COOPERATIVE SENSOR SYSTEM AND METHOD

Description

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 in such a way 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 distributed execution logic 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] The closest prior art document EP 3 874 480 describes a facility monitoring system for assessing the safety of anomalies or an abnormal state of a facility by performing a learning phase based on hidden Markov chains (HMM).

[0007] There is therefore a need for an improved cooperative detection system and process. General definition of the invention

[0008] To this end, a cooperative detection system is proposed, comprising a detection array for monitoring a surveillance area, the detection array comprising a plurality of detection devices. Advantageously, the detection system includes: a transition rate matrix determination unit configured to estimate a transition rate matrix, for each candidate group among one or more candidate groups of detection devices in the set, by performing a Hidden Markov Chain (HMM) learning phase, from an initial dataset indicating the activity states of the detection devices in 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, a group characteristic quantity determination unit 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 including at least one cooperation metric relative to a determined entropy for the candidate group; a grouping determination unit configured to determine at least one grouping of detection devices from the set of group characteristic quantities determined for each candidate group, a detection grouping comprising at least two networked detection devices capable of cooperating with each other.

[0009] The cooperative detection system is capable of using a determined grouping for monitoring the surveillance area.

[0010] In some 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 L R< of possible activity states for all the R detection devices for the candidate group, each detection device having a number L of activity states.

[0011] 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.

[0012] The surveillance area can be located around the detection devices of the detection system.

[0013] In some 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 off-diagonal terms of each row of the transition rate matrix so that their sum is unit, thus providing a probability vector. V i for each row i of the transition rate matrix, comprising probability values, each corresponding to one of the terms of row i of the transition rate matrix, with the exception of the diagonal term, said probability values p ik of the probability vector V i obtained for a line i representing the probabilities of transitions to an arrival state, the probability vectors V i obtained for all rows of the transition rate matrix forming the rows of said probability matrix P, the cooperation metric relative to an entropy of the candidate group being calculated from the probability matrix.

[0014] The calculation of the cooperation metric relative to an entropy of the candidate group may include, for each line i from the probability matrix P, the determination of an entropy value, the entropy values ​​determined for the different rows of the probability matrix forming an entropy vector including entropy values h i associated with each line i of the probability matrix P, the cooperation metric relative to an entropy of the candidate group being determined from the entropy vector .

[0015] In some embodiments, the entropy value h i associated with a line iof the probability matrix P can be a Shannon entropy, determined according to the following equation: h i = − ∑ k = 1 N − 1 p ik ln p ik

[0016] In one respect, the cooperation metric can be an average entropy calculated by averaging the components of the entropy vector. weighted by applying a weighting coefficient α j to each component h j of the entropy vector .

[0017] Cooperative detection system according to claim 8, wherein the weighting coefficients α j constitute the components of a vector η of average steady state defined by: η = 1 n exp τ . M T 1 ⋮ 1 , Or n denotes the dimension of the transition rate matrix M and τ is a parameter representing a time value.

[0018] The time parameter τ may be equal to τ = 10 3< × max( λ i ), λ i denoting the eigenvalues ​​of the transition rate matrix.

[0019] The set of characteristic group values ​​can be a triplet of values ​​comprising the list L q detection devices for the candidate group G q , average entropy < H q >, and the number of measurements K q used to calculate the transition rate matrix.

[0020] In one embodiment, the grouping determination unit may be capable of generating a representation of the candidate groups selected in the detection set comprising n detection devices, 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 { L q , 〈 〉 , K q } , and in which: Each detection device for a candidate group is represented by a point in the representation space, for each candidate group comprising a list L q of p 200 detection devices, the mechanical system includes p elastic links connecting the representative points of the candidate group detection devices to the center of a hypersphere circumscribed to p points, in the representation space; The empty length l of the p elastic bonds are defined by the average entropy 〈 〉; the elastic stiffness constant k of the p Elastic bonds are proportional to the number K q .

[0021] In some respects, the mechanical system may also include elastic damping type friction forces or fluid brake type friction forces related to friction coefficients chosen to bring the mechanical system into a stable state.

[0022] In some 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.

[0023] Depending on 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 representative points of the detection devices in the mechanical system, in the steady state.

[0024] Furthermore, a cooperative detection method is proposed for monitoring a surveillance area using a detection array comprising a plurality of detection devices. The method includes the steps of: determine one or more candidate groups of detection devices from the detection set, determine a transition rate matrix for each candidate group by performing a Hidden Markov Chain (HMM) learning phase, from an initial dataset indicating the activity states of the previously detected detection devices in the 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, determine a set of group characteristic quantities for each candidate group from the transition rate matrix obtained for the candidate group,the set of characteristic group quantities including at least one cooperation metric relative to an entropy calculated for the candidate group; determine at least one grouping of detection devices from the set of characteristic group quantities determined for each candidate group, a detection grouping including at least two networked detection devices capable of cooperating with each other.

[0025] The cooperative detection process is capable of using each determined grouping for the surveillance of the surveillance area. Brief Description of the Figures

[0026] Other features, details and advantages of the invention will become apparent from the description provided with reference to the accompanying drawings given by way of example, which represent, respectively: [ Fig.1 ] - There figure 1 represents a cooperative detection system according to various embodiments. Fig.2 ] - There figure 2 represents a control device, according to various embodiments. Fig.3 ] - There figure 3 is an example of an activity status observation table obtained from a set of observed data. Fig.4 ] - There figure 4 illustrates an example of dividing the state observation table into state submatrices. Fig.5 ] - There figure 5 illustrates the generation of transition rate matrices from the two state sub-matrices obtained in the example of the figure 4 . [ Fig.6 ] There figure 6 shows state transition diagrams obtained from the two example transition rate matrices of the figure 4 . [ Fig.7 ] - There figure 7 illustrates the calculation of the average entropy for a first candidate group of a set of detection devices. Fig.8 ] - There figure 8 illustrates the calculation of the average entropy for a second candidate group from the same set of detection devices as that of the figure 7 . [ Fig.9 ] - There figure 9 illustrates the calculation of the average entropy for a third candidate group from the same set of detection devices as that of the figure 7 . [ Fig.10 ] - There figure 10 illustrates the calculation of the average entropy for a fourth candidate group from the same set of detection devices as that of the figure 7 . [ Fig.11 ] - There figure 11 is an example of a mechanical system used to model the detection ensemble from the group characteristic quantities calculated for the candidate groups. Fig.12 ] - There figure 12 represents the mechanical system of the figure 11 after relaxation. Fig.13 ] - There figure 13 is a flowchart representing the cooperative detection process according to various embodiments. Fig.14 ] - There figure 14 illustrates a step in determining the state chaining logic of a grouping, according to an example implementation. Fig.15 ] - There figure 15 illustrates another step in determining the state chaining logic of a grouping, according to the example of the implementation of the figure 14 . Detailed description of the request

[0027] There figure 1 represents a cooperative detection system 100 comprising a detection set 2 comprising a plurality of detection devices 200 (at least two).

[0028] 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 can, for example, be located around the detection devices 200 (e.g., in an area of ​​airspace).

[0029] 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.

[0030] A detection device 200 could be, for example, a radar or sonar device.

[0031] Detection array 2 may, for example, include a plurality of 200 ground-based radar devices that cooperate to observe the sky (surveillance mission).

[0032] The rest of the description will be made primarily to an application of the invention to radar-type detection devices, by way of non-limiting example.

[0033] 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.

[0034] The cooperative detection system 100 includes a control device 1 configured to control the cooperation between the different detection devices 200 of the detection set to perform the monitoring mission in the monitored 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 sequencing logic for each grouping (also called 'state sequencing rules'), and to control the detection devices 200 of a grouping 20, according to the sequencing logic determined for the grouping to perform the monitoring mission in the monitored area.

[0035] 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.

[0036] A detection device (in transmit mode) 200 of set 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 about 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: A first value, V1, indicates the device's active state (or "ON" state) (i.e., indicating that the detection device is operating or switched on); a second value, V2, indicates the device's inactive state ("OFF" state) (i.e., indicating that the detection device is switched off); or a third value, V3, indicates that the active state is unavailable when the device's active state could not be determined at the given time. The third value, V3, thus indicates an indeterminate state characterizing 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.

[0037] There figure 2 schematically represents the control device 1 according to certain embodiments.

[0038] The control device 1 includes a modeling unit 10 capable of providing a model of the detection set 2 comprising n 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.

[0039] 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.

[0040] A 200 detection device can have a target search mode, in which the 200 detection device is configured to detect a target (object for example) in the surveillance area, and a tracking mode, in which a 200 detection device measures the coordinates of a detected target and uses the measured information to determine the target's trajectory and / or predict its future position.

[0041] 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.

[0042] The control device 1 further includes a transition rate matrix determination unit 12 configured to determine a transition rate matrix M q , for each candidate group from among one or more candidate groups G q of 200 detection devices from set 2, by performing a Hidden Markov Chain (HMM) learning phase, from dataset 3 indicating observations of activity states of the detection devices from detection set 2 (activity states previously detected at different previous times) and the modeling of detection set 2 provided by modeling unit 10. The Hidden Markov Chain (HMM) learning phase includes a data sampling step which can be at variable time step or constant time step.

[0043] The transition rate matrix of a candidate group G q It includes coefficients, each coefficient representing a transition rate from one state to another determined for the associated candidate group. A coefficient in the transition rate matrix has a first index corresponding to a starting state (row index, for example) and a second index corresponding to an ending state (column index, for example).

[0044] 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 G q from the transition rate matrix M q obtained for the candidate group G q . The set of characteristic group values ​​can be a P-tuple comprising at least one quantity related to a calculated entropy (also called a 'cooperation metric') for the candidate group G q 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 L q 200 detection devices from the candidate group G q , the average entropy < H q and the number of states K q associated with the transition rate matrix M q (total number of possible states of the candidate group corresponding to the transition rate matrix).

[0045] 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.

[0046] 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.

[0047] 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).

[0048] Because of 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 the state information values ​​V1, V2 or V3.

[0049] It should be noted that the position of the 200 detection devices generally varies very little over time. It is also assumed that the position of the various 200 detection devices is known. In a real-world situation, the observer's position (e.g., a receiver in flight) can be adjusted to be able to listen to the emissions of all 200 detection devices. The control device 1, according to the embodiments of the invention, can determine the optimal grouping of the 200 detection devices using only information relating to the activity status of the detection devices (first value V1 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.

[0050] In one embodiment, the observed activity state dataset 3 can be modeled as an activity state observation table that represents, at each instant (each row of the table corresponds to a detection instant), the different observed states of the detection devices 200 in the detection set 2 (each column corresponds to a detection device in set 2), located in the geographical area of ​​interest. These states are represented in the state observation table by a state value based on the activity state of the detection device 200 in question. The state value can be a Boolean value taking the first value V1 (for example, 1) or the second value V2 (for example, 0) depending on whether the detection device 200 is active (value 1) or not (value 0), or the third value V3 ("NaN," for example) indicating that activity information for the detection device 200 is not available.

[0051] There figure 3 illustrates an example of an activity status observation table. In the example of the figure 3 Four detection devices are considered in the scene (#1, #2, #3, #4), and at different times, the activity state of each detection device is indicated. For example, at time t=241 s, detection devices #1 and #2 are inactive (value "0"), but no status 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 inactive (value "0").

[0052] A partitioning process is then applied to the activity state observation table corresponding to detection set 2 in order to extract a set of state submatrices, each corresponding to a group of candidate detection devices. More precisely, the partitioning of the activity table into state submatrices is performed such 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 (the third state information value V3, such as "NaN", for example). A submatrix of the state observation table therefore contains only active state values ​​(the first value V1, such as the value 1) and / or inactive state values ​​(the second value V2, such as the value 0).It can be made up of elements from columns or rows of the table, whether continuous or not. A state sub-matrix thus corresponds to state information 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).

[0053] Each sub-state matrix thus obtained corresponds to a candidate group 20 of detection devices 200 and provides the activity state information of the candidate group from the state data 3, at different times t of the initial state observation table, without including any indeterminate information (i.e. third value V3 of activity state information indicating that the activity state is unavailable such as "NaN").

[0054] There figure 4 This illustrates an example of dividing a state observation table 50 into two state submatrices 53 and 54 corresponding to two candidate groups. The submatrix division can be carried out in such a way as to isolate as many rectangular submatrices devoid of "NaN" elements (third V3 value of activity state information) as possible for different combinations of detection devices 200. This division can be performed in such a way as to have state submatrices as large as possible, each state submatrix corresponding to a candidate group of detection devices 200.

[0055] In the example of the figure 4 State submatrix 53 corresponds to the rows of state observation table 50 between t=241 and t=253 and to the first two columns of state observation table 50 corresponding to detection devices #1 and #2. State submatrix 53 is a rectangular partition such that it contains only elements 0 (inactive state) or 1 (active state). State submatrix 53 is thus associated with the candidate group of detection devices comprising devices {#1, #2}.

[0056] 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 submatrix 54 contains only elements 0 (inactive state) or 1 (active state). State submatrix 54 is thus associated with the candidate group of detection devices comprising devices {#3, #4}.

[0057] The number of combinations used to determine the state submatrices can vary and be as high as possible.

[0058] Each resulting state submatrix (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 different detection devices associated with the state submatrix, at the given time t, 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: the detection device is in an active state (value V1 such as the boolean value 1 for example), that is to say it is in an emission state (state 'ON'), or the device is in an inactive state (value V2 such as the boolean value 0 for example), that is to say in a state where it does not emit ("state OFF').

[0059] In the example of the figure 4 , the state vector corresponding to time t=246 is '11' for submatrix 53.

[0060] It is important to note that although referred to as "state submatrices" and "state vectors" for simplicity, these data structures correspond respectively to state observation submatrices and state observation vectors. Indeed, while 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 ​​V1 and V2 (0 and 1, for example) may correspond to false positives or false negatives, so the state submatrices and state vectors (corresponding to the observations) may not exactly reflect the actual states.

[0061] According to this model, a set 2 of n detection devices can be associated with a number of states (the states of the 200 devices it comprises) up to 2 n< different possible states, in cases where each of the n devices can have one state among two states (active or inactive state).

[0062] The state vector therefore contains boolean values ​​reflecting the observed activity ('ON') or non-activity ('OFF') of a detection device 200.

[0063] 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 transition rate matrix, including at least one value related 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 entropy values ​​of the different candidate groups. The control device 1 can further determine the state sequence 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).

[0064] In the activity state observation table, it is assumed that the transitions from one activity state to another occur independently of variations in the environment, that is to say that whatever the results of measurements made 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).

[0065] Although the description is made primarily with reference to a Boolean (specifically 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 can have two activity states). More generally, a state of a detection device 200 can be characterized by a Q-tuple of state values, the different values ​​of the Q-tuple providing at least the activity state of the associated detection device 200 and additional information relating to the object detection performed by the detection device 200.For example, the Q-tuple can be a pair (Q=2) of state values ​​denoted 'x1 x2' where x1 characterizes the activity 'ON' or inactivity '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., set to 'ON' or active) and off (set to '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 x 1 only provides an indication of whether a detection device 200 is emitting a signal (value V1 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 x 2 complements this indication by providing an indication of the detection of an object in the vicinity of the detection device.

[0066] Thus, in this example, the state of a detection device 100 can take the values ​​'00' (x1 = 0 indicating an inactive state and x2 = 0 indicating a non-recent detection), '01' (x1 = 0 indicating an inactive state and x2 = 1 indicating a recent detection), '10' (x1 = 1 indicating an active state and x2 = 0 indicating a non-recent detection), or '11' (x1 = 1 indicating an active state and x2 = 1 indicating a non-recent detection). The use of such a Q-tuple of state values ​​can therefore account for the causal relationship that may exist between a detection and the activity of the different detection devices 200.

[0067] The activity state datasets can be updated dynamically based on the activity states of the 200 environment 2 detection devices detected by an observer, with the modeling unit 10 able to update the model periodically or dynamically.

[0068] Control device 1 is thus capable of defining one or more candidate groups G q 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 from the detection set 2, according to different combinations.

[0069] The unit for determining the transition rate matrix 12 is then configured to determine a transition rate matrix associated with each candidate group G q corresponding to a state submatrix.

[0070] To determine the transition rate matrix associated with a candidate group G q From 200 detection devices, the transition rate matrix determination unit 12 is capable of learning the state-switching logic of the 200 detection devices from active to inactive and vice versa ('ON'↔'OFF'), which is "hidden" behind the detected state datasets. This is achieved by implementing a Hidden Markov Chain (HMM) learning phase and using 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 200 detection devices. Since the activity state of a 200 detection device is represented by the state vector that lists its activity in a state submatrix, there can be up to 2 n< 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.

[0071] The set of detection devices 200 in detection set 2 thus behaves like 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 that state, towards which state(s) it will evolve, or which state it is likely to evolve (a single state in a deterministic case or a choice among several states in the probabilistic case). The determined information is then structured in a transition rate matrix that represents the transitions between activity states for each detection device in the candidate group. G q considered.

[0072] The determination of the transition rate matrix from the state vectors can, for example, be determined using HMM modeling.

[0073] 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 200 sensing devices.

[0074] 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 Learning and Decoding of the Continuous-Time Hidden Markov Model for Disease Progression Modeling. arXiv preprint arXiv:2110.13998, 2021, designed to track disease progression, 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 method described in RABINER, Lawrence R. A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE, 1989, vol. 77, no. 2, p. 257-286 (RABINER).

[0075] The HMM-based algorithm described in LIU, Yu-Ying, MORENO, Alexander, XU, Maxwell A., et al. Efficient Learning and Decoding of the Continuous-Time Hidden Markov Model for Disease Progression Modeling. arXiv preprint arXiv:2110.13998, 2021 (LIU et al ), particularly on page 12, takes as input observations at different times and a set of possible states.

[0076] To apply this method, the unit for determining the transition rate matrix 12 can take as input a sub-matrix of states (observations at different times), and the set of 2 n< Possible states of the detection set 2. The applied process then determines the number of times a transition from one initial state to another occurs, and the average time it takes, thus determining an initial transition rate matrix. Next, using the initial transition rate matrix, the transition rate matrix determination unit 12 applies the iterative HMM algorithm, which in its sixth step uses the process 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 constant time steps. Each iteration of the HMM-based iterative algorithm provides a current transition rate matrix.

[0077] Between two consecutive observations of the submatrix, the transition rate matrix determination unit 12 can consider 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 consider 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, notably takes into account the probability of false positives and false negatives in the input state sub-matrix.

[0078] The transition rate matrix obtained for a candidate group G q is a matrix comprising a set of rows, each row comprising a set of coefficients. Each row corresponds to a starting state.

[0079] The coefficients associated with a row of the transition rate matrix indicate the speed at which a candidate group detection device arrives in another state from an arrival state).

[0080] The speed represented by a coefficient of the transition rate matrix is ​​a transition speed, therefore in s -1< , or in "state / s" (state per second).

[0081] There figure 5 illustrates the transition rate matrices obtained for each candidateG 53 and G 54 corresponding respectively to the state submatrices 53 and 54 of the figure 4 derived from the breakdown of state observation table 50, as an illustrative example. The figure 5 only shows the state vectors drawn respectively from the state submatrices 53 and 54 (components representing the activity states in a boolean form).

[0082] The coefficients associated with a row of the transition rate matrix (for example M 53 and M 54) indicate the speed at which a candidate group detection device (e.g. G 53 and G 54 respectively) arrives in another state from an arrival state.

[0083] For example, the index coefficient (2,1) (second row, first column) of the matrix M53 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 s⁻¹. It will therefore take 2 seconds to get there.

[0084] The index coefficient (1,1) (first row, first column) of the matrix M 53 has a value of -0.1, which means that from state 1 (row number), we move to state 1 (column number) at a speed of -0.1s. The minus sign "-" means that we leave this state. The value 0.1 therefore means that it takes 10 seconds to leave it.

[0085] The columns of the transition rate matrix (e.g. M 53 and M 54) thus correspond to different possible arrival states of the detection set 2 while the lines correspond to different departure states.

[0086] By construction, the diagonal terms of the transition rate matrix (e.g. M 53 and M54) are negative, and the sum of the elements in the same row is zero. Row 'k' of a transition rate matrix indicates that from state 'k', one moves towards state 'l' 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. Therefore, 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 row 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 initial speed.

[0087] According to another example, considering a detection set of 2 n< =4 possible states (case where set 2 includes two detection devices 200 each having two possible states), an example of a transition rate matrix could be: − 0 , 1 0 0 , 1 0 0 , 5 − 0 , 5 0 0 0 0 − 0 , 25 0 , 25 0 0 , 33 0 − 0 , 33

[0088] In this matrix example, for the first row, it can be observed that, starting from state [1], the initial state corresponding to the first row, we arrive at state [1], the destination state corresponding to the first column, with a transition rate (speed) of -0.1 (1st < coefficient of the first row of the transition rate matrix), and at state [3] (the destination 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].

[0089] 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., number of devices in the candidate group 200) 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 2 includes n detection devices 200, the total number of possible states then being at most equal to 2 n< states, the transition rate matrix is ​​square, of size 2 n< × 2 n< .

[0090] Each transition rate matrix thus obtained reflects the state movements in the associated candidate group, as illustrated by diagrams 63 and 64 of the figure 6 which describe the transitions between states corresponding to the matrices M 53 andM 54 of figures 4A and 4B.

[0091] The transition rate matrix, calculated by learning from the state dataset, can be sparse or non-sparse. A sparse matrix contains mostly zero coefficients (the percentage of non-zero coefficients is low).

[0092] In particular, if within the same row of a transition rate matrix only two coefficients are non-zero, and specifically 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 in question 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.

[0093] Such a hollow aspect of the transition rate matrix can be advantageously exploited by the grouping unit 14 to determine at least one grouping of detection devices 200.

[0094] A group of 200 detection devices operates in a network and has a deterministic state-sequencing logic or one that includes very little randomness. If the state-sequencing logic of a group of detection devices is perfectly deterministic, this means that if a transition rate matrix is ​​calculated from 200 detection devices from the same group, this transition rate matrix contains only a few non-zero elements, namely the diagonal elements and only one other non-zero element per row.

[0095] Since the transition rate matrix is ​​derived from an estimate obtained from measurements (observed state data) which may be subject to errors (for example in cases of non-detection or false positives), it is not generally obtained to obtain transition rate matrices in which most of the elements (coefficients) are strictly zero.

[0096] For example, it can be considered a matrix M 1 corresponding to a candidate group G 1 and a matrix M 2 corresponding to a candidate group G 2 defined by the following coefficients: M 1 = − 0 , 104 0 , 001 0 , 1 0 , 003 0 , 5 − 0 , 5045 0 , 003 0 , 0015 0 , 0041 0 , 0012 − 0 , 2553 0 , 25 0 , 0009 0 , 33 0 , 002 − 0 , 3329 M 2 = − 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

[0097] The matrix M1 can reasonably be considered a sparse matrix, so the corresponding candidate group G1 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.

[0098] Thus, the transition rate matrix M1 can be considered quasi-deterministic, while the transition rate matrix M2 is more random. It should be noted that in practice, obtaining absolute zeros is virtually impossible, 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 zero for certain coefficients if an infinite number of iterations were performed, and a stopping criterion is applied when the result remains roughly unchanged from one iteration to the next.

[0099] For a strictly deterministic transition rate matrix, each row should contain only zeros except for two terms: one diagonal term and one other term. In practice, the value is never exactly zero but almost zero. The transition rate matrix M1 illustrates a case that closely resembles a strictly deterministic matrix, as there are several orders of magnitude differences between the terms with significant weight and the others within each row.

[0100] It can therefore be assumed that the state data 3 used to estimate the transition rate matrix M 2 comes from detection devices 200 that do not operate in a network and conversely, in the case of the transition rate matrix M 1, it can be assumed that the state data 3 used comes from a grouping that operates in a network.

[0101] The unit for determining group characteristic values ​​13 is configured to determine a K-tuple of group characteristic values ​​comprising at least one quantity related to group entropy ('cooperation metric') for each candidate group G q whose value indicates how a transition rate matrix associated with the candidate group G q is hollow and thus the level of cooperation of the detection devices 200 of the candidate group 20 considered.

[0102] 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. Specifically, 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. i of the transition rate matrix: The diagonal term of line i is removed first, while the other terms are retained, each of the remaining terms of the 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, thus providing a probability vector V i comprising probability values, each corresponding to one of the terms in the considered row i of the transition rate matrix, excluding the diagonal term (the probability vector therefore has one fewer component than the considered row). The probability values ​​of the probability vector V i obtained for the line i considered represent the probabilities of transitions to an arrival state (the list of subsequent probable states, without information on speed).

[0103] The different probability vectors V i obtained for all rows of the transition rate matrix form a probability matrix P (the i-th row of the probability matrix is ​​the vector V i obtained for the line i of the transition rate matrix).

[0104] For example, considering matrix examples M 1 and M 2, the transition probabilities obtained are given by the probability matrices for the matrix M 1 and for the matrix M 2: P 1 = 0 , 0096 0 , 9615 0 , 0288 0 , 9911 0 , 0059 0 , 0030 0 , 0161 0 , 0047 0 , 9792 0 , 0027 0 , 9913 0 , 0060 P 2 = 0 , 3200 0 , 4000 0 , 2800 0 , 4762 0 , 3810 0 , 1429 0 , 3462 0 , 1731 0 , 4808 0 , 2297 0 , 4459 0 , 3243

[0105] The probability matrix P thus obtained for a transition rate matrix includes probability coefficients pik represents the transition probabilities to an arrival state for each row of the transition rate matrix (corresponding to an initial state). The unit for determining group characteristic values ​​13 can then estimate how well the probabilities converge to the same arrival state from the probability matrix P.

[0106] In particular, in one embodiment, the unit for determining characteristic values ​​of group 13 can be configured to determine the Shannon entropy entropy, which quantifies the spread of the probability distribution of arrival states from a given starting state. A low entropy value therefore indicates that there is a preferred arrival state, while a high entropy value indicates the absence of a preferred arrival state.

[0107] Assuming the transition rate matrix is ​​a square matrix of size N × N,the probability matrix P includes N lines, each line i being associated with a vector V i comprising N - 1 components representing the probability coefficients p ik .

[0108] For each row i of the probability matrix P, an entropy value is determined. Thus, for the transition rate matrix of size N × N, N Entropy values ​​are determined, with one entropy value for each row. N Entropy values ​​form an entropy vector including entropy values h i associated with each row i of the probability matrix P.

[0109] In one embodiment, the entropy value h i associated with a row i of the probability matrix P is a Shannon entropy, determined according to the following equation (1): h i = − ∑ k = 1 N − 1 p ik ln p ik

[0110] Each component of the entropy vector is an entropy value corresponding to a state of a detection device 200.

[0111] The entropy vector therefore provides as many entropy values ​​as there are states.

[0112] By construction, entropy 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 outcome states are equally probable. Such an entropy vector H This indicates whether a logic of state chaining of a candidate group is rather deterministic or random.

[0113] 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 H moy components of the entropy vector , to determine the optimal groupings of candidate devices.

[0114] In the examples of probability matrices And obtained respectively for the matrices M 1 and M 2, the entropy vectors And are: H 1 = 0 , 1845 0 , 0566 0 , 1123 0 , 0553 H 2 = 1 , 0876 0 , 9990 1 , 0229 1 , 0632

[0115] In one embodiment, the unit for determining characteristic group values ​​13 can determine a mean H moy values ​​of the entropy vector (also referred to below as "average entropy"), for each transition rate matrix M q (corresponding to a candidate group) G q ), by applying a weighting coefficient α j to each component h j of the entropy vector , For j between 1 and the number of states N q associated with the transition rate matrix M q according to equation (2): H moy = ∑ j = 1 N i α j h j N i

[0116] In one embodiment, the entropy values h j can be weighted using a vector η representing the average steady state including coefficients α j distinct a priori.

[0117] Given the transition rate matrices M q by calculating their exponential over a long time, the average steady-state vector, which is a mixture between the N q states, can be calculated according to the formula: η = 1 N exp τ . M q T 1 ⋮ 1

[0118] In equation 3, N denotes the dimension of the transition rate matrix M q (in this case N is at most equal to 2 n< and the size of the matrix is ​​then equal to 2 n< × 2 n< ) And τ denotes a "large" time value. For example, by noting λ q the eigenvalues ​​of the matrix M q (i.e. roots of the characteristic polynomial of the matrix), τ can be chosen equal to τ = 10 3< × max( λ i ).

[0119] According to equation (3), using the vector η The entropy of each line can be weighted by the presence of a state over time. Thus, a frequently recurring state will have a greater weight than a very rare one.

[0120] Considering the example of the two transition rate matrices M 1 and M 2, which are of dimension n = 4, the average steady-state coefficient η 1 defined for the matrix M 1 and the average steady-state coefficient η 2 defined for the matrix M 2 are: η 1 = 1 4 exp τ . M 1 T 1 1 1 1 = 0 , 5240 0 , 1070 0 , 2078 0 , 1612 And η 2 = 1 4 exp τ . M 2 T 1 1 1 1 = 0 , 4944 0 , 1066 0 , 2472 0 , 1519

[0121] It should be noted that the matrix examples M 1 and M 2 are used to illustrate two extreme cases: a case of a quasi-deterministic transition rate matrix M 1 and a case of a random transition rate matrix M 2.

[0122] Weighting the average entropy is advantageous because the contribution of entropy is greater when it relates to a frequently reached state.

[0123] Taking into account the values η 1 and η 2, the average entropy H moy ( M 1) = 〈 and average entropy H moy ( M 2 ) = 〈 〉 corresponding respectively from the entropy vector obtained for M 1 and the entropy vector obtained for M 2 are then equal to: H 1 = 0 , 1350 H 2 = 1 , 0586

[0124] The rest of the description will be made with reference to a cooperation metric of the average entropy type. H moy ( M q ) =< H q > , weighted by an average steady-state coefficient η 2, by way of non-limiting example. The figures 7 , 8, 9 et 10 illustrate the determination of the average entropy for four transition rate matrices M 3, M 4 , M 5 and M 6 obtained for 4 distinct candidate groups from the same set of detection devices 2 comprising three detection devices #1, #2, and #3, from an initial state observation table.

[0125] More specifically, the figure 7 illustrates the steps in determining average entropy H moy (M 3 ), still noted 〈 〉, in the case of another example of a transition rate matrix M 3 associated with a candidate group {#1,#2,#3}.

[0126] There figure 8 illustrates the step of calculating average entropy H moy (M 4 ), still noted 〈 〉, in the case of another example of a transition rate matrix M 3 associated with a second candidate group {#1,#2}.

[0127] There figure 9 illustrates the steps involved in calculating average entropy H moy ( M 5 ), also noted 〈 〉, in the case of another example of a transition rate matrix M 3 associated with a third candidate group {#1,#3}.

[0128] There figure 10 illustrates the steps involved in calculating average entropy H moy ( M 6 ), also noted 〈 〉, in the case of another example of a transition rate matrix M 4 associated with a third candidate group {#2,#3}.

[0129] Thus, the entropy obtained for the different groups is: 〈 〉 = 0.58 for the candidate group {#1, #2, #3} ; 〈 〉 = 0.86 for the candidate group {#1, #2} ; 〈 〉 = 0.17 for the candidate group {#1, #3} ; 〈 〉 = 0.59 for the candidate group {#2, #3};

[0130] Based on cooperation metrics related to entropy, such as average entropies 〈 〉, obtained from the transition rate matrices M q associated with the different candidate groups corresponding to the state sub-matrices, the grouping determination unit 14 is configured to determine at least one grouping of the detection devices 200 by determining which candidate group 20 among the different candidate groups 20 considered contains detection devices 200 with the highest probability of belonging to the same network.

[0131] In the example of matrices M 1 and M 2 corresponding to two different candidate groups, the grouping determination unit 14 is thus able to use the entropy averages calculated for each transition rate matrix in order to determine whether it is more probable that the detection devices 200 from group no. 1 (which resulted in the matrix M 1) belong to the same network as those from group no. 2 (which resulted in the matrixM 2).

[0132] In embodiments, the cooperation metrics obtained for the different candidate groups, such as average entropies 〈 〉, can be compared with each other or compared to a threshold to determine the grouping of 200 detection devices that minimizes the average entropy and therefore has the greatest probability of cooperation.

[0133] The cooperation metric related to entropy (e.g., average entropy) thus provides a likelihood of network operation (or cooperation of detection devices).

[0134] According to another example, in the case of the 4 candidate groups considered in the figures 7 , 8, 9 et 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.

[0135] Thus, for each candidate group, the transition rate matrix is ​​determined, and then the cooperation metric related to entropy (e.g., average entropy) is derived 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.

[0136] 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: The list L q detection devices 200 from candidate group 20 (designated by G q ); the cooperation metric related to entropy such as average entropy < H q > determined for this candidate group based on its transition rate matrix M q ; The number K q de measures used to calculate the transition rate matrix M q (K q represents the number of components, and therefore rows, in the state submatrix used to determine the transition rate matrix).

[0137] In the following description, the cooperation metric related to entropy will be considered to be the average entropy < H q > as an illustrative example, and the triplet of characteristic group values ​​is therefore denoted { L q , 〈 〉 , K q } .

[0138] The triplets { L q , 〈 〉 , K q} obtained for the different candidate groups G q thus provide trend information through the cooperation metric related to entropy 〈 〉, without directly giving the estimate of belonging or not to the same cooperative network of detection devices 200.

[0139] In one embodiment, the grouping determination unit 14 can be configured to determine groupings of detection devices 200 into networks from all triplets { L q , 〈 〉 , K q} calculated for the different candidate groups G q using a representation of candidate groups and their triplets { L q , 〈 〉 , K q} associated in the form of a mechanical system within a representational space.

[0140] To generate such a representation in a mechanical system, for a set of n detection devices, the representation space is an n-1 dimension space in which point mechanics laws are applied. In this representation space, each real detection device is represented as an associated point, which is a point capable of being subjected to one or more forces.

[0141] Each triplet { L q , 〈 〉 , K q} is an indicator of the level of cooperation between certain 200 detection devices (i.e., it indicates how well they appear to cooperate). If a triplet { L q , 〈 〉 , K q} corresponds to a candidate group involving p detection devices 200 (i.e., p is the number of devices in the list) L q ) , the mechanical system used to represent the candidate group G q and the triplet { L q , 〈 〉 , K q} associated in the representation space further includes p elastic links connecting the p representative points of the detection devices 200 to the center of a hypersphere circumscribed by the p points (hypersphere passing through the p points), in the representation space. The unstretched length, denoted l q , The average entropy of these elastic bonds is defined by the average entropy 〈 〉 of the triplet of values ​​and the elastic stiffness constant of these elastic connections, denoted k is proportional to the number of measurements K q given by the triplet of values.

[0142] Thus, the representative points of the 200 detection devices are attracted if the entropy 〈 〉 is weak or repelled from each other if entropy 〈 〉 is strong with a strength that depends on the number of measurements K q , and therefore the reliability of this entropy. Elastic connections between the p points are used to ensure that all representative points of the 200 detection devices 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, so at most n - 1 (in the case where p = n,that is, in the case of a triplet which involves all detection devices).

[0143] There figure 11 is an example of a mechanical system 500 corresponding to such a representation, in the representation space, of the triplet { L q , 〈 〉 , K q } obtained for a candidate group 20, in which n = 3.

[0144] In this example, 3 detection devices 200 ( n=3 ) are considered, designated by A, B, and C. The representation space is therefore a 2-dimensional space. A first triplet is considered, which corresponds to a candidate group. G ( A,B,C ) comprising the three detection devices A, B and C. Connections therefore link the point O ABC , center of the circle circumscribed about triangle ABC, at 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. Elastic links therefore connect the midpoint of segment [AC] to points A and C.

[0145] In the example of the figure 11 , it is assumed that the unladen length l ABC for the group G ( A,B,C ) is large while the length l AC of the candidate group G ( A, C ) is small. k ABC And k AC are the stiffness constants of the elastic joints respectively for the group G ( A, B, C ) and the candidate group G ( A, C ) .

[0146] In the example of the figure 11 , the elastic force originating from the point O ABC which acts on point A (representing a first detection device) is expressed in the form: F → O ABC → A = k ABC AO ABC − l ABC ⋅ AO ABC → AO ABC

[0147] If entropy 〈 〉 of the triplet { L ABC , 〈 〉 , K ABC } associated with the group G ABC including devices A, B and C is strong but that of the triplet { L AC , 〈 〉 , K AC } associated with the group G AC including devices A and C is weak, so after relaxation of the mechanical system, the point O ABC must be "far" from points A, B and C while the point O AC must be close to points A and C.

[0148] Placing it in a two-dimensional representation space (n = 3) allows us to establish links to the point O ABC so that these links can reach their unstretched length, and also allows points A and C to move closer to each other without impacting the tension of the links around the point O ABC . Indeed, points A and C can move closer together by sliding along circle 50 shown on the figure 11 .

[0149] In some embodiments, frictional forces can 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 stiffness constant k q The resistance of each spring thus serves to arbitrate between the forces of the springs. However, once relaxation is achieved, the opposing springs (the "losing" spring as well as the "winning" spring) do not, in practice, reach zero potential energy but minimal potential energy.

[0150] Friction forces can be elastic damping type friction forces or braking type friction forces in a fluid medium.

[0151] 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: F → amortissement = − f amortissement × v → I . IO → IO

[0152] Thus, in the example of the connection between a point A and the center O ABC of the figure 11 The elastic damping force can be expressed as follows: F → amortissement = − f amortissement × v → A . AO ABC → AO ABC

[0153] 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: F → fluide = − f fluide × v → I In the example of the connection between a point A and the center O ABC of the figure 11 The elastic damping force is expressed as follows: F → fluide = − f fluide × v → A

[0154] In equations (6) and (7), the values ​​of the friction coefficients f amortissement And f fluide 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 the resolution of a differential system associated with the point mechanics equations that govern the mechanical system. The friction coefficients f amortissement and f fluide can be adjusted for optimal performance. 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 and hinder its convergence towards equilibrium.

[0155] The simulation of the mechanical system can be carried out, after introducing a braking force to prevent oscillations to allow the elements to move and slowing them down so that they stabilize into a state of relaxation.

[0156] The differential equations of the resulting mechanical system can be solved by any suitable solver. In the system simulation, potential energy is converted into kinetic energy as the elements are set in motion. The mechanical energy of the system is equal to the sum of the potential energy and the kinetic energy, which is consumed by the braking forces. The mechanical energy then decreases until 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 DBscan (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.

[0157] There figure 12 is a diagram representing the mechanical system 500 of the figure 12 , after relaxation.

[0158] As illustrated, the set of elastic links allows the points to be brought closer together A And C if entropy 〈 〉 calculated for the group G AC is weak while being consistent with entropy 〈 〉, strong group G ABC including the points A, B, C.

[0159] 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 { L q , 〈 〉 , K q } such as : Each detection device 200 of a candidate group is represented by a point in the representation space; for each candidate group comprising a list L q of p detection devices 200, the mechanical system used to represent this candidate group G q includes p elastic links connecting the representative points of the 200 detection devices of the group to the center of a hypersphere circumscribed at p points, in the representation space. The empty length, denoted l, of the pelastic bonds are defined by the average entropy < H q >; the elastic stiffness constant k of the p Elastic bonds are proportional to the number of measurements K q . Frictional forces can be applied to the mechanical system 500 to bring it into a state of relaxation.

[0160] In one embodiment, to position the hypersphere in the representation space, the grouping unit 14 can calculate the center of the hypersphere circumscribed at p points in dimension space n - 1 using vectors e i such as: e 1 = u 1 u 1

[0161] And : ∀ i ∈ 2 ; p − 1 e i = u i − ∑ k = 1 i − 1 u i ⋅ e k e k u i − ∑ k = 1 i − 1 u i ⋅ e k e k

[0162] Vectors e i constitute p - 1 basis vectors.

[0163] A projection matrix R of size ( p - 1) × ( n - 1) can then be used as follows: R = ⋮ e i T ⋮ i ∈ 1 ; p − 1

[0164] The matrix R allows us to project an element of dimension n - 1 into the orthonormal basis that has been created (the orthonormal basis consists of the vectors e i , the construction of the base ( e 1, e 2, e 3 , etc.) following the Gramm-Schmidt orthonormalization process). It should be noted that the index i 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).

[0165] The coordinates Y i of the p points in the coordinate system centered at X p and whose basis vectors are the e i are then defined according to the following formula (11):

[0238] ∀ i ∈ 1 p , Y i = R X i − X p

[0166] By construction, Y p = 0.

[0167] In this basis, the center of the circumscribed hypersphere can then be calculated.

[0168] By definition, the center of the hypersphere, denoted Ω̃, satisfies the following equation: Y i − Ω ˜ = Y j − Ω ˜ , ∀ i , j ∈ 1 p

[0169] This equation can also be written as: Y i − Ω ˜ T Y i − Ω ˜ = Y j − Ω ˜ T Y j − Ω ˜ Y i T Y i + Ω ˜ T Ω ˜ − Ω ˜ T Y i − Y i T Ω ˜ = Y j T Y j + Ω ˜ T Ω ˜ − Ω ˜ T Y j − Y j T Ω ˜ Y i T Y i − 2 Y i T Ω ˜ = Y j T Y j − 2 Y j T Ω ˜ Y i T Y i − Y j T Y j = 2 Y i T − Y j T Ω ˜

[0170] THE p - The following equations (17) and (18) can then be solved to calculate the center of the hypersphere: Y i T Y i − Y p T Y p = 2 Y i T − Y p T Ω ˜ , ∀ i ∈ 1 ; p − 1 Y i T Y i = 2 Y i T Ω ˜ , ∀ i ∈ 1 ; p − 1

[0171] Furthermore, we consider the vector B following size p - 1 and the matrix A of size ( p - 1) × ( p - 1)) :: B = ⋮ Y i T Y i ⋮ i ∈ 1 ; p − 1 A = ⋮ 2 Y i T ⋮ i ∈ 1 ; p − 1

[0172] If the Y i 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 invertible.

[0173] The center Ω can then be calculated from the following equation (21): Ω ˜ = A − 1 B

[0174] Ω̃ represents the position of the center of the hypersphere in another frame of reference. Indeed, initially, the elements are positioned according to the vectors X i 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 has the position of the point 0 in this new coordinate system.

[0175] Ω̃ can then be expressed in the initial frame of reference according to formula (22): Ω = R T Ω ˜ + X p = R T A − 1 B + X p

[0176] The point Ω thus calculated represents the center of the hypersphere to which are attached all the elastic links leading to each of the p points.

[0177] Based on the representation of n detection devices 200 of the detection set 2 in the dimension representation space n- 1, in the form of a mechanical system 500, the grouping unit 14 is capable of grouping the detection devices 200 operating in networks together, while keeping apart those that do not seem a priori not work together, from the representation of elastic links between points of the same candidate group.

[0178] The grouping unit 14 can be configured to then apply the grouping algorithm (or "clustering") 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.

[0179] The clustering algorithm (such as, for example, the DB-Scan algorithm) is a method that uses a threshold defining the neighborhood ε of a point. For each point, the method determines which points are in the neighborhood of the point (i.e., at a distance less than ε from the point in question). The selected points (points in the neighborhood) are then added together to form a cluster. The method thus performs a clustering of points representing detection devices 200 by step. The neighborhood threshold ε is predetermined or predefined in a manner appropriate to the application of the invention. Indeed, if the threshold ε is too small, each point can form a cluster of which it is the sole member. Conversely, if the threshold ε is too large, a single cluster encompassing all the points can be determined.

[0180] The state-sequence logic determination unit 16 can determine the state-sequence logic of the determined grouping from the transition rate matrices determined for the different candidate groups by unit 12. The state-sequence logic defines the transition rules from one state to another for each detection device of the determined grouping.

[0181] To determine the state chaining logic of a given grouping, the state chaining logic determination unit 16 can select all transition rate matrices that are associated only with 200 detection devices 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.

[0182] In particular, for each grouping obtained, the state chaining logic determination unit 16 selects all the resulting transition rate matrices corresponding to candidate groups including a detection device 200 of the grouping under consideration. For example, if the grouping under consideration is a grouping comprising three detection devices #1, #2, and #3 such as =[#1,#2,#3], the state chaining logic determination unit 16 selects the four transition rate matrices M 13, M 23 and M 123 associated respectively with the four candidate groups [#1,#2], [#1,#3], [#2,#3], [#1,#2,#3], as illustrated on the figure 14 The state chaining logic determination unit 16 is then capable of reconstructing a resulting transition rate matrix. M Res based on the selected transition rate matrices, taking into account the Ldetection devices for the grouping under consideration (for example, three detection devices in the preceding example), such that the size of the resulting transition rate matrix M r East 2 L< (2 3< = 8 in the preceding example where the grouping (includes 3 detection devices). To determine the resulting transition rate matrix M Res , it is assumed that each transition rate matrix M q determined by the unit of determination of the transition rate matrix 14, has a weight k , 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 four weights k 12 , k 13 , k 23 and k 123 are respectively associated with the different transition rate matricesM 13, M 12 , M 23 and M 123.

[0183] The state chaining logic determination unit 16 can initially determine the diagonal terms of the transition rate matrix M Res to be reconstructed from the selected transition rate matrices. Each of these diagonal terms corresponds to the speed at which the system corresponding to the grouping leaves each state. To determine such a diagonal term, as illustrated on the figure 14 The state chaining logic determination unit 16 can identify all terms corresponding or potentially corresponding to the starting speed from the first state, i.e., state

[000] in the example of the 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 the grouping The state chaining logic determination unit 16 then considers each of the values ​​as a measurement tainted by a Gaussian error, whose variance is: σ 2 = 1 k × 2 r

[0184] In equation (23), r denotes the number of detection devices 200 not taken into account by a selected transition rate matrix, among the detection devices in the grouping Thus, in the example of the figure 14 he comes σ 123 2 = 1 k 123 × 2 0 (0 detection devices not taken into account by the matrix) M 123 among the group detection devices #1, #2, and #3), σ 12 2 = 1 k 12 × 2 1 (1 detection device not taken into account in the matrix) M12, i.e., detection device #3), σ 13 2 = 1 k 13 × 2 1 (1 detection device not taken into account in the matrix) M 13, i.e., detection device #2), σ 23 2 = 1 k 23 × 2 1 (1 detection device not taken into account in the matrix) M 23, i.e., detection device #1).

[0185] 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] .

[0186] Such a calculation amounts to determining x such as the likelihood is maximal, where is given by: L = e − x − x 000 , 000 123 2 2 σ 123 2 × e − x − x 00 ⋅ , 00 ⋅ 12 2 2 σ 12 2 × e − x − x 0 ⋅ 0 , 0 ⋅ 0 13 2 2 σ 13 2 × e − x − x ⋅ 00 , ⋅ 00 23 2 2 σ 23 2

[0187] Maximizing as defined by equation (24) amounts to minimizing the quantity: x − x 000 , 000 123 2 σ 123 2 + x − x 00 ⋅ , 00 ⋅ 12 2 σ 12 2 + x − x 0 ⋅ 0 , 0 ⋅ 0 13 2 σ 13 2 + x − x ⋅ 00 , ⋅ 00 23 2 σ 23 2

[0188] The quantity defined by equation (25) is minimal when: x − x 000 , 000 123 σ 123 2 + x − x 00 ⋅ , 00 ⋅ 12 σ 12 2 + x − x 0 ⋅ 0 , 0 ⋅ 0 13 σ 13 2 + x − x ⋅ 00 , ⋅ 00 23 σ 23 2 = 0

[0189] Equation (27) allows us to deduce x

[000] ,

[000] : x 000 , 000 = x 000 , 000 123 σ 123 2 + x 00 ⋅ , 00 ⋅ 12 σ 12 2 + x 0 ⋅ 0 , 0 ⋅ 0 13 σ 13 2 + x ⋅ 00 , ⋅ 00 23 σ 23 2 1 σ 123 2 + 1 σ 12 2 + 1 σ 13 2 + 1 σ 23 2

[0190] The state chaining logic determination unit 16 then repeats the same steps to estimate the starting speed of the next state, i.e., state

[001] in the example of the figure 14 (second iteration) and determine the second diagonal term of the resulting transition rate matrix M Res to build. In the example of the figure 14 The terms circled in dotted 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. M Res to be built.

[0191] The state chaining logic determination unit 16 then repeats the same steps to estimate the starting speed of subsequent states, until all the terms on the diagonal of the resulting transition rate matrix are obtained. M Res .

[0192] For off-diagonal terms, the state chaining logic determination unit 16 can perform row-by-row normalization of the selected transition rate matrices by dividing each row of a selected transition rate matrix by the absolute value of the row's diagonal term. The normalized sum of the off-diagonal terms in each selected transition rate matrix is ​​therefore 1.

[0193] 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 by the figure 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 dotted lines for the state change

[000] →

[011] . It should be noted that not all selected transition rate matrices are necessarily involved, as the element that could correspond to the desired state change is sometimes diagonal and therefore ignored.

[0194] 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 M Res (such as the terms x̃

[000] ,

[001] , x̃

[000] ,

[010] , x̃

[000] ,

[011] , etc..), such as for example: x ˜ 000 , 001 = x 000 , 001 123 σ 123 2 + x 0 ⋅ 0 , 0 ⋅ 1 13 σ 13 2 + x ⋅ 00 , ⋅ 01 23 σ 23 2 1 σ 123 2 + 1 σ 13 2 + 1 σ 23 2 , x ˜ 000 , 010 = x 000 , 010 123 σ 123 2 + x 0 ⋅ 0 , 0 ⋅ 1 12 σ 12 2 + x ⋅ 00 , ⋅ 10 23 σ 23 2 1 σ 123 2 + 1 σ 12 2 + 1 σ 23 2 , x 000 , 011 = x 000 , 011 123 σ 123 2 + x 00 ⋅ , 01 ⋅ 12 σ 12 2 + x 0 ⋅ 0 , 0 ⋅ 1 13 σ 13 2 + x ⋅ 00 , ⋅ 11 23 σ 23 2 1 σ 123 2 + 1 σ 12 2 + 1 σ 13 2 + 1 σ 23 2 , etc .

[0195] Since the selected transition rate matrices were previously normalized, the off-diagonal terms of the resulting transition rate matrix M Res are obtained by then performing the following calculations: x 000 , 001 = x ˜ 000 , 001 × x 000 , 000 , x 000 , 010 = x ˜ 000 , 010 × x 000 , 000 , x 000 , 011 = x ˜ 000 , 011 × x 000 , 000 , etc.

[0196] In the example of the figure 12 The generated mechanical system 500 allows us to determine that 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. M AC for the grouping {A,C} and a transition rate matrix M B for grouping {B} respectively from the data observed for detection devices A and C on the one hand and for the detection device B on the other hand. In this example, the transition rate matrix M AC is at most 4x4 in size (since there are at most 22 possible states) while the transition rate matrix M B is at most 2x2 in size (because there are at most 21 possible states). These transition rate matrices are in principle sparse, that is to say they contain few non-zero elements, which allows them to be used.

[0197] 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).

[0198] Advantageously, control device 1 is able to transpose the problem of grouping detection devices 200 into the domain 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 'clustering' algorithm to determine the groupings of detection devices 200 that operate cooperatively. From the groupings obtained, the previously calculated transition rate matrices allow the orchestration logic of each grouping to be determined.

[0199] There figure 13 is a flowchart illustrating a cooperative detection process for monitoring a surveillance area using detection set 2, according to certain embodiments.

[0200] At step 900, a model of the 200 detection devices of the detection set 2 is received. This model provides a model of the detection set 2 in the form of a macro-system that changes from one state to another as soon as a 200 detection device switches from the active state ('ON') to the inactive state ('OFF') or vice versa.

[0201] 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.

[0202] Step 902 advantageously uses Hidden Markov Chain (HMM) learning to determine transition rate matrices.

[0203] In step 904, candidate groups are determined corresponding to different combinations of detection devices 200 from set 2.

[0204] 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 can notably be the triplet { L q , 〈 〉, K q} .

[0205] At 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.

[0206] At 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.

[0207] In step 910, the logic of the chaining of states 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.

[0208] The 200 detection device groupings 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.

[0209] 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 even directly in flight for radar-type detection devices. The determination of a grouping can notably be performed 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 adjusted to obtain a rapid result.

[0210] 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, including 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 on computer-readable media.

[0211] Furthermore, the invention is not limited to the embodiments described above by way of non-limiting example. It encompasses all alternative embodiments that could be considered by a person skilled in the art.

Claims

1. A cooperative detection system (100) comprising a detection assembly (2) for monitoring a monitoring zone, the detection assembly comprising a plurality of detection devices (200), characterized in that it comprises: - a transition rate matrix determination unit (12) configured to estimate a transition rate matrix, for each candidate group among one or several candidate groups of detection devices of the assembly (2), by carrying out a learning phase based on hidden Markov chains (HMM), from an initial dataset indicating activity states of the detection devices (200) of the detection assembly (2) detected beforehand and from a modeling of the detection assembly (2), the transition rate matrix of a candidate group comprising coefficients, each one representing a transition speed from one activity state to the other for each detection device (200) of the associated candidate group, - a characteristic group value determination unit (13) configured to determine a set of characteristic values for each candidate group from a transition rate matrix obtained for the candidate group, the set of characteristic group values comprising at least one cooperative metric relative to an entropy determined for the candidate group; - a regrouping determination unit (14) configured to determine at least one regrouping (20) of detection devices (200) from the set of characteristic group values determined for each candidate group, a detection regrouping comprising at least two detection devices (200) connected in a network and able to cooperate together; the cooperative detection system being able to use a regrouping determined for the monitoring of the monitoring zone.

2. The detection system according to claim 1, wherein a coefficient of the transition rate matrix has a first index corresponding to an initial state and a second index corresponding to a final 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 LR of possible activity states for all the R detection devices of the candidate group, each detection device having a number L of activity states.

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

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

5. The cooperative detection system according to one of claims 2 to 4, wherein the characteristic group 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 line of the transition rate matrix so that their sum is unitary, which provides a probability vector Vi for each line i of the transition rate matrix, comprising probability values, each one in correspondence with one of the terms of the line i of the transition rate matrix, except for the diagonal term, said probability values pik of the probability vector Vi obtained for a line i representing the probabilities of transitions to a final state, said probability vectors Vi obtained for all the lines of the transition rate matrix forming the lines of said probability matrix P, the cooperative metric relative to an entropy of the candidate group being calculated from the probability matrix.

6. The cooperative detection system according to claim 5, wherein the calculation of the cooperative metric relative to an entropy of the candidate group comprises, for each line i of the probability matrix P, determining an entropy value, the entropy values determined for tha various lines of the probability matrix forming an entropy vector H comprising entropy values hi associated with each line i of the probability matrix P, the cooperative metric relative to an entropy of the candidate group being determined from the entropy vector H.

7. The cooperative detection system according to claim 6, wherein the entropy value hi associated with a line i of the probability matrix P is a Shannon entropy, determined according to the following equation (1): h i = − ∑ k = 1 N − 1 p ik ln p ik 8. The cooperative detection system according to claim 7, wherein the cooperative metric is an entropy average calculated by taking an average of the components of the entropy vector H, weighted by applying a weighting coefficient αj to each component hj of the entropy vector H.

9. The cooperative detection system according to claim 8, wherein the weighting coefficients αj constitute the components of a vector η of average stationary state defined by: η = 1 n exp τ . M T 1 ⋮ 1 , where n designates the dimension of the transition rate matrix M and τ is a parameter representing a time value.

10. The cooperative detection system according to claim 9, wherein the time parameter τ is equal to τ = 103 x max(λi), λi designating the eigenvalues of the transition rate matrix.

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

12. The cooperative detection system according to claim 11, wherein the regrouping determination unit (14) is able to generate 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 value triplet 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 connections connecting the points representative of the detection devices (200) of the candidate group at the center of a hypersphere (50) circumscribed at p points, in the representation space; - The non-load length I of said p elastic connections is defined by the average entropy 〈Hq〉; - the elastic stiffness constant k of the p elastic connections is proportional to the number Kq.

13. The cooperative detection system according to claim 12, wherein the mechanical system further comprises friction forces of the elastic damping type or friction forces of the braking type in a fluid medium relative to friction coefficients chosen to bring the mechanical system to a stable state.}14. The cooperative detection system according to one of claims 12 and 13, wherein the regrouping unit (14) is able to cause the mechanical system to change to a stable state by implementing a resolution of a differential system associated with equations that govern the mechanical system.

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

16. A cooperative detection method (100) for monitoring a monitoring zone by using an detection assembly (2) comprising a plurality of detection devices (200), characterized in that it comprises the steps consisting of: - defining one or more candidate groups of detection devices (200) of the detection assembly (2), - determining a transition rate matrix (12) for each candidate group by carrying out a learning phase learning phase based on hidden Markov chains (HMM), from an initial dataset indicating activity states of detection devices of the detection assembly (2) detected beforehand and a modeling of the detection assembly (2), the transition rate matrix of a candidate group comprising coefficients, each coefficient representing a transition speed from one state to the other for each detection device (200) of the associated candidate group, - determining a set of characteristic group values (13) for each candidate group from the transition rate matrix obtained for the candidate group, the set of characteristic group values comprising at least one cooperative metric relative to an entropy calculated for the candidate group; - determining at least one regrouping (20) of detection devices (200) from the set of characteristic group values determined for each candidate group, a detection regrouping comprising at least two detection devices (200) connected in a network and able to cooperate together; the method for cooperative detecting being able to use each determined regrouping for the monitoring of the monitoring zone.