Cooperative detection system and method

Abstract

A cooperative detection system (100) is proposed, configured to: - estimate (12) a transition rate matrix for each candidate group of a set of detection devices (2) by performing hidden Markov chain learning from activity state data 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) in the associated candidate group; - determine (13) a cooperation metric related to the entropy of each candidate group from the associated transition rate matrix; - determine (14) at least one grouping (20) of networked detection devices (200) capable of cooperating with each other, from the cooperation metrics, the cooperative detection system being capable of using each grouping to monitor an area. Abbreviated: 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 radar devices, may be present and may be required to cooperate with each other for the purpose of the same detection or surveillance mission (joint mission) in a surveillance area.

[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 accomplish the common mission.

[0004] Such control is achieved using execution logic that governs the various cooperating detection devices. This execution logic, distributed across the different 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 performed by an operator, and is therefore not optimized.

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

[0007] General definition of the invention

[0008] To this end, a cooperative detection system is proposed comprising a detection set for monitoring a surveillance area, the detection set comprising a plurality of detection devices. Advantageously, the detection system comprises:

[0009] - a unit for determining a transition rate matrix configured for to estimate a transition rate matrix, for each candidate group among one or more candidate groups of detection devices from the set, by performing a Hidden Markov Chain (HMM) learning phase, from an initial dataset indicating the activity states of the detection devices from the previously detected set and a model 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 in the associated candidate group,

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

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

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

[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 ending 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 R detection devices of the candidate group, each detection device having a number L of activity states.

[0014] In certain aspects, the system may further include a state chaining rule 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 candidate groups comprising at least one grouping detection device and a weight associated with the transition rate matrices, the state chaining rules determined for a grouping defining the activity state transitions of the grouping detection devices, the cooperative detection system being able to control each determined grouping for the surveillance of the surveillance area, according to the state chaining rules determined for the grouping.

[0015] The surveillance area can be located around the detection devices of the detection assembly.

[0016] In embodiments, the unit for determining characteristic group values ​​can 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, thus providing 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, with the exception of the diagonal term, said probability values ​​of the vector

[0017]

[0018] probabilities Ç- obtained for a rowz representing the probabilities of transitions to an arrival state, the probability vectors Çz obtained for all 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. The calculation of the cooperation metric relative to an entropy of the candidate group may include, 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 relative to an entropy of the candidate group being determined from the entropy vector H. In some embodiments, the entropy value associated with a row of the probability matrix n can be a Shannon entropy, determined according to the following equation _ y7V-l ni~ ~^k^PikmPik

[0019] According to one aspect, the cooperation metric can be an average entropy 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, wherein the weighting coefficients aj constitute the components of a mean steady-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( A- ) ' denoting the eigenvalues ​​of the transition rate matrix.

[0024] The set of characteristic group values ​​may be a triplet of values ​​comprising the list Lq of 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 grouping determination unit may be capable of generating a representation of the candidate groups selected in the detection set comprising detection devices, in the form of a system mechanics, in the n-1 dimension representation space, from the triplet of values ​​determined for each candidate group {Lq, ( Hq ), Æç], and in which:

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

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

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

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

[0030] In certain aspects, the mechanical system may further include 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 towards a stable state by implementing a resolution of a differential system associated with the equations that govern the mechanical system.

[0032] According to some aspects, the grouping unit may be able 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, in the steady state.

[0033] A cooperative detection method is further proposed for monitoring a surveillance area using a detection array comprising a plurality of detection devices. The method comprises the steps of:

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

[0035] - determine a transition rate matrix for each candidate group in performing a Hidden Markov Modeling (HMM) learning phase, from an initial dataset indicating the activity states of the detection devices in the previously detected detection set and a model 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 in the associated candidate group,

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

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

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

[0039] Other features, details and advantages of the invention will become apparent from the description given with reference to the accompanying drawings provided by way of example, which represent, respectively:

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

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

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

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

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

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

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

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

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

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

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

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

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

[0053] [Fig. 14] - The [Fig. 14] illustrates a step in determining the logic sequence of states of a grouping, according to an example of implementation.

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

[0055] Detailed description of the application

[0056] Fig. 1 represents a cooperative detection system 100 comprising a detection set 2 comprising a plurality of detection devices 200 (at least two).

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

[0058] The cooperative detection system 100 implements active monitoring. Thus, each detection device 200 emits electromagnetic waves (which can be radio frequency or optical waves) or acoustic waves, and is configured to deduce 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 can be, for example, a radar or sonar device.

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

[0061] The rest of the description will be made primarily 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 can be an active state ('ON') in which the detection device is emitting or in an inactive state ('OFF') otherwise.

[0063] The cooperative detection system 100 includes a control device 1 configured to control the cooperation between the various detection devices 200 of the detection set to perform the surveillance mission in the surveillance area. 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 area.

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

[0065] A detection device (in transmit mode) 200 of assembly 2 emits waves that an observer (i.e., a receiving device) can intercept to identify state information about the detection device 200 at different past times. When the observer is sufficiently close, they can obtain, for each transmitting detection device 200, 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, a receiver mounted in an aircraft), their distance from the various detection devices 200 fluctuates, so 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 that instant is information indicating the unavailability of the information. Thus, the state dataset used by the control device 1 (and derived from observations collected by at least one observer at different times) can include different values ​​relating to the activity state of each detection device 200 in set 2, corresponding to different past detection times. A value relating to an activity state is thus associated with a given detection device 200 and a detection time and can take one of the following values:

[0066] - a first value VI indicating an activity state (or "ON" state) of the device (i.e. 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 (i.e., indicating that the detection device is off); or

[0068] - a third value V3 indicating state unavailability information The third value, V3, indicates an indeterminate state characterized by the absence of information, which can be noted, for example, as 'N / A' (Not Available) or NaN (Not a Number). In the remainder of this description, the third value will be referred to as "NaN" as a non-limiting example.

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

[0070] The control device 1 includes a modeling unit 10 capable of providing a model of the detection assembly 2 comprising detection devices 200 in the form of a macro-system switching 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 model 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 can have a target search operating mode, in which the detection device 200 is configured to detect a target (object for example) in the surveillance area, and a tracking 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 set 2. The embodiments of the invention advantageously use hidden Markov chains (HMM, acronym for the corresponding Anglo-Saxon expression 'Hidden Markov Model') to control the cooperations (or collaborations) between several detection devices 200 of the detection set 2 and to determine at least one grouping of detection devices 200.

[0074] The control device 1 further includes 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 set 2, by performing a hidden Markov chain (HMM) learning phase, from the dataset 3 indicating observations of activity states of the detection devices of the detection set 2 (activity states previously detected at different previous times) and the modeling of the detection set 2 provided by the modeling unit 10. The hidden Markov chain (HMM) learning phase includes a data sampling step which can be with variable time step or 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 The first index corresponds to a starting state (row index for example) and the second index corresponds to an ending state (column index for example).

[0076] The control device 1 also includes 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 ​​can be a P-tuple comprising at least one quantity related to a calculated entropy (also called the 'cooperation metric') for the candidate group Gq. In one embodiment, the cooperation metric can be an average entropy. The P-tuple can 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 (the total number of possible states of the candidate group corresponding to the transition rate matrix).

[0077] The control device also includes a grouping determination unit 14 (hereafter referred to as "grouping unit") configured to determine at least one grouping of detection devices 200 that belong to the same cooperation network from the set of characteristic group values ​​obtained for each candidate group.

[0078] The control device 1 may include 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 in 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 (so-called "networked" devices).

[0080] Due to the observer's mobility, the observer may have insufficient information regarding the activity status of the various detection devices 200 so that the state data set 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 various detection devices 200 is known. In a real-world situation, the position of the observer (e.g., a receiver in flight) can be adjusted so as to be able to listen to the emissions 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 using only information relating to the activity state of the detection devices (first value VI in case of activity, second value in case of inactivity, or third value V3 in case of unavailable information), and does not use information on the trajectories of the detected targets.

[0082] In one embodiment, the observed activity state dataset 3 can be modeled as 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 state value can be a boolean value taking the first value VI (e.g. 1) or the second value V2 (e.g. 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] Figure 3 illustrates an example of an activity state observation table. In the example in Figure 3, four detection devices 200 are considered in the scene (#1, #2, #3, #4), and different times are indicated the activity state of each detection device 200. 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 detection set 2 so as to extract a set of state sub-matrices, each corresponding to a group of candidate detection devices. More precisely, the partitioning of the activity table into state sub-matrices is performed so that each state submatrix 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 elements indicating unavailability of state information (third value V3 of state information such as "NaN", for example). A submatrix of the state observation table therefore contains only active state values ​​(first value VI such as the value 1) and / or inactive state values ​​(second value V2 such as the value 0). It can be composed of elements from continuous or non-continuous columns or rows of the table. A state submatrix thus corresponds to state information from at least two detection devices 200 of the detection set 2 (i.e., it contains elements from at least two columns of the initial state observation table).

[0085] Each state submatrix 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 indeterminate information (i.e. third value V3 of activity state information indicating that the activity state is unavailable such as "NaN").

[0086] Figure 4 illustrates an example of the segmentation of a state observation table. 50 into two state sub-matrices 53 and 54 corresponding to two candidate groups. The sub-matrices can be divided into two sub-matrices so as to isolate as many rectangular sub-matrices devoid of "NaN" elements (third V3 value 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 in [Fig. 4], the state submatrix 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 detection devices #1 and #2. The state submatrix 53 is a rectangular partition such that it contains only elements 0 (inactive state) or l (active state). The state submatrix 53 is thus associated with the candidate group of detection devices comprising devices {#1, #2}.

[0088] The state submatrix 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 detection devices #3 and #4. It also corresponds to a rectangular partition such that the submatrix 54 contains only elements 0 (inactive state) or 1 (active state). The state submatrix 54 is thus associated with the candidate group of detection devices including devices {#3, #4}.

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

[0090] Each state submatrix thus obtained (53 or 54, for example) comprises a set of state vectors, each state vector corresponding to a row of the state submatrix associated with a given time t, and represents the observed state of the various detection devices 200 associated with the state submatrix. The state vector thus comprises a set of components, corresponding to the various detection devices associated with the state submatrix, 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 indicating whether, at the given time t:

[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 an emission 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 in [Fig.4], the state vector corresponding to time t=246 is '11' for submatrix 53.

[0094] It should be noted that although referred to as "state submatrix" and "state vector" for simplicity, these data structures correspond respectively to state observation submatrices 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 submatrices and state vectors (corresponding to the observations) may not exactly correspond 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 200 devices it includes) up to 2” different possible states, in cases where each of the n devices can have one state among 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 submatrices, 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, and then at least one characteristic quantity of the candidate group from the rate matrix. of transition, including at least one value relative to the entropy of the candidate group. The control device is then capable of determining at least one grouping of 200 detection devices that collaborate based on the relative entropy values ​​of the different candidate groups. The control device 1 can further determine the state chaining logic associated with each grouping based on the modeling performed by the modeling unit 10 and 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 take place independently of variations in the environment, that is to say that whatever the results of measurements carried out by the detection devices 200 (in transmission), the 'ON' / 'OFF' switching sequences remain unchanged, whether they are strictly deterministic or probabilistic (i.e. it is assumed that all 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 primarily with reference to a Boolean (in particular binary) representation of the activity state of the detection devices 200, those skilled in the art will readily 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 may 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 performed by the detection device 200.For example, the Q-tuple can be a pair (Q=2) of state values ​​denoted 'xix2' where Xi characterizes the activity ('ON' or 'OFF') of the detection device 200, and x2 characterizes whether an object has recently been detected 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 potentially hostile detection and therefore continues to switch its set of detection devices 200 on (i.e., turn 'ON' or active) and off (turn 'OFF' or inactive) at its usual rate (i.e., without taking the object detection into account).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 in question, the detection device is emitting a radar wave) or not (value V2 meaning that on the date in question, 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 causal relationship that may exist between a detection and the activity of the different detection devices 200.

[0101] The activity state datasets can be updated dynamically 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 partitioning 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 unit for determining the transition rate matrix 12 is then configured to determine a transition rate matrix associated with each candidate group Gq corresponding to a state submatrix.

[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 capable of learning the state-switching logic 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 datasets by implementing a learning phase based on Hidden Markov Models (HMMs) and using the state submatrices derived from the state observation table (and in particular the state vectors associated with the different detection devices in the candidate group). This learned state-switching logic can then be used by the grouping unit 14 to determine the cooperative groupings of detection devices 200.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 environment 2, in the case where a device has two possible activity states.

[0105] The set of detection devices 200 in the detection set 2 therefore behaves as a state machine, the unit of determination of the transition rate matrix 12 being able to reconstruct the state transition logic and the temporality of this state machine. In particular, for each state, the unit of determination of the transition rate matrix 12 is able to determine how long it takes for each detection device 200 to leave this state, towards which state(s) it will evolve, or it is probable 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 that represents the transitions between activity states for each detection device in 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 transition rates 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 can use the algorithm described in LIU, Yu-Ying, MORENO, Alexander, XU, Maxwell A., et al. Efficient Leaming and Decoding of the Continuous-Time Hidden Markov Model for Disease Progression Modeling. arXiv preprint arXiv:2110.13998, 2021, designed to track the progression of a disease, either in continuous time (i.e., data sampling is performed at variable time steps) as described in this article, or by adapting it to operate at constant time steps. This algorithm notably uses, in one step, the procedure 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 Leaming and Decoding of the Continuous-Time Hidden Markov Model for Disease Progression Modeling. arXiv preprint arXiv:2110.13998, 2021 (LIU et al), in particular on 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 sub-matrix of states (observations at different times), and the set of 7 possible states of the detection set 2. The applied method then determines the number of times a transition from one initial state to another occurs, and after what average time, which makes it possible to determine an initial transition rate matrix. Then, starting from the initial transition rate matrix, the transition rate matrix determination unit 12 applies the iterative HMM algorithm, which in its sixth step uses the procedure 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 observations of the submatrix, the transition rate matrix determination unit 12 can take into account all the probabilities of changes in the considered state between these two observations. Potentially, a state could have changed a large number of times, 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 estimation of the transition rate matrix. The algorithm is 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 sub-state matrix, the convergence of the current estimate of the transition rate matrix to be 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 the next, since in this case it is considered that this estimate is sufficiently good (the variation in 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 less than this threshold, the stopping condition of the process is reached, i.e. the iterations are stopped and the current transition rate matrix obtained in the current iteration is returned as a 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 submatrix.

[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 speed 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 transition 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 submatrices 53 and 54 of [Fig. 4], derived from the decomposition of the state observation table 50, as an illustrative example. [Fig. 5] shows only the state vectors drawn respectively from the state submatrices 53 and 54 (components representing the activity states in 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 M53 matrix has a value of 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 M53 matrix has the value -0.1, which means that from state 1 (row number), one moves to state 1 (column number) at a speed of -0.1 s*. The minus sign "-" means that one leaves this state. The value 0.1 therefore means that it takes 10 seconds to leave it.

[0119] The columns of the transition rate matrix (e.g. 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 entries of the transition rate matrix (e.g., Af53 and ^54) are negative, and the sum of the elements in the same row is zero. The 'k' row of a transition rate matrix indicates that from state 'k', one moves towards the state '1' corresponding to the column index. Thus, from a state 'k', it is not possible to move to that same state; it is only possible to leave it, regardless of 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 one remains in the state indefinitely.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 each subsequent possible state is reached with a cumulative speed equal to the starting speed.

[0121] According to another example, considering a detection set with 2‰ = 4 possible states (the case where set 2 includes 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 initial state corresponding to the first row, we arrive in state [1], the final 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] (final 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 reach state [3].

[0124] The transition rate matrix can be a square matrix. The dimension of the transition rate matrix associated with a candidate group of size R (i.e., the number of devices in the candidate group) is defined by the total number LR of possible activity states for all R detection devices in 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 comprises n detection devices, the total number of possible states being then at most equal to 2ⁿ states, the transition rate matrix is ​​square, of size 2ⁿ x 2ⁿ.

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

[0126] The transition rate matrix calculated by learning from the state dataset can be sparse or non-spouted. A sparse matrix consists mainly of nuisance coefficients (the percentage of non-nuisance coefficients is low).

[0127] In particular, if within the same row of a transition rate matrix, only two coefficients are non-zero, 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 one 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 hollow 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 200 detection devices operates in a network and has a deterministic state-sequencing logic or one that includes only a few random variables. If the The logic of the chaining of 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 contains only 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 estimation obtained from measurements (observed state data) which may be subject to errors (for example in cases of non-detection or false positives), it is not generally obtained from transition rate matrices 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 can be considered, defined by the following coefficients:

[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 a sparse matrix, so that the corresponding candidate group Gj can be considered to use deterministic logic. In the case of the second matrix M2, however, the corresponding state-chaining logic can be considered non-deterministic.

[0135] Thus, the transition rate matrix Mi can be considered quasi-deterministic, while the transition rate matrix M2 is more random. It should be noted that in practice, it is virtually impossible to obtain absolute zeros, since the algorithm used to generate the transition rate matrices is an iterative process that allows a certain number of iterations. These iterations 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 approximately unchanged from one iteration to the next.

[0136] For a strictly deterministic transition rate matrix, each row should contain only zeros except for two terms, namely a diagonal term and another term. In practice, the value is never exactly zero but almost zero. The transition rate matrix M5 illustrates a case that much closer to a strictly deterministic matrix since there are several orders of magnitude between the terms that 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 unit for determining characteristic group values ​​13 is configured to determine a K-tuple of characteristic group values ​​comprising at least one quantity relating to the entropy of the group ('cooperation metric') for each candidate group Gq whose value indicates how sparse a transition rate matrix associated with the candidate group Gq is 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 can be configured to scan each row of the transition rate matrix and, for each row, to check only the off-diagonal terms. In particular, the group characteristic value determination unit 13 is configured to normalize the off-diagonal terms of each row of the matrix so that their sum is unity (normalization operation). The following steps are performed to carry out 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 retained terms,

[0141] - each of the remaining terms in 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 equals 1, yielding a probability vector Ç; comprising probability values, each corresponding to one of the terms in the considered row i of the transition rate matrix, except for the diagonal term (the probability vector therefore has one fewer component than the considered row). The probability values ​​of the probability vector obtained for the considered row i represent the probabilities of transitions to an arrival state (the list of subsequent probable states, without information about the velocity).

[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 The probability matrix is ​​the vector obtained for row f of the transition rate matrix.

[0143] For example, considering the example matrices and the Ode transition probabilities obtained 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 includes probability coefficients Pjk representing the transition probabilities to a final state for each row of the transition rate matrix (corresponding to a starting state). The unit for determining group 13 characteristic values ​​can then estimate the extent to which the probabilities converge to the same final state from the probability matrix FI.

[0147] In particular, in one embodiment, the unit for determining group characteristic values ​​13 can be configured to determine the Shannon entropy, which quantifies the spreading of the probability distribution of arrival states from a single starting state. A low entropy value thus indicates the existence of a preferred arrival state, while a high entropy indicates 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 Shannon 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 number 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. Conversely, it is at its maximum when the arrival states are equally probable. Such an entropy vector H thus indicates whether a state-chaining logic of a candidate group is more deterministic or random.

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

[0156] In the example 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 unit for determining characteristic group values ​​13 can determine an average Hmoy of the values ​​of the entropy vector (hereafter also referred to as "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 can 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] Given the transition rate matrices M^, by calculating their exponential With a long time, the average steady-state vector, which is a mixture of the Nq states, can be calculated using 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, denoting the eigenvalues ​​of the matrix Mq (i.e., roots of the characteristic polynomial of the matrix) by 4, r can be chosen equal to T - ] ÿ x max^ ) • According to equation (3), using vector 7, the entropy of each line can be weighted by the presence of a state over time. Thus, a frequently recurring state will weigh more than a very rare condition. Considering the example of the two transition rate matrices M1 and M2, which are of dimension n = 4, the average steady-state coefficient [7] defined for the matrix M1 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 should be noted 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 average entropy is advantageous because the entropy input is all the more significant as it concerns a frequently affected condition. Taking into account the values ​​7 and 72, the average entropy - (HJ and the average entropy corresponding respectively from the 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 remainder 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 M5 transition rate matrices obtained for four 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 specifically, Figure 7 illustrates the steps for determining the average entropy, again numbered (H3), in the case of another example 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 a transition rate matrix M3 associated with a second candidate group {#1,#2}.

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

[0179] Figure 10 illustrates the steps for calculating the average entropy j, again noted (H6), in the case of another example of a 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 the candidate group {#1,#2, #3};

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

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

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

[0185] From the entropy-related cooperation metrics, such as the average entropies (Hq), obtained from the transition rate matrices Mq associated with the different candidate groups corresponding to the state submatrices, 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 contains detection devices 200 with the greatest probability of belonging to the same network.

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

[0187] In embodiments, the cooperation metrics obtained for the different candidate groups, such as average entropies (Hq), can be compared with 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 related to entropy (e.g. 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 the detection devices #1 and #3 of the candidate group {#1, #3} having the lowest entropy cooperate while the detection device #2 operates alone.

[0190] Thus, for each candidate group, the transition rate matrix is ​​determined, and then the cooperation metric related to entropy (e.g., average entropy) is determined 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 characteristic group values ​​comprising:

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

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

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

[0195] In the following description, the cooperation metric with respect to entropy will be considered to be the average entropy < Hq > as an illustrative example, and the triplet of characteristic group values ​​will therefore be denoted {Hq), Kq],

[0196] The triplets [Lq, ( Hq), Kq] obtained for the different candidate groups Gq thus provide trend information through the cooperation metric related to 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 grouping determination unit 14 can be configured to determine groupings of detection devices 200 into networks from all 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 an n-1 dimension space in which point mechanics laws are applied. In this representation space, each real detection device 200 is represented as 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 200 detection devices between them (i.e. it indicates how well they appear to cooperate). If a triplet {Lq, (Hq), Kq] corresponds to a candidate group involving p detection devices (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 representative points of the detection devices to the center of a hypersphere circumscribed by the p points (a hypersphere passing through the p points) in the representation space. The unstretched 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 that depends on the number of measurements Kq, and therefore on the reliability of this entropy. Elastic connections between the p points are used to ensure that all the representative points of the detection devices 200 are equidistant 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, and thus at most n - 1 (in the case where P = n, i.e., in the case of a triplet involving 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, three 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, corresponding to a candidate group G(A, B, C) comprising the three detection devices A, B, and C. Therefore, connections link the point Oabc, the center of the circle circumscribed about triangle ABC, to the points A, B, and C. A second triplet is considered, corresponding to a candidate group G(A, C) comprising only the two detection devices A and C. Therefore, elastic connections link the midpoint of segment [AC] to the points A and C.

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

[0204] In the example in Figure 11, the elastic force from point ^abc acting 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 devices A, B and C is high but that of the triplet {LAC, ( , Kac} associated with the group GAC comprising devices A and C is small, so after relaxation of the mechanical system, the point OABC must be "far" from points A, B and C while the point OAC must be close to points A and C.

[0207] Placement in a two-dimensional representation space (n = 3) allows the establishment of links towards the point OABC so that these links can reach their unloaded length, and also allows points A and C to get closer to each other without impacting the tension of the links around the point ^abc- Indeed, points A and C can get closer by sliding along the circle 50 shown in [Fig.1 1].

[0208] In some embodiments, frictional forces may be applied to the mechanical system 500. In this case, the frictional forces added to the representation of the mechanical system of candidate groups allow the mechanical system 500 to relax rather than undergo perpetual oscillations, thus resulting in a system 500 where the elastic potential energy becomes minimal. In some cases, there may indeed be tension in the sense that springs may come into conflict. The spring constant kq of each spring is thus used to arbitrate between the forces of the springs. However, once relaxation is achieved, the conflicting springs (both the "losing" and "winning" springs) do not, in practice, reach zero potential energy but rather a minimum.

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

[0210] In the embodiment where a friction force of the elastic damping type 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 amortization ~ ' J amortization 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, 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. 1 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 reach a stable state, the grouping unit 14 can evolve the mechanical system representing the candidate groups in the representation space by implementing a solution of a differential system associated with the point mechanics equations that govern the mechanical system. The friction coefficients / ,. ^etdef., ., can They must be adjusted as precisely as possible. Small values ​​for the friction coefficients, for example, can allow the mechanical system 500 to oscillate for a long time before stabilizing. Conversely, large values ​​for the friction coefficients can dampen the oscillations of the mechanical system 500 as well as its 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 slowing them down so that they stabilize until they reach the relaxation 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 as the elements are set in motion. The energy The mechanical energy of the system is equal to the sum of its potential energy and kinetic energy, which is consumed by braking forces. The mechanical energy then decreases until the system reaches a stabilization state. In this stabilization state, a clustering algorithm can be applied to the system to determine at least one grouping of detection devices. 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-based classification algorithm, such as a DBscan algorithm (for 'Density-based Spatial Clustering of Applications with Noise').The stabilization state is reached once the springs of the mechanical system have reached their minimum potential energy.

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

[0221] As illustrated, the set of elastic links allows points A and C to move closer together if the entropy (HAC) calculated for the group GAC is low while being consistent with the high entropy (HABCL) of the group GABC 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 representational space;

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

[0225] - The unstretched length, denoted l, of the p elastic joints is defined by the entropy average < Hq > ;

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

[0227] - frictional forces can be applied to the mechanical system 500 for bring him 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 about the points in the n-1 dimension 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 such that :

[0234] y <10) Æ = I e, I

[0235] The matrix R allows the projection of a one-dimensional element into the orthonormal basis that has been created (the orthonormal basis consists of the vectors ei, the construction of the basis (ei' e2' etc.) being carried out according to the Gramm-Schmidt orthonormalization process). 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 basis 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, denoted Q, satisfies the following equation:

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

[0242] This equation can also be written as:

[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 coincident, then the matrix A, created from a family of free vectors, is reversible.

[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 along the vectors. Equation (11) was then used to redefine the position of each element in an orthonormal coordinate system centered around the point with index p. Equation (11) thus shows that the point pa, as the position in this new coordinate system, is the point 0-

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

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

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

[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 separating those which do not seem a priori to operate together, from the representation of the elastic links between the points of the same candidate group.

[0261] The grouping unit 14 can be configured to then apply the grouping algorithm (or "clusterization") 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 process that uses a threshold defining the neighborhood e of a point. For each point, the process determines which points are in the neighborhood of the point (i.e., at a distance less than e from the point in question). The selected points (points in the (neighborhood) points are then added together to form a group. The method thus groups points representing detection devices 200 by point. The neighborhood threshold s is predetermined or predefined appropriately depending on the application of the invention. Indeed, if the threshold s is too small, each point can form a group of which it is the sole member. Conversely, if the threshold e is too large, a single group encompassing all 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 given grouping, the state chaining logic determination unit 16 can select all the transition rate matrices that are associated only with detection devices 200 belonging to the given grouping, and perform a weighted average 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 grouping obtained, the state chaining logic determination unit 16 selects all the resulting transition rate matrices corresponding to candidate groups comprising a detection device 200 of the grouping under consideration. For example, if the grouping under consideration 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, associated respectively with the four candidate groups [#1,#2], [#1,#3], [#2,#3], [#1,#2,#3], as illustrated in Figure 14.The state chaining logic determination unit 16 is then capable of reconstructing a resulting transition rate matrix Res from the selected transition rate matrices, taking into account the L detection devices of the considered grouping (e.g., 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 grouping P123 includes 3 detection devices). To determine the resulting transition rate matrix MRes, it is assumed 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 to (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 can initially 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 grouping p leaves each state. To determine such a diagonal term, as illustrated in Figure 14, the state chaining logic determination unit 16 can identify all terms corresponding or potentially corresponding to the departure speed from the first state, i.e., state

[000] in the example in Figure 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 grouping p.The state chaining logic determination unit 16 then considers each of the values ​​as a measure tainted by a Gaussian error, whose variance is: . <72 = | x 2' (23) In equation (23), r denotes the number of detection devices not taken into account by a selected transition rate matrix, among the detection devices in grouping p. Thus, in the example in Figure 14, we have ^2 — -L. x 9O (0 detection device not taken into account by matrix M123 among the detection devices in grouping #1, #2, and #3), — dL x (1 detection device not taken into account in 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 in Figure 14 (second iteration), and to determine the second diagonal term of the resulting transition rate matrix MRes to be constructed. In the example in Figure 14, the terms circled with dashed lines are those 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 subsequent states, until all the terms of the diagonal of the resulting transition rate matrix MRes are obtained.

[0280] For off-diagonal terms, the state chaining logic determination unit 16 can perform a normalization of the different selected transition rate matrices, row by row, 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 off-diagonal terms of each selected transition rate matrix, after normalization, is therefore 1.

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

[000] —>

[001] , these identified terms are outlined in solid lines, in dashes for the state change

[000] —>

[010] , and in dashes for the state change

[000] —>

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

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

[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 in Figure 12, the generated mechanical system 500 determines that the detection devices 200 A and C belong to the same grouping, while 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 MAC for the grouping {A,C] and a transition rate matrix MMB for the grouping {B} respectively from the observed data for the detection devices A and C on the one hand and for the detection device B on the other.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, meaning they contain few non-nuisance elements, which allows them to be used.

[0285] The embodiments of the invention thus make it possible to determine groups of detection devices 200 in optimal cooperation networks, from simple initial state data (Boolean elements without the complexity of all 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 suitable for 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 as a mechanical system where the devices are represented by points connected by elastic links. This representation allows the use of the algorithm of 'Clustering' is used to determine the groupings of 200 detection devices that operate cooperatively. From the resulting groupings, the previously calculated transition rate matrices allow the orchestration logic of each grouping to be determined.

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

[0288] In step 900, a model of the detection devices 200 of the detection set 2 is received. This model provides a model of the detection set 2 in the form of a macro-system switching 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) learning to determine transition rate matrices.

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

[0292] In step 906, a Q-tuple of characteristic group values ​​is determined for each candidate group from the transition rate matrices, the set of characteristic values ​​including at least the cooperation metric related to entropy, estimated for the candidate group (statistical entropy in the sense of information theory). The set of characteristic values ​​for the candidate group 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 dimension 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 networked (cooperating) detection devices 200 are determined by applying a clustering algorithm to the mechanical system 500, after relaxation.

[0295] At 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 groups 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 area.

[0297] The control device 1 can initiate the determination of a grouping at different phases of a detection mission, such as upon return from the mission, once on the ground, during analysis, or directly in flight for radar-type detection devices 200. The determination of a grouping can notably be carried out in real time. In this case, the actual data 3 relating to the state of the detection devices 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 embodiments of the invention can be implemented in various ways by hardware, software, or a combination of hardware and software, in particular in the form of program code that can be distributed as a program product in various forms. In particular, the program code can be distributed using computer-readable media, which may include computer-readable storage media and communication media. The methods described herein can, in particular, be implemented in the form of computer program instructions executable by one or more processors in a computer system. These computer program instructions can also be stored in computer-readable media.

[0299] Furthermore, the invention is not limited to the embodiments described above by way of non-limiting example. It encompasses all the variant embodiments that could be envisaged by a person skilled in the art.< / hq>

Claims

Demands

1. A cooperative detection system (100) comprising a detection set (2) for monitoring a surveillance area, the detection set 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 in the set (2), by performing a Hidden Markov Chain (HMM)-based learning phase, from an initial dataset indicating the activity states of the detection devices (200) in the detection set (2) previously detected and a model of the detection set (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 quantity determination unit (13) configured to determine a set of characteristic quantities 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 relative to a determined entropy 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 quantities determined for each candidate group,a detection grouping comprising at least two networked detection devices (200) capable of cooperating with each other; the cooperative detection system being capable of using a specific grouping for monitoring the surveillance area.

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. A cooperative detection system according to any one of the preceding claims, further comprising a state chaining rule 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 candidate groups comprising at least one grouping detection device and a weight associated with said transition rate matrices, the state chaining rules determined for a grouping defining the activity state transitions of the grouping detection devices, the cooperative detection system (100) being capable of controlling each determined grouping (20) for monitoring the monitoring area, according to the state chaining rules determined for the grouping.

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

5. A cooperative detection system according to any 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 1 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 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 relative 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 relative to an entropy of the candidate group being determined from the entropy vector H.

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

8. Cooperative detection system according to claim 7, wherein the cooperation metric is an average entropy 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. Cooperative detection system according to claim 8, wherein the weighting coefficients ai constitute the components of a mean steady-state vector H defined by: q = ^exp(T.MT) ( P \ 1 ! where 11 denotes the dimension of the transition rate matrix M and T is a parameter representing a time value.

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

11. Cooperative detection system according to any one of the preceding claims 8 to 10, wherein the set of characteristic group values ​​is a value triplet comprising the list Lq of 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 to the P points, in the representation space;- The unstretched 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. 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 claims 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 that govern the mechanical system.

15. Cooperative detection system according to claim 12 to 14, wherein the grouping unit (14) is capable of determining 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 steady state.

16. Cooperative detection method (100) for monitoring a surveillance area using a detection set (2) comprising a plurality of detection devices (200), characterized in that it comprises the steps of: - define one or more candidate groups of detection devices (200) from the detection set (2), - determine a transition rate matrix (12) for each candidate group by performing a Hidden Markov Chain (HMM) learning phase, from an initial dataset indicating activity states of the detection devices of the detection set (2) previously detected and a model 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, - determine 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 relative to an entropy calculated for the candidate group;- determine at least one grouping (20) of detection devices (200) from the set of characteristic group 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 process being able to use each determined grouping for the surveillance of the surveillance area.

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