JP6553994B2 - Flying object position calculation system, flying object position calculation method, and flying object position calculation program - Google Patents

Description

  Embodiments of the present invention relate to a projectile position calculation system, a projectile position calculation method, and a projectile position calculation program.

  Conventionally, a triangulation method is known as a method for measuring a spatial position of an observation target. In the case where the position of the projectile is calculated by triangulation based on the image captured by the camera, it is necessary to place the camera at a different relative position with respect to the projectile to shoot the projectile. Specifically, the position of the projectile can be geometrically calculated based on the azimuth and elevation angle of the projectile photographed by a plurality of cameras installed at different positions.

  In addition, as an application of triangulation, a technology for calculating the position of an object with a single camera has been devised (see, for example, Patent Document 1). In this technique, a single camera is moved to capture an object from different positions, thereby obtaining a plurality of images similar to those captured by a plurality of cameras. That is, even with a single camera, if the object is photographed from a plurality of directions by moving the camera, the spatial position of the object can be calculated by triangulation.

International Publication No. 2007/142267

  However, when the observation target is a flying object such as a missile that moves at high speed, it is difficult to measure the spatial position of the target with the conventional method. For example, in the case of photographing an object with a plurality of cameras, it is necessary to install each camera at an appropriate position in advance so that the object falls within the field of view of each camera. Moreover, when the distance between the object and the camera is large, it is necessary to increase the distance between the cameras in order to reduce the measurement error. For this reason, when photographing an object moving at high speed using a plurality of cameras, it is necessary to predict in advance the movement path of the object.

  On the other hand, when shooting a projectile such as a missile by a conventional method using a single camera, the speed sufficient to follow the projectile in order to shoot the project at different positions sufficiently separated. It is necessary to move the camera. That is, it is necessary to move the camera in the same direction as the flying object at the same speed as the flying object. For this reason, even in the case of shooting a flying object by moving a single camera, it is necessary to predict in advance the moving direction of the flying object.

  Therefore, an object of the present invention is to make it possible to easily measure the spatial position of a projectile whose movement direction is uncertain.

A projectile position calculation system according to an embodiment of the present invention includes a launch direction calculation unit and a projectile position calculation unit. The launch direction calculation unit is movement information of a flying object that flies without thrust deflection while maintaining the thrust, and the movement of the flight object is calculated based on the acquisition information at three or more different times by an image sensor. The launch orientation on the horizontal plane of the projectile is calculated by performing approximation to be regarded as uniform linear motion . The flying object position calculation unit calculates the flying object's spatial position based on the shooting direction of the flying object, the shooting direction of the flying object by the image sensor, the spatial position of the image sensor, and the emitting position of the flying object. .
Further, the flying object position calculation method according to the embodiment of the present invention is the capture information of the flying object that flies without deflecting the thrust while maintaining the thrust, and the capture information at three or more different times by the image sensor. Calculating an emission orientation on the horizontal plane of the projectile by performing approximation based on the movement of the projectile as constant velocity linear motion, the emission orientation of the projectile, and the flight by the image sensor Calculating a spatial position of the flying object based on a shooting direction of the body, a spatial position of the image sensor, and a launch position of the flying object.
In addition, the flying object position calculation program according to the embodiment of the present invention causes a computer to function as a launching direction calculation unit and a flying object position calculation unit. The launch direction calculation unit is movement information of a flying object that flies without thrust deflection while maintaining the thrust, and the movement of the flight object is calculated based on the acquisition information at three or more different times by an image sensor. The launch orientation on the horizontal plane of the projectile is calculated by performing approximation to be regarded as uniform linear motion . The flying object position calculation unit calculates the flying object's spatial position based on the shooting direction of the flying object, the shooting direction of the flying object by the image sensor, the spatial position of the image sensor, and the emitting position of the flying object. .

The functional block diagram which shows the structure of the flying body position calculation system which concerns on embodiment of this invention. FIG. 2 is a diagram showing a geometrical positional relationship between a camera and a flying object when shooting a flying object in a state where the camera shown in FIG. 1 is mounted on an aircraft. The figure which projected the positional relationship of the camera shown in FIG. 2 and a project object on the horizontal surface. The figure which shows the definition of the parameter for calculation of the injection direction of a projectile, and a space position. The flowchart which shows the flow at the time of calculating the space position of a flying body by the flying body position calculation system shown in FIG.

  A flying object position calculation system, a flying object position calculation method, and a flying object position calculation program according to an embodiment of the present invention will be described with reference to the accompanying drawings.

(Configuration and function)
FIG. 1 is a functional block diagram showing a configuration of a flying object position calculation system according to an embodiment of the present invention.

  The flying object position calculation system 1 is a system that measures the spatial position of the flying object O by photographing the flying object O that flies without deflecting thrust while maintaining the thrust. For this purpose, the flying object position calculation system 1 includes a camera 2, a navigation device 3, a launching direction calculation unit 4, a flying object position calculation unit 5, an input device 6, and a display device 7.

  The camera 2 is an image sensor provided with an imaging element 2A for imaging the projectile O and an angle detection device 2B for detecting the imaging direction. The angle detection device 2B can be configured by sensors such as an angle sensor and a tilt sensor. The camera 2 can be mounted on the aircraft 8 as an example of a moving body together with the navigation device 3. The navigation device 3 is a device that calculates the spatial position of the mounted aircraft 8. Accordingly, the spatial position of the aircraft 8 and the camera 2 can be calculated by the navigation device 3. The camera 2 and the navigation device 3 may be provided as equipment of the aircraft 8.

  Therefore, the flying object position calculation system 1 includes at least a launching direction calculation unit 4 and a flying object position calculation unit 5. The launching direction calculation unit 4 and the flying object position calculation unit 5 can be constructed by causing the computer 9 to read the flying object position calculation program. In other words, the flying object position calculation program is a program that causes the computer 9 to function as the launching direction calculation unit 4 and the flying object position calculation unit 5. The flying object position calculation program can be recorded on an information recording medium and distributed as a program product.

  However, a circuit may be used to configure the launch direction calculation unit 4 and the flying object position calculation unit 5. The computer 9 is also configured by an electronic circuit. Therefore, if the computer 9 is regarded as a kind of circuit, it can also be said that the launch direction calculation unit 4 and the flying object position calculation unit 5 can be configured by a circuit.

  The camera 2 and the navigation device 3 are provided as components of the aircraft position calculation system 1 as necessary. Also, the camera 2 may be mounted on a mobile object such as a car or a ship. Also in that case, a known position sensor is mounted on the moving body together with the camera 2. Alternatively, the camera 2 may be stationary without being mounted on a moving body. In that case, if the spatial position of the camera 2 is known, the position sensor is unnecessary. Hereinafter, the case where the camera 2 is mounted on the aircraft 8 and the spatial position of the camera 2 is measured by the navigation device 3 will be described as an example.

  As the navigation device 3, an inertial navigation device, a Global Positioning System (GPS) navigation device, and a Doppler radar navigation device are known. The inertial navigation device is a device that detects the spatial position and velocity of a mobile unit mounted using an inertial measurement sensor such as a gyro that detects a change in posture and an accelerometer that detects a change in velocity. The GPS navigation device is a system that detects the spatial position of a mobile unit mounted by receiving radio waves from a plurality of GPS satellites with a GPS receiver. The Doppler radar navigation system is a navigation system that utilizes the fact that the frequency of the reflected beam of a radio wave beam emitted toward the ground changes by the Doppler effect. Further, a navigation sensor such as a radio wave altimeter may be used as the navigation device 3 in combination.

  FIG. 2 is a diagram showing a geometrical positional relationship between the camera 2 and the projectile O in the case of shooting the projectile O in a state where the camera 2 shown in FIG. 1 is mounted on the aircraft 8.

  As shown in FIG. 2, when shooting the moving object O with the camera 2 mounted on the aircraft 8, the projecting object coordinate system centering on the projecting position of the projecting object O and the spatial position of the camera 2 are the center. Sensor coordinate system to be defined. The projectile coordinate system can be defined as a three-dimensional space coordinate system having a north-south axis, an east-west axis, and a vertical axis in the height direction. The sensor coordinate system can also be defined as a three-dimensional space coordinate system having a north-south axis, an east-west axis, and an upper and lower axis in the height direction.

  The spatial position of the camera 2 can be identified by the navigation device 3. On the other hand, the launch position of the projectile O can be obtained in advance by any method. As a specific example, it is possible to identify in advance the launch position of the flying object O by a position detection system using the United States Defense Support Program (DSP) satellite. A position detection system using DSP satellites is a system that transmits coordinates of feature points detected by three or more satellites equipped with an infrared sensor to a ground base station. Of course, other position detection systems can be used to identify the launch position of the projectile O. Alternatively, the launch position of the flying object O may be specified by user observation.

  The projectile O may be launched from a stationary launcher or may be launched from a self-propelled launcher. That is, as long as it is possible to specify the launch position of the flying object O, the launching apparatus of the flying object O may be a stationary facility or a self-propelled launching apparatus. In particular, when the launcher of the projectile O is a stationary installation, the launch position of the projectile O may be known by observation by a DSP satellite or the like. In that case, detection of the launch position of the flying object O can be omitted. On the other hand, even if the launcher of the projectile O is self-propelled, the launch position of the projectile O can be detected with sufficient accuracy by a DSP satellite or the like.

  If the flying object O flies without thrust deflection while maintaining the thrust, the flying object O moves without meandering in the atmosphere. Therefore, the trajectory of the projectile O can be considered to be in the same plane orthogonal to the horizontal plane. Specifically, the trajectory of the flying object O is considered to be in the same plane according to the emitting direction of the flying object O. As an example of a flying object O that flies without thrust deflection while maintaining thrust, missiles that do not have guidance devices such as rockets, rockets that do not carry explosives, and airplanes that fly linearly without meandering, etc. Is mentioned. Airplanes are categorized as fixed wing aircraft with propulsion devices in a narrow sense.

  In particular, rockets with explosives and rockets without explosives often fly at a speed exceeding the speed of sound in order to reach far enough. In the case where the flying object O moves at supersonic speed without thrust deflection while maintaining the thrust in the atmosphere, the trajectory of the flying object O at a predetermined time after the emission time of the flying object O can be regarded as a linear trajectory. it can. The reason is as follows.

When the height H of the projectile O is sufficiently small with respect to the radius of the earth, the surface can be regarded as a plane. Therefore, the equation of motion of the flying object O is expressed by equations (1-1) and (1-2).
dv / dt = −gsinγ + (P / m) cos α _t −D / m (1-1)
v (dγ / dt) = − g cos γ + (P / m) sin α _t (1-2)
However, in Formula (1-1) and Formula (1-2),
v: velocity of flying object O γ: angle of flying path of flying object O with respect to horizontal plane t: time g: acceleration of gravity P: thrust of flying object O m: mass of flying object O α _t : angle of attack of flying object O D : The drag of flying object O. Incidentally, drag D is defined as the product QSC _D dynamic pressure q, the reference area S and the drag coefficient _{C D.}

When the flying object O flies at a speed exceeding the sound velocity, it can be approximated as the attack angle α _t 00 and g / v ≒ 0. Therefore, dγ / dt ≒ 0 in equation (1-2). This means that the time change of the angle γ of the flying object O can be regarded as zero, so that the trajectory of the flying object O can be regarded as a linear trajectory. Even if the velocity of the flying object O is not supersonic in practice, the velocity of the flying object O should be fast enough to be able to approximate the attack angles α _t 0 0 and g / v 0 0. In this case, the trajectory of the flying object O can be regarded as a straight trajectory.

  Furthermore, if the velocity of the projectile O is supersonic or sufficiently fast, the velocity change of the projectile O in a sufficiently short time of 1 second or less can be ignored. Therefore, when a flying object O that flies at supersonic speed or sufficiently high speed, such as a ballistic missile in the fuel combustion stage, is observed at a sufficiently short time interval, the flying object O is tens of seconds after the launch. It can be regarded as a constant velocity linear motion.

  When the trajectory of the projectile O can be considered to be in the same plane orthogonal to the horizontal plane, the spatial position of the projectile O should be expressed with the launch orientation Ω, the flight distance X and the height H as parameters as shown in FIG. Can do. The launch orientation Ω is an angle (azimuth angle) from a reference position of a line segment obtained by projecting the trajectory of the projectile O on a horizontal plane. The flight distance X is the length of a line segment obtained by projecting the trajectory of the projectile O on a horizontal plane. In the example shown in FIG. 2, the north direction of the projectile coordinate system is the reference position of the angle of the emission direction Ω.

  On the other hand, when the flying object O is photographed by the camera 2 mounted on the aircraft 8, the direction of the line segment connecting the camera 2 and the flying object O can be expressed using the azimuth ψ and the elevation angle θ as parameters. The azimuth ψ is an angle formed by a line segment connecting a point obtained by projecting the space position of the flying object O on the ground surface and the space position of the camera 2 and the north-south axis in the sensor coordinate system. The elevation angle θ is an angle between a plane parallel to the east-west axis and the north-south axis in the sensor coordinate system, and a line connecting the spatial position of the camera 2 and the spatial position of the projectile O. That is, the direction of the flying object O photographed by the camera 2 can be represented by the azimuth ψ and the elevation angle θ.

  The azimuth angle 仰 and the elevation angle θ of the flying object O photographed by the camera 2 can be detected by the angle detection device 2B. In particular, a camera 2 has also been developed that automatically calculates the azimuth angle ψ and the elevation angle θ of the flying object O based on the position on the image of the flying object O reflected in the image. In addition, a camera 2 that automatically detects a flying object O reflected in an image by threshold processing or the like has been developed. Therefore, the user inputs the position on the image of the flying object O to the camera 2 by marking the position of the flying object O on the image, or the position on the image of the flying object O by the object detection function of the camera 2 Is automatically detected, the azimuth ψ and elevation angle θ of the flying object O can be calculated.

  The azimuth angle 仰 and the elevation angle θ of the flying object O are geometrically calculated based on the orientation and elevation angle of the central axis of the lens of the camera 2 and the distance and angle from the center of the photographing field on the image of the flying object O Can. Therefore, if at least the azimuth and elevation angle of the central axis of the lens of the camera 2 are detected by the angle detection device 2B, the azimuth ψ and elevation angle θ of the flying object O are geometrically determined based on the image data in which the flying object O is reflected. Can be calculated.

  Therefore, the azimuth ψ and elevation angle θ of the flying object O may be detected by the angle detection device 2B, or the azimuth and elevation angle of the center axis of the lens of the camera 2 may be detected by the angle detection device 2B. Alternatively, the azimuth ψ and elevation angle θ of the flying object O may be calculated separately based on the image data in which.

  Also, if the projectile O is photographed with a size sufficiently large relative to the size of the field of view, or if the projectile O is photographed near the center of the field of view, the azimuth of the central axis of the lens of the camera 2 And the elevation angle can be regarded as the azimuth ψ and the elevation angle θ of the flying object O. In that case, the azimuth and elevation angle of the center axis of the lens of the camera 2 detected by the angle detection device 2B can be regarded as the azimuth ψ and elevation angle θ of the flying object O. In this case, the process of detecting the projectile O from the image data and the specification of the position of the projectile O on the image become unnecessary.

  Therefore, as a method of determining the shooting direction of the flying object O represented as the azimuth angle 仰 and the elevation angle θ of the flying object O, the image data in which the flying object O is reflected, the direction of the central axis of the lens of the camera 2 and the elevation angle There are a method for obtaining the shooting direction of the flying object O more accurately and a method for regarding the azimuth and elevation angle of the central axis of the lens of the camera 2 as the shooting direction of the flying object O. In the latter case, since the image data of the flying object O itself is unnecessary, it is only necessary that the capturing information of the flying object O is recorded in the camera 2 as the lens direction of the camera 2.

  The launching direction calculation unit 4 and the flying object position calculation unit 5 are configured so that the flying object O is based on the spatial position of the camera 2, the azimuth ψ and elevation angle θ of the flying object O photographed by the camera 2, and the launching position of the flying object O. It has a function to calculate the spatial position of the flying object O by performing approximation with constant velocity linear motion locally.

  The emitting direction calculation unit 4 has a function of calculating the emitting direction Ω on the horizontal plane of the flying object O based on the capture information of the flying object O at three or more different times by the camera 2. The launch direction Ω of the flying object O is geometrically calculated based on the captured information of the flying object O corresponding to three or more different times by performing an approximation that regards the movement of the flying object O as a constant velocity linear motion. can do.

  The flying object O may be photographed by a plurality of cameras 2 or may be photographed by a single camera 2. That is, the launch direction Ω of the flying object O can be calculated based on the capturing information of the flying object O by the single camera 2 or can be calculated based on the capturing information of the flying object O by the plurality of cameras 2. You can also.

  Various methods can be considered as a method for calculating the launch direction Ω of the flying object O. Here, the flying object O is launched based on image data of at least three frames of the flying object O taken by the camera 2 at different times. Based on the first method for calculating the azimuth Ω, the shooting direction of the flying object O expressed as the azimuth ψ and the elevation angle θ of the flying object O, the spatial position of the camera 2 and the launch position of the flying object O. The second method of calculating the launch direction will be described.

  First, the first method will be described. The first method can be used when the camera 2 can be regarded as stationary.

  FIG. 3 is a diagram in which the positional relationship between the camera 2 and the flying object O shown in FIG. 2 is projected on a horizontal plane.

  When the trajectory of the flying object O is in the same plane perpendicular to the horizontal plane, when the trajectory of the flying object O is projected onto a horizontal plane of an arbitrary height, the launch position of the flying object O is the starting point as shown in FIG. It becomes a straight track. Further, the launch orientation Ω of the projectile O is the azimuth angle of the linear trajectory on the horizontal surface, that is, the angle between the linear direction and the north direction which is the reference direction.

  When the projectile O is photographed at different times by the camera 2, the projectile O flying in different spatial positions can be photographed. For example, as shown in FIG. 3, the projectile O moves from position A to position B on the horizontal surface when a certain time elapses, and moves from position B to a position C after a certain time elapses. Therefore, the flight object O flying on the position A, the position B and the position C on the horizontal plane can be imaged by the imaging element 2A of the camera 2.

  Then, if it can be considered that the camera 2 is at rest, the projectile O at the position A, the position B and the position C is projected to the position A ′, the position B ′ and the position C ′ of the imaging device 2A, respectively. . That is, the position A, the position B and the position C of the projectile O are projected in the projection directions connecting the position A, the position B and the position C of the projectile O and the focal point of the camera 2. As a result, the position A, the position B and the position C of the projectile O are projected to the position A ′, the position B ′ and the position C ′ of the imaging device 2A, respectively.

  When the flying object O is photographed at three different positions A, B, and C with the camera 2 that can be regarded as stationary, the position A ′, position B ′, and position C ′ of the flying object O projected onto the image sensor 2A. It is possible to geometrically calculate the launch direction Ω in the horizontal plane of the flying object O based on the above. Specifically, the distance A′B ′ between the position A ′ and the position B ′ of the flying object O projected on the image sensor 2A, and the distance between the position B ′ and the position C ′ of the flying object O. Based on the ratio of B′C ′ (A′B ′ / B′C ′), the launch orientation Ω of the flying object O can be calculated as follows.

  If the projectile O at three positions A, B and C is photographed at a sufficiently short imaging interval so that the change in velocity of the projectile O can be ignored, the projectile O performs uniform linear motion as described above. Can be considered. In other words, if the shooting interval of the flying object O is set so that the speed change of the flying object O becomes a predetermined rate or less, the motion of the flying object O is approximated as a constant-velocity linear motion with accuracy according to the rate of speed change. can do.

  When the motion of the projectile O can be regarded as uniform linear motion, if the image data of the three frames of the projectile O at the position A, the position B and the position C are photographed at equal intervals, The distance AB and the distance BC between the position B and the position C are equal to each other.

  However, the distance A′B ′ between the position A ′ and the position B ′ projected onto the imaging device 2A and the distance B′C ′ between the position B ′ and the position C ′ are not necessarily equal. The distance A′B ′ and the distance B′C ′ are equal only when the trajectory of the projectile O on the horizontal plane is parallel to the plane of the imaging device 2A. On the other hand, when the flying object O is away from the camera 2, the distance A'B 'is longer than the distance B'C'. Conversely, when the flying object O approaches the camera 2, the distance A'B 'is shorter than the distance B'C'.

  That is, the ratio (A′B ′ / B′C ′) between the distance A′B ′ and the distance B′C ′ is uniquely determined corresponding to the launch direction Ω. Therefore, by measuring the ratio (A'B '/ B'C') of the distance A'B 'and the distance B'C', the launch orientation Ω can be geometrically calculated. For example, if the ratio of distance A'B 'to distance B'C' (A'B '/ B'C') is 1, then the launch orientation Ω of the projectile O is equal to the orientation of the camera 2 in the horizontal plane become. The ratio of the distance A′B ′ to the distance B′C ′ (A′B) depends on whether the angle difference between the azimuth of the camera 2 on the horizontal plane and the launch azimuth Ω of the flying object O is the positive direction or the negative direction. '/ B'C') will increase or decrease proportionally from 1.

  Therefore, the relationship between the distance A'B 'and the distance B'C' (A'B '/ B'C'), the orientation of the camera 2 and the launch orientation Ω of the flying object O are obtained in advance, The launch azimuth Ω can be calculated based on the relational expression for calculating the launch azimuth Ω using the ratio of A′B ′ to the distance B′C ′ (A′B ′ / B′C ′) and the orientation of the camera 2 as parameters. it can. The orientation of the camera 2 can be acquired by the angle detection device 2B.

  Practically, the distance A′B ′ and the distance B′C ′ can be measured as the movement distance of the projectile O displayed on the image enlarged and displayed on the display device 7 at a predetermined magnification. In this case, the enlargement ratio of the display image is also used for calculating the launch direction Ω.

  The movement distance of the projectile O may be measured by the user visually and manually input to the launch direction calculation unit 4 or may be automatically detected by the launch direction calculation unit 4. Alternatively, the user may observe the images of a plurality of frames displayed on the display device 7 to check the position of the projectile O by visual observation, and the position of the projectile O may be marked by the operation of the input device 6. In that case, the moving direction of the flying object O can be calculated as the distance between the plurality of marking positions input as the position of the flying object O by the operation of the input device 6 in the emitting direction calculation unit 4.

  When the emission direction calculation unit 4 automatically detects the position of the projectile O and measures the movement distance of the projectile O, known contour extraction processing including processing such as threshold processing and binarization processing Alternatively, the flying object O is automatically detected from image data of a plurality of frames by image recognition processing such as template matching, and the moving distance of the flying object O is determined as a moving distance between frames of representative positions such as the center of gravity of the detected flying object O. Can be calculated.

  The detection of the position of the flying object O and the measurement of the moving distance of the flying object O described above can also be performed by the camera 2. In that case, the detection of the position of the projectile O and the measurement of the movement distance of the projectile O may be automatically performed by the camera 2 or the user may refer to the image displayed on the monitor of the camera 2 May mark the position of the flying object O. When the camera 2 detects the position of the flying object O and measures the moving distance of the flying object O, the result of detecting the position of the flying object O and the measuring result of the moving distance of the flying object O are calculated from the camera 2 as the launch direction. It is transferred to the part 4.

  As described above, the first distance between the first position and the second position of the flying object O projected on the imaging element 2A of the camera 2 and the flying object projected on the imaging element 2A of the camera 2 The second distance between the second position and the third position of O is obtained, and the first distance and the first distance are obtained by performing an approximation that regards the movement of the flying object O as a constant linear motion locally. The launch orientation Ω on the horizontal plane of the projectile O can be calculated on the basis of the ratio between the distance of two.

  In addition, when the imaging | photography time of the flying object O is not equal intervals, the radiation | emission azimuth | direction Ω can be similarly calculated by multiplying the ratio of imaging | photography time intervals as a coefficient.

  In addition, if the frame rate of the video is set sufficiently large and the shooting interval is shortened, even if the camera 2 is actually mounted on a moving vehicle such as the aircraft 8 and moving, It can be considered that the camera 2 is stationary at the time of shooting.

  In addition, the image data of four or more frames of the projectile O may be continuously photographed, and the calculation accuracy of the emission direction Ω may be enhanced by calculating the average value of the ratio between the projected positions of the projectile O. When the image data of the flying object O is captured as a moving image, the frame rate of the image data generally captured is constant. Since the moving distance of the flying object O per frame on the image is the moving distance of the flying object O per unit time, it is the apparent speed of the flying object O. Therefore, the rate of change of the movement distance of the projectile O between successive frames corresponds to the apparent acceleration of the projectile O.

  In other words, the flying object O, which is considered to be locally moving at a constant linear velocity, moves on the image based on the acceleration obtained from the image using the relationship that the moving object O moves on the image with an acceleration corresponding to the launch direction Ω. The launch orientation Ω of O can be calculated. Therefore, in order to obtain the apparent acceleration of the flying object O, it is necessary to capture image data of three or more frames. Then, when image data of four or more frames is captured, the apparent acceleration of the flying object O can be obtained by fitting.

  Furthermore, each of the flying objects O is photographed using a plurality of cameras 2, and the average of the plurality of launch azimuths calculated based on the image data photographed by the plurality of cameras 2 is used to calculate the launch azimuth Ω. May be increased. Alternatively, the launch azimuth Ω of the flying object O may be calculated by the above-described method based on image data of three or more frames taken at different times by a plurality of cameras 2.

  Next, a second method of more accurately calculating the launch orientation Ω of the projectile O based on the spatial position of the camera 2, the azimuth ψ and elevation angle θ of the projectile O taken from the camera 2 and the launch position of the projectile O A method will be described.

  FIG. 4 is a diagram showing the definition of the launch orientation Ω of the projectile O and parameters for calculation of the spatial position.

As shown in FIG. 4, the center of the projectile coordinate system, which is the launch position of the projectile O shown in FIG. 2, is the longitude λ _O0 , latitude in the earth centered, earth fixed (ECEF) orthogonal coordinate system. It can be represented by a position vector r _O0 (λ _O0 , φ _O0 , h _O0 ) having φ _O0 and height h _O0 as elements. On the other hand, the center of the sensor coordinate system, which is the spatial position at the time t _i of the camera 2 shown in FIG. 2, is a position vector r _Si (λ) having longitude λ _Si , latitude φ _Si and altitude h _Si as elements in the ECEF orthogonal coordinate system It can be represented by _Si , φ _Si , h _Si ).

The ECEF orthogonal coordinate system is an orthogonal coordinate system fixed to the earth with the center of gravity of the earth as the origin. In the ECEF orthogonal coordinate system, the Z _ECEF axis is the rotation axis of the earth, the X _ECEF axis is the direction of the Greenwich meridian perpendicular to the Z _ECEF axis, and the Y _ECEF axis is the direction orthogonal to the X _ECEF axis and the Z _ECEF axis.

Expressions for converting the longitude λ, the latitude φ, and the altitude h into the X _ECEF coordinates, the Y _ECEF coordinates, and the Z _ECEF coordinates in the ECEF orthogonal coordinate system are Expressions (2-1), (2-2), and (2-3). ).
X _ECEF = (N + h) cos φ cos λ (2-1)
Y _ECEF = (N + h) cos φ sin λ (2-2)
Z _ECEF = {N (1-e ² ) + h} sinφ (2-3)
However, in Formula (2-1), Formula (2-2), and Formula (2-3),
N = a / (1-e ² sin ² φ) ^1/2
e ² = 2f−f ²
a: Equatorial plane average radius f: Flatness, WGS 84 (World Geodetic System 1984), which is a GPS reference coordinate system,
a = 6378137m
f = 1 / 298.252923563
It is defined as

When the flying object O is imaged three times at equal intervals in time with the camera 2, the spatial position of the flying object O at the imaging time t _i (i = 1, 2, 3) is the spatial coordinate (X in the ECEF orthogonal coordinate system). It can be represented by a position vector r _Oi (X _Oi , Y _Oi , Z _Oi ) whose elements are _Oi , Y _Oi , Z _Oi ). Position in photographing time _{t i} of the projectile O vector _{r Oi (X Oi, Y Oi} , Z Oi) , as shown in equation (3), the camera 2 in the imaging time _{t i} of the projectile O longitude lambda _Si, A function f (λ _Si , φ _Si) having parameters of latitude φ _Si and altitude h _Si , orientation ψ _i and elevation angle θ _{i of} flying object O viewed from camera 2, and distance d _i between camera 2 and flying object O , H _Si , ψ _i , θ _i , d _i ).
r _Oi (X _Oi , Y _Oi , Z _Oi ) = f (λ _Si , φ _Si , h _Si , ψ _i , θ _i , d _i ) (3)

The function f in equation (3) can be determined geometrically. Specifically, the function f is a flight in the sensor coordinate system represented by the azimuth ψ _i and the elevation angle θ _{i of} the flying object O viewed from the camera 2 and the distance d _i between the camera 2 and the flying object O as elements. This is a function that performs coordinate transformation of the position vector r _{O_Si} (ψ _i , θ _i , d _i ) of the body O and addition of the position vector r _Si (λ _Si , φ _Si , h _Si ) of the camera 2.

Note that on the right side of Expression (3), the azimuth ψ _i and the elevation angle θ _i of the flying object O viewed from the camera 2 can be acquired as angle measurement values, and the position vector r _Si (λ _Si , φ _{Si of the} camera 2 is obtained. , H _Si ) can be obtained from the navigation device 3. Accordingly, the unknown on the right side of Equation (3) is only the distance d _i between the camera 2 and the flying object O at the shooting time t _i of the flying object O. That is, the position vector r _Oi (X _Oi , Y _Oi , Z _Oi ) at the photographing time t _i of the flying object O in the ECEF orthogonal coordinate system represents the distance d _i between the camera 2 and the flying object O as a parameter. Can do.

On the other hand, the spatial position of the flying object O at the imaging time t _i is a position (X _i , H _i ) on a two-dimensional (2D: two-dimensional) plane using the flying distance X _i and the altitude H _i of the flying object O as parameters. ). The 2D plane in which the position (X _i , H _i ) of the flying object O exists is uniquely determined by the launch position (λ _O0 , φ _O0 , h _O0 ) of the flying object O and the launch direction Ω. Therefore, as shown in the equation (4), the space coordinates (X _Oi , Y _Oi , Z _Oi ) of the projectile O in the ECEF orthogonal coordinate system can be expressed by the emission position (λ _O0 , φ _O0 , h _O0 ) of the projectile O And, it is possible to convert into 2D position (X _i , H _i ) by a function g (X _Oi , Y _Oi , Z _Oi , λ _O0 , φ _O0 , h _O0 , Ω) which takes the launch direction Ω as a parameter.
(X _i , H _i ) = g (X _Oi , Y _Oi , Z _Oi , λ _O0 , φ _O0 , h _O0 , Ω) (4)

The function g in equation (4) can be determined geometrically. Specifically, the function g is the position vector _r Oi projectile O in ECEF Cartesian coordinate system _{(X Oi, Y Oi, Z} Oi) position vector in ECEF Cartesian coordinate system indicating the firing position of the projectile O from _{r O0} (Λ _O0 , φ _O0 , h _O0 ) is subtracted to obtain a function for performing coordinate conversion using the launch direction Ω of the flying object O and the longitude λ _O0 and the latitude φ _O0 of the launch position of the flying object O as parameters.

When the spatial coordinates (X _Oi , Y _Oi , Z _Oi ) of the flying object O in the ECEF orthogonal coordinate system of the expressions (3) to (4) are deleted, as shown in the expression (5), the camera 2 and the flying object O And the function h for determining the distance d _i between
d _i = h (λ _Si , φ _Si , h _Si , ψ _i , θ _i , λ _O0 , φ _O0 , h _O0 , Ω) (5)

The unknowns on the right side of the equation (5) are only the launch direction Ω of the flying object O. That is, Expression (5) is an expression representing the relationship between the distance d _i between the camera 2 and the flying object O at the shooting time t _i of the flying object O and the launch direction Ω of the flying object O.

A vector l _i (ΔXo _i , ΔY _Oi , ΔZ _Oi ) representing the moving distance and moving direction of the flying object O between the shooting times t _{i + 1} and t _i of the flying object O is expressed by Expression (6).
l _i (ΔX o _i , ΔY _Oi , ΔZ _Oi )
= R _{Oi + 1} (X _{Oi + 1} , Y _{Oi + 1} , Z _{Oi + 1} ) −r _Oi (X _Oi , Y _Oi , Z _Oi ) (6)

That is, photographing time _{t i} + 1, _{t i} vector representing the moving distance and the moving direction of the projectile O between _{l i} projectile _{O (ΔXo i, ΔY Oi,} ΔZ Oi) is the photographing time _{t i + 1} of the projectile O This is a vector obtained by subtracting the position vector r _Oi (X _Oi , Y _Oi , Z _Oi ) at the shooting time t _i of the flying object O from the position vector r _{Oi + 1} (X _{Oi + 1} , Y _{Oi + 1} , Z _{Oi + 1} ).

Since the flying object O can be regarded as a constant velocity linear motion, Expression (7) is established.
l _{i + 1} (ΔXo _{i + 1} , ΔY _{Oi + 1} , ΔZ _{Oi + 1} )
= L _i (ΔXo _i , ΔY _Oi , ΔZ _Oi ) (7)

Equation (8) can be derived from Equation (6) and Equation (7).
r _O3 (X _O3 , Y _O3 , Z _O3 )
_{= 2r O2 (X O2, Y} O2, Z O2) -r O1 (X O1, Y O1, Z O1) (8)

Substituting equation (3) into equation (8), the linear equations for the distances _{d 1,} d 2, _{d 3} between the camera 2 and the projectile O at each imaging time _{t 1,} t 2, _{t 3} and coefficient Is obtained. Accordingly, the distance _d 1, the formula showing the relation between _{d 2} and a distance _{d 3} (9) is obtained.
d ₃ = k (d ₁ , d ₂ ) (9)

  Furthermore, if equation (5) is substituted into equation (9), a nonlinear equation in which only the launching direction Ω of the flying object O is unknown can be obtained. A non-linear equation having the launch orientation Ω of the projectile O as an unknown can be solved by a known numerical analysis method such as the Newton method. Thereby, the launch direction Ω of the flying object O can be calculated.

That is, the second method of calculating the launch orientation Ω of the flying object O is the spatial coordinates (λ _O0 , φ _O0 , h _O0 ) indicating the launching position of the flying object O, and the camera 2 at the shooting time t _i of the flying object O Geometrically and three-dimensionally based on the spatial coordinates (λ _Si , φ _Si , h _Si ) and the azimuth ψ _i and elevation angle θ _i of the flying object O viewed from the camera 2 at the photographing time t _i of the flying object O. This is a method of calculating the launch direction Ω of the flying object O.

  According to the second method, the launch orientation Ω of the flying object O can be calculated regardless of whether the camera 2 is moving. That is, even when the camera 2 moves, the launching direction of the flying object O can be calculated based on the shooting direction of the flying object O by the moving camera 2 and the spatial position of the moving camera 2.

  When the launch orientation Ω of the projectile O is calculated in the launch orientation calculation unit 4, the launch orientation Ω of the calculated flight object O is given to the projectile position computation unit 5.

The flying object position calculation unit 5 calculates the shooting direction Ω of the flying object O calculated by the shooting direction calculation unit 4, the azimuth ψ _{i of the} flying object O indicating the shooting direction at the shooting time t _i of the flying object O by the camera 2, and the elevation angle. θ _i , spatial coordinates (λ _Si , φ _Si , h _Si ) indicating the spatial position of the camera 2 at the shooting time t _i of the flying object O, and spatial coordinates (λ _O0 , φ _O0 , h indicating the launch position of the flying object O) _It has a function of calculating space coordinates (X _Oi , Y _Oi , Z _Oi ) indicating the space position of the projectile O based on O 0).

Specifically, in the positional relationship shown in FIG. 4, the launch direction Ω of the flying object O, the spatial coordinates (λ _Si , φ _Si , h _Si ) of the camera 2 at the shooting time t _i of the flying object O, the flying object O Substituting the azimuth 角_i and elevation angle θ _{i of} the flying object O seen from the camera 2 at the shooting time t _i and the spatial coordinates (λ _O0 , φ _O0 , h _O0 ) indicating the emitting position of the flying object O into the equation (5) For example, the distance d _i between the camera 2 and the flight object O at the shooting time t _i of the flight object O can be obtained.

Further, the distance d _i between the camera 2 and the flying object O at the shooting time t _i of the flying object O obtained by the equation (5), the spatial coordinates (λ _Si) of the camera 2 at the shooting time t _i of the flying object O, phi _Si, substituting _{h Si)} and orientation [psi _i and elevation theta _i of the projectile O as viewed from the camera 2 at the shooting time _{t i} of the projectile O in equation (3), projectile at photographing time _{t i} O Spatial coordinates (X _Oi , Y _Oi , Z _Oi ) can be calculated.

Further, the spatial position of the flying object O can also be expressed by using the flight distance X _i and the altitude H _i of the flying object O by Expression (4).

As described above, the spatial position of the flying object O can also be calculated regardless of whether the camera 2 is moving. That is, even when the camera 2 moves, the azimuth ψ _i and the elevation angle θ _{i of the} flying object O indicating the shooting direction of the flying object O by the moving camera 2 and the spatial coordinates indicating the spatial position of the moving camera 2. The spatial position of the projectile O in the desired coordinate system can be calculated based on (λ _Si , φ _Si , h _Si )

(Operation and action)
Next, a flying object position calculation method using the flying object position calculation system 1 will be described.

  FIG. 5 is a flow chart showing the flow when calculating the spatial position of the projectile O by the projectile position calculation system 1 shown in FIG.

  First, in step S1, the launch position of the flying object O is specified by an arbitrary method or system. The specified launch position of the flying object O is input to the flying object position calculation unit 5 by operating the input device 6.

  Next, in step S2, the flying object O is imaged by the camera 2. For shooting, the camera 2 installed on the ground so that the flying object O is within the field of view for shooting may be used, or the camera 2 mounted on a moving object such as the aircraft 8 so that the flying object O can be shot. It is good. The projectile O is photographed for at least three frames at a sufficiently short imaging interval so as to be considered as moving with constant velocity linear motion. In other words, the flying object O is photographed at three different points with sufficiently short photographing intervals.

  The azimuth angle 仰 and the elevation angle θ of the flying object O taken from the camera 2 are detected by the angle detection device 2B, and given to the emitting direction calculation unit 4 and the flight object position calculation unit 5. In addition, when the camera 2 used for photographing is mounted on a moving body such as the aircraft 8 and moves, the spatial position of the camera 2 is determined from the position sensor of the navigation device 3 or the like mounted on the moving body. 4 and the flying object position calculation unit 5. Further, when the image data of the flying object O is used for calculating the launching direction Ω of the flying object O, the image data of the flying object O is given from the camera 2 to the launching direction calculating unit 4.

  Transfer of information from the position sensors such as the camera 2 and the navigation device 3 may be performed wirelessly in real time, or may be performed after the return of a moving body such as the aircraft 8. Alternatively, the launching direction calculation unit 4 and the flying object position calculation unit 5 are also mounted on the moving body, and information from the position sensors such as the camera 2 and the navigation device 3 is sent to the launching direction calculation unit 4 and the flying object position calculation unit 5 in real time. It may be transferred.

  Next, in step S3, the emission direction calculation unit 4 performs the first method based on the image data of the projectile O shown in FIG. 3 or the second method based on the geometry data of the projectile O and the camera 2 shown in FIG. The launch direction Ω on the horizontal plane of the flying object O is calculated by the method.

  Next, in step S <b> 4, the flying object position calculation unit 5 obtains the flying object O as the spatial position of the camera 2 from the launching direction of the flying object O calculated by the launching direction calculation unit 4 and the position sensor such as the navigation device 3. The spatial position of the flying object O is geometrically calculated on the basis of the shooting position of the flying object O, the shooting direction of the flying object O acquired from the angle detection device 2B, and the emitting position of the flying object O. When shooting the object O with the camera 2 at rest, the coordinate position of the camera 2 is directly given instead of the spatial position of the camera 2 being given from the position sensor such as the navigation device 3 to the projectile position calculation unit 5 Then, the flying object position calculation unit 5 inputs the imaging position of the image data of the flying object O.

  In other words, the flying object position calculation system 1 as described above regards the movement of the flying object O flying at supersonic speed or sufficiently high speed without performing thrust deflection while maintaining the thrust as local constant velocity linear motion, and By separately acquiring the launch position of the projectile O, the spatial position of the projectile O can be easily measured based on the capture information of the projectile O by the camera 2.

(effect)
For this reason, according to the flying object position calculation system 1, it is possible to measure the spatial position of the flying object O whose flying direction is uncertain with a very simple configuration. Specifically, by approximating according to the characteristics of the flying object O that the trajectory after a certain time of the flying object O flying at supersonic speed without performing thrust deflection while maintaining the thrust is regarded as a linear trajectory, The spatial position of the flying object O can be obtained without performing conventional triangulation.

  For this reason, as in the prior art, the camera is moved at a sufficiently high speed with respect to the velocity of the object to obtain the spatial position of the object moving at high velocity, or the object moving at high velocity is within the shooting field of view. Thus, unrealistic work such as arranging a plurality of cameras at appropriate and sufficiently separated positions is not necessary. In other words, conventionally, it has been difficult to obtain the spatial position of an object whose moving direction is uncertain and moves at high speed by triangulation. However, according to the flying object position calculating system 1, the moving object position can be calculated at high speed in any direction. Even if the flying object O moves, the spatial position of the flying object O can be measured if there is no thrust deflection.

  Further, according to the flying object position calculation system 1, the spatial position of the flying object O can be obtained without relying on triangulation, so the spatial position of the flying object O can be obtained using a single camera 2 .

  For this reason, it is possible to rapidly measure the spatial position of the projectile O even in the case of the projectile O which can be launched in a sudden and uncertain direction such as a ballistic missile. Therefore, the vehicle position calculation system 1 can also contribute to the security of the people and the maintenance of world peace.

  In addition, the flying object O which moves while maintaining the thrust by air resistance in the atmosphere loses the thrust outside the atmosphere. For this reason, the flight object O which arrived out of the atmosphere draws a curvilinear orbit by the gravity of the earth and falls to the earth. Therefore, when the flying object O reaches the outside of the atmosphere, by detecting the completion of combustion of the flying object O, the flying object O is detected by Kepler's law based on the space position and velocity of the flight object O at the completion of combustion. The trajectory to land can be estimated. There is a known method for detecting the end of combustion of the flying object O outside the atmosphere.

  On the other hand, there is a known method for calculating the dropping trajectory of the flying object O based on the spatial position and velocity of the flying object O at the end of combustion. That is, if the spatial position and velocity of the flying object O at the end of combustion are known, the falling trajectory of the flying object O can be calculated by a known method.

  Therefore, the spatial position and velocity of the flying object O at the end of combustion of the flying object O can be estimated based on the spatial position of the flying object O in the atmosphere estimated by the flying object position calculation system 1. Thereby, it is possible to easily calculate the dropping trajectory of the flying object O.

  Although the specific embodiments have been described above, the described embodiments are merely examples and do not limit the scope of the invention. The novel methods and apparatus described herein may be embodied in various other ways. Various omissions, substitutions, and changes can be made in the method and apparatus described herein without departing from the spirit of the invention. The appended claims and their equivalents include such various forms and modifications as are encompassed by the scope and spirit of the invention.

  For example, in the embodiment described above, the case where the image sensor is the camera 2 has been described as an example, but another image sensor such as an infrared sensor that receives infrared light and converts it into an electric signal may be used. In other words, any image sensor that can capture the flying object O can be used.

DESCRIPTION OF SYMBOLS 1 Flying object position calculation system 2 Camera 2A Image pick-up element 2B Angle detection apparatus 3 Navigation apparatus 4 Launch direction calculation part 5 Flying object position calculation part 6 Input device 7 Display apparatus 8 Aircraft 9 Computer O Flying object

Claims (7)

Based on the captured information of a flying object flying without thrust deflection while maintaining the thrust, and based on the captured information at three or more different times by the image sensor , the movement of the flying object is regarded as constant velocity linear motion A launch direction calculation unit that calculates a launch direction on the horizontal plane of the projectile by performing approximation ;
A flying object position calculating unit that calculates the flying object's spatial position based on the shooting direction of the flying object, the shooting direction of the flying object by the image sensor, the spatial position of the image sensor, and the emitting position of the flying object;
A flying object position calculation system. Wherein said firing orientation calculation unit, shooting direction of the flying object, the spatial position and the projectile firing position the flying object according to claim 1 configured to calculate the firing azimuth based on said image sensor Flying object position calculation system. The launch direction calculation unit is projected onto a first distance between the first position and the second position of the flying object projected onto the image sensor of the image sensor, and onto the image sensor of the image sensor. Obtaining a second distance between the second position and the third position of the flying object, and based on a ratio between the first distance and the second distance, the flying object The flying object position calculating system according to claim 1 , wherein the flying object position calculating system is configured to calculate a launch azimuth on a horizontal plane. Wherein said firing orientation calculation unit, based on the acquisition information of the flying object with a single image sensor, according to any one of constituted claims 1 to 3 so as to calculate the firing direction of the projectile Flying object position calculation system. The launch direction calculation unit calculates the launch direction of the flying object based on the shooting direction of the flying object by the moving image sensor and the spatial position of the moving image sensor,
The projectile position calculating unit, said moving said flying object photographing direction and the movement on the basis of the spatial position of the image sensor the projectile according to claim 2 configured to calculate the spatial position of which by the image sensor Flying object position calculation system. Based on the captured information of a flying object flying without thrust deflection while maintaining the thrust, and based on the captured information at three or more different times by the image sensor , the movement of the flying object is regarded as constant velocity linear motion Calculating a launch direction on the horizontal plane of the flying object by approximating ;
Calculating the space position of the flying object based on the shooting direction of the flying object, the shooting direction of the flying object by the image sensor, the spatial position of the image sensor, and the launch position of the flying object;
A flying object position calculation method comprising: Computer,
Based on the captured information of a flying object flying without thrust deflection while maintaining the thrust, and based on the captured information at three or more different times by the image sensor , the movement of the flying object is regarded as constant velocity linear motion A launch direction calculation unit that calculates a launch direction on the horizontal surface of the projectile by performing approximation, a launch direction of the projectile, a shooting direction of the projectile by the image sensor, a spatial position of the image sensor, and A projectile position calculation unit that calculates the spatial position of the projectile based on the launch position of the projectile;
Spacecraft position calculation program to function as.

Images