Cooperative detection system and method

Abstract

A cooperative detection system (100) is provided, configured to: - estimate (12) a transition rate matrix, for each candidate group of a set of detection devices (2), by performing hidden Markov chain-based learning, from data on activity states of the detection devices (2), the coefficients of the transition rate matrix representing the transition speeds from one activity state to another for each detection device (200) of the associated candidate group, - determine (13) a cooperation metric relating to the entropy of each candidate group from the associated transition rate matrix; - determine (14) at least one grouping (20) of detection devices (200) connected in a network and capable of cooperating with each other, from the cooperation metrics, the cooperative detection system being capable of using each grouping to monitor an area. Abstract: Fig. 2

Description

Title of the invention: Cooperative detection system and method Technical field

[0001] The invention relates generally to detection systems and in particular to a cooperative detection system and method.

[0002] In a given environment, several detection devices, such as for example radar devices, may be present and be required to cooperate with each other for the purposes of the same detection or surveillance mission (common mission) in a surveillance zone.

[0003] This set of detection devices is controlled so as to assign a set of tasks to the different cooperating detection devices which must then execute them in order to achieve the common mission.

[0004] Such control is achieved by using execution logic that governs the various cooperating detection devices. This distributed execution logic across the various detection devices must be more efficient than if each detection device operated in isolation and independently of the others.

[0005] In existing solutions, the selection of detection devices that must cooperate together to carry out a surveillance mission is carried out by an operator and is therefore not optimized.

[0006] There is thus a need for an improved cooperative detection system and method.

[0007] General definition of the invention

[0008] For this purpose, a cooperative detection system is proposed comprising a detection assembly for monitoring a surveillance zone, the detection assembly comprising a plurality of detection devices. Advantageously, the detection system comprises:

[0009] - a transition rate matrix determination unit configured to estimating a transition rate matrix, for each candidate group among one or more candidate groups of detection devices of the set, by performing a learning phase based on hidden Markov chains (HMM), from an initial data set indicating activity states of the detection devices of the detection set previously detected and a modeling of the detection set, the transition rate matrix of a candidate group comprising coefficients, each representing a transition speed from one activity state to another for each detection device of the associated candidate group,

[0010] - a unit for determining group characteristic quantities configured to determine a set of characteristic quantities for each group candidate from the transition rate matrix obtained for the candidate group, the set of group characteristic quantities comprising at least one cooperation metric relating to an entropy determined for the candidate group;

[0011] - a grouping determination unit configured to determine at least a grouping of detection devices from the set of group characteristic quantities determined for each candidate group, a detection grouping comprising at least two detection devices connected in a network and capable of cooperating with each other.

[0012] The cooperative detection system being capable of using a determined grouping for monitoring the surveillance zone.

[0013] In embodiments, a coefficient of the transition rate matrix has a first index corresponding to a starting state and a second index corresponding to an arrival state, the transition rate matrix being a square matrix, the dimension of the transition rate matrix associated with a candidate group of size R being defined by the total number £ R of possible activity states for all the R detection devices of the candidate group, each detection device having a number L of activity states.

[0014] According to certain aspects, the system may further comprise a state chaining rules determination unit configured to determine state chaining rules for each determined grouping, from the transition rate matrices determined by the transition rate matrix determination unit for the candidate groups comprising at least one detection device of the grouping and a weight associated with the transition rate matrices, the state chaining rules determined for a grouping defining the activity state transitions of the detection devices of the grouping, the cooperative detection system being able to control each determined grouping for the monitoring of the monitoring zone, according to the state chaining rules determined for the grouping.

[0015] The monitoring area may be located around the detection devices of the detection assembly.

[0016] In embodiments, the group characteristic value determination unit may be configured to determine a probability matrix from the transition rate matrix associated with a candidate group, by normalizing the non-diagonal terms of each row of the transition rate matrix so that their sum is unity, which provides a probability vector Ç- for each row i of the transition rate matrix, comprising probability values, each corresponding to one of the terms of row * of the transition rate matrix, except for the diagonal term, said probability values ​​of the vector of

[0017]

[0018] probabilities Ç- obtained for a rowz representing the probabilities of transitions to an arrival state, the probability vectors Çz obtained for all the rows of the transition rate matrix forming the rows of said probability matrix n, the cooperation metric relating to an entropy of the candidate group being calculated from the probability matrix. The calculation of the cooperation metric relating to an entropy of the candidate group may comprise, for each row z of the probability matrix, the determination of an entropy value, the entropy values ​​determined for the different rows of the probability matrix forming an entropy vector H comprising entropy values ​​h{ associated with each row 1 of the probability matrix fl, the cooperation metric relating to an entropy of the candidate group being determined from the entropy vector H. In embodiments, the entropy value associated with a row of the probability matrix n may be a Shanon entropy, determined according to the following equation _ y7V-l ni~ ~^k^PikmPik

[0019] According to one aspect, the cooperation metric may be an entropy average calculated by averaging the components of the entropy vector H, weighted by applying a weighting coefficient aj to each component hj of the entropy vector H.

[0020] Cooperative detection system according to claim 8, in which the weighting coefficients aj constitute the components of an average stationary state vector 7 defined by:

[0021] it ?; = râexp(rAf

[0022] where n denotes the dimension of the transition rate matrix M and r is a parameter representing a time value.

[0023] The time parameter T can be equal to T — ] (px max( À- ) ' denoting the eigenvalues ​​of the transition rate matrix.

[0024] The set of group characteristic values ​​can be a triplet of values ​​comprising the list Lq of the detection devices of the candidate group G^, the average entropy < Hq >, and the number of measurements Kg used to calculate the transition rate matrix.

[0025] In one embodiment, the clustering determination unit may be capable of generating a representation of the candidate clusters selected from the detection set comprising n detection devices, in the form of a system mechanical, in the representation space of dimension n- 1, from the triplet of values ​​determined for each candidate group {Lq, ( Hq ), Æç], and in which:

[0026] - each detection device of a candidate group is represented by a point in the representation space,

[0027] - for each candidate group comprising a list Lq of p devices of detection 200, the mechanical system comprises p elastic links connecting the representative points of the detection devices of the candidate group to the center of a hypersphere circumscribed at the p points, in the representation space;

[0028] - The empty length1 of the p elastic bonds is defined by the average entropy (Hq);

[0029] - the elastic stiffness constant & of the p elastic bonds is proportional to the Kq number.

[0030] According to certain aspects, the mechanical system may further comprise elastic damping type friction forces or fluid brake type friction forces relating to friction coefficients chosen to bring the mechanical system into a stable state.

[0031] In embodiments, the grouping unit may be capable of evolving the mechanical system toward a stable state by implementing a resolution of a differential system associated with the equations that govern the mechanical system.

[0032] According to aspects, the clustering unit may be able to determine at least one clustering of detection devices by applying a clustering algorithm to the mechanical system using the distance between representative points of the detection devices in the mechanical system, in the steady state.

[0033] Further provided is a cooperative detection method for monitoring a surveillance area using a detection assembly comprising a plurality of detection devices. The method comprises the steps of:

[0034] - determine one or more candidate groups of detection devices the detection set,

[0035] - determine a transition rate matrix for each candidate group in performing a learning phase based on hidden Markov chains (HMM), from an initial data set indicating activity states of the detection devices of the detection set previously detected and a modeling of the detection set, the transition rate matrix of a candidate group comprising coefficients, each coefficient representing a transition speed from one state to another for each detection device of the associated candidate group,

[0036] - determining a set of group characteristic quantities for each candidate group from the transition rate matrix obtained for the group candidate, the set of group characteristic quantities including at least one cooperation metric relating to an entropy calculated for the candidate group;

[0037] - determine at least one grouping of detection devices from the set of group characteristic quantities determined for each candidate group, a detection grouping comprising at least two detection devices connected in a network and capable of cooperating with each other.

[0038] The cooperative detection method being capable of using each determined grouping for monitoring the surveillance zone. Brief Description of the Figures

[0039] Other characteristics, details and advantages of the invention will emerge on reading the description given with reference to the appended drawings given by way of example and which represent, respectively:

[0040] [Fig-1] - [Fig.l] represents a cooperative detection system according to modes of realization.

[0041] [Fig.2] - [Fig.2] represents a control device, according to embodiments.

[0042] [Fig.3] - [Fig.3] is an example of an activity state observation table obtained from an observed data set.

[0043] [Fig.4] - [Fig.4] illustrates an example of dividing the state observation table into state sub-matrices.

[0044] [Fig.5] - [Fig.5] illustrates the generation of transition rate matrices from the two state sub-matrices obtained in the example of [Fig.4].

[0045] [Fig.6] [Fig.6] shows state transition diagrams obtained from the two examples of transition rate matrices of [Fig.4].

[0046] [Fig.7] - [Fig.7] illustrates the calculation of the average entropy for a first candidate group of a set of detection devices.

[0047] [Fig.8] - [Fig.8] illustrates the calculation of the average entropy for a second candidate group of the same set of detection devices as that of [Fig.7].

[0048] [Fig.9] - [Fig.9] illustrates the calculation of the average entropy for a third candidate group of the same set of detection devices as that of [Fig.7].

[0049] [Fig. 10] - [Fig. 10] illustrates the calculation of the average entropy for a fourth candidate group of the same set of detection devices as that of [Fig.7].

[0050] [Fig. 11] - [Fig. 11] is an example of a mechanical system used to model the detection assembly from the group characteristic quantities calculated for the candidate groups.

[0051] [Fig. 12] - [Fig. 12] represents the mechanical system of [Fig. 11] after relaxation.

[0052] [Fig. 13] - [Fig. 13] is a flowchart representing the detection process cooperative according to embodiments.

[0053] [Fig. 14] - [Fig. 14] illustrates a step in the determination of the logic of state chaining of a grouping, according to an example of implementation.

[0054] [Fig. 15] - [Fig. 15] illustrates another step in determining the logic of state chaining of a grouping, according to the example of realization of [Fig.14],

[0055] Detailed description of the application

[0056] [Fig.l] represents a cooperative detection system 100 comprising a detection assembly 2 comprising a plurality of detection devices 200 (at least two).

[0057] The cooperative detection system 100 is configured to determine one or more groupings of detection devices 200, a grouping comprising at least two networked detection devices 200 capable of cooperating with each other to carry out a surveillance mission in a surveillance zone. The surveillance zone may for example be located around the detection devices 200 (for example in an airspace zone).

[0058] The cooperative detection system 100 implements active monitoring. Thus, each detection device 200 emits electromagnetic waves (which may be radiofrequency or optical waves) or acoustic waves, and is configured to deduce therefrom the presence of an object (detect an object or more generally a target) in its detection zone based on the signal received in return.

[0059] A detection device 200 may be, for example, a radar or sonar device.

[0060] The detection assembly 2 may for example comprise a plurality of radar devices 200 on the ground which cooperate to observe the sky (surveillance mission).

[0061] The remainder of the description will be made mainly to an application of the invention to radar type detection devices 200, by way of non-limiting example.

[0062] A detection device 200 has an activity state which may be an active state ('ON') in which the detection device is transmitting or an inactive state ('OFF') otherwise.

[0063] The cooperative detection system 100 comprises a control device 1 configured to control the cooperation between the different detection devices 200 of the detection assembly to carry out the surveillance mission in the surveillance zone. The control device 1 is configured to determine at least one grouping of detection devices 200 from a set of state data 3 collected (i.e. observed or detected) by at least one observer at different past times, to determine a state chaining logic for each grouping (also called 'state chaining rules') and to control the detection devices 200 of a grouping 20, according to the sequence logic determined for the grouping to carry out the surveillance mission in the surveillance zone.

[0064] The control device can be arranged at any suitable location and is capable of communicating with the various detection devices 200 of the detection assembly 2.

[0065] A detection device (in transmission mode) 200 of the set 2 in fact transmits waves that an observer (i.e. receiver device) can intercept to identify information on the state of the detection device 200 at different past times. When the observer is in sufficient proximity, he can obtain, for each detection device 200 which is in transmission, an associated timing diagram indicating the activity state (“active” or “inactive”) of the detection device 200. The timing diagram can be a sequence of Boolean elements (of the true / false type) over time. If the observer moves over time (for example receiver mounted in an aircraft), his distance from the different detection devices 200 fluctuates, so that the Boolean information on the activity state of the detection devices is not always available.Indeed, non-detection does not necessarily mean that the emitting detection device is inactive and may indicate that it is out of range. In this case, the detection information obtained by the observer at this time is information of non-availability of the information. Thus, the state data set used by the control device 1 (and resulting from the observations collected by at least one observer at different times) may comprise different values ​​relating to the state of activity of each detection device 200 of the set 2, corresponding to different past detection times. A value relating to a state of activity is thus associated with a given detection device 200 and a detection time and may take a value from among: .

[0066] - a first value VI indicating an activity state (or “ON” state) of the device (ie indicating that the detection device is in operation or switched on);

[0067] - a second value V2 indicating an inactivity state (“or OFF state”) of the device (ie indicating the detection device is off); or

[0068] - a third value V3 indicating information on the unavailability of the state activity when the activity state of the device could not be determined at the time in question. The third value V3 thus indicates an indeterminate state characterizing the absence of information, which can be noted for example 'N / A' (Not Available) or NaN (Not a Number). In the remainder of the description, the third value will be designated by "NaN" as a non-limiting example.

[0069] [Fig.2] schematically represents the control device 1 according to certain embodiments.

[0070] The control device 1 comprises a modeling unit 10 capable of providing a modeling of the detection assembly 2 comprising n detection devices 200 in the form of a macro-system passing from one state to another as soon as a detection device 200 switches from the active state ('ON') to the inactive state ('OFF') or vice versa.

[0071] The modeling unit 10 is capable of providing a modeling of the sequence of operating states of a given detection device 200 in the form of a state observation table.

[0072] A detection device 200 may have a target search type operating mode, in which the detection device 200 is configured to detect a target (object for example) in the monitoring zone, and a tracking type operating mode, in which a detection device 200 measures the coordinates of a detected target and uses the measured information to determine the trajectory of the target and / or predict its future position.

[0073] Advantageously, the control device 1 is configured to perform this modeling of the sequence of operating modes not from the point of view of a single detection device 200 considered in isolation but from the point of view of the cooperation between the different detection devices 200 of the detection assembly 2. The embodiments of the invention advantageously use hidden Markov chains (HMM, acronym for the corresponding English expression 'Hidden Markov Model') to control the cooperation (or collaboration) between several detection devices 200 of the detection assembly 2 and determine at least one grouping of detection devices 200.

[0074] The control device 1 further comprises a transition rate matrix determination unit 12 configured to determine a transition rate matrix Mq, for each candidate group among one or more candidate groups Gq of detection devices 200 of the set 2, by performing a learning phase based on hidden Markov chains (HMM), from the data set 3 indicating observations of activity states of the detection devices of the detection set 2 (activity states previously detected at different previous times) and from the modeling of the detection set 2 provided by the modeling unit 10. The learning phase based on hidden Markov chains (HMM) comprises a data sampling step which can be at variable time step or at constant time step.

[0075] The transition rate matrix of a candidate group G^ comprises coefficients, each coefficient representing a transition rate from one state to another determined for the associated candidate group. A coefficient of the transition rate matrix has a first index corresponding to a starting state (row index for example) and a second index corresponding to an arrival state (column index for example).

[0076] The control device 1 also comprises a group characteristic value determination unit 13 configured to determine a set of characteristic values ​​for each candidate group Gq from the transition rate matrix Mq obtained for the candidate group Gq. The set of group characteristic values ​​may be a P-tuple comprising at least one quantity relating to a calculated entropy (also called 'cooperation metric') for the candidate group Gq. In one embodiment, the cooperation metric may be an average entropy. The P-tuple may then be, for example, a triplet of values ​​(P=3) comprising the list Lq of the detection devices 200 of the candidate group Gq, the average entropy < Hq > and the number of states Kq associated with the transition rate matrix Mq (total number of possible states of the candidate group corresponding to the transition rate matrix).

[0077] The control device also comprises a grouping determination unit 14 (hereinafter also called “grouping unit”) configured to determine at least one grouping of detection devices 200 which belong to the same cooperation network from the set of group characteristic values ​​obtained for each candidate group.

[0078] The control device 1 may comprise a state chaining logic determination unit 16 (also called “state chaining rules”) configured to determine the state chaining logic within the same grouping of detection devices 200, for each grouping determined by the grouping unit 14 from the transition rate matrices determined by the transition rate matrix determination unit 12. The state chaining logic determined for a grouping defines the activity state transitions of the detection devices of the grouping.

[0079] To model the detection devices 200, the modeling unit 10 considers the point of view of at least one mobile observer (receiver capable of receiving the waves emitted by the detection devices 200) who moves in a geographical area where the n detection devices 200 forming the detection set 2 are arranged, and from which the activity state data set 3 is obtained. The detection set 2 thus corresponds to the set of detection devices 200 which are located in this geographical area which is chosen according to the surveillance area, some of the detection devices 200 in this detection set 2 are configured to cooperate with each other (devices called "networked").

[0080] Due to the mobility of the observer, the observer may have insufficient information regarding the activity status of the different detection devices 200 so that the set of state data observed by an observer at different times may include state information values ​​VI, V2 or V3.

[0081] It should be noted that the position of the detection devices 200 generally varies very little over time. It is also assumed that the position of the different detection devices 200 is known. In a real situation, the position of the observer (receiver flying over for example) can be adjusted so as to be able to listen to the transmissions of all the detection devices 200. The control device 1 according to the embodiments of the invention can determine the optimal grouping of detection devices 200 by using only the information relating to the activity state of the detection devices (first value VI in the case of activity, second value in the case of inactivity or third value V3 in the case of unavailable information), and does not use information on the trajectories of the detected targets.

[0082] In one embodiment, the observed activity state data set 3 can be modeled in the form of an activity state observation table which represents at each instant (each row of the table corresponds to a detection instant) the different observed states of the detection devices 200 of the detection set 2 (each column corresponds to a detection device of the set 2), located in the geographical area of ​​interest, these states being represented in the state observation table by a state value as a function of the activity state of the detection device 200 considered. The status value may be a Boolean value taking the first value VI (for example 1) or the second value V2 (for example 0) depending on whether the detection device 200 is active (value 1) or not (value 0), or the third value V3 (“NaN” for example) indicating that the activity information of the detection device 200 is not available.

[0083] [Fig. 3] illustrates an example of an activity state observation table. In the example of [Fig. 3], four detection devices 200 are considered in the scene (#1, #2, #3, #4) and different times for which the activity state of each detection device 200 is indicated. For example, at time t=241 s, detection devices #1 and #2 are inactive (value “0”), but no state information is available (value “NaN”) on the activity state of detection devices #3 and #4. Similarly, at time t=254 s, no information on the activity state of detection device #1 is available (value “NaN”) while detection devices #2 and #3 are active (value “1”) and detection device #4 is not active (value “0”).

[0084] A partitioning is then applied to the activity state observation table corresponding to the detection set 2 so as to extract a set of state sub-matrices, each corresponding to a candidate detection device group. More precisely, the partitioning of the activity table into state sub-matrices is carried out so that each state sub-matrix is ​​a rectangular matrix corresponding to an area of ​​the state observation table, defined by the intersection of a set of rows and a set of columns, devoid of state information unavailability elements (third state information value V3 such as "NaN" for example). A sub-matrix of the state observation table therefore only comprises activity state values ​​(first value VI such as the value 1) and / or inactivity state values ​​(second value V2 such as the value 0). It may be made up of elements from columns or rows of the table, whether continuous or not. A state sub-matrix thus corresponds to state information of at least two detection devices 200 of the detection assembly 2 (i.e. comprises elements of at least two columns of the initial state observation table).

[0085] Each state sub-matrix thus obtained corresponds to a candidate group 20 of detection devices 200 and provides the activity state information of the candidate group from the state data 3, at different times t of the initial state observation table, without including any undetermined information (i.e. third value V3 of activity state information indicating that the activity state is unavailable such as “NaN”).

[0086] [Fig.4] illustrates an example of the breakdown of a state observation table 50 into two state sub-matrices 53 and 54 corresponding to two candidate groups. The division into state sub-matrices can be carried out so as to isolate as many rectangular sub-matrices devoid of “NaN” elements (third value V3 of activity state information) as possible for different combinations of detection devices 200. This division can be carried out so as to have state sub-matrices as large as possible, each state sub-matrix corresponding to a candidate group of detection devices 200.

[0087] In the example of [Fig.4], the state sub-matrix 53 corresponds to the rows of the state observation table 50 between t=241 and t=253 and to the first two columns of the state observation table 50 corresponding to the detection devices #1 and #2. The state sub-matrix 53 corresponds to a rectangular division such that the sub-matrix 53 only comprises elements 0 (inactive state) or l (active state). The state sub-matrix 53 is thus associated with the candidate group of detection devices comprising the devices {#1, #2}.

[0088] The state sub-matrix 54 corresponds to the rows of the state observation table between t=249 and t=256 and to the last two columns of the state observation table corresponding to the detection devices #3 and #4. It also corresponds to a rectangular division such that the sub-matrix 54 only comprises elements 0 (inactive state) or 1 (active state). The state sub-matrix 54 is thus associated with the candidate group of detection devices comprising devices {#3, #4}.

[0089] The number of combinations used to determine the state sub-matrices can vary and be as high as possible.

[0090] Each state sub-matrix thus obtained (53 or 54 for example) comprises a set of state vectors, each state vector corresponding to a row of the state sub-matrix associated with a time t, and represents the observed state of the different detection devices 200 associated with the state sub-matrix. The state vector thus comprises a set of components, corresponding to the different detection devices associated with the state sub-matrix, at the time considered, each component of the state vector corresponding to an observed activity state value (taking for example the Boolean values ​​0 or 1) of the associated detection device 200 and indicates whether, at the time t considered:

[0091] - the detection device is in an active state (value V1 such that the value boolean 1 for example), that is to say that it is in a transmitting state (state 'ON'), or

[0092] - the device is in an inactive state (value V2 such that the Boolean value 0 by example), that is to say in a state where it does not emit ('OFF state').

[0093] In the example of [Fig.4], the state vector corresponding to the instant t=246 is '11' for the sub-matrix 53.

[0094] It should be noted that although referred to as "state sub-matrix" and "state vector" for simplification, these data structures correspond respectively to state observation sub-matrices and state observation vectors. Indeed, although the third activity state information value V3 which indicates that the activity state is unavailable ("NaN" for example) is removed from these data structures, the first and second values ​​VI and V2 (0 and 1 for example) may correspond to false positives or false negatives, so that the state sub-matrices and the state vectors (corresponding to the observations) may not correspond exactly to the actual states.

[0095] According to this modeling, a set 2 of n detection devices can be associated with a number of states (the states of the devices 200 that it comprises) ranging up to 2 different possible states, in cases where each of the n devices can have one of two states (active or inactive state).

[0096] The state vector therefore contains Boolean values ​​reflecting the activity ('ON') or non-activity ('OFF') observed of a detection device 200.

[0097] From the determined state sub-matrices, associated with different candidate groups of detection devices, the embodiments of the invention make it possible to determine a transition rate matrix for each candidate group, then at least one characteristic quantity of the candidate group from the rate matrix. transition, comprising at least one value relating to the entropy of the candidate group. The control device is then able to determine at least one grouping of detection devices 200 which collaborate from the values ​​relating to the entropy of the different candidate groups. The control device 1 can further determine the state chaining logic associated with each grouping from the modeling carried out by the modeling unit 10 and from HMM-based learning (modeling in the form of transition rate matrices).

[0098] In the activity state observation table, it is assumed that the transitions from one activity state to another occur independently of variations in the environment, i.e. whatever the results of measurements made by the detection devices 200 (in transmission), the 'ON' / 'OFF' switching sequences remain unchanged, whether they are rigorously deterministic or probabilistic (i.e. it is assumed that all of the detection devices 200 continue to operate at their usual rate whether or not they have detected the presence of an object that would be potentially hostile to them).

[0099] Although the description is made mainly with reference to a Boolean representation (in particular binary) of the activity state of the detection devices 200, those skilled in the art will easily understand that the invention is not limited to such a Boolean representation of the activity state of a detection device 200 (according to which the detection device can have two activity states). More generally, a state of a detection device 200 can be characterized by a Q-tuple of state values, the different values ​​of the Q-tuple providing at least the activity state of the associated detection device 200 and additional information relating to the object detection carried out by the detection device 200.For example, the Q-tuple may be a pair (Q=2) of state values ​​denoted 'xix2' where Xi characterizes the activity 'ON' or inactivity 'OFF' of the detection device 200 and x2 characterizes the recent detection or not of an object by the detection device 200 itself or one of its neighboring detection devices. In this example, it is assumed that the detection system 100 does not react to a detection that would be potentially hostile to it and that it therefore continues to turn on (i.e. put to 'ON' or active state) and turn off (put to 'OFF' or inactive state) its set of detection devices 200 at its usual rate (i.e. without taking into account the detection of the object).Thus, the activity state ('ON' or 'OFF') represented by the value Xi only provides an indication of whether a detection device 200 is emitting a signal (value VI meaning that on the date considered, the detection device is emitting a radar wave) or not (value V2 meaning that on the date considered, the detection device is not emitting a radar wave), while the value x2 comes . supplement this indication by providing an indication of the detection of an object in the vicinity of the detection device.

[0100] Thus, in this example, the state of a detection device 100 can take the values ​​'00' (xi=0 indicating an inactive state and x2=0 indicating a non-recent detection), '01' (xi=0 indicating an inactive state and x2=1 indicating a recent detection), '10' (xi=1 indicating an active state and x2=0 indicating a non-recent detection), or '11' (xi=1 indicating an active state and x2=1 indicating a non-recent detection). The use of such a Q-tuple of state values ​​can thus take into account the causality that there may be between a detection and the activity of the different detection devices 200.

[0101] The activity state data sets can be dynamically updated based on the activity states of the detection devices 200 of the environment 2, detected by an observer, the modeling unit 10 being able to update the model periodically or dynamically.

[0102] The control device 1 is thus able to define one or more candidate groups Gq of detection devices 200 among the devices of the detection set 2, from the division of the state observation table 50 into state sub-matrices (52, 53 for example) which correspond to several combinations of detection devices of the detection set 2, according to different combinations.

[0103] The transition rate matrix determination unit 12 is then configured to determine a transition rate matrix associated with each candidate group Gq corresponding to a state sub-matrix.

[0104] To determine the transition rate matrix associated with a candidate group Gq of detection devices 200, the transition rate matrix determination unit 12 is able to learn the logic for chaining the state switches of the detection devices 200 from the active state to the inactive state and vice versa ('ON'<->'OFF'), which is "hidden" behind the detected state data sets by implementing a learning phase based on hidden Markov chains HMM and by using the state sub-matrices derived from the state observation table (and in particular the state vectors associated with the different detection devices of the candidate group). This learned state chaining logic can then be used by the grouping unit 14 to determine the groupings of detection devices 200 which cooperate.The activity state of a detection device 200 being represented by the state vector which lists its activity in a state sub-matrix, there can be up to 2 different activity state values ​​used in the learning phase, n being the number of detection devices 200 present in the environment 2, in the case where a device has two possible activity states.

[0105] The set of detection devices 200 of the detection set 2 therefore behaves like a state machine, the unit for determining the transition rate matrix 12 being able to reconstitute the state transition logic and the temporality of this state machine. In particular, for each state, the unit for determining the transition rate matrix 12 is able to determine after how much time each detection device 200 leaves this state, towards which state(s) it will evolve or it is likely that it will evolve (a single state in a deterministic case or a choice among several states in the probabilistic case), the determined information then being structured in a transition rate matrix which represents the transitions between activity states for each detection device of the candidate group Gq considered.

[0106] The determination of the transition rate matrix from the state vectors can for example be determined using HMM modeling.

[0107] HMM modeling is an iterative process that converges to a matrix providing the rates of transitions from one state to another. The iterative HMM process is used by the transition rate matrix determination unit 12 to model the sequence of activity states of the detection devices 200.

[0108] The iterative HMM process applied by the transition rate matrix determination unit 12 may use the algorithm described in LIU, Yu-Ying, MORENO, Alexander, XU, Maxwell A., et al. Efficient Learning and Decoding of the Continuous-Time Hidden Markov Model for Disease Progression Modeling. arXiv preprint arXiv:2110.13998, 2021, intended to follow the evolution of a disease, either in continuous time (i.e., the data sampling is carried out at variable time steps) as provided in this article, or by adapting it to operate at constant time steps. This algorithm uses in particular, in one step, the method described in RABINER, Lawrence R. A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE, 1989, vol. 77, no. 2, p. 257-286 (RABINER).

[0109] The HMM-based algorithm described in LIU, Yu-Ying, MORENO, Alexander, XU, Maxwell A., et al. Efficient Learning and Decoding of the Continuous-Time Hidden Markov Model for Disease Progression Modeling. arXiv preprint arXiv:2110.13998, 2021 (LIU et al), especially page 12, takes as input observations at different times and a set of possible states.

[0110] To apply this method, the transition rate matrix determination unit 12 can take as input a state sub-matrix (observations at different times), and all 7 possible states of the detection set 2. The applied method then determines the number of times a transition from one starting state to another takes place, and after how long on average, which makes it possible to determine an initial transition rate matrix. Then, from the initial transition rate matrix, the transition rate matrix determination unit 12 applies the iterative HMM algorithm, which uses in its sixth step the method described in RABINER, Lawrence R. A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE, 1989, vol. 77, no. 2, pp. 257-286 (RABINER) in continuous time (data sampling is performed at variable time steps) or at constant time steps. Each iteration of the HMM-based iterative algorithm provides a current transition rate matrix.

[0111] Between two consecutive observation times of the sub-matrix, the transition rate matrix determination unit 12 can take into account all the probabilities of evolutions of the state considered between these two observations. Potentially, a state could have changed a large number of times by passing through a multitude of possible states between two observations. The transition rate matrix determination unit 12 can take into account all the possible paths that could have occurred between two observations. The probabilities of each path are governed by the current estimate of the transition rate matrix. The algorithm described in LIU, Yu-Ying, MORENO, Alexander, XU, Maxwell A., et al. Efficient Learning and Decoding of the Continuous-Time Hidden Markov Model for Disease Progression Modeling. arXiv preprint arXiv:2110.13998, 2021 can thus be applied to allow, using all the observations of a state sub-matrix, to converge the current estimate of the transition rate matrix so that it is the most likely given all the observations made. The iterative algorithm is stopped if it is detected that the likelihood of the current estimate of the transition rate matrix no longer varies much from one iteration to another, since in this case it is considered that this estimate is sufficiently good (the variation of the likelihood of the estimate between the current iteration and the previous iteration can for example be compared to a predefined threshold and if it is lower than this threshold, the stopping condition of the process is reached, i.e. the iterations are stopped and the current transition rate matrix obtained at the current iteration is returned as the transition rate matrix 12).The determination of the transition rate matrix 12 according to the aforementioned algorithms, takes into account in particular the probability of false positives and false negatives in the input state sub-matrix.

[0112] The transition rate matrix obtained for a candidate group Gq is a matrix comprising a set of rows, each row comprising a set of coefficients. Each row corresponds to a starting state.

[0113] The coefficients associated with a row of the transition rate matrix indicate the rate at which a detection device of the candidate group arrives in another state from an arrival state).

[0114] The speed represented by a coefficient of the transition rate matrix is ​​a passage speed, therefore in s1, or in “state / s” (state per second).

[0115] Figure 5 illustrates the transition rate matrices obtained for each candidate G53 and G54 corresponding respectively to the state sub-matrices 53 and 54 of [Fig.4] resulting from the division of the state observation table 50, as an illustrative example. [Fig.5] only shows the state vectors drawn respectively from the state sub-matrices 53 and 54 (components representing the activity states in a Boolean form).

[0116] The coefficients associated with a row of the transition rate matrix (e.g. Af53 and M54) indicate the rate at which a detection device of the candidate group (e.g. G53 and G54 respectively) arrives in another state from an arrival state.

[0117] For example, the index coefficient (2,1) (second row, first column) of the matrix M53 has the value 0.5, which means that from state 2 (row number), we go to state 1 (column number) at a speed of 0.5 s1. It will therefore take 2 seconds to get there.

[0118] The index coefficient (1,1) (first row, first column) of the matrix M53 has the value -0.1, which means that from state 1 (row number), we go to state 1 (column number) at the speed of -0.1s *. The sign "-" means that we leave this state. The value 0.1 means that it takes 10 seconds to leave it.

[0119] The columns of the transition rate matrix (eg M53 and thus correspond to different possible arrival states of the detection set 2 while the rows correspond to different departure states.

[0120] By construction, the diagonal terms of the transition rate matrix (for example Af53 and ^54) are negative and the sum of the elements of the same row is zero. Row 'k' of a transition rate matrix indicates that from state 'k', we go to state '1' corresponding to the column index. Thus from a state 'k', it is not possible to go to this same state and it is only possible to leave it, whatever the speed, whether fast or slow. Leaving a state is equivalent to "going backwards", hence the use of a negative sign. Thus, by construction, a component on the diagonal of the transition rate matrix, with index (k, k), is negative or possibly zero if we remain in the state forever.Furthermore, the sum within each line is zero ('0') since state 'k' is left with the speed indicated by the diagonal term (k,k) and we arrive in each following possible state with a cumulative speed equal to the starting speed.

[0121] According to another example, considering a detection set with 2”=4 possible states (case where the set 2 comprises two detection devices 200 each having two possible states), an example of a transition rate matrix can be:

[0122] / -0.1 0 0.1 0 \ 0.5 -0.5 0 0 0 0 -0.25 0.25 0 0.33 0 -0.33 /

[0123] In this example matrix, for the first row, it can be observed that, starting from state [1], the starting state corresponding to the first row, we arrive in state [1], the arrival state corresponding to the first column, with a transition rate (speed) equal to -0.1 (1st coefficient of the first row of the transition rate matrix), and in state [3] (arrival state corresponding to the third column) with a rate of 0.1 (3rd coefficient of the first row of the transition rate matrix). In other words, state [1] is left after 10s to join state [3].

[0124] The transition rate matrix may be a square matrix. The dimension of the transition rate matrix associated with a candidate group of size R (i.e. number of devices 200 of the candidate group) is defined by the total number LR of possible activity states for all the R detection devices of the candidate group, each detection device being able to have the same number L of activity states. The case L = 2 is the Boolean case. If the detection set 2 comprises n detection devices 200, the total number of possible states then being at most equal to 2” states, the transition rate matrix is ​​square, of size 2” x 2”-

[0125] Each transition rate matrix thus obtained translates the state movements in the associated candidate group, as illustrated by diagrams 63 and 64 of Figure 6 which describe the transitions between states corresponding to matrices M53 and Af54 of Figures 4A and 4B.

[0126] The transition rate matrix calculated by learning from the state data set can be sparse or non-sparse. A sparse matrix mainly contains harmful coefficients (the percentage of non-harmful coefficients is low).

[0127] In particular, if within the same row of a transition rate matrix, only two coefficients are not nullified, and in particular the element of the row located on the diagonal of the matrix (diagonal element) and any other element of the row, this indicates that when the detection device considered 200 leaves a state, it arrives in another state. If, on the other hand, a row is filled with non-zero coefficient values, there is uncertainty about the arrival state.

[0128] Such a sparse aspect of the transition rate matrix can advantageously be exploited by the grouping unit 14 to determine at least one grouping of detection devices 200.

[0129] A grouping of detection devices 200 operates in a network and has a deterministic state chaining logic or one that includes only a few random events. If the The logic of chaining states of a grouping of detection devices is perfectly deterministic, this means that if a transition rate matrix is ​​calculated from 200 detection devices from the same grouping, this transition rate matrix only contains a few rare non-null elements, namely the diagonal elements and only one other non-zero element per row.

[0130] Since the transition rate matrix is ​​derived from an estimate obtained from measurements (observed state data) which may be subject to errors (for example in cases of non-detection or false positives), transition rate matrices are generally not obtained in which most of the elements (coefficients) are rigorously harmed.

[0131] For example, a matrix corresponding to a candidate group Gf and a matrix M2 corresponding to a candidate group G2 defined by the following coefficients can be considered:

[0132] / -0.104 0.001 0.1 0.003 1 0.5 -0.5045 0.003 0.0015 0.0041 0.0012 - 0.2553 0.25 10.0009 0.33 0.002 -0.3329 /

[0133] -0.25 0.08 0.1 0.07 0.5 -1.05 0.4 0.15 0.18 0.09 -0.52 0.25 0.17 0.33 0.24 -0.74 /

[0134] The matrix can reasonably be considered as a sparse matrix so that it can be considered that the corresponding candidate group Gj uses deterministic logic. In the case of the second matrix M2, it can be considered on the other hand that the corresponding state chaining logic is not deterministic.

[0135] Thus, it can be considered that the transition rate matrix Mi is quasi-deterministic while the transition rate matrix M2 is more random. It should be noted that in practice, it is almost not possible to rigorously obtain zeros since the algorithm applied to generate the transition rate matrices is an iterative process that allows a certain number of iterations that would only converge to 0 for certain coefficients if an infinite number of iterations were performed, and a stopping criterion is applied when the result remains roughly unchanged from one iteration to the next.

[0136] For a case of a rigorously deterministic transition rate matrix, it would be necessary, for each row, to have only zeros except for two terms, namely a diagonal term and another. In practice, the value is never rigorously equal to zero but almost equal to zero. The transition rate matrix M5 illustrates a case which comes very close to a rigorously deterministic matrix since there are several orders of magnitude between the terms which weigh and the others within each row.

[0137] It can therefore be assumed that the state data 3 used to estimate the transition rate matrix M2 come from detection devices 200 which do not operate in a network and conversely, in the case of the transition rate matrix it can be assumed that the state data 3 used come from a grouping operating in a network.

[0138] The group characteristic value determination unit 13 is configured to determine a K-tuple of group characteristic values ​​comprising at least one quantity relating to the group entropy ('cooperation metric') for each candidate group Gq whose value indicates to what extent a transition rate matrix associated with the candidate group Gq is sparse and thus the level of cooperation of the detection devices 200 of the candidate group 20 considered.

[0139] To determine the Q-tuple of group characteristic values ​​(and thus determine whether the state chaining logic of a transition rate matrix is ​​deterministic), the group characteristic value determination unit 13 may be configured to scan each row of the transition rate matrix and, for each row, to check only the non-diagonal terms. In particular, the group characteristic value determination unit 13 is configured to normalize the non-diagonal terms of each row of the matrix so that their sum is unity (normalization operation). The following steps are performed to perform the normalization operation for each row ' of the transition rate matrix:

[0140] - the diagonal term of the line * is first removed while the others are kept terms,

[0141] - each of the remaining terms of line i (each term except the diagonal term), is then divided by the sum of all remaining terms (the result of the division can be rounded to the nearest tenth) so that the sum of the remaining terms is 1, which provides a probability vector Ç; comprising probability values, each corresponding to one of the terms of the row i considered in the transition rate matrix, except the diagonal term (the probability vector therefore includes 1 component less than the row considered). The probability values ​​of the probability vector obtained for the row 1 considered represent the probabilities of transitions to an arrival state (the list of the following probable states, without information on the speed).

[0142] The different probability vectors obtained for all the rows of the transition rate matrix form a probability matrix fl (the j-th row of the Probability matrix is ​​the vector obtained for row f of the transition rate matrix).

[0143] For example, considering the examples of matrices and the obtained transition probabilities Ode are given by the probability matrices II, for the matrix and n2 j day the matrix M2:

[0144] (0.0096 0.9615 0.0288) T~T __ , (0.9911 0.0059 0.0030) n( = (0.0161 0.0047 0.9792) (0.0027 0.9913 0.0060)

[0145] ' (0.3200 0.4000 0.2800) (0.4762 0.3810 0.1429) n2= (0.3462 0.1731 0.4808) (0.2297 0.4459 0.3243)

[0146] The probability matrix FI thus obtained for a transition rate matrix comprises probability coefficients Pjk representing the transition probabilities to an arrival state for each row of the transition rate matrix (corresponding to a departure state). The group characteristic value determination unit 13 can then estimate to what extent the probabilities converge to the same arrival state from the probability matrix FI.

[0147] In particular, in one embodiment, the group characteristic value determination unit 13 may be configured to determine the Shannon entropy which quantifies the spread of the probability distribution of arrival states from the same departure state. A low entropy value therefore indicates that there is a preferred arrival state, while a high entropy marks the absence of a preferred arrival state.

[0148] Assuming that the transition rate matrix is ​​a square matrix of size N x N, the probability matrix FI comprises N rows, each row z being associated with a vector Çt- comprising N- 1 components representing the probability coefficients Pik.

[0149] For each row ' of the probability matrix H, an entropy value is determined. Thus, for the transition rate matrix of size N x N, N entropy values ​​are determined, with one entropy value for each row. The N entropy values ​​form an entropy vector H comprising entropy values ​​h, associated with each row z of the probability matrix U.

[0150] In one embodiment, the entropy value associated with a row of the probability matrix FF is a Shanon entropy, determined according to the following equation (1):

[0151] , _ y"! , (1) -Lk=lPik^Pik

[0152] Each component of the entropy vector H is an entropy value corresponding to a state of a detection device 200.

[0153] The entropy vector H therefore provides as many entropy values ​​as there are numbers of states.

[0154] By construction, the entropy H has a minimum value when the probability distribution is reduced to 100% in one place and 0% elsewhere. On the contrary, it is maximum in the case where the arrival states are equiprobable. Such an entropy vector H thus indicates whether a state chaining logic of a candidate group is rather deterministic or random.

[0155] In one embodiment, the grouping unit 14 may use a cooperation metric corresponding to a quantity derived from this entropy vector, such as the average Httmy of the components of the entropy vector H, to determine the optimal groupings of candidate devices.

[0156] In the examples of probability matrices H, and n2 obtained respectively for the matrices and Af2, the entropy vectors H1 and H2 are:

[0157] / 0.1845\ 0.0566 0.1123 ' 0.0553 /

[0158] / 1.08763 0.9990 H2“ 1.0229 1.0632 /

[0159] In one embodiment, the group characteristic value determination unit 13 can determine an average Hmoy of the values ​​of the entropy vector (hereinafter also called “average entropy”), for each transition rate matrix Mq (corresponding to a candidate group Gq\ by applying a weighting coefficient aj to each component hj of the entropy vector H, for j between 1 and the number of states Nq associated with the transition rate matrix Mq according to equation (2):

[0160] (2) Hmoy —

[0161] In one embodiment, the entropy values ​​hj may be weighted using a vector 7 representing the average steady state comprising a priori distinct coefficients aj.

[0162]

[0163]

[0164]

[0165]

[0166]

[0167]

[0168]

[0169]

[0170]

[0171]

[0172]

[0173]

[0174] Considering the transition rate matrices M^ by calculating their exponential with a long time, the average steady state vector, which is a mixture between the Nq states, can be calculated according to the formula: 1 / U1^) In equation 3, N denotes the dimension of the transition rate matrix (in this case N is at most equal to 2” and the size of the matrix is ​​then equal to 2” x 2”) and T denotes a “large” time value. For example, by denoting 4 the eigenvalues ​​of the matrix Mq (i.e. roots of the characteristic polynomial of the matrix), r can be chosen equal to T - ] ÿ x max^ ) • According to equation (3), using vector 7, the entropy of each row can be weighted by the presence of a state over time. Thus, a state returning often will weigh more than a very rare condition. Considering the example of the two transition rate matrices and M2, which are of dimension n = 4, the average steady-state coefficient 7] defined for the matrix and the average steady-state coefficient % defined for the matrix M2 are: m ?7{ = {exp(Tjff) J / 0.5240) 0.1070 0.2078 J),1612 / (4A) And 11 / / 0.4944) 0.1066 0.2472 )0.1519 / (4B) It is worth noting that the examples of matrices M1 and M2 are used to illustrate two extreme cases: a case of quasi-deterministic transition rate matrix M1 and a case of random transition rate matrix M2. Weighting the entropy average is advantageous because the entropy contribution is all the greater as it concerns a frequently affected condition. Considering the values ​​7, and 72, the average entropy - (HJ and the average entropy corresponding respectively from the entropy vector H, obtained for and of the entropy vector H2 obtained for M2 are then equal to: (HJ = 0.1350 (HJ = 1.0586

[0175] The rest of the description will be made with reference to a cooperation metric of the average entropy type Hmoy(Mq) = <hq>, weighted by an average steady-state coefficient as a non-limiting example. Figures 7, 8, 9 and 10 illustrate the determination of the average entropy for four transition rate matrices M5 and obtained for 4 distinct candidate groups of the same set of detection devices 2 comprising three detection devices #1, #2, and #3, from an initial state observation table.

[0176] More precisely, Figure 7 illustrates the steps of determining the average entropy still numbered (H3), in the case of another example of matrix of M3 transition rate associated with a candidate group {#1,#2,#3}.

[0177] Figure 8 illustrates the step of calculating the average entropy also noted (H4), in the case of another example of transition rate matrix M3 associated with a second candidate group {#1,#2}.

[0178] Figure 9 illustrates the steps of calculating the average entropy again denoted (H5}, in the case of another example of transition rate matrix M3 associated with a third candidate group {#1,#3}.

[0179] Figure 10 illustrates the steps of calculating the average entropy j, again denoted (H6), in the case of another example of transition rate matrix M4 associated with a third candidate group {#2,#3}.

[0180] Thus, the entropy obtained for the different groups is:

[0181] W - 0.58 for candidate group {#1,#2, #3};

[0182] (H4) = 0.86 for candidate group {#1, #2};

[0183] (H5) = 0.17 for candidate group {#1, #3};

[0184] - 0.59 for candidate group {#2, #3};

[0185] From the cooperation metrics relating to the entropy, such as the average entropies (Hq), obtained from the transition rate matrices Mq associated with the different candidate groups corresponding to the state sub-matrices, the grouping determination unit 14 is configured to determine at least one grouping of the detection devices 200 by determining which candidate group 20 among the different candidate groups 20 considered comprises detection devices 200 having the greatest probability of belonging to the same network.

[0186] In the example of the matrices Mi and M2 corresponding to two different candidate groups, the grouping determination unit 14 is thus able to use the entropy averages calculated for each transition rate matrix in order to determine whether it is more probable that the detection devices 200 from the group n°1 (having resulted in the matrix) belong to the same network as those from group n°2 (having resulted in matrix M2).

[0187] In embodiments, the cooperation metrics obtained for the different candidate groups, such as the average entropies (Hq), may be compared to each other or compared to a threshold to determine the grouping of detection devices 200 that minimizes the average entropy and therefore has the greatest probability of cooperation.

[0188] The cooperation metric relating to entropy (for example average entropy) thus provides a likelihood of network operation (or cooperation of detection devices).

[0189] According to another example, in the case of the 4 candidate groups considered in figures 7, 8, 9 and 10, it is likely that detection devices #1 and #3 of the candidate group {#1, #3} having the lowest entropy cooperate while detection device #2 operates alone.

[0190] Thus, for each candidate group, the transition rate matrix is ​​determined, then the cooperation metric relating to the entropy (for example the average entropy) from the transition rate matrix determined for the candidate group. The cooperation metrics (average entropies) can then be used to determine one or more groupings of detection devices.

[0191] In one embodiment, for each candidate group 20 considered corresponding to a possible combination of cooperating detection devices 200, the control device 1 can determine a triplet of group characteristic values ​​comprising:

[0192] - The list of detection devices 200 of the candidate group 20 (designated by

[0193] - the cooperation metric relative to entropy such as the average entropy < Hq > determined for this candidate group from its transition rate matrix Mq-

[0194] - The number Kq of measurements used to calculate the transition rate matrix Mq (Kq represents the number of components, therefore rows, in the state sub-matrix used to determine the transition rate matrix).

[0195] In the remainder of the description, it will be considered that the cooperation metric relating to the entropy is the average entropy < Hq > as an illustrative example, and that the triplet of group characteristic values ​​is therefore noted {Hq), Kq],

[0196] The triplets [Lq, (Hq), Kq] obtained for the different candidate groups Gq thus provide trend information through the cooperation metric relating to the entropy (Hq), without directly giving the estimate of belonging or not to the same cooperative network of detection devices 200.

[0197] In one embodiment, the clustering determination unit 14 may be configured to determine clusters of detection devices 200 into networks from all the triplets {Lq, (Hq), Kq] calculated for the different candidate groups Gq, using a representation of the candidate groups and their associated triplets {Lq^(Hq), Kq] in the form of a mechanical system in a representation space.

[0198] To generate such a representation in a mechanical system, for a set 2 of n detection devices 200, the representation space is a space of dimension n -1 in which laws of point mechanics are applied. In this representation space, each real detection device 200 is represented in the form of an associated point, which is a point capable of being subjected to one or more forces.

[0199] Each triplet {Lq, (Hq), Kq] is an indicator of the level of cooperation of certain detection devices 200 with each other (i.e., it indicates to what extent they appear to cooperate). If a triplet {Lq, (Hq), Kq] corresponds to a candidate group involving p detection devices 200 (i.e. p is the number of devices in the list ), the mechanical system used to represent the candidate group Gq and the associated triplet {Lq, (Hq), Kq] in the representation space further comprises p elastic links connecting the p points representative of the detection devices 200 to the center of a hypersphere circumscribed at the p points (hypersphere passing through the p points), in the representation space. The empty length, denoted lq, of these elastic links is defined by the average entropy (Hq) of the triplet of values ​​and the elastic stiffness constant of these elastic links, denoted is proportional to the number of measurements Kq given by the triplet of values.

[0200] Thus, the representative points of the detection devices 200 are attracted if the entropy (Hq) is low or repelled from each other if the entropy (Hq) is high with a force which depends on the number of measurements Kq, and therefore on the reliability of this entropy. The elastic connections between the p points are used to ensure that all the representative points of the detection devices 200 are at equal distance from the same central point (i.e. the center of the hypersphere). The evolution space of the mechanical system must therefore be of dimension p -1, therefore at most n -1 (in the case where P = n, i.e. in the case of a triplet which involves all the detection devices).

[0201] Figure 11 is an example of a mechanical system 500 corresponding to such a representation, in the representation space, of the triplet {Lq, (Hq), Kq] obtained for a candidate group 20, in which n = 3.

[0202] In this example, 3 detection devices 200 (H=3) are considered, designated by A, B and C. The representation space is therefore a 2-dimensional space. It a first triplet is considered which corresponds to a candidate group G(A, B, C) comprising the three detection devices A, B and C. Bonds therefore link the point O abc, center of the circle circumscribed to the triangle ABC, to the points A, B and C. A second triplet is considered which corresponds to a candidate group G(A, C) comprising the two detection devices A and C only. Elastic bonds therefore link the middle of the segment [AC] to the points A and C.

[0203] In the example of Figure 11, it is assumed that the empty length lAgç for the group G(AB, C) is large while the length lAC of the candidate group G(A, C) is small, and kAC are the stiffness constants of the elastic bonds respectively for the group G(A, B, C) and the candidate group G(A, C).

[0204] In the example of figure 11, the elastic force from point ^abc which is exerted on point A (representing a first detection device) is expressed in the form:

[0205] (5) r Oahc-*A - K asc ( AU^ - ) ■ AO

[0206] If the entropy (H^) of the triplet {G abc, {^abc] associated with the group comprising the devices A, B and C is high but that of the triplet {LAC, ( , Kac} associated with the GAC group including devices A and C is small, so after relaxation of the mechanical system, the OABC point should be “far” from points A, B and C while the OAC point should be close to points A and C.

[0207] The placement in a two-dimensional representation space (n = 3) makes it possible to establish links towards the point OABC so that these links can reach their empty length, and also allows the points A and C to move closer to each other without impacting the tension of the links around the point ^abc- Indeed, the points A and C can move closer by sliding along the circle 50 represented in [Fig.l 1].

[0208] In embodiments, frictional forces may be applied to the mechanical system 500. In this case, the frictional forces are added into the representation of the mechanical system of the candidate groups to allow the mechanical system 500 to relax rather than have perpetual oscillations, which makes it possible to obtain a system 500 where the elastic potential energy becomes minimal. In some cases, there may indeed be pulls in the sense that springs may enter into contradiction. The stiffness constant kq of each spring thus serves to arbitrate between the forces of the springs. However, once relaxation is reached, the springs in contradiction (the "losing" spring as well as the "winning" spring) do not in practice reach zero but minimal potential energy.

[0209] The friction forces can be elastic damping type friction forces or brake type friction forces in a fluid medium.

[0210] In the embodiment where an elastic damping type friction force is used, the elastic damping force can be expressed in the following form, considering the example of a connection between a point I (representing a detection device) of a candidate group and the center O of the hypersphere of the mechanical system representing the candidate group:

[0211] (6) depreciation J depreciation D

[0212] Thus, in the example of the connection between a point A and the center OABC of [Fig. 11], the elastic damping force can be expressed as follows:

[0213] -> va-AOabc r depreciation ~ ' J depreciation X

[0214] In the embodiment where a brake-type friction force in a fluidic medium is used, the fluid friction force can be expressed in the following form by considering the example of a connection between a point I (representing a detection device) of a candidate group and the center O of the hypersphere of the mechanical system representing the candidate group:

[0216] In the example of the connection between a point A and the center of the [Fig.l 1], the elastic damping force is expressed as follows: / 7. fyv fhude J fluid A

[0217] In equations (6) and (7), the values ​​of the friction coefficients f and f are predefined to allow the mechanical system to stabilize and do not correspond to a physical quantity. To arrive at a stable state, the grouping unit 14 can evolve the mechanical system representing the candidate groups in the representation space by implementing a resolution of a differential system associated with the point mechanics equations which govern the mechanical system. The friction coefficients / ,. ^etdef., ., can be adjusted as best as possible. Small values ​​of the friction coefficients can, for example, allow the mechanical system 500 to oscillate for a long time before stabilizing. Conversely, large values ​​of the friction coefficients can slow down the oscillations of the mechanical system 500 and the convergence towards the equilibrium state.

[0218] The simulation of the mechanical system can be carried out, after introducing a braking force to avoid oscillations to allow the elements to move and slow them down so that they stabilize until the relaxed state.

[0219] The differential equations of the mechanical system thus obtained can be solved by any suitable solver. In the simulation of the system, the potential energy is converted into kinetic energy with the setting in motion of the elements. The energy mechanical energy of the mechanical system is equal to the sum of the potential energy and the kinetic energy, which is consumed by the braking forces. The mechanical energy then decreases until a stabilization state of the system is reached. In the stabilization state of the mechanical system, a clustering algorithm can be applied to the mechanical system 500 to determine at least one grouping of detection devices 200. The clustering algorithm uses in particular the Euclidean distance between the representative points of the detection devices in the stabilization state. The applied clustering algorithm can be a density classification algorithm such as for example a DBscan type algorithm (for 'Density-based Spatial Clustering of Applications with Noise' meaning 'Spatial grouping based on the density of applications with noise').The stabilization state is reached once the springs of the mechanical system have reached their minimum potential energy.

[0220] [Fig. 12] is a diagram showing the mechanical system 500 of [Fig. 12], after relaxation.

[0221] As illustrated, the set of elastic links makes it possible to bring points A and C closer together if the entropy (HAC) calculated for the GAC group is low while being in line with the strong entropy (HABCL) of the GABC group comprising points AB,C

[0222] Thus, the grouping unit 14 is capable of generating a representation of the candidate groups selected in the detection set 2 comprising the n detection devices 200, in the form of a mechanical system, in a representation space of dimension n - 1, from the triplet of values ​​determined for each candidate group {Lq, (HqL} such that:

[0223] - each detection device 200 of a candidate group is represented by a point in the representation space;

[0224] - for each candidate group comprising a list Lq of detection devices 200, the mechanical system used to represent this candidate group Gq comprises elastic links connecting the representative points of the detection devices 200 of the group to the center of a hypersphere circumscribed at the p points, in the representation space.

[0225] - The empty length, noted l, of the p elastic bonds is defined by the entropy average < Hq > ;

[0226] - the elastic stiffness constant £ of the p elastic connections is proportional to the number of measurements Kq.

[0227] - frictional forces may be applied to the mechanical system 500 to bring it to a state of relaxation.

[0228] In one embodiment, to position the hypersphere in the representation space, the grouping unit 14 can calculate the center of the hypersphere circumscribed at the points in the n-1 dimensional space using vectors ei such as:

[0229] . _ ±i_ (8)

[0230] And:

[0231] (9)

[0232] The vectors eî constitute p -1 basis vectors.

[0233] A projection matrix R of size (p-1) X (n-1) can then be used as that :

[0234] y <10) Æ = I e, I

[0235] The matrix R makes it possible to project an element of dimension 1 into the orthonormal basis that has been created (the orthonormal basis is made up of the vectors ei, the construction of the basis (ei' e2' etc.) being done according to the Gramm-Schmidt orthonormalization method). It should be noted that the index * used in the calculation of the center of the hypersphere is independent of the index i used in the preceding description in relation to the transition rate matrices (in particular as a row index).

[0236] The coordinates Yj of the p points in the frame centered at Xp and whose base vectors are the ۔ are then defined according to the following formula (11):

[0237] Life Œhp]], Y^R^-Xp) (11)

[0238] By construction, Yp = 0.

[0239] In this basis, the center of the circumscribed hypersphere can then be calculated.

[0240] By definition, the center of the hypersphere, noted Q, verifies the following equation:

[0241] U^-Qll = ||yrQ||, Vf, [ l;pl (12)

[0242] This equation is also written:

[0243] (yrà)T(y;--Û) = (Yj-&)T(Yj-&) (13)

[0244] yfy.+ôrQ-ôryryfô= y}yy+Qrô-Qryr yjû (14)

[0245] y^Yf - 2Y^Ù = Y^Y; - 2Y^l (15)

[0246] Yi - Y?Yj = 2 (Y[ - Yj) Q (16)

[0247] The following p-1 equations (17) and (18) can then be solved to calculate the center of the hypersphere:

[0248] Y{Yj-YTpYp=2(Y{ -YTp)a Vi&mp-l] (17)

[0249] ^^ = 2^^7 / ^1^^-131(18)

[0250] Furthermore, we consider the following vector B of size p-1 and the matrix A of size (P~l) x (P-1)) :: 102511 (19)

[0252] A_Lyr\ <2°) ' ' zeW-ll!

[0253] If the Yj are all different, which is in principle the case if the points are not initially confused, then the matrix A, created from a family of free vectors, is invertible.

[0254] The center H can then be calculated from the following equation (21):

[0255] 0 = ^(21)

[0256] □ represents the position of the center of the hypersphere in another frame of reference. Indeed, Initially, the elements are positioned according to the vectors. Equation (11) was then used to redefine the position of each element in an orthonormal frame centered around the point with index p. Equation (11) thus shows that the point pa as position in this new frame is the point 0-

[0257] Û can then be expressed in the initial frame according to the formula (22):

[0258] Q = Rt&. + Xp = RtAaB + Xp (22)

[0259] The point thus calculated represents the center of the hypersphere to which all the elastic links leading to each of the p points are attached.

[0260] From the representation of the n detection devices 200 of the detection set 2 in the representation space of dimension n - 1, in the form of a mechanical system 500, the grouping unit 14 is able to group the detection devices 200 operating in networks together, while distancing those which do not seem a priori to operate together, from the representation of the elastic connections between the points of the same candidate group.

[0261] The grouping unit 14 can be configured to then apply the grouping (or “clustering”) algorithm to the mechanical system obtained after relaxation to determine at least one grouping of the detection devices 200 of the representation space, using the distances between the points representing the detection devices, in the mechanical system, such as for example the DB-Scan type algorithm.

[0262] The clustering algorithm (such as for example the DB-Scan algorithm) is a method that uses a threshold defining the neighborhood e of a point. For each point, the method determines which points are in the neighborhood of the point (i.e. at a distance less than £ from the point considered). The selected points (points in the neighborhood) are then added to form a grouping. The method thus performs a grouping of points representing detection devices 200 from near to far. The neighborhood threshold s is predetermined or predefined in a suitable manner depending on the application of the invention. Indeed, if the threshold £ is too small, each point can form a grouping alone of which it is the only member. If, conversely, the threshold e is too large, a single grouping encompassing all the points can be determined.

[0263] The state chaining logic determination unit 16 can determine the state chaining logic of the determined grouping from the transition rate matrices determined for the different candidate groups by the unit 12. The state chaining logic defines the transition rules from one state to another for each detection device of the determined grouping.

[0264] To determine the state chaining logic of a determined grouping, the state chaining logic determination unit 16 may select all transition rate matrices that are associated only with detection devices 200 belonging to the determined grouping, and perform an average weighted by the number of measurement points, which provides a resulting transition rate matrix that represents the chaining logic within the grouping.

[0265] In particular, for each obtained grouping, the state chaining logic determination unit 16 selects all the obtained transition rate matrices corresponding to candidate groups comprising a detection device 200 of the considered grouping. For example, if the considered grouping is a grouping Pi 23 comprising three detection devices #1, #2, and #3 such that Pi23=[#1,#2,#3], the state chaining logic determination unit 16 selects the four transition rate matrices Af13, and associated respectively with the four candidate groups [#1,#2], [#1,#3], [#2,#3], [#1,#2,#3], as illustrated in FIG. 14.The state chaining logic determination unit 16 is then able to reconstruct a resulting transition rate matrix Res from the selected transition rate matrices by taking into account the L detection devices of the grouping considered (for example three detection devices in the preceding example), so that the size of the resulting transition rate matrix Mr is 2L (23 = 8 in the preceding example where the grouping P123 comprises 3 detection devices). To determine the resulting transition rate matrix MRes, it is considered that each transition rate matrix Mq determined by the transition rate matrix determination unit 14 has a weight &, which corresponds to the amount of information used to obtain it. This weight value corresponds (i.e. is equal) to the stiffness constant used for the mechanical relaxation of the mechanical system 500. In the grouping example P123, four .

[0266]

[0267]

[0268]

[0269]

[0270]

[0271]

[0272]

[0273] weights kn, ^13, k23 and kl23 are respectively associated with the different transition rate matrices Ml3, Mn, ^23 and M123. The state chaining logic determination unit 16 may first determine the diagonal terms of the transition rate matrix MRes to be reconstructed from the selected transition rate matrices. Each of these diagonal terms corresponds to the speed at which the system corresponding to the grouping p leaves each state. To determine such a diagonal term, as illustrated in FIG. 14, the state chaining logic determination unit 16 may identify all the terms corresponding or capable of corresponding to the departure speed from the first state, i.e., state

[000] in the example of FIG. 14 (solid circles). The states corresponding to the rows and columns identify a possible detection device 200 not taken into account by a selected transition rate matrix, among the detection devices of the grouping p.The state chain logic determination unit 16 then considers each of the values ​​as a measurement affected by a Gaussian error, the variance of which is: . <72 = | x 2' (23) In equation (23), r denotes the number of detection devices 200 not taken into account by a selected transition rate matrix, among the detection devices of the grouping p. Thus, in the example of Figure 14, it comes ^2 — -L. x 9O (0 detection devices not taken into account by the matrix M123 among the detection devices of the grouping #1, #2, and #3), — dL x (1 detection device not taken into account in the matrix Af12, i.e. detection device #3), — _L x 2] detection device not taken into account in the 13 kl3 matrix Mi3, i.e. detection device #2), ^2, — — x 21 (1 detection device 23 k.: not taken into account in the Af23 matrix, i.e. detection device #1). The state chaining logic determination unit 16 then performs a maximum likelihood calculation to obtain the estimate of the diagonal term sought, namely the starting speed of state

[000] . Such a calculation amounts to determining x such that the likelihood A is maximal, where A is given by: xex e- (24) t 2«, Maximizing A as defined by equation (24) amounts to minimizing the quantity: .(13) ' WW! 4(w-ooi) (25)

[0274] The quantity defined by equation (25) is minimal when:

[0275] x*4(W()oof x'x[woo] ~ (26) 23 + ^2 + ^13 + ^3 " U

[0276] Equation (27) allows us to deduce ^[OOOHOOO]:

[0277] (27) X

[000]

[000] = " J_+_L+^+_L

[0278] The state chaining logic determination unit 16 then repeats the same steps to estimate the starting speed of the next state, i.e., state

[001] in the example of FIG. 14 (second iteration) and determine the second diagonal term of the resulting transition rate matrix MRes to be constructed. In the example of FIG. 14, the terms surrounded by dotted lines are those which are taken into account in the second iteration implemented by the state chaining logic determination unit 16 to determine the second diagonal term of the resulting transition rate matrix MRes to be constructed.

[0279] The state chaining logic determination unit 16 then repeats the same steps to estimate the starting speed of the following states, until all the terms of the diagonal of the resulting transition rate matrix MRes are obtained.

[0280] For the non-diagonal terms, the state chaining logic determination unit 16 can perform a normalization of the different selected transition rate matrices, by rows, by dividing each row of a selected transition rate matrix by the absolute value of the diagonal term of the row. The sum of the non-diagonal terms of each selected transition rate matrix, after normalization, is therefore equal to 1.

[0281] The state chaining logic determination unit 16 can then identify the terms corresponding or capable of corresponding to the state change concerned in the selected transition rate matrices, with the exception of the diagonal terms as illustrated by [Fig.15]. For example, for the state change

[000] —>

[001] , these identified terms are surrounded by solid lines, by dashes for the state change

[000] —>

[010] , and by dotted lines for the state change

[000] —>

[011] . It should be noted that not all the selected transition rate matrices necessarily intervene because the element capable of corresponding to the desired state change is sometimes diagonal, and therefore remains ignored.

[0282] The state chaining logic determination unit 16 may use formula (24) to calculate an estimate of the searched term of the resulting transition rate matrix MRes (such as the terms ^[oooÿooi], %wo][oio], *[00Q|[0iy, etc.), such as:

[0283] Since the selected transition rate matrices have been previously normalized, the off-diagonal terms of the resulting transition rate matrix MRes are obtained by then performing the following calculations: *

[000]

[001] = *[000100 i] x 1 *[0001(000] | ' *[000K010] - *

[000]

[010]

[0284] In the example of Figure 12, the generated mechanical system 500 makes it possible to determine that the detection devices 200 A and C are part of the same grouping, while the entity B is isolated, due to their respective distances, after relaxation. In this example, to determine the chaining logic of the groupings thus obtained, the grouping unit 14 can recalculate the resulting transition rate matrices corresponding to these groupings, by calculating a transition rate matrix M AC for the grouping {A,C] and a transition rate matrix MB for the grouping {B} respectively from the data observed for the detection devices A and C on the one hand and for the detection device B on the other hand.In this example, the MAC transition rate matrix is ​​at most 4x4 in size (because there are at most 22 = 4 possible states) while the MB transition rate matrix is ​​at most 2x2 in size (because there are at most 2l = 1 possible states). These transition rate matrices are in principle sparse, i.e. they contain few unharmed elements, which allows them to be exploited.

[0285] The embodiments of the invention thus make it possible to determine groupings of detection devices 200 in optimal cooperation networks, from simple initial state data (Boolean elements without the complexity of the entirety of the information collected during the interception of an electromagnetic / acoustic signal emanating from one of the detection devices present).

[0286] Advantageously, the control device 1 is capable of transposing the problem of grouping the detection devices 200 into the field of point mechanics, by representing the candidate groups of the detection set 2 in the form of a mechanical system where the devices are represented by points connected by elastic links. This representation makes it possible to use the algorithm of 'clustering' to determine the groupings of detection devices 200 that operate cooperatively. From the groupings obtained, the transition rate matrices already calculated make it possible to determine the orchestration logic of each grouping.

[0287] [Fig. 13] is a flowchart illustrating a cooperative detection method for monitoring a surveillance area using the detection assembly 2, according to certain embodiments.

[0288] In step 900, a modeling of the detection devices 200 of the detection assembly 2 is received. This modeling provides a modeling of the detection assembly 2 in the form of a macro-system passing from one state to another as soon as a detection device 200 switches from the active state ('ON') to the inactive state ('OFF') or vice versa.

[0289] In step 902, the transition rate matrices are determined by performing a learning phase from the observed state data sets 3, from the modeling of the detection devices 200.

[0290] Step 902 advantageously uses hidden Markov chain (HMM)-based learning to determine transition rate matrices.

[0291] In step 904, candidate groups are determined corresponding to different combinations of detection devices 200 of the set 2.

[0292] In step 906, a Q-tuple of group characteristic values ​​is determined for each candidate group from the transition rate matrices, the set of characteristic values ​​comprising at least the cooperation metric relating to the entropy, estimated for the candidate group (statistical entropy in the sense of information theory). The set of candidate group characteristic values ​​may in particular be the triplet {Lq, (Hq}, Kq}.

[0293] In step 907, a representation of the n devices of the detection set 2 is generated in the n-1 dimensional representation space in the form of the mechanical system 500 using the set of characteristic values ​​determined for the candidate groups.

[0294] In step 908, one or more groupings of detection devices 200 operating in a network (cooperating) are determined by applying a clustering algorithm to the mechanical system 500, after relaxation.

[0295] In step 910, the state chaining logic of each grouping obtained in step 908 is determined by generating a resulting transition rate matrix from the transition rate matrices determined in step 902.

[0296] The groupings of detection devices 200 can then be used according to the state chaining logics determined in step 910 to carry out a common detection or surveillance mission in the surveillance zone.

[0297] The control device 1 can initiate the determination of a grouping in different phases of a detection mission, such as for example on return from the mission, once on the ground, in analysis, or directly in flight for radar-type detection devices 200. The determination of a grouping can in particular be carried out in real time. In this case, the real data 3 relating to the state of the detection devices resulting from the observations can be collected dynamically and the computing power is adapted to obtain a rapid result.

[0298] Those skilled in the art will understand that the system or subsystems according to the embodiments of the invention may be implemented in various ways by hardware, software, or a combination of hardware and software, in particular in the form of program code that may be distributed as a program product, in various forms. In particular, the program code may be distributed using computer-readable media, which may include computer-readable storage media and communication media. The methods described in the present disclosure may in particular be implemented in the form of computer program instructions executable by one or more processors in a computer computing device. These computer program instructions may also be stored in a computer-readable medium.

[0299] Furthermore, the invention is not limited to the embodiments described above as a non-limiting example. It encompasses all the variant embodiments which may be envisaged by those skilled in the art.< / hq>

Claims

Claims

1. Cooperative detection system (100) comprising a detection assembly (2) for monitoring a monitoring area, the detection assembly comprising a plurality of detection devices (200), characterized in that it comprises: - a transition rate matrix determination unit (12) configured to estimate a transition rate matrix, for each candidate group among one or more candidate groups of detection devices of the assembly (2), by performing a learning phase based on hidden Markov chains (HMM), from a set of initial data indicating activity states of the detection devices (200) of the detection assembly (2) previously detected and from a modeling of the detection assembly (2), the transition rate matrix of a candidate group comprising coefficients,each representing a transition rate from one activity state to another for each detection device (200) of the associated candidate group, - a group characteristic magnitude determination unit (13) configured to determine a set of characteristic magnitudes for each candidate group from the transition rate matrix obtained for the candidate group, the set of group characteristic magnitudes comprising at least one cooperation metric relating to an entropy determined for the candidate group; - a grouping determination unit (14) configured to determine at least one grouping (20) of detection devices (200) from the set of group characteristic magnitudes determined for each candidate group,a detection grouping comprising at least two detection devices (200) connected in a network and capable of cooperating with each other; the cooperative detection system being capable of using a determined grouping for monitoring the surveillance zone.,

2. A detection system according to claim 1, wherein a coefficient of the transition rate matrix has a first index corresponding to a starting state and a second index corresponding to an ending state, the transition rate matrix being a matrix square, the dimension of the transition rate matrix associated with a candidate group of size R being defined by the total number LR of possible activity states for all R detection devices in the candidate group, each detection device having a number L of activity states.

3. Cooperative detection system according to one of the preceding claims, further comprising a state chaining rules determination unit (16) configured to determine state chaining rules for each determined grouping (20), from the transition rate matrices determined by the transition rate matrix determination unit (12) for the candidate groups comprising at least one detection device of the grouping and a weight associated with said transition rate matrices, the state chaining rules determined for a grouping defining the activity state transitions of the detection devices of the grouping, the cooperative detection system (100) being able to control each grouping (20) determined for monitoring the monitoring zone, according to the state chaining rules determined for the grouping.

4. Cooperative detection system according to one of the preceding claims, wherein the monitoring zone is located around the detection devices of the detection assembly (2).

5. A cooperative detection system according to one of claims 2 to 4, wherein the group characteristic value determination unit (13) is configured to determine a probability matrix from the transition rate matrix associated with a candidate group, by normalizing the non-diagonal terms of each row of the transition rate matrix so that their sum is unity, which provides a probability vector Çj for each row i of the transition rate matrix, comprising probability values, each corresponding to one of the terms of row • of the transition rate matrix, with the exception of the diagonal term, said probability values P& of the probability vector Çj obtained for a row i representing the probabilities of transitions to an arrival state,said probability vectors Çj obtained for all the rows of the transition rate matrix forming the rows of said probability matrix n, the cooperation metric, relative to an entropy of the candidate group being calculated from the probability matrix.

6. Cooperative detection system according to claim 5, wherein the calculation of the cooperation metric relating to an entropy of the candidate group comprises, for each row i of the probability matrix n, the determination of an entropy value, the entropy values determined for the different rows of the probability matrix forming an entropy vector H comprising entropy values h, associated with each row i of the probability matrix H, the cooperation metric relating to an entropy of the candidate group being determined from the entropy vector H.

7. Cooperative detection system according to claim 6, in which the entropy value h, associated with a row i of the probability matrix n is a Shanon entropy, determined according to the following equation (1): hi = G)

8. A cooperative detection system according to claim 7, wherein the cooperation metric is an entropy average calculated by averaging the components of the entropy vector H, weighted by applying a weighting coefficient ai to each component hj of the entropy vector H.

9. A cooperative detection system according to claim 8, wherein the weighting coefficients ai constitute the components of an average steady-state vector H defined by: q = ^exp(T.MT) ( P \ 1 ! where 11 denotes the dimension of the transition rate matrix M andT is a parameter representing a time value.

10. A cooperative detection system according to claim 9, wherein the time parameter T is equal to T — [Q3 X max ( À ) ' denoting the eigenvalues of the transition rate matrix.

11. Cooperative detection system according to one of the preceding claims 8 to 10, in which the set of group characteristic values is a triplet of value comprising the list Lq of the detection devices (200) of the candidate group Gq, the average entropy < Hq >, and the number of measurements Kq used to calculate the transition rate matrix.

12. Cooperative detection system according to claim 11, wherein the grouping determination unit (14) is capable of generating a representation of the candidate groups selected in the detection set (2) comprising n detection devices (200), in the form of a mechanical system, in the representation space of dimension n -1, from the triplet of values determined for each candidate group {Lq, (Hq), Kq], and wherein: - each detection device (200) of a candidate group is represented by a point in the representation space, - for each candidate group comprising a list Lq of P detection devices 200, the mechanical system comprises P elastic links connecting the representative points of the detection devices (200) of the candidate group to the center of a hypersphere (50) circumscribed at the P points, in the representation space;- The empty length 1 of said P elastic links is defined by the average entropy (Hq); - the elastic stiffness constant k of the P elastic links is proportional to the number Kq.;

13. A cooperative detection system according to claim 12, wherein the mechanical system further comprises elastic damping type friction forces or fluid brake type friction forces relating to friction coefficients chosen to bring the mechanical system into a stable state.

14. Cooperative detection system according to claim 12 and 13, wherein the grouping unit (14) is capable of evolving the mechanical system towards a stable state by implementing a resolution of a differential system associated with the equations which govern the mechanical system.

15. A cooperative detection system according to claim 12 to 14, wherein the grouping unit (14) is adapted to determine at least one grouping of detection devices by applying a grouping algorithm to the mechanical system using the distance between the representative points of the detection devices in the mechanical system (500), in the stable state.

16. A cooperative detection method (100) for monitoring a surveillance area using a detection assembly (2) comprising a plurality of detection devices (200), characterized in that it comprises the steps of: - defining one or more candidate groups of detection devices (200) of the detection assembly (2), - determining a transition rate matrix (12) for each candidate group by performing a learning phase based on hidden Markov chains (HMM), from an initial data set indicating activity states of the detection devices of the detection set (2) previously detected and a modeling of the detection set (2), the transition rate matrix of a candidate group comprising coefficients, each coefficient representing a transition speed from one state to another for each detection device (200) of the associated candidate group, - determining a set of group characteristic quantities (13) for each candidate group from the transition rate matrix obtained for the candidate group, the set of group characteristic quantities comprising at least one cooperation metric relating to an entropy calculated for the candidate group;- determining at least one grouping (20) of detection devices (200) from the set of group characteristic quantities determined for each candidate group, a detection grouping comprising at least two detection devices (200) connected in a network and capable of cooperating with each other; the cooperative detection method being able to use each determined grouping for monitoring the surveillance area.

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