the same effects and benefits as in the position estimation method according to this embodiment.

[0198] "Seventh Embodiment" Referring to Figures 3, 4, 8, and 11, a position estimation method, position estimation program, and position estimation system according to the seventh embodiment will be described.

[0199] "Position estimation method" Referring to Figures 8 and 11, the method for estimating the position of the aircraft 1 according to this embodiment will be described. The relationship between the aircraft 1, the radar 2, and the n receiving devices 11 according to this embodiment, and the parameters based on that relationship, are the same as in the fifth embodiment, except that n is 3.

[0200] As shown in FIG. 11, the position estimation method according to this embodiment includes an information acquisition step S71 and a position calculation step S72. The information acquisition step S71 is the same as the information acquisition step S31 of the third embodiment, except that it acquires eavesdropping information on parameters using the altitude. The position calculation step S72 is the same as the position calculation step S32 of the third embodiment, except that the measurement information, the predetermined information, the variables, and the intermediate variables are defined as follows.

[0201] The measurement information includes the angle φ s , the distance L i and the altitude k. The predetermined information includes the angle φ i , the horizontal distance D i , the altitude K i and the altitude K S . The position information of the aircraft 1 can be calculated based on the angle difference Δφ, the horizontal distance d, the angle φ s and the altitude k. The angle difference Δφ and the horizontal distance d are unknown information and variables, and the distances e i and the distance x are intermediate variables.

[0202] When estimating the position of the aircraft 1, the angle difference Δφ and the horizontal distance d can be calculated as follows. First, the distance x can be defined as in the above relational expression 83. x = [L i 2 - D i 2 - K i 2 + K S 2 + 2(K i - K S )k + 2D i d{cos(φ S - φ i )cosΔφ - sin(φ S - φ i )sinΔφ)}] / 2L i

[0203] Next, constants P i , constants Q i and constants R i are defined as in the following relational expression 121. Pi =L i 2 -D i 2 -K i 2 +K S 2 +2(K i -K s )k Q i =D i cos(φ s -φ i ) R i =D i sin(φ s -φ i )

[0204] When i is 1, applying relation 121 to relation 83 yields the following relation 122. x={P1+2(Q1cosΔφ-R1sinΔφ)d} / 2L1

[0205] When i is 2, applying relation 121 to relation 83 yields the following relation 123. x={P2+2(Q2cosΔφ-R2sinΔφ)d} / 2L2

[0206] When i is 3, applying relation 121 to relation 83 yields the following relation 124. x={P3+2(Q3cosΔφ-R3sinΔφ)d} / 2L3

[0207] Based on relations 122 and 123, the horizontal distance d is derived as shown in relation 125. d=-(L1P2-L2P1) / 2{(L1Q2-L2Q1)cosΔφ-(L1R2-L2R1)sinΔφ}

[0208] Based on relations 123 and 124, the horizontal distance d is derived as shown in relation 126. d=-(L2P3-L3P2) / 2{(L2Q3-L3Q2)cosΔφ-(L2R3-L3R2)sinΔφ}

[0209] Based on relations 125 and 126, the following relation 127 is derived. (L1P2-L2P1){(L2Q3-L3Q2)cosΔφ-(L2R3-L3R2)sinΔφ} =(L2P3-L3P2){(L1Q2-L2Q1)cosΔφ-(L1R2-L2R1)sinΔφ}

[0210] The constants α and β are defined as shown in relation 128 below. α=Q1(L2P3-L3P2)+Q2(L3P1-L1P3)+Q3(L1P2-L2P1) β=R1(L2P3-L3P2)+R2(L3P1-L1P3)+R3(L1P2-L2P1)

[0211] Applying relation 128 to relation 127 yields relation 129. αcosΔφ-βsinΔφ=0

[0212] By substituting the angle Δφ with the variable t using Weierstrass substitution, we obtain the following relation 130. t = tan(Δφ / 2) cosΔφ=(1-t 2 ) / (1+t 2 ) sinΔφ=2t / (1+t 2 )

[0213] Applying relation 130 to relation 129 yields relation 131. α(1-t 2 )-2βt=0 αt 2 -2βt-α=0

[0214] The angular difference Δφ can be calculated using relational equations 130 and 131. As mentioned above, the horizontal distance d can be calculated using relational equation 125 or 126.

[0215] "Location estimation program and location estimation system" Referring to Figures 3, 4, and 11, the position estimation program and position estimation system of the aircraft 1 according to this embodiment will be described. Referring to Figure 11, the position estimation program according to this embodiment causes a computer to execute multiple steps, each corresponding to one of the multiple steps of the position estimation method according to this embodiment.

[0216] The multiple steps include an information acquisition procedure corresponding to the information acquisition step S71 and a position estimation procedure corresponding to the position calculation step S72. The position estimation program can be stored in a computer-readable storage medium.

[0217] Referring to Figures 3 and 4, the position estimation system according to this embodiment is the same as that of the third embodiment, except that it enables the execution of the information acquisition procedure and the position estimation procedure of the position estimation program according to this embodiment.

[0218] As described above, the position estimation method according to this embodiment can be used to obtain the same effects and benefits as in the third embodiment. The position estimation program and position estimation system according to this embodiment can also be used to obtain the same effects and benefits as in the position estimation method according to this embodiment.

[0219] "Eighth Embodiment" Referring to Figures 3, 4, 8, and 12, a position estimation method, position estimation program, and position estimation system according to the eighth embodiment will be described. "Position estimation method"

[0220] Referring to Figures 8 and 12, the method for estimating the position of the aircraft 1 according to this embodiment will be described. The relationship between the aircraft 1, the radar 2, and the n receiving devices 11, and the parameters based on that relationship, according to this embodiment are the same as in the fifth embodiment, except that n is 4.

[0221] As shown in Figure 12, the position estimation method according to this embodiment includes an information acquisition step S81 and a position calculation step S82. The information acquisition step 81 is the same as the information acquisition step S41 of the fourth embodiment, except that it acquires intercepted information regarding parameters using altitude above sea level. The position calculation step S82 is the same as the position calculation step S42 of the fourth embodiment, except that it defines the measurement information, default information, variables and parameter variables as follows.

[0222] Measurement information: angle φ s and distance L i Includes. Default information is angle φ i , horizontal distance D i , sea level K i and altitude K S The position information of aircraft 1 includes the angle difference Δφ, horizontal distance d, and angle φ. s It can be calculated based on the altitude k above sea level. The angle difference Δφ, horizontal distance d, and altitude k above sea level are unknown information and variables, and the distance e i And the distance x is a parameter.

[0223] In estimating the position of aircraft 1, the angular difference Δφ, horizontal distance d, and altitude k above sea level can be calculated as follows. First, the distance x can be defined as shown in relational equation 83 above. x=[L i 2 -D i 2 -K i 2 +K S 2 +2(K i -K S )k+2D i d{cos(φ S -φ i )cosΔφ-sin(φ S -φ i )sinΔφ)}] / 2L i

[0224] As shown in the following relation 141, the constant P i , constant Q i and the constant R i Define. P i =L i 2 -D i 2 -K i 2 +K S 2 Q i =D i cos(φ s -φ i ) R i =D i sin(φ s -φ i ) H i =K i -K S

[0225] When i is 1, applying relation 141 to relation 83 yields relation 142. x={P1+2H1k+2(Q1cosΔφ-R1sinΔφ)d} / 2L1

[0226] When i is 2, applying relation 141 to relation 83 yields the following relation 143. x={P2+2H2k+2(Q2cosΔφ-R2sinΔφ)d} / 2L2

[0227] When i is 3, applying relation 141 to relation 83 yields relation 144. x={P3+2H3k+2(Q3cosΔφ-R3sinΔφ)d} / 2L3

[0228] When i is 4, applying relation 141 to relation 83 allows us to derive the following relation 145. x={P4+2H4k+2(Q4cosΔφ-R4sinΔφ)d} / 2L4

[0229] Based on relations 142 and 143, the following relation 146 is derived. (L1P2-L2P1)+2(L1H2-L2H1)k+2{(L1Q2-L2Q1)cosΔφ-(L1R2-L2R1)sinΔφ}d=0

[0230] Based on relations 143 and 144, the following relation 147 is derived. (L2P3-L3P2)+2(L2H3-L3H2)k+2{(L2Q3-L3Q2)cosΔφ-(L2R3-L3R2)sinΔφ}d=0

[0231] Eliminating the altitude k from equations 146 and 147 yields equation 148. 2[{(L1H2-L2H1)(L2Q3-L3Q2)-(L2H3-L3H2)(L1Q2-L2Q1)}cosΔφ-{(L1H2-L2H1)(L2R3-L3R2)-(L2H3-L3H2)(L1R2-L2R1)}sinΔφ]d =(L2H3-L3H2)(L1P2-L2P1)-(L1H2-L2H1)(L2P3-L3P2)

[0232] Eliminating the horizontal distance d in relational equations 146 and 147 yields relational equation 149. 2[{(L1H2-L2H1)(L2Q3-L3Q2)-(L2H3-L3H2)(L1Q2-L2Q1)}cosΔφ-{(L1H2-L2H1)(L2R3-L3R2)-(L2H3-L3H2)(L1R2-L2R1)}sinΔφ]k =-[{(L1P2-L2P1)(L2Q3-L3Q2)-(L2P3-L3P2)(L1Q2-L2Q1)}cosΔφ-{(L1P2-L2P1)(L2R3-L3R2)-(L2P3-L3P2)(L1R2-L2R1)}sinΔφ]

[0233] The constants α, β, γ, δ, and ε are defined as shown in the following relation 150. α=Q1(L2H3-L3H2)+Q2(L3H1-L1H3)+Q3(L1H2-L2H1) β=R1(L2H3-L3H2)+R2(L3H1-L1H3)+R3(L1H2-L2H1) γ=Q1(L2P3-L3P2)+Q2(L3P1-L1P3)+Q3(L1P2-L2P1) δ=R1(L2P3-L3P2)+R2(L3P1-L1P3)+R3(L1P2-L2P1) ε=H1(L2P3-L3P2)+H2(L3P1-L1P3)+H3(L1P2-L2P1)

[0234] Applying relation 150 to relation 148, the horizontal distance d is derived as shown in relation 151. d = ε / 2(αcosΔφ - βsinΔφ)

[0235] Applying relation 150 to relation 149, the altitude k above sea level is derived as shown in relation 152. k=-(γcosΔφ-δsinΔφ) / 2(αcosΔφ-βsinΔφ)

[0236] Applying relations 151 and 152 to relation 142 yields relation 153. x=[P1-H1{(γcosΔφ-δsinΔφ) / (αcosΔφ-βsinΔφ)}+ε{(Q1cosΔφ-R1sinΔφ) / (αcosΔφ-βsinΔφ)}] / 2L1

[0237] Applying relations 151 and 152 to relation 145, we can derive the following relation 154. x=[P4-H4{(γcosΔφ-δsinΔφ) / (αcosΔφ-βsinΔφ)}+ε{(Q4cosΔφ-R4sinΔφ) / (αcosΔφ-βsinΔφ)}] / 2L4

[0238] Based on relations 153 and 154, the following relation 155 is derived. L4{P1(αcosΔφ-βsinΔφ)-H1(γcosΔφ-δsinΔφ)+ε(Q1cosΔφ-R1sinΔφ)} =L1{P4(αcosΔφ-βsinΔφ)-H4(γcosΔφ-δsinΔφ)+ε(Q4cosΔφ-R4sinΔφ)}

[0239] By substituting the angle Δφ with the variable t using Weierstrass substitution, we obtain the following relation 156. t = tan(Δφ / 2) cosΔφ=(1-t 2 ) / (1+t 2 ) sinΔφ=2t / (1+t 2 )

[0240] Applying relation 156 to relation 155 yields relation 157. L4[P1{α(1-t 2 )-2βt}-H1{γ(1-t 2 )-2δt}+ε{Q1(1-t 2 )-2R1t}] =L1[P4{α(1-t 2 )-2βt}-H4{γ(1-t 2 )-2δt}+ε{Q4(1-t 2 )-2R4t}] {(L1P4-L4P1)α-(L1H4-L4H1)γ+(L1Q4-L4Q1)ε}t 2 +2{(L1P4-L4P1)β-(L1H4-L4H1)δ+(L1R4-L4R1)ε}t -{(L1P4-L4P1)α-(L1H4-L4H1)γ+(L1Q4-L4Q1)ε} =0

[0241] The constants a and b are defined as shown in the following relation 158. a=(L1P4-L4P1)α-(L1H4-L4H1)γ+(L1Q4-L4Q1)ε b=(L1P4-L4P1)β-(L1H4-L4H1)δ+(L1R4-L4R1)ε

[0242] Applying relation 158 to relation 157 yields relation 159. at 2 +2bt-a=0

[0243] The angular difference Δφ can be calculated using relational equations 156 and 159. As mentioned above, the horizontal distance d can be calculated using relational equation 151. The altitude k above sea level can be calculated using relational equation 152.

[0244] "Location estimation program and location estimation system" Referring to Figures 3, 4, and 12, the position estimation program and position estimation system of the aircraft 1 according to this embodiment will be described. Referring to Figure 12, the position estimation program according to this embodiment causes a computer to execute a plurality of steps corresponding to a plurality of steps of the position estimation method according to this embodiment.

[0245] The multiple steps include an information acquisition procedure corresponding to the information acquisition step S81 and a position estimation procedure corresponding to the position calculation step S82. The position estimation program can be stored in a computer-readable storage medium.

[0246] Referring to Figures 3 and 4, the position estimation system according to this embodiment is the same as that of the fourth embodiment, except that it enables the execution of the information acquisition procedure and the position estimation procedure of the position estimation program according to this embodiment.

[0247] As described above, the position estimation method according to this embodiment can be used to obtain the same effects and benefits as in the fourth embodiment. The position estimation program and position estimation system according to this embodiment can also be used to obtain the same effects and benefits as in the position estimation method according to this embodiment.

[0248] Although embodiments of the present invention have been described so far, the present invention is not limited to the embodiments described above, and the present invention can be modified and changed based on its technical concept. [Examples]

[0249] Examples 1 to 5 and Comparative Example 1 are described below.

[0250] "Example 1" In Example 1, the position of aircraft 1, which is assumed to be flying around Kadena Air Base, was estimated by simulation using an algebraic solution method, similar to the position estimation method in the First Embodiment. Aircraft 1 was assumed to be as follows: For the landing path, the approach gradient was set to 3 degrees and the flight speed to 250 m / sec. For the takeoff path, the climb gradient was set to 7.6 degrees and the flight speed to 300 m / sec.

[0251] The radar 2 to be installed at the airfield was assumed to be as follows: Radar 2 was assumed to be an SSR. The rotation period of the antenna 2a of radar 2 was assumed to be 4 seconds. The frequency of inquiries from radar 2 was assumed to be 250 times / sec. The beam width of radar 2 was assumed to be 3 degrees. Radar 2 was assumed to be installed at the position of origin O in the plan view of Figure 13A.

[0252] In Example 1, n was set to 2. The first and second measuring devices 11 were installed at the marks M1 and M2 in the plan view of Figure 13A. The first and second measuring devices 11 were installed only on one side in the width direction of the flight path of the aircraft 1.

[0253] In Example 1, the condition was to acquire first and second interception information obtained by intercepting a group of radio waves, including a second radio wave transmitted from aircraft 1 based on a first radio wave transmitted from radar 2, using first and second receiving devices 11. Under this condition, measurement information obtained based on the first and second interception information was calculated by simulation based on predetermined information determined based on radar 2 and the first and second receiving devices 11. Furthermore, the horizontal position and altitude of aircraft 1 were calculated by simulation based on the predetermined information and measurement information acquired in advance.

[0254] In the simulation of Example 1, it was assumed that the transponder 1a would respond when the aircraft 1 was positioned within a 3-degree beamwidth of the radar 2. Therefore, for one theoretically correct position of the aircraft 1, approximately 10 responses were obtained from the aircraft 1 per rotation of the radar 2. The simulation of Example 1 was performed with a time resolution of 100 ps.

[0255] Example 2 Embodiment 2 was the same as Embodiment 1, except that the first and second measuring devices 11 were installed so as to straddle the flight path of the aircraft 1. In Embodiment 2, the radar 2 was installed at the position of the origin O in the plan view of Figure 14A. The first and second measuring devices 11 were installed at the marks M1 to M2 in the plan view of Figure 14A.

[0256] "Example 3" In Example 3, the position of aircraft 1, which is assumed to be flying around Kadena Air Base, was estimated by simulation using an algebraic solution method, similar to the position estimation method in the second embodiment. The conditions for Example 3 were the same as in Example 2, except that n was set to 3. In Example 3, radar 2 was installed at the origin O in the plan view of Figure 15A. The first to third measuring devices 11 were installed at the marks M1 to M3 in the plan view of Figure 15A.

[0257] "Example 4" In Example 4, the position of aircraft 1, which is assumed to be flying around Kadena Air Base, was estimated by simulation using an algebraic solution method, similar to the position estimation method in the third embodiment. The conditions for Example 4 were the same as those for Example 3. In Example 4, radar 2 was installed at the origin O in the plan view of Figure 16A. The first to third measuring devices 11 were installed at the marks M1 to M3 in the plan view of Figure 16A.

[0258] Example 5 In Example 5, the position of aircraft 1, which is assumed to be flying around Kadena Air Base, was estimated by simulation using an algebraic solution method, similar to the position estimation method in the fourth embodiment. The conditions in Example 5 were the same as in Example 2, except that n was set to 4. In Example 5, radar 2 was installed at the origin O in the plan view of Figure 17A. The first to fourth measuring devices 11 were installed at the X marks M1 to M4 in the plan view of Figure 17A.

[0259] "Comparative Example 1" Comparative Example 1 was the same as Example 1, except that one measuring device was used. In Comparative Example 1, radar 2 was installed at the origin O in the plan view of Figure 18A. The one measuring device was installed at the X mark M1 in the plan view of Figure 18A.

[0260] The simulation results for Examples 1-5 and Comparative Example 1 are shown in Figures 13-18. In the plan views of Figures 13A-18A, the X-axis represents the east-west position (m) of aircraft 1, and the Y-axis represents the north-south position (m) of aircraft 1. In the time-altitude change diagrams of Figures 13B-18B, the T-axis represents time (sec), and the Z-axis represents the altitude (m) of aircraft 1.

[0261] In the plan views of Figures 13A-18A and the time-altitude change diagrams of Figures 13B-18B, the dashed circles indicate the theoretically correct position of aircraft 1, and the points indicate the position of aircraft 1 calculated by simulation. Ten points representing the simulated positions of aircraft 1 are plotted for each circle indicating the theoretically correct position of aircraft 1. Furthermore, in the time-altitude change diagrams of Figures 13B-18B, the data on the left side of the Z-axis (from the perspective of the paper) indicates the landing trajectory of aircraft 1, and the data on the right side indicates the takeoff trajectory of aircraft 1.

[0262] Referring to the plan views in Figures 13A to 17A, the horizontal position of most aircraft 1 calculated by the simulations in Examples 1 to 5 matched the theoretically correct horizontal position of aircraft 1. In particular, it was confirmed that the positional accuracy of aircraft 1 improved as the number of measuring devices 11 increased. On the other hand, referring to the plan view in Figure 18A, the positions of many aircraft 1 calculated by the simulation in Comparative Example 1 deviated from the theoretically correct position of aircraft 1.

[0263] Furthermore, referring to the time-altitude change diagrams in Figures 15B and 17B, the altitudes of most aircraft 1 calculated by the simulations in Examples 3 and 5 matched the theoretically correct altitude of aircraft 1. In addition, in the time-altitude change diagrams in Figures 13B, 14B, and 16B, the altitudes of most aircraft 1 calculated by the simulations in Examples 1, 2, and 4 were barometric altitudes obtained from the interrogation signals from aircraft 1, and therefore naturally matched the theoretically correct altitude of aircraft 1. Thus, it was confirmed that the position estimation method according to the first to fourth embodiments improves the accuracy of estimating the position of aircraft 1.

[0264] Furthermore, comparing Examples 1 and 2 with reference to the plan views in Figures 13A and 14A, the accuracy of the horizontal position of aircraft 1 calculated by the simulation in Example 2 was higher than the accuracy of the horizontal position of aircraft 1 calculated by the simulation in Example 1. This is thought to be due to the fact that in Example 1, the first and second measuring devices 11 were installed only on one side in the width direction relative to the flight path of aircraft 1. [Explanation of Symbols]

[0265] 1...Aircraft, 2...Radar, 11...Receiving equipment S11,S21,S31,S41,S51,S61,S71,S81...Information acquisition process S12,S22,S32,S42,S52,S62,S72,S82...Position calculation process φ s ...the horizontal angle of the principal lobe in the first radio wave relative to a specific direction. φi ...the angle of the i-th receiver 11 as seen from radar 2, based on a specific direction. Δφ…The horizontal angular difference between the direction of the main lobe in the first radio wave and the direction of aircraft 1, with reference to radar 2. L i ...the distance from radar 2, via aircraft 1, to the i-th receiving device 11 D i ...horizontal distance from radar 2 to the i-th receiver 11 d...Horizontal distance from radar 2 to aircraft 1 H i ...height of the i-th receiver 11 relative to radar 2 h... Altitude of aircraft 1 relative to radar 2 K i ...the altitude of the i-th receiving device 11 K S ...Radar 2's altitude k... Altitude of aircraft 1

Claims

1. An information acquisition step in which first and second intercepted information is obtained by intercepting a group of radio waves, including a second radio wave transmitted from an aircraft based on a first radio wave transmitted from radar, using first and second receiving devices, respectively; A position calculation step that calculates the position information of the aircraft based on measurement information obtained based on the first and second intercepted information and predetermined information determined based on the radar and the first and second receiving devices. A method for estimating the position of an aircraft, including, In the position calculation step, The aforementioned measurement information is The horizontal angle φ of the principal lobe in the first radio wave with respect to a specific direction. ｓ and, The distance L from the radar to the receiving device i (where i is an integer between 1 and 2) via the aircraft. ｉ and, The altitude h of the aircraft relative to the radar and It has, The aforementioned default information is, The angle φ of the i receiving device as seen from the radar, with respect to the aforementioned specific direction. ｉ and, The horizontal distance D from the radar to the i-receiving device ｉ and, The height H of the i receiving device relative to the radar ｉ and It has, The aircraft's identification information is The horizontal angular difference Δφ between the direction of the main lobe in the first radio wave and the direction of the aircraft, with respect to the radar, The horizontal distance d from the radar to the aircraft, The angle φ ｓ and, The aforementioned altitude h and Calculated based on, The angle difference Δφ and the horizontal distance d are, P ｉ =L ｉ ２ -D ｉ ２ -H ｉ ２ +2H ｉ h Q ｉ =D ｉ φ ｓ -φ ｉ ) R ｉ =D ｉ sin (φ) ｓ -φ ｉ ) α=L １ P ２ -L ２ P １ β=L １ Q ２ -L ２ Q １ γ=L １ R ２ -L ２ R １ t=tan(Δφ / 2) cosΔφ=(1-t ２ ) / (1+t ２ ) sinΔφ=2t / (1+t ２ ) a=(Q) １ a-P １ b) ２ -(L) １ a) ２ -(2L) １ (hb) ２ b=4{(Q) １ a-P １ b)(R １ a-P １ c)-(2L) １ W) ２ γγ} c=2{(Q １ a-P １ b) ２ -2(R) １ a-P １ c) ２ +(L) １ a) ２ -(2L) １ W) ２ (b) ２ -2c ２ )} If defined as follows, at ４ +bt ３ -ct ２ -bt+a=0 d=-α / 2(βcosΔφ−γsinΔφ) A method for estimating the position of an aircraft, calculated based on [the specified formula / data].

2. An information acquisition step of acquiring first, second, and third intercepted information obtained by intercepting a group of radio waves, including a second radio wave transmitted from an aircraft based on a first radio wave transmitted from radar, using first, second, and third receiving devices, respectively, A position calculation step that calculates the position information of the aircraft based on measurement information obtained based on the first, second, and third intercepted information and predetermined information determined based on the radar and the first, second, and third receiving devices. A method for estimating the position of an aircraft, including, In the position calculation step, The aforementioned measurement information is The horizontal angle φ of the principal lobe in the first radio wave with respect to a specific direction. ｓ and, The distance L from the radar to the receiving device i (i = an integer from 1 to 3) via the aircraft. ｉ and It has, The aforementioned default information is, The angle φ of the i receiving device as seen from the radar, with respect to the aforementioned specific direction. ｉ and, The horizontal distance D from the radar to the i-receiving device ｉ and, The height H of the i receiving device relative to the radar ｉ and It has, The aircraft's identification information is The horizontal angular difference Δφ between the direction of the main lobe in the first radio wave and the direction of the aircraft, with respect to the radar, The horizontal distance d from the radar to the aircraft, The altitude h of the aircraft with respect to the aforementioned radar, The angle φ ｓ and Calculated based on, The angle difference Δφ, the horizontal distance d, and the altitude h are, P ｉ =L ｉ ２ -D ｉ ２ -H ｉ ２ Q ｉ =D ｉ φ ｓ -φ ｉ ) R ｉ =D ｉ sin (φ) ｓ -φ ｉ ) α=Q １ (L ２ H ３ -L ３ H ２ )+Q ２ (L ３ H １ -L １ H ３ )+Q ３ (L １ H ２ -L ２ H １ ) β=R １ (L ２ H ３ -L ３ H ２ )+R ２ (L ３ H １ -L １ H ３ )+R ３ (L １ H ２ -L ２ H １ ) γ=Q １ (L ２ P ３ -L ３ P ２ )+Q ２ (L ３ P １ -L １ P ３ )+Q ３ (L １ P ２ -L ２ P １ ) δ=R １ (L ２ P ３ -L ３ P ２ )+R ２ (L ３ P １ -L １ P ３ )+R ３ (L １ P ２ -L ２ P １ ) ε=H １ (L ２ P ３ -L ３ P ２ )+H ２ (L ３ P １ -L １ P ３ )+H ３ (L １ P ２ -L ２ P １ ) t=tan(Δφ / 2) cosΔφ=(1-t ２ ) / (1+t ２ ) sinΔφ=2t / (1+t ２ ) a=(P １ a-H １ γ+Q １ e) ２ -L １ ２ (c) ２ +e ２ ) b=4{(P) １ a-H １ γ+Q １ e)(P １ β-H １ d+R １ e)-L １ ２ } c=2{(P １ a-H １ γ+Q １ e) ２ -2(P) １ β-H １ d+R １ e) ２ -L １ ２ (c) ２ -2d ２ -e ２ )} If defined as follows, at ４ +bt ３ -ct ２ -bt+a=0 d=ε / 2(αcosΔφ−βsinΔφ) h=-(γcosΔφ−δsinΔφ) / 2(αcosΔφ−βsinΔφ) A method for estimating the position of an aircraft, calculated based on [the specified formula / data].

3. An information acquisition step of acquiring first, second, and third intercepted information obtained by intercepting a group of radio waves, including a second radio wave transmitted from an aircraft based on a first radio wave transmitted from radar, using first, second, and third receiving devices, respectively, A position calculation step that calculates the position information of the aircraft based on measurement information obtained based on the first, second, and third intercepted information and predetermined information determined based on the radar and the first, second, and third receiving devices. A method for estimating the position of an aircraft, including, In the position calculation step, The aforementioned measurement information is The horizontal angle φ of the principal lobe in the first radio wave with respect to a specific direction. ｓ and, The distance L from the radar to the receiving device i (where i is an integer from 1 to 3) via the aircraft. ｉ and, The altitude h of the aircraft relative to the radar and It has, The aforementioned default information is, The angle φ of the i receiving device as seen from the radar, with respect to the aforementioned specific direction. ｉ and, The horizontal distance D from the radar to the i-receiving device ｉ and, The height H of the i receiving device relative to the radar ｉ and It has, The aircraft's identification information is The horizontal angular difference Δφ between the direction of the main lobe in the first radio wave and the direction of the aircraft, with respect to the radar, The horizontal distance d from the radar to the aircraft, The angle φ ｓ and, The aforementioned altitude h and Calculated based on, The angle difference Δφ and the horizontal distance d are, P ｉ =L ｉ ２ -D ｉ ２ -H ｉ ２ +2H ｉ h Q ｉ =D ｉ φ ｓ -φ ｉ ) R ｉ =D ｉ sin (φ) ｓ -φ ｉ ) α=Q １ (L ２ P ３ -L ３ P ２ )+Q ２ (L ３ P １ -L １ P ３ )+Q ３ (L １ P ２ -L ２ P １ ) β=R １ (L ２ P ３ -L ３ P ２ )+R ２ (L ３ P １ -L １ P ３ )+R ３ (L １ P ２ -L ２ P １ ) t=tan(Δφ / 2) cosΔφ=(1-t ２ ) / (1+t ２ ) sinΔφ=2t / (1+t ２ ) If defined as follows, at ２ +2β-α=0 d=-(L １ P ２ -L ２ P １ ) / 2{(L １ Q ２ -L ２ Q １ )cosΔφ-(L １ R ２ -L ２ R １ )sinΔφ or d=-(L ２ P ３ -L ３ P ２ ) / 2{(L ２ Q ３ -L ３ Q ２ )cosΔφ-(L ２ R ３ -L ３ R ２ )sinΔφ A method for estimating the position of an aircraft, calculated based on [the specified formula / data].

4. An information acquisition step of acquiring intercepted information, the first, second, third, and fourth, obtained by intercepting a group of radio waves, including a second radio wave transmitted from an aircraft based on a first radio wave transmitted from radar, using first, second, third, and fourth receiving devices, respectively; A position calculation step for calculating the aircraft's position information based on measurement information obtained based on the first, second, third, and fourth intercepted information, and predetermined information determined based on the radar and the first, second, third, and fourth receiving devices. A method for estimating the position of an aircraft, including, In the position calculation step, The aforementioned measurement information is The horizontal angle φ of the principal lobe in the first radio wave, relative to a specific direction. ｓ and, The distance L from the radar to the receiving device i (where i is an integer from 1 to 4) via the aircraft. ｉ and It has, The aforementioned default information is, The angle φ of the i receiving device as seen from the radar, with respect to the aforementioned specific direction. ｉ and, The horizontal distance D from the radar to the i-receiving device ｉ and, The height H of the i receiving device relative to the radar ｉ and It has, The aircraft's identification information is The horizontal angular difference Δφ between the direction of the main lobe in the first radio wave and the direction of the aircraft, with respect to the radar, The horizontal distance d from the radar to the aircraft, The altitude h of the aircraft with respect to the aforementioned radar, The angle φ ｓ and Calculated based on, The angle difference Δφ, the horizontal distance d, and the altitude h are, P ｉ =L ｉ ２ -D ｉ ２ -H ｉ ２ Q ｉ =D ｉ φ ｓ -φ ｉ ) R ｉ =D ｉ sin (φ) ｓ -φ ｉ ) α=Q １ (L ２ H ３ -L ３ H ２ )+Q ２ (L ３ H １ -L １ H ３ )+Q ３ (L １ H ２ -L ２ H １ ) β=R １ (L ２ H ３ -L ３ H ２ )+R ２ (L ３ H １ -L １ H ３ )+R ３ (L １ H ２ -L ２ H １ ) γ=Q １ (L ２ P ３ -L ３ P ２ )+Q ２ (L ３ P １ -L １ P ３ )+Q ３ (L １ P ２ -L ２ P １ ) δ=R １ (L ２ P ３ -L ３ P ２ )+R ２ (L ３ P １ -L １ P ３ )+R ３ (L １ P ２ -L ２ P １ ) ε=H １ (L ２ P ３ -L ３ P ２ )+H ２ (L ３ P １ -L １ P ３ )+H ３ (L １ P ２ -L ２ P １ ) t=tan(Δφ / 2) cosΔφ=(1-t ２ ) / (1+t ２ ) sinΔφ=2t / (1+t ２ ) a=(L １ P ４ -L ４ P １ )α-(L １ H ４ -L ４ H １ )γ+(L １ Q ４ -L ４ Q １ )ε b=(L) １ P ４ -L ４ P １ )b-(L １ H ４ -L ４ H １ )δ+(L １ R ４ -L ４ R １ )e If defined as follows, at ２ +2bt-a=0 d=ε / 2(αcosΔφ−βsinΔφ) h=-(γcosΔφ−δsinΔφ) / 2(αcosΔφ−βsinΔφ) A method for estimating the position of an aircraft, calculated based on [the specified formula / data].

5. An information acquisition step in which first and second intercepted information is obtained by intercepting a group of radio waves, including a second radio wave transmitted from an aircraft based on a first radio wave transmitted from radar, using first and second receiving devices, respectively; A position calculation step that calculates the position information of the aircraft based on measurement information obtained based on the first and second intercepted information and predetermined information determined based on the radar and the first and second receiving devices. A method for estimating the position of an aircraft, including, In the position calculation step, The aforementioned measurement information is The horizontal angle φ of the principal lobe in the first radio wave with respect to a specific direction. ｓ and, The distance L from the radar to the receiving device i (where i is an integer between 1 and 2) via the aircraft. ｉ and, The altitude k of the aforementioned aircraft and It has, The aforementioned default information is, The angle φ of the i receiving device as seen from the radar, with respect to the aforementioned specific direction. ｉ and, The horizontal distance D from the radar to the i-receiving device ｉ and, The altitude K of the receiving device i mentioned above ｉ and, The radar's altitude K Ｓ and It has, The aircraft's identification information is The horizontal angular difference Δφ between the direction of the main lobe in the first radio wave and the direction of the aircraft, with respect to the radar, The horizontal distance d from the radar to the aircraft, The angle φ ｓ and, The aforementioned altitude k and Calculated based on, The angle difference Δφ and the horizontal distance d are, P ｉ =L ｉ ２ -D ｉ ２ -K ｉ ２ +K Ｓ ２ +2(K ｉ -K ｓ )k Q ｉ =D ｉ φ ｓ -φ ｉ ) R ｉ =D ｉ sin (φ) ｓ -φ ｉ ) α=L １ P ２ -L ２ P １ β=L １ Q ２ -L ２ Q １ γ=L １ R ２ -L ２ R １ t=tan(Δφ / 2) cosΔφ=(1-t ２ ) / (1+t ２ ) sinΔφ=2t / (1+t ２ ) a=(Q １ α-P １ β) ２ - (L) １ (a) ２ -{2L １ (k-K Ｓ )β} ２ b=4[(Q) １ a-P １ b)(R １ a-P １ c)-{2L １ (K-K) Ｓ )} ２ [bg] c=2[(Q) １ a-P １ b) ２ -2(R) １ a-P １ c) ２ +(L) １ a) ２ -{2L １ (K-K) Ｓ )} ２ (b) ２ -2c ２ )] If defined as follows, at ４ +bt ３ -ct ２ -bt+a=0 d=-α / 2(βcosΔφ−γsinΔφ) A method for estimating the position of an aircraft, calculated based on [the specified formula / data].

6. An information acquisition step of acquiring first, second, and third intercepted information obtained by intercepting a group of radio waves, including a second radio wave transmitted from an aircraft based on a first radio wave transmitted from radar, using first, second, and third receiving devices, respectively, A position calculation step that calculates the position information of the aircraft based on measurement information obtained based on the first, second, and third intercepted information and predetermined information determined based on the radar and the first, second, and third receiving devices. A method for estimating the position of an aircraft, including, In the position calculation step, The aforementioned measurement information is The horizontal angle φ of the principal lobe in the first radio wave with respect to a specific direction. ｓ and, The distance L from the radar to the receiving device i (where i is an integer from 1 to 3) via the aircraft. ｉ and It has, The aforementioned default information is, The angle φ of the i receiving device as seen from the radar, with respect to the aforementioned specific direction. ｉ and, The horizontal distance D from the radar to the i-receiving device ｉ and, The altitude K of the receiving device i mentioned above ｉ and, The radar's altitude K Ｓ and It has, The aircraft's identification information is The horizontal angular difference Δφ between the direction of the main lobe in the first radio wave and the direction of the aircraft, with respect to the radar, The horizontal distance d from the radar to the aircraft, The altitude k of the aforementioned aircraft above sea level, The angle φ ｓ and Calculated based on, The angle difference Δφ, the horizontal distance d, and the altitude k above sea level are, P ｉ =L ｉ ２ -D ｉ ２ -K ｉ ２ +K Ｓ ２ Q ｉ =D ｉ φ ｓ -φ ｉ ) R ｉ =D ｉ sin (φ) ｓ -φ ｉ ) H ｉ =K ｉ -K Ｓ α=Q １ (L ２ H ３ -L ３ H ２ )+Q ２ (L ３ H １ -L １ H ３ )+Q ３ (L １ H ２ -L ２ H １ ) β=R １ (L ２ H ３ -L ３ H ２ )+R ２ (L ３ H １ -L １ H ３ )+R ３ (L １ H ２ -L ２ H １ ) γ=Q １ (L ２ P ３ -L ３ P ２ )+Q ２ (L ３ P １ -L １ P ３ )+Q ３ (L １ P ２ -L ２ P １ ) δ=R １ (L ２ P ３ -L ３ P ２ )+R ２ (L ３ P １ -L １ P ３ )+R ３ (L １ P ２ -L ２ P １ ) ε=H １ (L ２ P ３ -L ３ P ２ )+H ２ (L ３ P １ -L １ P ３ )+H ３ (L １ P ２ -L ２ P １ ) ζ=P １ a-H １ γ+Q １ e n = P １ β-H １ d+R １ e ξ=γ+2Κ Ｓ a u=d+2K Ｓ b t=tan(Δφ / 2) cosΔφ=(1-t ２ ) / (1+t ２ ) sinΔφ=2t / (1+t ２ ) a=z ２ -L １ ２ (e) ２ +ξ ２ ) b = 4(ζη - L １ ２ ξυ) c=2{ζ ２ -2th ２ +L １ ２ (e) ２ -x ２ +2u ２ )} If defined as follows, at ４ +bt ３ -ct ２ -bt+a=0 d=ε / 2(αcosΔφ−βsinΔφ) k=-(γcosΔφ−δsinΔφ) / 2(αcosΔφ−βsinΔφ) A method for estimating the position of an aircraft, calculated based on [the specified formula / data].

7. An information acquisition step of acquiring first, second, and third intercepted information obtained by intercepting a group of radio waves, including a second radio wave transmitted from an aircraft based on a first radio wave transmitted from radar, using first, second, and third receiving devices, respectively, A position calculation step that calculates the position information of the aircraft based on measurement information obtained based on the first, second, and third intercepted information and predetermined information determined based on the radar and the first, second, and third receiving devices. A method for estimating the position of an aircraft, including, In the position calculation step, The aforementioned measurement information is The horizontal angle φ of the principal lobe in the first radio wave with respect to a specific direction. ｓ and, The distance L from the radar to the receiving device i (where i is an integer from 1 to 3) via the aircraft. ｉ and, The altitude k of the aforementioned aircraft and It has, The aforementioned default information is, The angle φ of the i receiving device as seen from the radar, with respect to the aforementioned specific direction. ｉ and, The horizontal distance D from the radar to the i-receiving device ｉ and, The altitude K of the receiving device i mentioned above ｉ and, The radar's altitude K Ｓ and It has, The aircraft's identification information is The horizontal angular difference Δφ between the direction of the main lobe in the first radio wave and the direction of the aircraft, with respect to the radar, The horizontal distance d from the radar to the aircraft, The angle φ ｓ and, The aforementioned altitude k and Calculated based on, The angle difference Δφ and the horizontal distance d are, P ｉ =L ｉ ２ -D ｉ ２ -K ｉ ２ +K Ｓ ２ +2(K ｉ -K ｓ )k Q ｉ =D ｉ φ ｓ -φ ｉ ) R ｉ =D ｉ sin (φ) ｓ -φ ｉ ) α=Q １ (L ２ P ３ -L ３ P ２ )+Q ２ (L ３ P １ -L １ P ３ )+Q ３ (L １ P ２ -L ２ P １ ) β=R １ (L ２ P ３ -L ３ P ２ )+R ２ (L ３ P １ -L １ P ３ )+R ３ (L １ P ２ -L ２ P １ ) t=tan(Δφ / 2) cosΔφ=(1-t ２ ) / (1+t ２ ) sinΔφ=2t / (1+t ２ ) If defined as follows, at ２ +2β-α=0 d=-(L １ P ２ -L ２ P １ ) / 2{(L １ Q ２ -L ２ Q １ )cosΔφ-(L １ R ２ -L ２ R １ )sinΔφ or d=-(L ２ P ３ -L ３ P ２ ) / 2{(L ２ Q ３ -L ３ Q ２ )cosΔφ-(L ２ R ３ -L ３ R ２ )sinΔφ A method for estimating the position of an aircraft, calculated based on [the specified formula / data].

8. An information acquisition step of acquiring intercepted information, the first, second, third, and fourth, obtained by intercepting a group of radio waves, including a second radio wave transmitted from an aircraft based on a first radio wave transmitted from radar, using first, second, third, and fourth receiving devices, respectively; A position calculation step for calculating the aircraft's position information based on measurement information obtained based on the first, second, third, and fourth intercepted information, and predetermined information determined based on the radar and the first, second, third, and fourth receiving devices. A method for estimating the position of an aircraft, including, In the position calculation step, The aforementioned measurement information is The horizontal angle φ of the principal lobe in the first radio wave with respect to a specific direction. ｓ and, The distance L from the radar to the receiving device i (where i is an integer from 1 to 4) via the aircraft. ｉ and It has, The aforementioned default information is, The angle φ of the i receiving device as seen from the radar, with respect to the aforementioned specific direction. ｉ and, The horizontal distance D from the radar to the i-receiving device ｉ and, The altitude K of the receiving device i mentioned above ｉ and, The radar's altitude K Ｓ and It has, The aircraft's identification information is The horizontal angular difference Δφ between the direction of the main lobe in the first radio wave and the direction of the aircraft, with respect to the radar, The horizontal distance d from the radar to the aircraft, The altitude k of the aforementioned aircraft above sea level, The angle φ ｓ and Calculated based on, The angle difference Δφ, the horizontal distance d, and the altitude k above sea level are, P ｉ =L ｉ ２ -D ｉ ２ -K ｉ ２ +K Ｓ ２ Q ｉ =D ｉ φ ｓ -φ ｉ ) R ｉ =D ｉ sin (φ) ｓ -φ ｉ ) H ｉ =K ｉ -K Ｓ α=Q １ (L ２ H ３ -L ３ H ２ )+Q ２ (L ３ H １ -L １ H ３ )+Q ３ (L １ H ２ -L ２ H １ ) β=R １ (L ２ H ３ -L ３ H ２ )+R ２ (L ３ H １ -L １ H ３ )+R ３ (L １ H ２ -L ２ H １ ) γ=Q １ (L ２ P ３ -L ３ P ２ )+Q ２ (L ３ P １ -L １ P ３ )+Q ３ (L １ P ２ -L ２ P １ ) δ=R １ (L ２ P ３ -L ３ P ２ )+R ２ (L ３ P １ -L １ P ３ )+R ３ (L １ P ２ -L ２ P １ ) ε=H １ (L ２ P ３ -L ３ P ２ )+H ２ (L ３ P １ -L １ P ３ )+H ３ (L １ P ２ -L ２ P １ ) t=tan(Δφ / 2) cosΔφ=(1-t ２ ) / (1+t ２ ) sinΔφ=2t / (1+t ２ ) a=(L １ P ４ -L ４ P １ )α-(L １ H ４ -L ４ H １ )γ+(L １ Q ４ -L ４ Q １ )ε b=(L) １ P ４ -L ４ P １ )b-(L １ H ４ -L ４ H １ )δ+(L １ R ４ -L ４ R １ )e If defined as follows, at ２ +2bt-a=0 d=ε / 2(αcosΔφ−βsinΔφ) k=-(γcosΔφ−δsinΔφ) / 2(αcosΔφ−βsinΔφ) A method for estimating the position of an aircraft, calculated based on [the specified formula / data].

9. An aircraft position estimation program that causes a computer to execute the aircraft position estimation method described in any one of claims 1 to 8.

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