Waveform recognition system and method

Abstract

A method for recognizing the waveform of a signal received from a transmitter, comprising electromagnetic pulses, using a waveform model based on a hidden Markovian process, comprising a comb of values ​​representing process states corresponding to possible values ​​of a pulse parameter, a transition matrix between consecutive values ​​of the comb, and the measurement standard deviations of the states, the method comprising: - receiving measurements of the pulse parameter, - determining a score by traversing (606) a tree whose node corresponds to one of the process states and provides a measurement prediction of the pulse parameter, - recognizing the waveform of the signal from the score, the score being updated (607) iteratively for each traversed node of the tree associated with a process state according to a precondition indicating whether the prediction reaches a pulse. (Figure 6)

Description

Title of the invention: Waveform recognition system and method technical field

[0001] The invention relates generally to radar systems and in particular to a device and a method for recognizing pseudo-random radar waveforms.

[0002] Some known radar systems use a transmitter that emits a signal comprising a series of electromagnetic pulses defining a pseudo-random pulsed waveform of the signal and a receiver capable of receiving the signal. The emission of such a signal consists of emitting radar pulses with at least one parameter that takes random values ​​from a set of possible values.

[0003] This parameter is generally the time interval between consecutive pulses. In other cases, the parameter may represent the carrier frequency or another characteristic parameter of the pulses, the differential arrival time being able to be independently pseudo-random or deterministic.

[0004] The recognition function implemented by the receiver implies the ability to recognize a waveform already intercepted previously, even if it is not necessarily identified, i.e., it is not necessarily associated with a radar name, carrier, and type of radar function that it executes, or it is not entered in a waveform identification library.

[0005] In some cases, waveform recognition can be done "on the fly", at the same time as the received pulses are deinterlaced and fed into sensor tracks - usually in small analysis time windows of less than a second, rather on the order of 100 ms.

[0006] Various known solutions have addressed the waveform recognition problem as a multi-class identification problem, notably by using machine learning such as deep neural network-based learning.

[0007] For example, identification can be performed at the level of the output signal of the analog-to-digital encoder, as described in: -PM Aashir Afnan. Et al. AI based radar waveform classification System. International research journal of engineering and technology 7(8):395-399. (Aug. 2020). - J.Lunden. V. Koivunen. Automatic radar waveform recognition. IEEE J. selected topics SP 1(1):124-136. (June 2007).

[0008] However, such approaches are complex, require a significant amount of computation, and necessitate retraining the models when a class is added or removed. Furthermore, multi-class classifiers are structurally incapable of handling cases where unlearned waveforms are presented as input. Yet, with the proliferation of transmitters and the widespread adoption of software-defined radars, whose parameters the operator can easily modify, it is necessary to be able to handle waveforms outside the reference library. Solutions offering ad-hoc mechanisms upstream or downstream of the classifier to detect an unknown input waveform, based on machine learning models complementary to the classifier, as disclosed, for example, in the following documents: - C. Tanner Frediau. Et al. Classification of common waveforms including a watchdog for unknown signals. arXiv [eess.SP]:2108.07339vl. Aug 2021. -RV Chakravarthy. Et al. Open-set radar waveform classification: Comparison of different features and classifiers. IEEE international radar conference. Washington DC, USA. (April 28-30, 2020).

[0009] More recent methods are also based on neural networks, such as W. Chao, et al. (including ZML). A radar signal deinterleaving method based on semantic segmentation with neural networks. arXiv [eess.SP]:2110.13706v2. (Feb. 2022).

[0010] Nevertheless, these known solutions remain limited due to the quantity and diversity of unknown waveforms.

[0011] Other known approaches address the waveform recognition problem in a similar way for characterized pulse streams, that is, most of the time as a multi-class identification problem.

[0012] A particular approach has been proposed in which the optimal transport distance is used to compare pre-sorted pulses with a list of candidates, as disclosed for example in: - M. Mottier, G. Chardon, F. Pascal. Radar emitter classification with optimal transport distance. Proc. 30th European signal processing conference (eusipco). Belgrade, Serbia. (29 Aug.-02 Sept. 2022).

[0013] This approach is however limited to the parameters of carrier frequency and pulse duration, which is restrictive because a very significant parameter of radar waveforms is the time difference between consecutive pulses (called PRI, acronym for "pulse repetition interval", also called DTOA, acronym for "differential time of arrival", when it is measured after interception by the listening receiver).

[0014] The choice of the Pulse Recurrence Period (PRI) is crucial in the design of radar systems, as indicated for example in N. Levanon. E. Mozeson. Radar signaling. Wiley. (2004). For radar operation, a certain regularity in the PRI is often desirable, but for reasons of stealth and jamming resistance, it is preferable to define long, non-repeating PRI sequences, among other constraints (as described, for example, in US 5 847677A). The resulting pseudo-random waveforms are indeed the most difficult to detect and recognize by a listening system when mixed in a stream of pulses from different, angularly unseparated transmitters.

[0015] Such a problem has rarely been addressed in the prior art despite its operational interest. Generally, identification approaches are based on PRI values ​​(moments) or on a range of PRI values, determined after deinterlacing and tracking, and compared to a library description to provide a similarity score. Other scores can be calculated based on other parameters, and the different scores are then combined to form an overall score and make a decision, as described in EP3491411. This type of approach requires considerable expertise in defining the scores and the methods for combining them. It depends, in particular, on the quality of the upstream deinterlacing and tracking, since it requires a sufficient number of pre-grouped pulses without too many errors to produce a sufficiently reliable score, and therefore cannot always be applied "on the fly" in analysis windows.

[0016] Another approach was described in HE Abou-Bakr-Hassan, KH Moustafa. Joint deinterleaving / identification of radar pulses using matrix differences. Proc. 5th International Conference on Electrical Engineering (ICEENG). Cairo, Egypt. (May 16-18, 2006). This approach consists of jointly deinterleaving and identifying the waveforms that make up a mixture. The approach advantageously calculates the arrival time differences between all pulse pairs and associates pulses whose DTOA is in the list of values ​​associated with a waveform (pseudo-random or regular). However, this approach requires a very large amount of memory (an array of size Ar x N, where N denotes the number of pulses in the analysis window) and only processes the DTOA parameter without considering other parameters characterizing the pulses. Furthermore, it is inefficient when several waveforms have PRI values ​​in common or in cases of significant pulse gaps.Another solution was proposed in EP1947472A to identify the presence or absence of a waveform that may have a long duration and a sparse energy distribution. This solution deals with the processing of very specific waveforms that are random and very spread out over time, with a very low pulse density. Pre-filtering on the DTOA (and optionally on the pulse duration) reduces the rate of received pulses, and then... Elementary statistics are calculated on the residual bursts to determine if they correspond to the waveform of interest. However, the performance of this approach is based on the very specific characteristics of the waveforms being sought and is not robust to denser situations.

[0017] In addition to the aforementioned limitations, these latter approaches only consider PRI (moment) values, along with other possible parameters, but do not take into account the temporal sequences of PRI (or other parameter) values, which can nevertheless be a useful characteristic for recognizing different pseudo-random waveforms, particularly when they are mixed, fragmented, and have relatively few pulses compared to the number of possible moments of PRI (or other parameter) values. Finally, they primarily perform an identification function since they require a priori reference library; they do not describe a way to overcome this by locally learning a statistical model useful for waveform recognition rather than identification.

[0018] These known solutions do not allow the resolution of problems which are located at a level further downstream of the receiving chain where the pulses are first detected and characterized by a limited number of parameters (arrival time, carrier frequency, level, duration, azimuth).

[0019] A first problem is to be able to recognize a waveform with good performance, given that its pseudo-random nature implies that the sequence of values ​​taken by the characteristic parameters of the pulses in the windows, such as the number of pulses, the arrival time, the carrier frequency, or the pulse duration, are different each time. This performance is all the more difficult to achieve since the analysis windows contain relatively few pulses of the waveform to be recognized compared to its variability, when it is present, and it is common for some pulses to be missed during reception.Furthermore, spurious pulses from other transmitters generally mix with the pulses of the waveform of interest, either because deinterlacing / tracking processes are imperfect, or because on-the-fly recognition must partially replace them.

[0020] It is therefore desirable that the probability of error (probability of wrongly recognizing a sequence of pulses as containing the waveform of interest) be low, while maximizing the probability of recognizing the waveform when it is present in the analysis window, in a very incomplete way and mixed with spurious pulses.

[0021] Another problem is to be able to automatically establish, in the short term (i.e., in the area of ​​operation during the duration of a mission), a probabilistic model of the pseudo-random waveform of interest which allows it to be recognized later with the difficulties mentioned.

[0022] There is therefore a need for an improved waveform recognition device and method.

[0023] General definition of the invention

[0024] To this end, the invention relates to a method for recognizing the waveform of a signal received by a receiver from a transmitter, the signal comprising a series of electromagnetic pulses defining a pseudo-random waveform of the signal. Advantageously, the method comprises the steps of: - determining a waveform model M = (ii,P,a) according to a hidden Markovian process, the model comprising a vector representing a comb of values, each value of the comb corresponding to a process state, the process states being possible values ​​of a given pulse parameter associated with the pulses, a transition matrix P between consecutive values ​​of the comb, the transition matrix being of size K x K, and a vector a E PA comprising a set of coefficients representing the measurement standard deviations of the states.

[0025] The process further comprises the steps of: - receive a dated sequence ordered in time of N measurements (x0 of the given pulse parameter, - determine a score, by traversing a tree comprising a set of branches, the branches comprising a set of nodes, each node of the tree corresponding to one of the process states Pk and providing a measurement prediction (xJ of the impulse parameter, the branches of the tree being traversed in a chosen order, the tree having a depth less than or equal to N, - recognize the waveform from the score.

[0026] Determining a score includes one or more iterations of the following steps, for each traversed node of the tree associated with a process state: - determine a prediction x of the impulse parameter from the prediction of the impulse parameter determined in the previous iteration and the process state Pk associated with the node, - determine if a precondition is met indicating that the prediction Xj reaches an impulse, - update the current score value, if the precondition is met, by incrementing the current score value by one value, - select the next branch to traverse,

[0027] the iterations being repeated until a stopping condition is met.

[0028] In one embodiment the method includes incrementing a shortage counter if the precondition is not met.

[0029] In particular, the tree traversal can go back to a higher level of the tree if the missing counter reaches a predefined maximum missing value.

[0030] In one embodiment, the precondition is verified if:

[0031] . MiM, min-ôr < t n &

[0032] denoting the measurement standard deviation of the impulse parameter etf designates an adjustable threshold.

[0033] In one embodiment, the calculated score can denote the maximum likelihood of the measures (xn) conditional on the model M.

[0034] In embodiments, the score can be updated at the score update step by adding to the current score value ii / [Mj2 \ or the / . MfV the quantity —^exp^ -min-^ - j quantity exp^ -min-^r )

[0035] Alternatively, the score can be updated at the score update step by incrementing the current score value.

[0036] In embodiments, the process can be repeated * times if the score obtained at the score determination step is less than a predefined score value, by initializing the prediction at the / + 1st measurement of the impulse parameter.

[0037] According to one aspect of the invention, the tree can be traversed in depth or in width.

[0038] In embodiments, the stopping condition is checked when all branches of the tree have been traversed or if the updated score value is greater than a threshold value S.

[0039] The method may further include training the model from reference data, the learning steps including the steps of: - filtering the reference data; - determine the number of process states; - determine the values ​​of the process states; - the number of process states and the values ​​of the process states being determined from the filtered reference data; - the process further comprising the determination of the transition matrix P and the standard deviations of state measurements, from the number of process states and the values ​​of the process states.

[0040] In one embodiment, the reference data is used to update a histogram representing on the ordinate the number of pulses detected in function of an index interval on the x-axis, the width of an interval being equal to a temporal resolution, such that: - the number of states corresponds to the number of connected components of the histogram with a cardinality at least equal to a given value, on its x-axis, a connected component corresponding to a number of consecutive intervals containing a non-zero number of pulses in the histogram, the number of intervals of a connected component defining the cardinality of the connected component; - The value of the process states is estimated by determining the median value of the midpoints of the intervals associated with each connected component, each median value providing the value of one of the K states of the comb

[0041] The method may further include the application of an optimization method to optimize the estimates obtained of the transition matrix vector P, and of the standard deviation, the optimization algorithm being initialized with the estimated values ​​P, eta, the optimization algorithm being able to jointly estimate the parameters P, et iteratively and optimally in the maximum likelihood sense.

[0042] In one embodiment, the method includes a correction of the predictions x{ by recentering them on the impulse reached by the prediction, in response to the verification of the precondition.

[0043] The method may include updating a prediction hit counter, the counter being incremented in response to the precondition check, the method further including a joint re-estimation of successive predictions after a given number of the prediction hit counter.

[0044] A waveform recognition receiver for a signal received from a transmitter is further proposed, the signal comprising a series of electromagnetic pulses defining a pseudo-random waveform of the signal, characterized in that the receiver comprises a waveform recognition unit configured to: - determine a waveform model M - (ji,P,cy ) according to a Markovian process, the model comprising a vector e P* representing a comb of values, each value of the comb corresponding to a process state, the process states being possible values ​​of a given impulse parameter associated with the impulses, a transition matrix P between consecutive values ​​of the comb, the transition matrix being of size K x K, and a vector e P^ comprising a set of coefficients representing the measurement standard deviations of the states.

[0045] Advantageously, the waveform recognition unit can be configured to: - receive a dated, time-ordered sequence of N measurements (xi) of the given impulse parameter, - determine a score, by traversing a tree comprising a set of branches, the branches comprising a set of nodes, each node of the tree corresponding to one of the process states and providing a measurement prediction (¾) of the impulse parameter, the branches of the tree being traversed in a chosen order, the tree having a depth less than or equal to N, - to recognize the waveform from the score,

[0046] the determination of a score comprising one or more iterations of the following steps, for each node traversed of the tree associated with a process state: - determine a prediction of the impulse parameter from the prediction of the impulse parameter determined in the previous iteration and the process state Pk associated with the node; - determine if a precondition is met indicating that the prediction reaches a certain point, - update the current score value, if the precondition is met, by incrementing the current score value $ by one value, - select the next branch to traverse,

[0047] the iterations being repeated until a stopping condition is met. Brief Description of the Figures

[0048] Other features, details and advantages of the invention will become apparent from the description given with reference to the accompanying drawings provided by way of example, which represent, respectively:

[0049] [Fig-1] - Fig. 1 represents an example of a detection system in which at least one receiver includes a waveform recognition device, according to embodiments of the invention.

[0050] [Fig.2] - The [Fig.2] is a diagram of time difference arrival (DTOAs) values ​​between consecutive pulses from a pseudo-random radar.

[0051] [Fig.3] - The [Fig.3] is a histogram of DTOA values ​​corresponding to the [Fig.2], according to an example of an embodiment of the invention in which the pulses are emitted by a naval radar intercepted at sea.

[0052] [Fig.4] - Figure 4 is an example of an estimated P transition matrix associated with the DTOAs of [Fig.3].

[0053] [Fig.5] - The [Fig.5] represents the structure of the waveform recognition device according to embodiments of the invention.

[0054] [Fig.6] - The [Fig.6] is a flowchart representing the process of calculating a score from the path of a decision tree, according to embodiments.

[0055] [Fig.7] - The [Fig.7] illustrates the preliminary calculation step to initialize the calculation of the score by traversing a tree, in the case where the impulse parameter is a differential type parameter such as the DTOA.

[0056] [Fig.8] - The [Fig.8] illustrates the first iteration of the score calculation steps of the process of the [Fig.6], in the case of a differential impulse parameter of type DTOA.

[0057] [Fig.9] - The [Fig.9] illustrates the best tree traversal when the process of the [Fig.6] is applied to the data of figures 2 and 3, in an analysis window.

[0058] [Fig. 10] - Figure 10 illustrates the learning process of the model M = (ft, P, a ), from reference data, according to embodiments of the invention.

[0059] [Fig. 11] - Figure 11 represents an enlargement of an H histogram around the first modes of the DTOA, in the example of the data in Figures 2 and 3 corresponding to a DTOA type impulse parameter.

[0060] [Fig. 12] - Figure 12 represents different False Alarm Probabilities as a function of the score threshold for different values ​​of the parameter d related to the temporal density of pulses in the environment of the receiver.

[0061] [Fig. 13] - Figure 13 represents the value of the score threshold (on the ordinate) as a function of (on the abscissa) for different False Alarm Probabilities.

[0062] [Fig. 14] - The [Fig. 14] illustrates the probability of recognition of the waveform of interest mixed with a Poisson process, as a function of the rate of mingling.

[0063] [Fig. 15] - The [Fig. 15] illustrates the results of the waveform recognition process applied to real data.

[0064] [Fig. 16] - The [Fig. 16] represents the pulse levels in a window where recognition is positive.

[0065] [Fig. 17] - The [Fig. 17] illustrates the DTOAs of the pulses extracted during waveform recognition (actual data).

[0066] [Fig. 18] - The [Fig. 18] is an enlargement (zoom) in ordinate of the [Fig. 17].

[0067] Detailed description of the application

[0068] Fig. 1 represents an example of a system 100 in which a method and a device for recognizing waveforms can be implemented, according to embodiments of the invention.

[0069] The system 100 may be a radar detection system configured to detect a transmitter 3 in an area (for example, a surveillance area). In certain applications of the invention, the detection system 100 may, for example, be a system configured to locate the transmitter 3 and / or identify and / or recognize the transmitter 3. The remainder of the description will primarily relate to a transmitter recognition application of the invention, by way of non-limiting example.

[0070] In the example of [Fig. 1], the system 100 comprises two carriers 20A and 20B, each comprising a receiver 2A and 2B respectively. The carriers 20A and 20B may, for example, be aerial carriers spaced a certain distance apart (for example, on the order of a kilometer) and simultaneously illuminated by the main lobe of a transmitter 3 to be located. The transmitter 3 may, for example, be a radar. The two receivers 2A and 2B may be configured to locate the transmitter 3. In the following description, a carrier will generally be designated by reference numeral 20 and a receiver will generally be designated by reference numeral 2. In an example application of the invention, a receiver 2 may, for example, be a passive listening sensor.

[0071] The transmitter 3 is configured to emit a signal comprising a series of electromagnetic pulses (radar pulses) defining a pseudo-random pulsed waveform of the signal.

[0072] According to embodiments of the invention, a receiver 2 is capable of receiving the signal emitted by the transmitter and of implementing a waveform recognition method to recognize the pseudo-random impulse waveform of the signal from the data relating to the received impulses.

[0073] Fig. 1 represents an embodiment of the system 100 in which each receiver 2A and 2B includes a waveform recognition device 10.

[0074] More generally, the waveform recognition device 10 can be provided in one or more receivers 2.

[0075] In one application example of the invention, a waveform recognition device 10 of the system 100 can exchange data with a transmitter recognition device 30 configured to perform transmitter recognition 3 via a data link 5 associated with a data rate. The recognition device can be provided on a centralized platform or in one of the receivers. In the example of [Fig. 1], each receiver 2A and 2B is equipped with a waveform recognition device 10 capable of exchanging data with a central transmitter recognition device 30, configured to recognize transmitter 3. In other application examples, the transmitter recognition device 30 can be replaced by a transmitter identification device 3 or by a transmitter 3 locating device.

[0076] The waveform recognition device 10 according to embodiments of the invention advantageously exploits two characteristics common to pseudo-random waveform radars. These two characteristics are linked to at least one parameter characterizing the pulses (also called "pulse parameter") such as, for example and without limitation, a parameter relating to the arrival times of the pulses.

[0077] According to embodiments of the invention, the waveform recognition device 10 is configured to recognize a waveform from: - a first characteristic representing a set of pulse parameters, comprising at least one pulse parameter, each pulse parameter of the set of pulse parameters being able to take values ​​within a finite set of possible values; and - a second characteristic corresponding to a characteristic of pseudo-random waveforms according to which the chaining of values ​​of the set of impulse parameters considered constitutes a Markovian process (P. Bremaud. Markov chains, Gibbs fields, Monte-Carlo simulations, and queues. Springer. 1998).

[0078] In one embodiment, the set of pulse parameters considered may be limited to a single pulse parameter or may be a tuple of pulse parameters comprising a plurality of pulse parameters.

[0079] In embodiments where the set of pulse parameters is limited to a single pulse parameter, the pulse parameter may be, for example, the pulse arrival time difference (PDT). In such an embodiment, the waveform recognition device 10 is configured to recognize a waveform from: - a first characteristic representing the difference in arrival time between two consecutive pulses (DTOA, differential time of arrival); and - a second characteristic corresponding to a characteristic of pseudo-random waveforms according to which the chaining of DTOA values ​​constitutes a Markovian process.

[0080] In this example, the first characteristic, which represents the difference in arrival time between two consecutive pulses, can take values ​​from a finite set of possible values. The pulse emission times can be chosen in the radar system from a comb of DTOA values. After a travel time that can be considered constant over the scale of a pulse train, the arrival times can be measured by the receiver 2, with Gaussian noise whose standard deviation is generally quite small compared to the difference between the nearest DTOAs.

[0081] Fig. 2 is a diagram of time difference arrival (DTOAs) values ​​between consecutive pulses from a pseudo-random radar and Fig. 3 is a histogram of corresponding DTOA values, according to an embodiment of the invention in which the pulses are emitted by a naval radar intercepted at sea.

[0082] As illustrated in Figure 2, the sequence of DTOAs does not exhibit any apparent regularity. The jumps in values ​​that fall outside the ordinate scale correspond either to missed pulses or to interruptions in radar illumination during its angular sweep. Figure 3 shows a histogram of DTOA values, as a proportion of intercepted pulses, which here number 2150. It can be noted that the values ​​are distributed over a comb of K = 32 average values ​​or "modes", denoted (jMp n,..., in an increasing order of values ​​including in order the value = 1538 qs, the value = 1541 qs, etc., up to the value f*K = 1631 qs, with a standard deviation around each mode which is small compared to the difference between the modes.

[0083] The second feature considered for pseudo-random waveform recognition relates to the fact that the sequence of DTOA values ​​constitutes a Markovian process. A sequence of DTOA values ​​is considered to constitute a Markovian process when the time interval between the '-th pair of consecutive pulses takes a random value in the comb of values ​​with a probability that depends only on the value taken by the time interval Tn between the previous pulse pair. More generally, when the set of pulse parameters is a tuple of pulse parameters, this definition can be generalized by considering vector PK values ​​where each component corresponds to a parameter (i.e., a tuple is a state).

[0084] In practice, this can be a "hidden" Markov model, or Hidden Markov Model (HMM) (LR Rabiner. A tutorial on hidden Markov models and selected applications in speech recognition. Proc. of the IEEE 77(2):257-286. (Feb. 1989)), because the DTOA modes are not observed directly but with a slightly noisy value around each mode due to measurement uncertainty. To facilitate understanding of the invention, in the following description, the measurement variance of DTOA will initially be neglected, for the sake of simplicity.

[0085] A Markov process is characterized, among other things, by a transition matrix P between states. The states of the transition matrix denote the histogram modes of DTOA. The transition matrix can be represented by a K x K array comprising the conditional probabilities - (Tn+1 ~ Pp\Tn-1 Pq}, - - -K, rows in line. For example, for the comb of K = 32 values ​​in Figure 2, the transition matrix can be estimated by counting all the sequences of two given modes of DTOA, in the case where the process is stationary, i.e. the conditional transition probabilities P(Tn+\ ~ Pp\Pn — Pq ) remain the same over time (i.e. do not depend on the index H).

[0086] Figure 4 is an example of an estimated P transition matrix associated with the DTOAs of [Fig.2].

[0087] As illustrated in [Fig. 4], each row 9 of the matrix (q = 1...32) includes the transition probabilities from state Tn = pq to one of the following states Tn+i = fi p - 1... 32. The sum of the coefficients in each row is therefore equal to 100%. Thus, in the first row of the matrix (q - 1), it can be observed that the non-nuisance coefficients are 45% and 55% in the columns p = 1 and p = 2, which means that, if at a given time the DTOA is the first value of the comb, in the example considered P, = 1539 qs, then the next DTOA is: - either once again the first value of the comb with a probability of 45%, - or the second value ^2 of the comb with a probability of 55%.

[0088] Similarly, it can be observed that in the second row of the matrix (q=2) that, if at a given time the DTOA is the second value of the comb (here = 1541 qs), then the next DTOA is: - either the third value ^3 of the comb with a probability of 50%, -or the fourth value ^4 of the comb with a probability of 50%, etc.

[0089] The method and device for waveform recognition according to embodiments of the invention are advantageously based on the exploitation of the first and second characteristics which make it possible to improve the performance of recognizing pseudo-random waveforms, and to optimize the amount of data necessary for learning a model^ M of the pseudo-random waveform.

[0090] It should be noted that the invention is not limited to first and second characteristics relating to a DTOA-type pulse parameter and applies more generally to any set of pulse parameters characterizing a waveform (single pulse parameter or tuple of pulse parameters) such as the transmitted carrier frequency, time-frequency pairs, or any other parameter or tuple of pseudo-random parameters characterizing the intercepted pulses. However, to facilitate understanding of the invention, the following description of certain embodiments will essentially be made with reference to the use of a first and second characteristic relating to a single pulse parameter linked to the pulse arrival times, and in particular to a DTOA-type differential pulse parameter, for recognizing waveforms, by way of non-limiting example.

[0091] The measurement of the pulse parameter or tuple of pulse parameters characterizing the nth intercepted pulse associated with the first and second characteristics will be denoted x«, with n = 1... N in the rest of the description.

[0092] The measurements (x„) correspond to at least some of the waveforms to be recognized.

[0093] As shown in [Fig. 5], the waveform recognition device 10 according to the embodiments of the invention comprises a recognition unit waveform 101 configured to recognize a pseudo-random waveform, modeled by a Markovian process according to a model M = ( fi, P, (y ), defined by: - ​​a vector g P& whose coefficients are a comb of K values ​​representing the states of the process, with KGN ; the process states (fi? , PK) are the coefficients of the comb and represent the moments of the considered impulse parameters, - a transition matrix P between consecutive values ​​of the comb, the transition matrix being of size K x K; the transition matrix P between states thus groups the probabilities of transitioning from a given state to the other states; and - a vector I ps comprising a set of coefficients, the coefficients representing the standard deviations of measurement of the states by receiver 2.

[0094] The waveform recognition device 10 further includes a learning unit 102 configured to implement model learning M = ( fi, P, cr ), from reference data.

[0095] Given a model M= ( fi, P,&) the waveform recognition unit 101 is configured to process the received pulses successively in the order of their interception over time.

[0096] The invention can be implemented for example to perform recognition of a pseudo-random radar waveform integrated into a passive listening sensor 2.

[0097] The waveform recognition unit 101 is thus capable of receiving as input a time-ordered dated sequence of measurements of the characteristic pulse parameter(s) of the waveform, and the waveform model M.

[0098] The waveform recognition unit 101 is configured to traverse a decision tree A, whose nodes correspond to the states through which the different possible realizations of the waveform can pass, the nodes being linked together through the depth levels of the tree in accordance with the transition matrix P of the model M.

[0099] The traversal of tree A consists of exploring the nodes, the waveform recognition unit 101 being configured, at each passage through a node, to: - calculate a predicted value of the considered pulse parameter(s), conditioned in particular by the state of the current node, - verify if a precondition relating to the comparison of the prediction and the input data (measurements of the received input pulse parameter(s)), within the measurement standard deviations given by M, - increment a missing value counter if the precondition is not met (no association between the prediction and the input measurements), - update a score by increasing its value if the precondition is verified (case of association between the prediction and one of the input measurements), the data reached by the prediction can then be stored in memory and / or the missing counter can then be reset (reset to zero).

[0100] The waveform recognition unit can then determine whether or not the waveform is recognized in the input data, based on the best score value among the values ​​obtained in the different branches of the tree traversed.

[0101] The waveform recognition unit 101 can be configured to determine the score from the measurements (xM) and the model M, by traversing the tree A with a depth less than N. In one embodiment, the calculated score can be the maximum likelihood of the measurements (xB) conditional on the model M.

[0102] It should be noted that, generally, not all measurements (xM) correspond to the waveform to be recognized. In particular, a subset of measurements (X„) may originate from a model other than M = when other forms waveforms are mixed with the waveform of interest (waveform to be recognized).

[0103] Figure 6 is a flowchart representing the method for calculating the score S from the traversal of tree A, according to various embodiments. The method for calculating the score S can be implemented by the waveform recognition unit 101.

[0104] The traversed tree A to calculate the score comprises a set of nodes arranged according to the tree structure between a root node and the leaf nodes.

[0105] Each node of the tree corresponds to one of the process states (1*2 -, PK) corresponding to the comb coefficients and provides a prediction of the measurements (xn). If the measurements (xw) correspond to measurements of a differential impulse parameter such as the DTOA, the phasing of the process states in the data is unknown, so the initial state is unknown. In this case, in an initial step 601 of the scoring calculation, the root node of the tree (initial node) can undergo cuts corresponding to as many hypotheses about the initial state, or alternatively, use additional information to reduce the number of cuts of the root node. A 'cut' operation, in the field of decision trees, refers to an operation of cutting into as many branches as there are possible successor nodes.

[0106] At step 602, the root node of the tree A is traversed. At step 602, the root node ('start') produces a prediction Xj of time of arrival (TOA, 'time of arrival' meaning "time of arrival"), equal to the first measured time of arrival XJ. At this step of the tree traversal, the score $ is initialized to 0 and the measurement of the parameter The impulse xi can be stored, for example in a buffer memory T Cbuffer ') of the device 10.

[0107] Figure 7 illustrates step 602 of score calculation by traversing a tree A, in the case where the differential impulse parameter is a DTOA type parameter (the process states considered are then the DTOA values).

[0108] As illustrated in Figure 7, the root node ('start') produces a prediction X| of time of arrival (TOA, 'time of arrival' meaning 'time of arrival'), equal to the first measured time of arrival xi. In this step of the tree traversal, the score S is initialized to 0 and the measurement of the impulse parameter xi can be stored, for example in the buffer.

[0109] With further reference to Figure 6, at step 604, at least one of the branches from the root node ('start') which leads to the initial state corresponding to one of the DTOAs of the comb of values ​​^1,...,¾ is explored.

[0110] The branches of the tree to be traversed can be explored in any order. Alternatively, the branches of the tree to be traversed can be explored in a chosen order. For example, the branches of the tree to be traversed can advantageously be explored in descending order of a probability value, also called 'marginal probability', representing the probability of a DTOA value appearing. Since the different DTOA values ​​do not necessarily all appear with the same probability, using such a branch traversal order linked to the marginal probability makes it possible to prioritize traversing the branches that have the greatest chance of leading to transmitter recognition and to interrupt the score calculation as soon as the score is large enough to recognize the waveform.According to Markov chain theory, under certain conditions, the transition matrix P has an eigenvalue equal to 1 with multiplicity 1, and the marginal probabilities of the states are then given by the associated eigenvector.

[0111] Regardless of considerations regarding the order of traversal of the tree branches, it is assumed that the branch selected at step 606 is a branch whose next node is associated with a process state P# with l <k<K, comme illustré par l’exemple de la figure 7. Le nœud correspondant à l’état Pk fournit alors une prédiction de mesure x? associée à la prochaine impulsion. Dans le cas où le paramètre d’impulsion considéré est le DTOA, x2 correspond au temps d‘arrivée de la prochaine impulsion qui est égal à la somme de la prédiction Xj déterminée à l’étape précédente 602 et du DTOA. Le score S est alors mis à jour à l’étape 607 selon qu’un échantillon des mesures ( x„) est proche de la prédiction x2 compte tenu de T écart-type de mesure ^k.

[0112] The score S can be updated at step 607, in the state if a precondition is satisfied (or verified) indicating that a pulse is reached, by incrementing the current value of the score $ by a chosen or calculated value V.

[0113]

[0114]

[0115]

[0116] In one embodiment, the score S can be updated at step 607, in the state , according to the following formula (3): min-07- < t Hit: S^S + —exp -min-5-2-n \ n / In formula (3), the precondition C is equal to , and the value V is mm-Tr?- st nk equaled a t / MM' \ • —7= exp -min -yf" J In formula (3), ak denotes the standard deviation of the measurement and * denotes an adjustable threshold to limit the terms contributing to the score calculation to significant values. For example, and without limitations, the threshold * can be equal to 3 (t = 3). The precondition C= is met if one of the measurements is sufficiently close to The prediction x? and can be associated with this prediction. The term 'Hit' (meaning 'reached') in formula (3) means that the prediction x9 'reaches' a pulse. A prediction is considered to reach a pulse if the precondition C is satisfied (i.e., verified).

[0117] If precondition C is satisfied, as indicated by formula (3), the current score S is significantly increased by the amount V, which may be equal to 1 ( -xf \ in the case of formula (3). Furthermore, the impulse minimum argument in precondition C (i.e., MM can be stored) in buffer T.

[0118] It should be noted that the invention is not limited to the score update equation 5 shown in formula (3) by way of non-limiting example (1 / k j2). Alternatively, other score calculation formulas S + —r^expl 5 can be used, and in particular adapted score calculation formulas to reduce the computational cost due to the exponential ('exp') in formula (3). For example, and without limitation, the score update equation 5 in formula (3) can be replaced by a simple increment 5S + 1 (in this case V is a fixed value of 1).

[0119] [Fig.8] illustrates the first iteration of steps 604 to 607 of [Fig.6] in the case of a differential impulse parameter of type DTOA.

[0120] If precondition C of formula (3) is not satisfied, a lack of pulse ('Miss') is detected, and a miss counter is then incremented, as illustrated in [Fig.8].

[0121] With further reference to Figure 6, the tree traversal continues iteratively after step 607, pruning branches if the miss counter reaches a predefined maximum miss value, i.e., when a number of consecutive misses corresponding to the maximum miss value is reached. At the (i - [)-emc iteration of step 607, with i ≥ 3, the score $ is updated, in one of the nodes fik, 1 L k < K, corresponding to the next node of the current branch, with the prediction x{ of the measurement of the impulse parameter (TOA for example).

[0122] The prediction X; can be determined from the previous estimation of the impulse parameter xiA and one of the successor states ^k of the current node (x(=xz j+ h If the If the impulse parameter is not a differential parameter, then the prediction is more simply defined by x^k, where k denotes the index of the state in the branch, after the current node is cut. If the state is vectorial, each component is predicted according to whether it is differential or not.

[0123] In embodiments where the process states correspond to a pulse parameter of type DTOA (differences in arrival time between consecutive pulses), the predictions associated with the nodes of the tree are the arrival times of the pulses, the first prediction Xj of the path coincides with the first measurement of the arrival time of the input data set, while the following predictions X, integrate the successive differences in arrival time.

[0124] In such an embodiment, the prediction Xj can correspond to the sum of the previous estimation of the impulse parameter and one of the successor states of the current node (x—X; j+ \.

[0125] In some embodiments, the S score can be updated at step 607 according to formula (3):

[0126] . i ( . (3) min-57- Hit: S S+—7== exp -min-5-7- nk crk^2ü \ f

[0127] As illustrated in Figure 8, the traversal proceeds in depth first. The states (states related to the DTOA, for example) that follow node ^k in tree A are indexed by <p(k, 1), ..., (p(k, où s* désigne le nombre de successeurs (nœuds successeurs) du nœud ^k- Par exemple, avec les données des figures 2, 3 et 4, le phasage de l’émetteur 3 dans les données est tel que l’état initial, fixé à la première itération des étapes 604 à 607 (i=2) est !*k ~ ^13- La matrice de transition, illustrée par la figure 4, indique que deux DTOAs peuvent succéder au niveau du nœud ^13 dans la second iteration of steps 604 to 607, corresponding to ^25 or ^26- Thus, the number of successors of the node ^3 is ^3 = 2 in the node ^13 since there are two possible values ​​subsequent to ^13, which are indexed by q>( 13,1) = 25 and 13,2) = 26.

[0128] In one embodiment, the order in which branches are traversed can be a decreasing conditional probability order. Indeed, at a given depth in the tree corresponding to a node conditionally to the following DTOAs, the subsequent DTOAs do not necessarily have the same probability, so it is advantageous to traverse first the branches that have the greatest chance of leading to the recognition of the sender 3 in order to interrupt the calculation of the score as soon as it is large enough to conclude. It should be noted that in Markov models, the conditional probability is represented by the transition matrix P, while the marginal probability is the stationary measure.

[0129] Regardless of the chosen order of traversal of the branches of tree A, assuming that the branch selected at step 606 is the one that leads to the state f^kiy with 1, step 607 is repeated at the next iteration by replacing the index & with (p(kl) (to similarly determine the predictions of TOA, the update of the score or the miss counter, and where appropriate to store the impulse reached by the prediction).

[0130] Thus, at a later iteration *, the score S can be updated, in the node corresponding to the next node of the current branch, with the prediction xt of the measurement of the impulse parameter (TOA for example) according to formula (3) above:

[0131] . ha-x] „ v 1 / - min;^ < t Hit: SS +---r=exp -min^-r— « r \ H ^«k» /

[0132] It should be noted that most of the time, branch exploration may not be successful, i.e., many consecutive gaps appear quickly (for example, if the initial phasing assumption and the various assumptions of DTOA value transitions are not correct, or if the data do not contain any realization of the M= model of the pseudo-random waveform). In such a case, tree exploration (i.e., "pruning" of branches) can be stopped and the process can go back up the path (to a level of the tree higher than the current level of the tree) to explore branches left aside in previous steps (according to a backtracking process).

[0133] When a stopping condition is satisfied in step 608, the process terminates in step 610, returning the largest score value S (i.e., the last updated score value). In step 610, other information may be returned, such as the path taken through the tree A and optionally the subset of impulses that were reached by the different predictions in the different depth levels of the best path. In one embodiment, the stopping condition can be satisfied (or verified) at step 608, when all branches have been explored and pruned.

[0134] Alternatively, to limit the number of calculations, the stopping condition of step 608 can be checked if the score S is greater than a threshold value Sseuii, because in this case the waveform is recognized, making it unnecessary to traverse the remaining branches (the score reaches a sufficiently high parameterable value, with the most probable nodes being explored first at each cut). However, the pulses of the waveform may not be fully extracted.

[0135] The stopping condition of step 608 can alternatively be checked if a configurable number of consecutive misses is reached by the miss counter, the last operations then being compensated in order to resume the journey from a higher level of the tree to another branch.

[0136] If the score returned in step 610 is too low, the waveform cannot be recognized. In this case, the procedure in Figure 6 can be repeated by initializing the first prediction of the measurement of the impulse parameter (TOA, for example) on the second sample, i.e., x = X7, then, if a further iteration of the procedure is again necessary (score S still insufficient), by then initializing jq on the third sample, i.e., Xj = X3, and so on, in order to take into account the fact that the emitter is not necessarily present at the beginning of the analysis window containing the data (xn). Since the maximum depth of the tree is decremented to N-j when Xj = Xj, the procedure is advantageously increasingly faster to execute.

[0137] If the waveform was recognized in an immediately preceding time window, it is generally not necessary to repeat the process with different initializations of the first prediction of the pulse parameter measurement (e.g., TOA). Alternatively, instead of being applied in adjacent windows, the process can also be applied in a sliding time window, thus avoiding repeating the process in the same window by resetting the first prediction of the pulse parameter measurement (e.g., TOA).

[0138] Fig. 9 illustrates the best tree traversal when the process of Fig. 6 is applied to the data of Figures 2 and 3, in an analysis window of 100 ms (in this example the pulse parameter used is DTOA), with branch pruning when three successive misses are detected (e.g., counted by the miss counter).

[0139] In the example in Figure 9, the phasing of emitter 3 in the data is such that the initial state ^]3 generates a first 'hit', i.e., the prediction in this state (node ​​^13) reaches a pulse (step 1). The exploration first passes through the node ^25 °where a first miss is detected (step 2), then by the nodes ^[g and ^3 where two other misses are detected (steps 3 and 4). With three consecutive misses detected, the tree traversal is stopped, indicated by a triangle at the end of branch ^13 " ^25 ' 18 ' ^3, and the backtracking operation moves up one level to explore the branch passing through ^4. Another miss being detected at this node (step 5), the exploration also stops at the end of branch ^13'^25'^18'^4. The backtracking operation then moves up two levels and continues the exploration along branch ^13'^25'^17. The miss counter at this stage is reset to 1, following the miss detected at node ^25. With further misses then detected at nodes ^17 and ^18'^7 (steps 6 and 7), the exploration stops at the end of branch ^13 "^25 "^17" and similarly at the end of branch ^13 "^25 "^17". ^\3^25~^\2^2 (step 8).

[0140] The backtracking operation then moves up 3 levels to begin exploring branch ^13' ^26. At node ^13, an impulse is reached by predicting the measurement of the impulse parameter (TOA in this example), which generates a 'hit' and triggers the score update (step 9). Note that the exploration of the branch passing through node ^19 is not shown in detail in [Fig. 9], although this branch is quickly pruned.

[0141] At node ^20, no pulse is reached by the prediction of the pulse parameter measurement (TOA in this example), which sets the miss counter to 1. The branch ^13' ^26' ^20' is then pruned and backtracking to the node Another hit is generated. The miss counter is reset to 0, and the exploration continues until all branches are explored or the score is large enough to stop the traversal. At each iteration of the process in Figure 6, the process returns the score, the best traversal of tree A (in the example in Figure 9, ^13”^26’^20 ~^8~ ^15’ “ ’ ), and optionally the impulses reached by the predictions of the impulse parameter measurement (TOA in the example in Figure 9) at nodes ^13, ^26, ^8, • • •• As used here, “the best traversal of the tree” refers to the path from the initial node to the final node (at the algorithm's stoppage) that corresponds to the best score.

[0142] In the case where the measured impulse parameter(s) xn are not differential parameters, the process can be simplified because the initial state is known. Indeed, the root node is directly the initial state, so it is not necessary to divide it into as many branches as there are possible initial states. It is also not necessary to integrate the measurement prediction; that is, it is not necessary to calculate the cumulative sum of the states (if the parameter is not differential, the transition to the next state does not involve summing the states to obtain a prediction of the parameter's value).

[0143]

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150]

[0151]

[0152]

[0153] A person skilled in the art will readily understand that the invention is not limited to the score calculation formula in Equation 1. In particular, the score calculation defined in Equation 1 corresponds to a likelihood calculation that can be adapted or simplified. The score can, alternatively, be a simple hit counter (counting the number of times predictions are achieved through pulses) to reduce the computational load represented by the exponential function. In another variant, the factor —!— can be ignored by considering that the standard deviations ak are constant even if the model (often learned with reference data) indicates that they are slightly different. Furthermore, the waveform recognition process is not limited to a depth-first tree scan. In an AI-based variant, tree A can alternatively be traversed using a breadth-first approach, that is, by first exploring all the nodes at a given depth in the tree. In the case of differential impulse parameters such as the DTOA, small errors in the state values ​​in the model can accumulate with each prediction and thus cause premature interruption of the process. To avoid such an accumulation of small errors in the state values ​​in an embodiment, step 607 of the waveform recognition process can include, in response to the generation of 'hit' (reaching a pulse by the prediction), a correction of the predictions x; by recentering them on the pulse reached by the prediction (i.e., the argument of the minimum in the precondition of equation 1), according to the following equations 4A or 4B: A. / (4A), x,- = argmm\—— / xn If the variances associated with the states are ignored, equation (4A) can be replaced by : argmin([x„-xH-^ I ) (4B) In another variant, step 607 of the waveform recognition process may include, in response to the generation of 'hit' (reaching of an impulse by the prediction), a joint re-estimation of successive predictions after a given number of hits, according to the following equation (5): Ei. (5) jnin-r-. t=ln Equation (5) is defined subject to the constraint that: ^r+i ~ for t -1... i -1 (6) In equation (6), the parameters for t = l... i -1 denote the states of the current path associated with "hits" and the parameters of, for t = l... i -1, denote X; = arg mm 7 y,-y the associated variances. In some embodiments, the variances can be ignored.

[0154] The waveform recognition method 10 according to embodiments of the invention thus makes it possible to recognize a realization of a pseudo-random waveform described by a model M = (fi, P, a) given a priori. In the case of an implementation of the invention in the form of the device 10, waveform recognition from the model M = (ji, P, <7) is implemented by the pattern recognition unit 101.

[0155] In embodiments, a method for learning the model M = (fl, P, a) from reference data is also proposed (also called 'model training method').

[0156] The learning of the model M consists of estimating as best as possible the states, i.e. the set of values ​​that can be taken by the pulse parameter(s) measured by the receiver 2, with the standard deviations of measurement as well as the transition matrix P between states, from reference data.

[0157] Figure 10 illustrates the method for learning the model M = (ji, P, a), from reference data, according to embodiments of the invention. The method can be implemented by the learning unit 102 of the waveform recognition device 10. The reference data are of the same nature as the received pulses. They can be intercepted beforehand and stored in memory for use in the model learning phase.

[0158] In step 800, the reference data is filtered. This filtering step consists of eliminating any mixtures in the reference data (possible minor spurious pulses). The reference data essentially comprises measurement data from the transmitter 3, whose model is to be learned. Such measurement data is obtained using acquisition means (the acquisition means may be, for example, the receiver 2 itself, i.e., the one that implements the waveform recognition method according to the embodiments of the invention) or other suitable acquisition means, such as other separate receivers used in previous intelligence missions and capable of providing data of the same nature as the receiver 2 that implements the waveform recognition method according to the embodiments of the invention.

[0159] However, depending on the means of acquiring the reference data, the reference data may also include a small proportion of measurements from other sources. Step 800 can be carried out using any suitable out-of-distribution (or 'outliers') sampling technique that eliminates non-significant measurements. Examples of suitable out-of-distribution sampling techniques include, without limitations, isolation forests, an outlier local factor, the nearest neighbor technique, the DBscan technique, etc. The filtering of step 800 is preferably not applied to each acquisition, because statistical representativeness of the sample is required, but advantageously to the implementation of the process.

[0160] At step 802, the number of states is estimated from the reference data filtered in step 800.

[0161] Knowing the sensor resolution, the estimation of the states ,l is based on a histogram H of the transmitter measurements (filtered reference data), with a step size adapted to the resolution. For example, in the case where the pulse parameter considered is the DTOA, the support of the histogram H can be limited to more than twice the lowest value of DTOA, so as not to take into account DTOAs due to missed pulses.

[0162] As used here, the expression "histogram support" refers to a set of values ​​where the histogram is not zero. Furthermore, the "upper bound" of the histogram refers to its maximum value (thus, the expression "upper bound" means "right-truncated" or "into larger values").

[0163] The histogram H represents the number of pulses detected as a function of an interval index. The abscissa of the histogram thus corresponds to the interval index whose width is equal to a resolution (in ps), while the ordinate of the histogram corresponds to the number of pulses belonging to the interval indexed on the abscissa.

[0164] In one embodiment, the number of states can be estimated from the histogram H, by counting the elements of the connected components of the histogram on its x-axis.

[0165] A connected component is a set of consecutive intervals (or steps ⇔step') of histograms containing a non-zero pulse count. Considering that K connected components are extracted, each of the connected components corresponds to a component value of the comb

[0166] The number of states then corresponds to the number of modes of the histogram H which is estimated by determining the number of connected components of sufficient cardinality (i.e. at least equal to 2) in the histogram.

[0167] Figure 11 shows an enlargement of an H histogram around the first modes of the DTOA, in the example of the data in Figures 2 and 3 corresponding to a DTOA type impulse parameter. A "DTOA mode" designates a local maximum of the DTOA histogram.

[0168] As illustrated in Figure 11, the first five intervals of the histogram H (indexed 1 to 5) contain a non-zero number of pulses and form the first connected component on the x-axis with a cardinality of 5. Similarly, the Histogram intervals with indices 31 to 35 form a second connected component, also with a cardinality of 5. A sufficient number of connected components (i.e., at least 2) allows us to estimate the number of histogram modes, that is, the number of states.

[0169] At step 804, the value of states 11 is estimated.

[0170] In one embodiment, the value of the states can be estimated by determining the median value of the centers of the intervals forming each connected component, each median value providing the value of one of the K states of the comb. Thus, for each connected component of cardinality N associated with a set of N consecutive interval indices, the value of the center of each of the intervals associated with these indices is determined (in ps), by considering the measurement resolution (the width of an interval index is equal to a measurement resolution) and then the median value or the average value of the values ​​of the centers of these intervals (sum of the values ​​of the N centers of the intervals of the connected component divided by N).

[0171] In the example in Figure 11, the first five index intervals 1 to 5, forming the first connected component, have centers at 1537.7 ps, 1537.8 ps, 1537.9 ps, 1538.0 ps, ​​and 1538.1 ps, respectively (the measurement resolution in the example in Figure 11 is 100 ns), which provides a median value of 1537.9 ps and thus the first value of the comb / z. An estimate of the K-1 other states and an estimate of the associated standard deviations can be obtained in a similar manner (in this example K = 32).

[0172] The standard deviation associated with the state & can be estimated using the standard estimator 2__, .2 with cmk denoting the ^-th interval center value ®k~ M ] ( ^mk " ) of the ^-th connected component and the corresponding mean. Alternatively, the standard deviation can be estimated with any other suitable estimator (e.g., with an unbiased estimator that divides the sum by M - 1 rather than M).

[0173] In embodiments, the estimation of the states can be further refined in various ways using any suitable statistical estimator that exploits knowledge of the number of states. For example, the EM algorithm (described, for instance, in (AP Dempster, NM Laird, DB Rubin, Maximum Likelihood from Incomplete Data via the EM Algorithm, Journal of the Royal Statistical Society B 39(1), pp. 1–38, 1977)) can be used to refine the estimation. The EM algorithm is a maximum likelihood optimal algorithm for estimating the modes of histograms if the measurement noise is Gaussian and centered. Such an algorithm also provides an optimal estimate of the standard deviation 17 associated with each state. By applying the EM algorithm at step 804, it is possible to obtain a very accurate estimation of the states and the associated measurement standard deviations 17. In one embodiment of In realization, at step 804, the values ​​and can first be estimated in step 804 above, and then the EM algorithm can be subsequently applied.

[0174] It should be noted that the use of an EM algorithm is only optional, the implementation of step 804 without application of the EM algorithm is generally sufficient.

[0175] At step 806, the transition matrix P can be estimated in a quasi-optimal way in the maximum likelihood sense, if the standard deviations n are small compared to the differences in values ​​between the states P. The coefficients of the matrix P can be estimated by counting all the transitions in the reference data (number of transitions between all pairs of states). Thus, the coefficient p.^ — p^^ of the matrix P, equal to the probability of having state Pj following state Pi, can be estimated by counting all the transitions from state Pi to state Pj and normalizing the value obtained (number of transitions from state Pi to state Pj) by the total number of transitions (state Pt is obtained when a measure xn is closer to Pi than to all other states, and state Pj is obtained when the next measure xn is closer to Pj than to all other states).The normalization operation refers to dividing the obtained value (number of transitions from state Mj to state Mj) by the total number of transitions.

[0176] In some embodiments, the estimates thus obtained of P, P, eta can be further optimized or refined by applying an optimization algorithm initialized with these estimated values ​​P, P, eta, such as the Baum-Welch algorithm, for example (LR Welch, Hidden Markov Models and the Baum-Welch Algorithm, IEEE Information Theory Society Newsletter 53(4), pp. 10-13, December 2003). Such an algorithm is capable of jointly estimating these parameters iteratively and optimally in the maximum likelihood sense, provided that a suitable initialization is obtained. Thus, once the values ​​1*, p, eta have been obtained using the method in [Fig. 10], it is optionally possible to optimize them further by applying the Baum-Welch algorithm to these values, which are then considered as initial values.

[0177] Embodiments of the invention advantageously enable the recognition of a statistical sample of pulses from a model M = (p, P, a) associated with a pseudo-random waveform. They provide a waveform recognition solution that is particularly robust to mixing, meaning that performance is only slightly affected if the sample of pulses from model M is mixed with another sample from a different model Ms, or even from the same model. Furthermore, such a solution is robust to missed pulses, meaning that performance is only slightly affected when not all pulses are intercepted. Furthermore, the waveform recognition method and device according to the embodiments of the invention have significant performance, even with a small number of intercepted pulses.

[0178] Advantageously, the waveform recognition method and device according to embodiments of the invention can "learn" the model M = characterizing the comb of values ​​the transition matrix P between values, and the 17 standard deviations of state measurements, from even a very partial set of waveform intercepts. While not limited to such applications, this type of learning is particularly advantageous if the device is used without extensive upstream capabilities to provide a priori radar models. It is also particularly advantageous in applications where the environment's radars are software-defined, allowing radar operators to relatively frequently modify the waveform characteristics and thus the associated model, rendering radar identification libraries ineffective. In this case, the learning functionality enables the recognition of emissions based on a recent history of intercepts in the operational area, without a priori libraries or models, and potentially anonymously (i.e., without necessarily associating a name with a transmitter).Such learning can also be advantageous in an application of the invention to an intelligence system, the learning then making it possible to automatically establish a more accurate and discriminating pseudo-random radar emitter model than current descriptions which are limited to minimum and maximum value intervals [ / / p or to the value comb ( / / ^ / / ,..., / / ^). .

[0179] In the following description, to illustrate the waveform recognition performance according to embodiments of the invention, the reference data examples in Figures 2 and 3, corresponding to a DTOA-type pulse parameter, will be considered in combination with a Poisson process (described, for example, in P. Bremaud, Markov chains, Gibbs fields, Monte-Carlo simulations, and queues. Springer, 1998) modeling spurious pulses from other emitters mixing with the pulses of the waveform of interest. The Poisson process is parameterized by the spurious pulse density (in y1), denoted 2, which varies. Furthermore, the measurement standard deviations of the DTOAs can all be considered identical, and the factors —L = & = 1 39 can be eliminated. in the calculation of the score (defined by equation 1). A person skilled in the art will readily understand that the invention is not limited to these examples, which are given only as a non-limiting illustration.

[0180] Figures 12 and 13 represent the score values ​​returned by the waveform recognition process (step 610 of Figure 6), applied to M = 1Q5 realizations of Poisson processes for different densities 2, in a time window of duration 100 ms. When the score values ​​are ordered in ascending order as in Figure 12, the m-th value corresponds to a score threshold corresponding to an erroneous decision in the waveform recognition with an empirical probability of error of 1- , m~ \ ...M- By analogy with the In detection theory, the probability of a false alarm is denoted by PFA (False Alarm Probability). Figure 12 represents different PFAs (logi0PFA on the y-axis) as a function of the score threshold (x-axis) for different values ​​of 2, while Figure 13 represents the value of the score threshold (y-axis) as a function of 2 (x-axis) for different PFAs.

[0181] Figure 13 thus represents the threshold value to be applied to the score to decide on waveform recognition as a function of parameter 2 for several PFA values. The range of values ​​for 2 relates to situations with relatively high pulse density. It is observed that a score threshold around 3 is generally sufficient to prevent false alarms.

[0182] It is assumed that the recognition method is applied to M = 10³ realizations of the waveform of interest, mixed with a Poisson process of fixed density 2 = 1000 F₁, and with a score threshold of 2.73 (for a PFA of 10² on [Fig. 13]), in a 100 ms window. A realization of the waveform is obtained by randomly fixing (i) the TOA of the first pulse, (ii) the phasing (i.e., the initial state of the waveform), and (iii) the transitions between states according to the probabilities in the model's transition matrix. The realizations of the waveform last 20 ms, so the number of pulses is generally 13, while the number of pulses in the Poisson process is around 100 (these are challenging situations, with significant mixing of spurious pulses). In practice, it is increasingly common for some pulses to be missed. The percentage of missed pulses is called the "fragmentation rate".

[0183] Figure 14 illustrates the probability of recognizing the waveform of interest mixed with a Poisson process, as a function of the interference rate. The probability of recognizing the waveform is denoted by PD (Detection Probability) by analogy with detection theory. The missed pulses are chosen randomly from the set of pulses of the waveform without interference on the one hand, and from the set of spurious pulses from the Poisson process without interference on the other.

[0184]

[0185]

[0186]

[0187] Figure 14 shows that the probability of waveform recognition reaches a maximum value of 1 for low dispersal rates and remains very robust up to the dispersal rate reaching 45%. Between 45% and 65%, recognition performance decreases but remains acceptable, with a recognition probability greater than 0.7. Above 65%, the recognition probability drops rapidly. Thus, as illustrated by Figure 14, the recognition process is very robust to dispersal and mixing. Figure 15 illustrates the results of the waveform recognition process applied to real data. More specifically, Figure 15 represents the levels of intercepted pulses as a function of time over 30 minutes of real recordings, in dB (with an unspecified change in level values). As shown in Figure 15, there are approximately 51,000 pulses, which corresponds to a much lower average density than in the simulations illustrated by the... previous figures. In this example, the waveform recognition method according to the embodiments of the invention was applied in small, adjacent time windows of approximately 100ms duration, in which the recognition of the pseudo-random waveform is tested. The recognition threshold is set at 2.2. The diamonds shown in [Fig. 15] indicate the extracted pulses when recognition is successful. It can be observed that transmitter 3 is present from 03:55. Around 04:10, the transmitter is no longer recognized in the data for a little over two minutes, before reappearing around 04:13. Even without having the reality on the ground which would indicate which transmitter each of the 51,000 pulses comes from, it is possible to establish by an examination of the recognized pulses that they form periodic radar antenna lobe passages, with an illumination every 2.5 s.

[0188] Figure 16 represents the pulse levels in a window where recognition is positive. Figure 16 is a magnification (zoom) of a lobe recognized by the waveform recognition method according to embodiments of the invention (from real data).

[0189] Figure 16 shows a lobe formed by the recognized pulses, of which there are only 5 pulses, while the number of DTOA moments is 32 (i.e., the number of state values). Classical prior art approaches based on minimum and maximum values ​​or on the DTOA histogram do not have enough information to recognize the waveform in this case where there are only 5 pulses.

[0190] Figures 17 and 18 show the DTOAs of the pulses extracted by the waveform recognition process according to embodiments of the invention.

[0191] [Fig. 17] illustrates the DTOAs of the pulses extracted during waveform recognition (actual data) while [Fig. 18] is an ordinate enlargement (zoom) of this [Fig. 17].

[0192] In Figures 17 and 18, the DTOAs of the extracted pulses take values ​​close to the states (i.e. the 32 DTOA moments of the waveform, which are values ​​close to 0 given the scale on the ordinate), as well as around 2.5 s, which is the time interval between two lobe passes (i.e. the antenna rotation period of a rotating radar).

[0193] In [Fig. 17], three 2.5 s harmonics, namely two at 5 s and one at 7.5 s, can be observed, representing a total of four missed lobes. Also observed in [Fig. 17] is a very large value of 130 s, corresponding to the approximate interval [04:10' - 04:13'] in [Fig. 15], where the transmitter is momentarily not visible. This result allows us to conclude that there are no recognition errors in this dataset.

[0194] The number of lobes recognized being 423 in total, it can be deduced that the probability of recognition of the waveform is around ~ 99% and that the probability of error is less than ___L__ ~ $ K)'5 since there are 10 windows of 100ms per second i.e. 30 x 60 x 10 windows in 30 min.

[0195] Thus, although they are not limited to such applications, the embodiments of the invention make it possible to recognize pseudorandom waveforms in difficult environments, with mixtures, lack of pulses, and / or a low number of pulses of the waveforms of interest in the tested data.

[0196] Those skilled in the art will understand that the system or subsystems according to embodiments of the invention can be implemented in various ways by hardware, software, or a combination of hardware and software, in particular in the form of program code that can be distributed as a program product in various forms. In particular, the program code can be distributed using computer-readable media, which may include computer-readable storage media and communication media. The methods described herein can, in particular, be implemented in the form of computer program instructions executable by one or more processors in a computer system. These computer program instructions can also be stored in computer-readable media.

[0197] Furthermore, the invention is not limited to the embodiments described above by way of non-limiting example. It encompasses all the variant embodiments that could be envisaged by a person skilled in the art.

Claims

1. Demands 1. A method for recognizing the waveform of a signal received by a receiver from a transmitter (3), said signal comprising a series of electromagnetic pulses defining a pseudo-random waveform of the signal, characterized in that the method comprises the steps of: - determine a waveform model M = (ji, P, c) according to a hidden Markov process, the model comprising a vector / / E representing a comb of values, each value of the comb corresponding to a process state, the process states being possible values ​​of a given impulse parameter associated with said impulses, a transition matrix P between consecutive values ​​of the comb, the transition matrix being of size K x Æ, and a vector <7 e P^ comprising a set of coefficients representing the measurement standard deviations of the states, and in that the process comprises the steps of: -receiving a dated, time-ordered sequence of V measurements x> of said given impulse parameter, - determine a score, by traversing a tree comprising a set of branches, said branches comprising a set of nodes, each node of the tree corresponding to one of said process states Pk and providing a measurement prediction (¾) of said impulse parameter, the branches of said tree being traversed in a chosen order, the tree having a depth less than or equal to N, - recognize the waveform from said score, the determination of a score comprising one or more iterations of the following steps, for each traversed node of the tree associated with a process state P& - determine a prediction of the impulse parameter from the prediction of the impulse parameter i determined in the previous iteration and the process state Pk associated with the node, - determine if a precondition is met indicating that the prediction Xj reaches an impulse, - update (607) the current score value, if the precondition is met, by incrementing the current score value $ by one value, - select the next branch to traverse, with iterations repeated until a stopping condition is met.

2. 2. A method according to claim 1, characterized in that it comprises incrementing a shortage counter if the precondition is not met.

3. 3. Method according to claim 2, characterized in that the path of the tree goes back up to a higher level of the tree if the missing counter reaches a predefined maximum missing value.

4. 4. A method according to any one of the preceding claims, wherein the precondition is verified if: . h» -'J ., mm-07- < f Tl K denoting the measurement standard deviation of the impulse parameter and f denoting an adjustable threshold.

5. 5. A method according to any one of the preceding claims, wherein the calculated score is the maximum likelihood of the measurements xe conditional on the model M.

6. A method according to any one of claims 1 to 4, wherein the score is updated at the score update step by adding to the current score value > / \ or the quantity —r=exp -min~5~r quantity exp^ 7. A method according to any one of claims 1 to 5, wherein the score is updated by incrementing the current score value.

6. 8. A method according to any one of the preceding claims, wherein the method comprises training said model from reference data, the learning steps comprising the steps of: - filtering the reference data; - determining the number of process states; - determining the values ​​of the process states; the number of process states and the values ​​of the process states being determined from the filtered reference data, the method further comprising determining the transition matrix P and the standard deviations of the state measurements, from the number of process states and the values ​​of the process states.

7. 9. A method according to claim 8, wherein the reference data are used to update a histogram representing on the ordinate the number of detected pulses as a function of an interval index on the abscissa, the width of an interval being equal to a temporal resolution, and wherein: - the number of states corresponds to the number of connected components of the histogram with cardinality at least equal to a given value, on its abscissa axis, a connected component corresponding to a number of consecutive intervals containing a non-zero number of pulses in the histogram, said number of intervals of a connected component defining the cardinality of the connected component, and - the value of the process states is estimated by determining the median value of the centers of the intervals associated with each connected component,each median value providing the value of one of the K states of the comb 10. Waveform recognition receiver of a signal received from a transmitter (3), said signal comprising a series of electromagnetic pulses defining a pseudo-random waveform of the signal, characterized in that the receiver (2) comprises a waveform recognition unit configured to: - determine a waveform model M = (z, P, a) according to a hidden Markovian process, the model comprising a vector fig p& representing a comb of values, each value of the comb corresponding to a process state, the process states being possible values ​​of a given pulse parameter associated with said pulses, a transition matrix P between consecutive values ​​of the comb, the transition matrix being of size K x K, and a vector oe P^ comprising a set of coefficients representing the measurement standard deviations of the states,and in that the waveform recognition unit is configured to: - receive a time-ordered, dated sequence of N measurements x> of said given pulse parameter, - determine a score by traversing a tree comprising a set of branches, said branches comprising a set, of nodes, each node of the tree corresponding to one of said process states and providing a measurement prediction (xJ) of said impulse parameter, the branches of said tree being traversed in a chosen order, the tree having a depth less than or equal to N, - to recognize the waveform from said score, the determination of a score comprising one or more iterations of the following steps, for each traversed node of the tree associated with a process state: - determine a prediction xi of the impulse parameter from the prediction of the impulse parameter x^j determined in the previous iteration and the process state associated with the node; - determine if a precondition is met indicating that the prediction reaches a certain point, - update (607) the current score value, if the precondition is met, by incrementing the current score value $ by one value, - select the next branch to traverse, with iterations repeated until a stopping condition is met.

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