EP4150298A1

EP4150298A1 - Method and system for generating a map of the probability of a carrier being located by a network of location sensors

Info

Publication number: EP4150298A1
Application number: EP21723710.6A
Authority: EP
Inventors: Hugo SEUTE; Marguerite LACROIX; Nicolas Breuil
Original assignee: Thales SA
Current assignee: Thales SA
Priority date: 2020-05-14
Filing date: 2021-05-04
Publication date: 2023-03-22
Also published as: FR3110232A1; WO2021228618A1; FR3110232B1

Abstract

Computer-implemented method for generating a map of the probability of a carrier being located by a network of a plurality of location sensors En, each having a maximum locating range p _n and a predefined locating precision, the method comprising the steps of: determining (101) a probability of presence of each location sensor E_n depending on its position, for each point M of a given geographic region, i. determining (102) the locating error achieved by the network of location sensors on the basis of the locating precision of each location sensor, ii. determining (103) a probability of being located by the network of location sensors to be equal to the integral, over a set of possible positions of the location sensors E_n, of the product of the probabilities of presence of each sensor E_n, if the locating error achieved by the network is lower than or equal to a predetermined threshold, and to be zero otherwise.

Description

DESCRIPTION

Title of the invention: Method and system for generating a probability map, for a carrier, of being located by a network of location sensors

The invention relates to the field of analysis of detection / location systems such as emitters / receivers of electromagnetic waves or more generally sensors, for example communication devices or radar devices.

[0002] The invention relates more specifically to a method for determining, for an allied platform, the probability of being located with a given precision by an adverse localization system based on radiofrequency transmission / reception means in an area given. The allied platform is, for example, on board an aircraft. Thus, the invention provides decision support for the pilot of the aircraft to determine the travel zones in which he is not likely to be located.

[0003] In the event that the location sensors have a fixed position, it is possible to determine their position, for example by using satellite location means or other means, once and for all before the departure of the aircraft.

[0004] When the opposing location sensors are mobile, this is more difficult because their positions can change between the time of location and the mission of the aircraft.

[0005] Furthermore, the adverse sensors to be located can be on board carriers of various types and in particular which can have variable sizes. For example, large span carriers are generally poorly mobile while medium span carriers may be more mobile.

[0006] During a surveillance mission, the position of the medium-sized adversary sensors is not known with certainty, which contributes to increasing the level of risk of the mission or to preventing overflight of large areas considered to be high. level of risk because with a high probability of the presence of this type of sensor. [0007] The risk zones are generally defined in relation to the ranges of the opposing sensors.

[0008] The general technical problem targeted by the invention consists, for an allied carrier, in estimating geographical areas in which the probability is high of being located with a given precision by opposing equipment having detection and localization capabilities.

[0009] The solutions of the prior art are most often based on the definition of zones of localization risk a priori, according to the assumed positions of the adverse detection / localization systems. The positions of the opposing sensors can be estimated from allied location sensors or by a priori information.

[0010] However, these solutions do not take into account the inaccuracies in the location of the adverse sensors which can lead to the definition of erroneous risk zones. They also do not take into account the phenomena of signal masking by the relief of the terrain.

[0011] Furthermore, these solutions do not take into account the overall location accuracy achieved by a network of opposing sensors either. Indeed, in the presence of a network of several collaborative opposing sensors communicating information with each other, the total location accuracy achieved by the opposing network is not simply dependent on the individual location accuracy of each sensor.

[0012] Indeed, in certain geographic sectors, a merged track resulting from a collaboration between two opposing sensors may be precise enough to precisely locate an allied platform, whereas each track taken individually would not have reached the required precision.

The invention proposes a method making it possible to generate a risk zone map corresponding to zones in which an allied platform is likely to be located, with a given precision, by an adverse system comprising several detection / localization sensors .

The invention takes into account the complementarity of several location sensors organized in a cooperative network as well as the relief of the terrain in order to best define the risk zones. The invention relates to a method, implemented by computer, for generating a probability map, for a carrier, of being located by a network of several location sensors E _n each having a range of maximum localization p _n and a predefined localization precision, the method comprising the steps of:

- Determine a probability of presence of each location sensor E _n as a function of its position,

- For each point M of a given geographical area, i. Determine the location error reached by the location sensor network from the location accuracy of each location sensor, ii. Determine a probability of being located by the network of localization sensors as being equal to the integral, over a set of possible positions of the localization sensors E _n , of the product of the probabilities of the presence of each sensor E _n , if the location error reached by the network is less than or equal to a predetermined error threshold, and is zero otherwise.

In an alternative embodiment, the invention comprises the steps of, for each point M of a given geographical area:

- Determine a covariance matrix associated with the location accuracy achieved by each location sensor En,

- Determine a covariance matrix associated with the location accuracy achieved by the network of location sensors,

- Determine the location error reached by the sensor network from the eigenvalues of the covariance matrix.

According to a particular aspect of the invention, the covariance matrix associated with the location accuracy achieved by each location sensor En is determined from a measurement of the location of the wearer located at point M by the sensor En, and a variance of that measure. According to a particular aspect of the invention, the measurement of the location of the wearer is a measurement of a pair {distance, angle}.

According to a particular aspect of the invention, said covariance matrix is a matrix with infinite eigenvalues if the distance between the point M and the location sensor En is less than the location range p _n .

In an alternative embodiment, the invention further comprises the steps of, for each location sensor En:

- Calculate information representative of the intervisibility between the wearer, located at point M, and the location sensor, taking into account the relief of the terrain,

- Assign said covariance matrix to a matrix with infinite eigenvalues if the carrier and the location sensor are not intervisible.

According to a particular aspect of the invention, the information representative of the intervisibility is determined from a digital model of the terrain by checking whether the line connecting the wearer and the location sensor does or does not intersect with the digital terrain model.

According to a particular aspect of the invention, the covariance matrix associated with the location precision of the location sensor network is equal to the inverse of the sum of the inverses of the covariance matrices associated with the location precision of each localization sensor In.

[0023] In an alternative embodiment, the invention further comprises a step of displaying the map on a viewing interface.

The invention also relates to a system for generating a probability map, for a carrier, of being located by a network of several location sensors Each having a maximum location range p _n and an accuracy. of predefined location, the system being configured to execute the steps of the method according to the invention.

[0025] Other characteristics and advantages of the present invention will emerge more clearly on reading the following description in relation to the following appended drawings. [0026] [Fig. 1] FIG. 1 represents a flowchart detailing the steps for implementing the method according to the invention,

[0027] [Fig. 2] Figure 2 shows a block diagram of the location of a platform located at a point M by a location sensor located at a point E,

[0028] [Fig. 3] FIG. 3 represents a block diagram of the location of a platform from two location sensors EI, E ₂ ,

[0029] [Fig. 4] Figure 4 shows an illustration of the principle of calculating a probability of being located by two location sensors,

[0030] [Fig. 5] Figure 5 is a diagram of a digital terrain model used to calculate intervisibility information between two points,

[0031] [Fig. 6] FIG. 6 represents an example of the probability density of the presence of two location sensors EI, E ₂ ,

[0032] [Fig. 7] FIG. 7 represents an example of a risk zone map corresponding to the two location sensors of FIG. 6,

[0033] [Fig. 8] Figure 8 shows a diagram of a system configured to perform the method according to the invention.

[0034] In the case of an adverse localization system comprising several collaborative sensors that can communicate their location information to each other, the location accuracy of the system does not simply depend on the range of each sensor. This is because in some geographic areas, the merged location information resulting from collaboration between multiple sensors may be more accurate than each individual location information from each sensor.

The location accuracy obtained by a network of location sensors depends on several factors: the possibility for each sensor to detect a target (depending on the range of the sensor and the relief of the terrain), the accuracy of the location measurements and the geometric arrangement of the sensors with respect to the target.

The steps of the method according to the invention are described in Figure 1. We consider a network of N sensors E ^.,., E _N present in an area of interest. This network seeks to locate an M coordinate platform

For each sensor £ _n , the first step 101 of the method consists in determining its probability density of presence f _En (x, y) ·

An estimate of the position of a sensor can be obtained more or less precisely by a conventional passive location method as described in the reference [Wil85]. This estimate is traditionally represented in the form of an ellipse, the axes of which are defined by the covariance matrix, and the center by the geographic coordinates of the estimate.

This location estimate can be provided by one or more sensors, for example a radar sensor, a passive sensor by triangulation, or an imaging sensor of the SAR imaging, visible optical or infrared optical sensor type. The sensors are, for example, on board the platform M or another allied platform.

By assuming a bi-normal distribution, it is possible to represent in two dimensions a map of the probability density of the presence of the sensor via the following relation:

With x = [xi, x ₂ ] ^T the coordinates of the point on the map where we want to evaluate the probability density of presence, m and å respectively the coordinates of the estimated position of the sensor and its covariance matrix associated, provided for example by a passive location method or any other possible method depending on the type of location sensor used.

By carrying out the integration of on tiles of small dimensions (pixels), it is possible to obtain a density map of probability of presence in the form of an image (matrix of pixels) at the desired resolution.

It is considered that there is no correlation between the positions of two separate sensors. The opposing sensors are located on the ground (zero height). In addition, it is considered that each sensor E _n is present with certainty within a closed zone Z _n . This amounts to saying that its presence probability density is zero outside this zone Z _n : ff _z f _En (x, y) dx dy = // _E2 f _En {x, y) dx dy = 1.

Each enemy sensor E _n is capable of estimating the position of the allied platform M, if the following conditions are met:

- The distance between E _n and M is less than or equal to the detection range p _n of the sensor E _n .

- When the influence of the relief is taken into account, there must be intervisibility between E _n and M.

The precision of the location measurements obtained by the sensor E _n on the platform M is defined by:

The angular measurement variance (azimuth) s _0h

The variance of distance measurement s _h

The covariance of the final estimate of the adverse sensor network is considered to result from the merging of the estimates of the N sensors.

For each point M of the area to be mapped, the following steps 102 and 103 are then applied.

Step 102 consists of a location error calculation performed by the sensor network to locate a platform at point M.

Step 103 consists of calculating the probability, for the platform, of being located with a given precision, at point M by the network of sensors.

The reasoning used to describe step 102 applies to a two-dimensional case, taking into account the location errors on distance and azimuth. It can be easily generalized to a three-dimensional case, taking into account in addition the location error in elevation.

First, we do not consider the relief of the terrain.

For a sensor E _n , the covariance matrix associated with the estimation of the position of M by E _n is given by: [0056] å _n = å _¥ otherwise

[0057] With:

Å _¥ a covariance matrix with infinite eigenvalues, such that å _¥ ^c =

0 0 0 0

Where r and Q are respectively the distance and the angle between E _n and M, as illustrated in FIG. 2.

By assuming that the angle and distance measurements are independent from one sensor to another, the covariance matrix of the merged estimate of the N sensors is given by the following relationship:

The mean squared error of the merged estimate is obtained by calculating:

With l _c and l ₂ the eigenvalues of the covariance matrix å.

According to the preceding equations, if we have N sensors, it is possible to construct the function a (E _l ..., E _N ) which gives the mean square error of the merged localization estimate of sensors of positions E, ..., E _N. s: Z ₁ x ... x Z _j -> IR.

The principle of merging covariances of the location estimation by two sensors E1 and E2 is shown in Figure 3.

The location error o (E ₁ ..., E _N ) for the point M is supplied at the output of step 102.

Then in step 103, we calculate, from the location error, a probability of being located at point M by the sensor network with a given precision a _e which corresponds to a standard deviation of measurement distance on the location of point M. The probability, for a platform located at point M, of being located by the network of sensors thus corresponds to the probability that the location estimated by the network of sensors is carried out with a precision lower than a _e .

This probability can be estimated via the following relation:

[0072] P (<j £ s,) = z 's) ds

F _a (s) is the probability density function associated with the average localization error of the sensor network.

By expressing this probability density f _a as a function of the probability density of presence f _E of the sensor network, it is shown that:

R (s £ a _e ) = 0 otherwise

Furthermore, assuming that the sensors are confined to restricted areas Zi, ... Z _n , we deduce that: R (s £ a _e ) = 0 otherwise

FIG. 4 illustrates, for a network of two sensors EI, E ₂ , the calculation of the probability R (s £ a _e ).

In an alternative embodiment, the method according to the invention further comprises a step 104 for calculating intervisibility between each sensor EI, .. E _N and the point M.

The notion of intervisibility corresponds to cases where masking related to the relief can reduce the range of an E sensor in certain areas. There is intervisibility when we can draw a line segment between points E and M without intercepting the terrain.

It is assumed that we have a digital terrain model making it possible to perform a function giving the altitude of the terrain at a point of coordinates (x, y). We denote this function z _DEM (x, y).

The condition of intervisibility between a sensor E of coordinates (. X _E , y _E , z _E ) and a platform located at a point M of coordinates (C _M> ΪM _> ^Z M) can be expressed like the following condition: the points E and M are intervisible if the following relation is respected:

Z _MNT (x _E + k (x _M - x _E ), y _E + k (y _M - y _E )) <z _E + k (z _M - z _E ), for any real number k between 0 and 1.

FIG. 5 represents an example of a digital terrain model and illustrates a situation where the points E and M are not intervisible because the straight line which connects them intercepts the relief.

The intervisibility calculation is taken into account in step 102 to refine the calculation of the covariance matrix å _n which becomes:

[0089] å _n = å _¥ otherwise

In fact, in order to be able to locate a platform at point M, each sensor and point M must be intervisible.

The steps 102,103 of the method are iterated for all the points M that it is desired to map. In the end, we obtain a risk zone map making it possible to define the zones in which a platform is likely to be located with a given precision.

In an alternative embodiment of the invention, in order to limit the complexity of the calculations required to determine the probability R (s <s _q ) for each point M, this calculation can be estimated by means of a method Monte-Carlo using the following algorithm:

[0093] J <- 0

[0094] For each printout k e [1, ..., K]:

For each opposing sensor E _n e [E _l ..., E _N ]:

Drawing a point P _n randomly according to the distribution f _En .

End For.

If s (R _1; ..., P _N ) <a _e :

J <- J + i. [0100] End If.

[0101] End For.

The calculation of the error function s (R _1; ..., P _N ) can be carried out using the following pseudo code:

[0103] Function s (C ₁ , ..., C _N ):

[° ¹⁰⁴ ΐ oo]

[0105] For i e [I, .., N]:

[0106] å _{j <} - calcul_covariance_censeur (X _j )

[0108] End For.

[0109] (li, l ₂ ) eigenvalues (F ^_1 )

[0110] Return | l _c | + | l ₂ |.

[0111] End of Function.

[0112] An example of application of the invention will now be described. In this example, the goal is to determine the areas to avoid so as not to run the risk of being located by a network of opposing sensors. The terrain is not very rugged, for reasons of simplicity we decide here not to take into account the relief.

[0113] In the area of interest are two sensors E ₁ and E ₂ . A geolocation system made it possible beforehand to determine a rough estimate of the position of the sensors. This information on the position is translated by ellipses of uncertainties, characterized by their centers m _{£ i} , m _¾ and their covariances . The sensors E ₁ and E ₂ are located inside the zone of interest Z.

A preliminary phase made it possible to identify these sensors and to determine their characteristics. Here, E ₁ and E ₂ are sensors of the same type, and share identical characteristics: namely their range p, their precision of angular measurement s _q and of distance a _r . In addition, it is estimated that the risk of being located is present for a platform when the network {E ₁ , E ₂ ) estimates the position of the platform with an uncertainty less than a _e . The probability density of the presence of the sensors can be represented in the form of a map, as illustrated in FIG. 6.

By applying the method according to the invention, we obtain the risk zone map defined in Figure 7.

[0117] This map makes it possible to highlight different areas. We first notice that a zone with a high probability of being located exists in the neighborhood of E ₁ and E ₂ . This corresponds to the locations where a single sensor is able to locate the platform precisely.

[0118] Next, a central zone highlights the locations where the fusion of the tracks of the two sensors makes it possible to obtain sufficient precision to locate the platform. In this example, a single sensor would not have achieved this precision. Note that at the very center of this area, the risk is lower: this corresponds to an area for which the geometry between the platform and the opposing sensors makes the fusion of tracks between E ₁ and E ₂ less effective.

[0119] Figure 8 shows a block diagram of an exemplary system 800 configured to implement the invention.

[0120] The system 800 comprises a module 801 for calculating a localization error function of a network of sensors, from data coming from a knowledge base B in particular giving information on the range of the sensors and their location accuracy.

[0121] The system 800 also includes an intervisibility calculation module 802 which interacts with the module 801 by using a digital terrain model MNT.

[0122] The system 800 finally comprises a calculation module 803 which receives LOC location information measured by a location sensor, calculates a probability of the presence of each sensor EI, .. EN then calculates a final probability of being located by the network of opposing sensors. The module 801 outputs a map of areas of risk of being located CZR.

Each of the elements of the system 800 according to the invention can be produced in software and / or hardware form using a processor and a memory. The processor can be a generic processor, a specific processor, an integrated circuit specific to an application (also known under the English name of ASIC for “Application-Specific Integrated Circuit”) or a network of programmable gates in situ (also known under the English name of FPGA for “Field-Programmable Gâte Array”).

[0124] The invention can also be implemented as a computer program comprising instructions for its execution. The computer program may be recorded on a recording medium readable by a processor. Reference to a computer program which, when executed, performs any of the functions described above, is not limited to an application program running on a single host computer. Rather, the terms computer program and software are used herein in a general sense to refer to any type of computer code (e.g., application software, firmware, firmware, or any other form of computer code). computer instruction) which can be used to program one or more processors to implement aspects of the techniques described herein. The computing means or resources can in particular be distributed (“Cloud computing”), possibly according to peer-to-peer technologies. Software code can be executed on any suitable processor (e.g., microprocessor) or processor core, or a set of processors, whether provided in a single computing device or distributed among multiple computing devices (e.g. example such as possibly accessible in the environment of the device). The executable code of each program allowing the programmable device to implement the processes according to the invention can be stored, for example, in the hard disk or in read only memory. In general, the program or programs can be loaded into one of the storage means of the device before being executed. The central unit can control and direct the execution of the instructions or portions of software code of the program or programs according to the invention, instructions which are stored in the hard disk or in the read only memory or else in the other aforementioned storage elements. The executable code can also be downloadable from a remote server.

The computer program can comprise a source code, an object code, an intermediate source code or a partially compiled object code or any other form of program code instructions suitable for implementing the invention in the form of a computer program. [0126] Such a program can have various functional architectures. For example, a computer program according to the invention can be broken down into one or more routines which can be adapted to execute one or more functions of the invention as described above. The routines can be saved together in the same executable file but can also be saved in one or more external files in the form of libraries which are associated with a main program in a static or dynamic way. Routines can be called from the main program but can also include calls to other routines or subroutines.

[0127] All the methods or steps of methods, programs or subroutines described in the form of flowcharts should be interpreted as corresponding to modules, segments or portions of program code which include one or more code instructions for implementing them. logic functions and the steps of the invention described.

[0128] The final probability map CZR can be returned to a user via a graphical interface, for example a display screen or any other equivalent means.

[0129] The system 800 can be carried on board a mobile carrier, for example an aircraft.

[01301 References

[0131] [WN85] R. G. Wiley: Electronic intelligence: the interception of radar signais, Artech House, 1985.

Claims

1. Method, implemented by computer, of generating a probability map, for a carrier, of being located by a network of several location sensors E _n each having a maximum location range p _n and an accuracy of predefined location of a carrier, the method comprising the steps of:

- Determine (101) a probability of the presence of each location sensor E _n as a function of its position,

- For each point M of a given geographical area, i. Determining (102) the location error reached by the location sensor network from the location accuracy of each location sensor, ii. Determine (103) a probability of being located by the network of localization sensors as being equal to the integral, over a set of possible positions of the localization sensors E _n , of the product of the probabilities of the presence of each sensor E _n , if the location error reached by the network is less than or equal to a predetermined error threshold, and is zero otherwise.

2. Method according to claim 1 comprising the steps of, for each point M of a given geographical area:

- Determine a first covariance matrix associated with the location precision reached by each location sensor E _n ,

- Determine a second covariance matrix associated with the location accuracy achieved by the network of location sensors,

- Determine (102) the localization error reached by the sensor network from the eigenvalues of the second covariance matrix.

3. Method according to claim 2, in which the first covariance matrix associated with the location precision reached by each sensor. of location E _n is determined from a measurement of the location of the carrier located at point M by the sensor E _n , and from a variance of this measurement.

4. Method according to claim 3, in which the measurement of the location of the wearer is a measurement of a pair {distance, angle}.

5. Method according to any one of claims 2 to 4 wherein said first covariance matrix is a matrix with infinite eigenvalues if the distance between point M and the location sensor E _n is less than the location range p _n. .

6. Method according to any one of claims 2 to 5 further comprising the steps of, for each location sensor E _n :

- Calculate (104) information representative of the intervisibility between the wearer, located at point M, and the location sensor, taking into account the relief of the terrain,

- Assign said first covariance matrix to a matrix with infinite eigenvalues if the carrier and the location sensor are not intervisible.

7. Method according to claim 6 wherein the information representative of the intervisibility is determined (104) from a digital model of the terrain by verifying whether the line connecting the wearer and the location sensor does or does not intersect with. the digital terrain model.

8. Method according to any one of claims 2 to 7 wherein the second covariance matrix associated with the location accuracy of the location sensor network is equal to the inverse of the sum of the inverses of the covariance matrices associated with the location accuracy of each location sensor E _n .

9. Method according to one of the preceding claims further comprising a step of displaying the map on a viewing interface.

10. System (800) for generating a probability map, for a carrier, of being located by a network of several location sensors E _n each having a maximum location range p _n and a location accuracy. predefined, the system being configured to perform the steps of the method according to any one of the preceding claims.