EP3227716A1 - Procede de determination d'une trajectographie par voie passive d'une source mobile par une methode de triangulation inverse - Google Patents
Procede de determination d'une trajectographie par voie passive d'une source mobile par une methode de triangulation inverseInfo
- Publication number
- EP3227716A1 EP3227716A1 EP15804814.0A EP15804814A EP3227716A1 EP 3227716 A1 EP3227716 A1 EP 3227716A1 EP 15804814 A EP15804814 A EP 15804814A EP 3227716 A1 EP3227716 A1 EP 3227716A1
- Authority
- EP
- European Patent Office
- Prior art keywords
- signal
- mobile source
- source
- signals
- arrival
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Withdrawn
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Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S11/00—Systems for determining distance or velocity not using reflection or reradiation
- G01S11/16—Systems for determining distance or velocity not using reflection or reradiation using difference in transit time between electrical and acoustic signals
Definitions
- the field of the invention relates to the reconstruction and / or estimation of a trajectory of a mobile source emitting signals during its displacement. More particularly, the invention relates to the field of methods based on the detection of arrival angles of signals from a source substantially in uniform rectilinear motion. STATE OF THE ART
- TMA Track Motion Analysis
- trajectography There is a first family of so-called “active” trajectories that can be implemented using radars or sonars. The general principle is based on the observer transmitting a signal in a portion of the space and receiving and analyzing signals reflected by a mobile source received by the observer. The available measurement is then a distance-angle pair giving the position of the source relative to the observer.
- passive trajectories that can be implemented by means of sensors receiving signals emitted by a mobile source in order to deduce its trajectory.
- This last family of trajectography has the advantage of allowing an estimation at lower cost while ensuring a maximum of discretion. In addition, they require less energy than active devices.
- the classic hypothesis of the implementation of passive tracking methods is that the source moves in a uniform rectilinear motion also designated by the acronym "MRU".
- Passive tracking methods can be implemented in different ways, depending on the available measurements.
- a passive tracking method is based on measurements of viewing angles of the waves emitted by a source. This method is particularly useful when the sources are in the far field relative to the observer. This configuration frees itself from surface or background reflections. However, it assumes a long observation time, at least 20 minutes. In addition, it requires the observer to change course or speed, so to maneuver, to obtain unambiguously the trajectory of the source.
- This method is particularly interesting for the estimation of source trajectories that are supposed to move rapidly relative to the observer.
- This method which requires the formation of frequency tracks downstream of the spectral analysis, can be implemented only if the signals radiated by the source are emitted in "very narrow band". In all these methods, the propagation time is neglected.
- the aim of the invention is to propose a method of passive trajectography from sight angle measurements of a mobile source S M emitting waves propagating at at least two different propagation speeds.
- the invention makes it possible to obtain, without ambiguity, the trajectory of the source substantially in uniform rectilinear motion with a minimum of angle measurements without the observer having to maneuver or dispose of a pair of geographically separated antennas. It does not require a particular information processing chain such as, for example, differential Doppler frequency line extractors, etc.
- the invention relates to a method for estimating the trajectory of a mobile source in a passive space plane, the mobile source generating at least a first signal and a second signal propagating respectively at two different speeds.
- the method comprises:
- ⁇ acquisition of signals by at least one antenna An estimate of angles of at least four angles of arrival of which at least one angle corresponds to a measurement of the angle of arrival of the first signal, and of which at least one angle corresponds to a measurement of the angle of arrival of the second signal by at least one antenna;
- the estimation of angles comprises: a first estimate of at least three arrival angles of the first signal at three different times by at least a first antenna;
- the estimation method comprises: a first estimation of the arrival angles at a first instant of each of the signals by at least one antenna; A second estimate of the arrival angles at a second instant of each of the signals by at least one antenna; An estimate of at least one position and a velocity vector of the mobile source at a given instant.
- the estimation of angles comprises: a first estimation of a plurality of angles of the first signal at N different times by at least a first antenna;
- the method comprises an estimation of at least two positions of the mobile source at two different times.
- the method comprises estimating the instantaneous position at a time t k by estimating the coordinates of the moving source in a plane and coordinates of its velocity vector from at least four angles d arrival of the received signals, said signals traveling at at least two different propagation speeds.
- the method comprises an estimation of six quantities corresponding to:
- the estimation of a trajectory of the mobile source is determined by integration over a given period of time of at least one estimated instantaneous position of the previously calculated mobile source and a plurality of speed vectors.
- the trajectory of the mobile source is substantially in uniform rectilinear motion on at least a portion of its trajectory.
- the estimation of at least one position of the mobile source is performed by an estimator using the least squares method.
- a calculation of the Cramer-Rao bound is made prior to estimating the trajectory of the source so as to:
- ⁇ collect, based on the estimated performance of new angle measurements, from a new acquisition.
- a calculation of the Cramér-Rao bound is made prior to estimating the trajectory of the source so as to:
- ⁇ collect, based on the estimated performance of new angle measurements, from a new acquisition.
- the calculation of the Cramér-Rao terminal makes it possible to determine at least four values associated with each of the four parameters corresponding to the coordinates of the mobile source in a plane and the coordinates of its velocity vector, each of said lowering values. the standard deviation of each parameter.
- a first signal is an electromagnetic or optical signal, the acquisition of the first signal being performed by an electromagnetic sensor or an optical sensor and the second signal is an acoustic signal, the acquisition of the second signal being performed. by an acoustic detector.
- a first signal is an acoustic signal propagating in a first medium and the second signal is an acoustic signal propagating in a second medium, the difference in propagation velocities of the acoustic waves in the first and second medium being greater than a predetermined threshold.
- the predetermined threshold is defined by a ratio between the difference between the fastest propagation speed and the slowest propagation speed greater than 4.
- the different antennas making it possible to collect angle measurements of the different signals are arranged substantially at the same position of the space.
- At least two antennas making it possible to collect angle measurements of the different signals are arranged at different positions of the space.
- the invention applies to sources emitting in a broad frequency band.
- one advantage is to make and exploit the estimates of angles at the same geographical position in which the different sensors are co-located. This configuration has the advantage of being simple to implement.
- Another object of the invention relates to a system for estimating the trajectory of a mobile source in a passive space plane, characterized in that it comprises:
- At least one first acoustic sensor and a second sensor for detecting waves propagating at the speed of light the two sensors being arranged in the same observation zone, the first sensor and the second sensor detecting a plurality of arrival angles of signals transmitted from a mobile source;
- a memory for storing the arrival angles detected by the sensors and
- a calculator for performing operations for deriving from the arrival angles at least one position in a plane of space and a velocity vector of said moving source Another object of the invention relates to a system for estimating the trajectory of a mobile source in a passive space plane, characterized in that it comprises:
- At least one first acoustic sensor and a second acoustic sensor the two sensors being arranged in the same observation zone, the first sensor and the second sensor detecting a plurality of signal arrival angles emitted from a mobile source, at least two signals being emitted in two different propagation media;
- a memory for storing the arrival angles detected by the sensors and;
- the system of the invention is configured to implement the method of the invention.
- FIG. 1 an example of a trajectory of a mobile source emitting a sound signal and an optical signal
- FIG. 2 the same example of FIG. 1 in which different angles of arrival of the signals are received at the observation point
- FIG. 3 the same example as that of FIG. 1 in which another selection of arrival angles is chosen to determine the trajectory of the mobile source
- FIG. 4 an embodiment representing a Monte Carlo simulation concerning the trajectory of a ship
- FIG. 5 an embodiment representing a Monte Carlo simulation concerning the trajectory of a helicopter
- FIG. 6 an embodiment representing a Monte Carlo simulation concerning the trajectory of an aircraft.
- FIG. 1 represents a trajectory of a mobile source S M , denoted TRAJ (S M ). Two positions POS A1 and POS E1 of the mobile source S M are represented on the trajectory TRAJ.
- the mobile source S M emits one or more signals detected by an observer noted OBS.
- the observer OBS is shown in Figure 1.
- the observer OBS is stationary.
- the invention is not limited to estimating a trajectory of a mobile from a fixed observation point.
- the invention is also applicable to the case of a mobile observer and / or different observation points, each observation point comprising at least one sensor.
- the positional deviations of the sensors are, in this case, taken into account in the method of the invention.
- the observer OBS is materialized by at least one antenna or a sensor capable of receiving at least one signal emitted by the mobile source S M.
- the term "sensor” or “antenna” is used interchangeably inasmuch as the invention relates to any type of signal that can be transmitted by a mobile source S M and detected by the observer.
- the invention is based on the use of measurements of arrival angles of signals coming from the mobile source S M and propagating at different propagation speeds. This difference in propagation speed may be due:
- signals carried by waves of different kinds such as, for example, an acoustic wave and an electromagnetic wave;
- the angle of view of the acoustic signal corresponds to a past position of the moving source S M
- the viewing angle of the signal of the electromagnetic or optical wave corresponds to the instantaneous position of the source.
- the method of the invention takes advantage of the differences in the arrival times of signals emitted by the mobile source so as to determine or estimate the trajectory of the mobile source S M.
- an acoustic signal denoted S A1
- an electromagnetic or optical signal S E1 is emitted by the mobile source S M when it is at POS position E1 .
- an acoustic sensor and a light or electromagnetic sensor located at the observation point OBS capture the acoustic signals S A1 and light or electromagnetic S E1 respectively.
- the angles of arrival ⁇ A1 and ⁇ E1 do not correspond to the same positions of the mobile source S M on its trajectory TRAJ during transmission of said signals.
- the method of the invention makes it possible to determine the portion of the trajectory TRAJ of the mobile source S M by solving a triangulation problem.
- This problem can be solved by considering the triangle formed of a POS 1 past position and an instantaneous position POS 2 of the mobile source S M and a position of an OBS observation point capturing at the same instant t 1 S A1 and S E1 signals from the two positions POS 1 and POS 2 of the mobile source S M.
- the speed of propagation of the signal is the speed of light
- the position of the moving source S M during the emission of the signal and its position when the same signal is detected by the observer OBS are considered to be identical. This approximation comes from the fact that the moving speed of the mobile source S M is negligible in front of the speed of light.
- the x, y coordinates of the position of the moving source S M in the plane at a chosen reference instant, such as, for example, the initial moment, the plane being provided with an orthonormal marker;
- An example of a marker used, especially in the field of the navy, can be defined on the surface of the earth.
- the axes of this landmark can be chosen according to the cardinal points and can correspond to East, North and Altitude. Each of these axes respectively defines the axis of abscissae, ordinates and altitudes.
- the "initial time” is the acquisition date of the first measurement and the “final time” is the acquisition date of the last measurement.
- the estimation of a single position and a plurality of velocity vectors of the mobile source makes it possible to reconstruct the trajectory from the method of the invention.
- the method of the invention remains valid in the 3D case. In this case, six quantities must be calculated or estimated: the coordinates x, y, z of position at a chosen reference instant, such as the initial moment, and the coordinates velocity vector. If the mobile remains at constant height, only the first two velocity coordinates are to be calculated or estimated.
- the calculation of the vector X, necessary for the identification of the trajectory of a mobile source S M requires at least four arrival angles of the signals emitted by the mobile source. At least two signals must propagate at different propagation speeds to form a triangle and allow this calculation unambiguously. According to one embodiment, an advantage is to perform the detection in the same observation position.
- 2 angle measurements of a first signal propagating at a first speed and 2 angle measurements of a second signal propagating at a second speed can be performed.
- the measurements are in this embodiment carried out at least two different times t 1 , t 2 .
- the measurements can be performed at 3 or 4 different times. Each acquisition can thus be performed at a chosen and predetermined time.
- the method of the invention can be realized on a time window during which angle of arrival measurements are made at regular time intervals.
- automatic measurement processing can be performed, for example, by programming measurements with predefined time sampling.
- the quality of the estimation of the trajectory of a mobile source increases with the number of measurements: the size of the confidence region decreases with increasing number of angle measurements used in the trajectory.
- FIG. 2 represents an exemplary case in which four angle measurements are made ⁇ A1 , ⁇ A2 , ⁇ E1 , ⁇ E2 .
- These angles are defined in an orthonormal frame and calculated according to a reference axis. In general, this reference axis is the ordinate axis and the positive direction is the inverse trigonometrical direction.
- the angle ⁇ i is the angle that makes the moving source in its position "i" with N seen from point OBS.
- the signals emitted by the mobile source S M are acoustic signals for the signals S A1 , S A2 and optical signals for the signals S E1 , S E2 .
- the optical signals may correspond, for example, to the image of the moving source S M in the field of view of the observation point OBS.
- the optical and acoustic sensors at the OBS position respectively pick up the signals S A1 and S E1 .
- the position of the mobile source S M corresponding to the transmission of the signal S A1 is denoted POS A1 .
- the position of the mobile source S M corresponding to the transmission of the signal S E1 is denoted POS E1 .
- the determined angles of the respective positions of the mobile source S M are respectively denoted ⁇ A1 , ⁇ E1. Consequently, the three points POS A1 , POS E1 and OBS form the vertices of a first triangle, of which two sides are represented in FIG. 2 by solid lines.
- the optical and acoustic sensors pick up the signals S A2 and S E2 at the position OBS.
- the position of the mobile source S M corresponding to the transmission of the signal S A2 is denoted POS A2 .
- the position of the mobile source S M corresponding to the emission of the signal S E2 is denoted POS E2 .
- the determined angles of the respective positions of the mobile source S M are respectively denoted ⁇ A2 , ⁇ E2 . Consequently, the three points POS A2 , POS E2 and OBS form the vertices of a second triangle, the three sides of which are represented in FIG. 2 by dashed lines.
- a measurement of angles of arrival at the observation point OBS of a first signal S A1 propagating at a first speed and three measurements of angles of second signals S E1 , S E2 , S E3 propagating at a second speed can be performed.
- the measurements are, in this embodiment, performed at least three different times noted t 1 , t 2 , t 3 .
- FIG. 3 represents an exemplary case in which four angle measurements are made ⁇ A1 , ⁇ E1 , ⁇ E2, ⁇ E3 . These angles are defined in an orthonormal frame and calculated according to a reference axis. In general, this reference axis is the ordinate axis and the positive direction is the inverse trigonometrical direction.
- the signals emitted by the mobile source S M are acoustic signals for the signal S A1 and optical signals for the signals S E1 , S E2 and S E3 .
- the optical signals may correspond, for example, to the image of the moving source S M in the field of view of the observation point OBS.
- the acoustic signal S A1 is picked up at a time t k , which can be chosen equal to one of the three instants t 1 , t 2 , t 3 to simplify the calculations subsequent to the acquisition of the signals.
- t k is chosen equal to t 1.
- t k may be chosen different from t 1 , t 2 , t 3 .
- the optical and acoustic sensors pick up signals S A1 and S E1 at position OBS.
- the position of the mobile source S M corresponding to the transmission of the signal S A1 is denoted POS A1 .
- the position of the mobile source S M corresponding to the transmission of the signal S E1 is denoted POS E1 .
- the determined angles of the respective positions of the mobile source S M are respectively denoted ⁇ A1 and ⁇ E1. Consequently, the three points POS A1 , POS E1 and OBS form the vertices of a first triangle whose sides are shown in FIG. 2.
- the optical sensor captures the signal S E2 at the position OBS.
- the position of the mobile source S M corresponding to the emission of the signal S E2 is denoted POS E2 .
- the determined angle of this position is noted ⁇ E2 .
- the optical sensor at the OBS position captures the signal S E3 .
- the position of the mobile source S M corresponding to the transmission of the signal S E3 is denoted POS E3 .
- the determined angle of this position is noted ⁇ E3 .
- a certain number of measurements are necessary to find the instantaneous TRAJ trajectory of the mobile source S M in space.
- the trajectory TRAJ of the mobile source S M is then integrated over a longer period.
- the signals are generally detected in the presence of noise, interference or any other phenomenon that interferes with the instantaneous angle measurements.
- the method of the invention makes it possible to take into account, for example, a noise quantization parameter that interferes with measurements and calculations in order to determine the trajectory TRAJ of the mobile source S M.
- This parameter makes it possible, for example, to define the number of measurements necessary to reduce the impact of the errors and approximations of the trajectory of the mobile source S M deduced.
- the observer at the origin of the reference, the azimuth and the distance between the observer and the source at time t are given by:
- the principle of the invention is to take advantage of additional azimuth corresponding to an earlier position of the source, the delay being due to the propagation time.
- the method of the invention thus makes it possible to solve the problem of the "non-uniqueness" of the solutions of the system of preceding equations.
- the corresponding system formed of four equations, has a unique solution.
- the method of the invention applies when one has any set of "instantaneous" azimuths and “delayed” azimuths so as to increase the accuracy of the reconstruction of the trajectory of the source mobile when measurements are noisy.
- the method of the invention applies when two signals propagate at different propagation speeds from the mobile source S M whose path is sought.
- it may be waves of different natures such as electromagnetic or light waves and acoustic waves.
- it may be waves of the same nature but propagating in different environments such as acoustic waves propagating in water and air.
- a first approximation consists in considering that the propagation delay of the signal propagating at the speed of light is negligible vis-à-vis the propagation delay of the signal propagating at the speed of sound.
- the angle of arrival of a propagating wave with a velocity lower than the speed of light is defined.
- the speed of the delayed wave corresponds to the speed of sound.
- the state vector X can be expressed as
- the estimator is that of the maximum likelihood, or equivalently that of the least squares when the noises are additive and Gaussian.
- ⁇ m (t k ) and ⁇ D, m (t k ) are respectively the instantaneous azimuth and the delayed azimuth measured at time t k
- ⁇ and ⁇ D are their respective standard deviations.
- These standard deviations can be determined by a predetermined numerical value as a function of the sensors used, the type of noise or even feedback from previous measurements. It is determined for a given configuration. These values are chosen during the configuration of the process of the invention. They can be, if necessary, adapted according to the changes of configurations.
- an algorithm such as the Gauss-Newton can be used to achieve the estimated vector X that minimizes the criterion C (X).
- the Cramér-Rao bound gives the asymptotic performances of the estimator and allows to build a confidence domain of the trajectory estimated from the measurements of angles of arrival.
- the Cramér-Rao bound is calculated by inverting the Fisher information matrix.
- the Fisher F (X) matrix is given by:
- trajectory TRAJ of the mobile source S M with i 1, 2, 3, 4:
- the first embodiment concerns the trajectory of a ship (figure 4)
- the second mode concerns the trajectory of a helicopter (figure 5)
- the third mode concerns the trajectory of a ship. plane ( Figure 6).
- an acoustic sensor and an optical capture device are arranged at the observation point OBS and can be used to capture:
- the optical device can be a periscope or a camera.
- a control system is coupled to the optical device and / or the acoustic sensor to take angle measurements at regular periods.
- the initial position of the mobile source S M is:
- the moving speed of the mobile source S M is 5m / s and its heading is 90 °.
- N 225 for each sensor.
- ⁇ CRLB is the asymptotic standard deviation calculated from the Cramér-Rao bound and ⁇ is the empirical standard deviation of the estimator.
- the bias is the difference between the empirical average of the estimator and the vector X. It is given for each of the components of the vector X.
- X init [ 1000, 1000, 0, 0] T.
- the trajectory of the source S M and the ellipses 40 and 41 of confidence are plotted at 90% of the positions estimated at the initial and final instants. These moments correspond to the first and the last moment of capture of the test.
- the 500 positions at the initial instant estimated at the end of the simulation are substantially obtained in the region delimited by the ellipse 40. Only a few estimated positions corresponding to different simulations are represented in FIG. at the initial moment for a better readability of the figure.
- the points obtained at the final moment are not represented in the figure.
- the x-axis represents a distance expressed in meters and oriented towards the East, denoted E.
- the ordinate axis represents a distance expressed in meters and oriented towards North, denoted N.
- a sensor acoustic and radar are arranged at observation point OBS.
- the scenario is defined as:
- T 2 the distances are expressed in meters.
- the moving speed of the mobile source S M is 50 m / s and its heading is 90 °
- the TABLE II table contains the same parameters as those shown in TABLE I of the first example.
- the trajectory of the source S M and the ellipses 50 and 51 of confidence are plotted at 90% of the positions estimated at the initial and final instants. These moments correspond to the first and the last moment of capture of the test.
- the 500 positions at the initial instant estimated at the end of the simulation are substantially obtained in the region delimited by the ellipse 50. Only a few estimated positions corresponding to different simulations are represented in FIG. at the initial moment for a better readability of the figure. The points obtained at the final moment are not represented in the figure.
- the x-axis represents a distance in meters and is oriented towards the East, denoted by E.
- the y-axis represents a distance in meters and oriented towards North, denoted N.
- an acoustic sensor and a radar are arranged at the observation point OBS.
- the initial position of the mobile source is P () [5 2000] T
- T 0 - 00 , the distances are expressed in meters.
- the moving speed of the mobile source S M is 150 m / s. ⁇ The head of the source is 90 °.
- Table TABLE III contains the same parameters as those shown in the tables TABLE I and TABLE II.
- the trajectory of the source S M and the ellipses 60 and 61 of confidence are plotted at 90% of the positions estimated at the initial and final instants. These moments correspond to the first and the last moment of capture of the test.
- the 500 positions at the initial moment estimated at the end of the simulation are substantially obtained in the region delimited by the ellipse 60. Only a few estimated positions corresponding to different simulations are represented in FIG. at the initial moment for a better readability of the figure. The points obtained at the final moment are not represented in the figure.
- the abscissa axis represents a distance expressed in meters and oriented towards the East, denoted E.
- the ordinate axis represents a distance expressed in meters and oriented towards North, denoted N.
- the preceding embodiments make it possible to validate the method of estimating the invention by assessing the proximity of the asymptotic and empirical standard deviations and by the low value of the bias of the estimator relative to the quantities to be estimated.
- the variance parameter can be determined instead of the standard deviation parameter to validate the method of the invention.
- the validations of the estimation method of the invention are verified for different types of mobile sources.
- the method of the invention thus makes it possible to have many applications relating to the estimation of trajectory for many types of sources capable of transmitting transmission signals. different natures or spreading in different environments.
- the method of the invention may include a preliminary step to pre-position the sensors at a given inclination or in a given orientation.
- a device may comprise the elements necessary to perform each of the steps.
- the sensors and antennas used to detect the arrival angles of the signals coming from a mobile source S M can be adapted to predefined types of sources. In this case, selective frequency ranges can be chosen. Another possibility is to choose antennas or "wide-band" sensors with noise filtering modules and signal processing. Any combination of sensors or antennas can be made according to the method of the invention to optimize the detection of signals from a mobile source S M.
- an optical sensor can be combined with one or more ultrasonic sensor (s) or one or more hydrophone (s).
- An electromagnetic antenna may be coupled with one or more ultrasonic sensors or one or more hydrophones.
- An underwater hydrophone and an emergent hydrophone can also be combined.
- filtering and signal processing modules can be applied to the received signals so as to optimize the quality of the detected angle.
- Sensors or redundancy antennas can be used to improve measurement accuracy.
- the receiving antennas may be linear, planar, spherical or geometric shapes imposed by the constraints related to the observer.
- the capture device for implementing the method of the invention may include a calculator for performing calculations corresponding for example to estimation algorithms from measurements made. The calculator makes it possible to determine the estimate of the vector X characterizing the trajectory of the source S M for a set of readings.
- a memory can be used in order to:
- ⁇ save a history of data including the measures used, the calculated estimators and their performance, and / or
- ⁇ perform processing operations in a deferred or real-time manner.
- the data of the various sensors can be collected jointly and indexed so as to discriminate the latter during calculation operations.
- the calculator can be configured to automatically execute certain operations in real time.
- an initial configuration makes it possible to define detection parameters including the capture times, the capture time, the accuracy of the measurements, the desired accuracy of the estimator, the number of sensors to be used as well as their type, etc.
- time intervals between each arrival angle measurement of each sensor and / or antenna can be set to synchronously control acquisitions.
- a common clock can be used for this purpose.
- a display can be combined with the device so as to display the estimated trajectory of the mobile source S M and of the trusted regions so that they can be exploited by an operator in real time.
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- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
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- Remote Sensing (AREA)
- Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)
- Position Fixing By Use Of Radio Waves (AREA)
Abstract
Description
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Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
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FR1461970A FR3029641B1 (fr) | 2014-12-05 | 2014-12-05 | Procede de determination d’une trajectographie par voie passive d’une source mobile par une methode de triangulation inverse |
PCT/EP2015/078715 WO2016087661A1 (fr) | 2014-12-05 | 2015-12-04 | Procede de determination d'une trajectographie par voie passive d'une source mobile par une methode de triangulation inverse |
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EP3227716A1 true EP3227716A1 (fr) | 2017-10-11 |
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EP15804814.0A Withdrawn EP3227716A1 (fr) | 2014-12-05 | 2015-12-04 | Procede de determination d'une trajectographie par voie passive d'une source mobile par une methode de triangulation inverse |
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EP (1) | EP3227716A1 (fr) |
FR (1) | FR3029641B1 (fr) |
WO (1) | WO2016087661A1 (fr) |
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DE3204874C2 (de) * | 1982-02-11 | 1994-07-14 | Atlas Elektronik Gmbh | Passives Verfahren zum Gewinnen von Zieldaten von einer Schallquelle |
US20110090762A1 (en) * | 2009-10-21 | 2011-04-21 | Mark Rhodes | Underwater navigation system |
-
2014
- 2014-12-05 FR FR1461970A patent/FR3029641B1/fr not_active Expired - Fee Related
-
2015
- 2015-12-04 WO PCT/EP2015/078715 patent/WO2016087661A1/fr active Application Filing
- 2015-12-04 EP EP15804814.0A patent/EP3227716A1/fr not_active Withdrawn
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FR3029641B1 (fr) | 2019-06-14 |
WO2016087661A1 (fr) | 2016-06-09 |
FR3029641A1 (fr) | 2016-06-10 |
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