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    • 专利摘要:
    The present invention relates to a passive detection method implemented by a device comprising one or more sensors, said method comprising a step of sampling the signals received on each sensor using different sub-Shannon sampling rate values. a step of transforming the signals sampled in the frequency domain by discrete Fourier transform, the frequency step AF being chosen constant, and for each time / frequency box, a step of calculating the normalized power in each reception channel, a step calculating the quadratic sum of the powers calculated taking into account the power of a possible parasite, and a thresholding step so as to ensure a given false alarm probability.
    公开号:FR3020157A1
    申请号:FR1400935
    申请日:2014-04-18
    公开日:2015-10-23
    发明作者:Meur Anne Le；Jean Yves Delabbaye
    申请人:Thales SA；
    IPC主号:
    专利说明:

    [0001] The present invention relates to the field of broadband passive reception (of the order of ten GigaHertz, for example) of electromagnetic signals such as for example communication signals or radar signals. The present invention relates more particularly to a passive digital detection method.
    [0002] For technological reasons, in the context of broadband listening of electromagnetic signals, of the order of ten GigaHertz for example, it is generally not possible to perform sampling at a frequency meeting the Shannon criterion, nor to carry out the processing of the data resulting from this sampling. This requires sampling at frequencies lower than Shannon's frequency, which introduces spectral overlap or aliasing problems. If only one useful signal is present in the whole of the analyzed band, this sampling principle does not cause any problems, neither for the detection, since the signal is isolated in the folded band, nor for the signal analysis. On the other hand, if several signals are present simultaneously in the total band, they can be superimposed in the folded band, even if they are not at the same frequency in reality. For very broadband electromagnetic signal listening systems such as communications signals or radar signals, it is not possible at the present time to simultaneously have a maximum interception probability and good capabilities. analysis. The systems that perform these interceptions can be arranged in two categories: A first category corresponds to the very broadband receivers. These receivers permanently cover the entire analysis band and have a probability of interception (or POI for "Probability of Intercept" in the English terminology) very large for strong signals, but are characterized by a low sensitivity and a capacity very limited in discriminating or analyzing electromagnetic signals. A second group corresponds to narrow-band receivers called "superheterodynes". These receivers, after multibit sampling of this band by a conventional method, allow fine analysis of the signal (with high sensitivity up to the search for the modulation after discrete Fourier transform), but obviously suffer from a degraded POI. since out-of-band signals are not processed. There are sequencing functions which consist in determining the partial listening plan in bands and listening time, but they only partially remedy this defect. In this context, it is interesting to propose a solution allowing to cumulate the advantages of these two families of receiver. Such a solution would allow continuous broadband monitoring and good multi-bit sampling for efficient signal processing. The conventional detectors found in the literature only take into account the thermal noise. As a result, the parasites which are themselves signals themselves are not taken into account by the detection method. It is also known in the prior art, in particular from US Pat. No. 7,482,967, a multi-bit sub-Shannon wideband digital receiver. However, this system does not deal with the possible problems of folding other signals. An object of the invention is notably to correct one or more of the disadvantages of the prior art by proposing a solution making it possible to detect one or more useful signals while being robust to parasitic signals. To this end, the subject of the invention is a method for passive detection of electromagnetic signals that is robust to refoldings implemented by a device comprising at least one antenna, said antenna comprising at least one sensor and said method comprising: A sampling step signals received on each sensor, during a common acquisition time AT, using M different sampling rate values fm not satisfying the Shannon criterion, the signals sampled at the same frequency forming a channel of sampling, M representing an integer greater than or equal to 2 and m, the index of the sampling frequency between 1 and M, at least two sampling being carried out with sampling frequencies fm and numbers of sampling points Nm different, the pair (Nm, fm) being chosen such that the ratio AT = Nm / fm remains constant whatever the index m, A stage of transformation of the sampled in the frequency domain by discrete Fourier transform on the Nm sampling points of the received signal, sampled at fm over the common time interval AT, the common spectral resolution for all samplings being AF = 1 / AT, signals being presented in a discrete time / frequency representation, the method further comprises, for each time / frequency box of said discrete representation, a step of calculating the normalized power in each sampling channel, a step of calculating the sum quadratic powers calculated taking into account the power of a parasite, A step of thresholding said quadratic sum with a predetermined threshold value. According to an alternative embodiment, the calculation of the quadratic sum S of the powers is carried out using the formula: 2 S = E y, n -1n [1 + - exp y. m = 1 mm = i Where y ,, 72 represents the normalized power in the frequency sampling channel fm indicates the possible presence of a parasite on one of the samplings with e.1_ a [0-2 R 20-12 represents the power of the potential parasite, 262 represents the power of the noise, a represents the probability of absence of parasite, and R represents the number of channels sampled at the frequency fm.
    [0003] According to an alternative embodiment, the method also comprises a step of finding the highest power value among the sampling channels, the quadratic sum being calculated excluding said highest value power and summing the values. (M-1) remaining powers, said highest value power being considered as the power of a spurious signal. According to an implementation variant, the signals are received over N time frequency boxes with N integer strictly greater than 1, the method further comprising the application of a non-linear function in each time / frequency box and a summation step the result obtained on the N time / frequency boxes. According to a variant embodiment, the nonlinear function is an increasing monotonic function whose representative curve is defined by its asymptotes, a first asymptote at 1 = 0 having for equation y = ql and a second asymptote for 1 -> + 00 having for equation y = 1 + In (q) where q represents a real between 0 and 1. According to an implementation variant, the threshold value is defined so as to ensure a predetermined false alarm probability. The invention also relates to a passive detection device 30 comprising a reception module comprising at least one antenna and a calculation module configured to implement the method according to one of the a a2 + 0-2 previous variants, said module of receiving being configured to receive surrounding electromagnetic signals and transmit them to the computing module for processing. According to an alternative embodiment, the receiving module comprises an interferometric antenna array. Other features and advantages of the present invention will appear more clearly on reading the following description, given by way of illustration and not limitation, and with reference to the accompanying drawings, in which: FIGS. 1a and 1b illustrate examples of implementation of the sampling step respectively in a single signal configuration and with two sampling channels; FIG. 2 represents an example of a curve representative of the specific non-linearity of the multicase detector; Figures 3 to 6 illustrate possible steps of the detection method according to the invention in different cases. It should be noted that the use of the terms "sampling" or "sampling path" refers to all the signals received by the receiving channels or measurement channels that are sampled with the same frequency. The principle of the invention is based on taking into account the phenomenon of aliasing in the modeling and processing of the received signal, that is to say in the mathematical resolution of the problem of broadband detection, in order to to ensure detection performance as close as possible to those which would be obtained without spectrum folding. The passive digital detection method according to the invention can mainly comprise a step of sampling the signal received on each sensor with several sub-Shannon frequency values, a step of filtering the signal by a Fourier transform filter bank. discrete and for each time / frequency box, a step of calculation of the normalized power in each sampling, a step of calculating the quadratic sum of the powers calculated taking into account the power of a possible parasite and a step of thresholding to the using a predetermined threshold value. The threshold value can be set to ensure a predetermined false alarm probability (see Testing Statistical Hypothesis, E.L. Lehmann, J.P. Romano, Springer 2005).
    [0004] The signal is received on an antenna or network of interferometric antennas. It will be assumed later that the reception device comprises P sensors where P represents a non-zero integer. During a sampling step, the signals received on the different sensors are sampled with several different frequency values fm (with m natural integer varying from 1 to M where M is an integer greater than or equal to 2 representing the number of frequencies used) Shannon sub ie that does not meet the Shannon-Nyquist criterion. M must be sufficient to allow the removal of ambiguities in frequency and depends on the width of the analysis band.
    [0005] The signals sampled at the same sampling frequency fm form a sampling path of index m. It is assumed that for each m from 1 to M, R sensors are sampled at the frequency fm.
    [0006] The different values of the sampling frequencies fm are chosen to satisfy two constraints: each frequency fm is chosen so that its value is much lower than the intercept band B of the signals but greater than the band of the signals to be analyzed. the frequency Fo of a pure sinusoid in the band B can be recovered unambiguously from the M signals sampled at the frequencies f1, ... fm.
    [0007] Thus, each sampling preserves the spectrum of the useful signal to be analyzed in its form, but the translation of a possible quantity which depends on the value of the frequency fm. Thus, advantageously, several samples at the fm frequencies technologically possible replace a traditional sampling frequency 2B that we do not know how to do, at the cost of a more elaborate treatment. By way of example, FIG. 1a illustrates the sampling method 10 in a single signal configuration and with 2 sampling channels. This is a simplifying block diagram, where it is assumed that one deals with analytic signals whose spectrum has no component in the negative frequencies. This type of sampling, which makes it possible to remove the frequency ambiguity without having to make a conventional sampling at the frequency 2B in order to comply with the Shannon criterion, upsets the conventional signal reception models and obliges to propose more elaborate treatments. especially in detection. Indeed, over the entire processed band B, there may be simultaneous signals during the duration of the discrete Fourier transform (or DFT for "Discrete Fourier Transform" according to the English terminology). It is possible that in one or more samplings, this simultaneity is translated into a mixture. By way of illustration, this case is represented in FIG. If a useful signal is at the frequency fo, and another useful signal is at the frequency fo = fo + k fmi, with k strictly positive or strictly negative integer (if k was zero it would mean that there is has a true mix) and with fmi one of the M different sample rate values, the frequencies of the 2 signals fall back to the same place in the fmi sampling. In other words, the 2 M-tuples representing the frequencies fo and fo in the M sampling channels have a common value. We measure a mixture of signals in the fmi sampling, while there is no mixing in reality. The signal at the frequency fo, although itself a useful signal, represents a parasite vis-à-vis the signal at the frequency fo.
    [0008] When a parasitic signal folds into one of the M channels corresponding to the frequency fo, while no signal is present at the frequency fo, the presence of the parasite can generate a false alarm. In a dense environment, the probability of presence of a parasite becomes significant, of the order of 10% or more, and incompatible with the performance required of most reception systems. A discrete Fourier transform is then applied to the Nm sampling points of the received signal, sampled at fm over a common acquisition time AT for each of the sensors. AF = 1 / AT is then the common spectral resolution for all samplings. In order to obtain synchronous information of the same spectral resolution, for the different sampling frequencies fm, it is necessary to obtain numbers of points of DFT Nm satisfying: N ,,,T ,,, = AT = 11 AF Where: Nm represents the number of sampling points at the frequency fm; Tm represents the sampling period at the frequency fm; AF represents the frequency step of the DFTs (independent of m) This implies that the number of points Nm is different from one sampling to another. This choice of sampling frequencies 1 / Tm so that they are multiples of the AF band implies that from one sampling to the next, the signal spectra are shifted by an integer number of filters.
    [0009] The next phase is to model the received signal after DFT. In a first step, we consider the case monocase that is to say that we place ourselves in a case where the signal is received only on a time / frequency box.
    [0010] We consider that we have P sensors and that for each m from 1 to M, R sensors are sampled at the frequency fm. It should be noted that the number R is chosen independent of m so as not to complicate the notations. This case is not limiting and we could consider a sensor structure with R dependent on m without modifying the reasoning that follows. We put: MR = Q MP Each sensor is therefore indexed by 2 indices, an index m for the 5 type of sampling with m integer between 1 and M and an index r for the number of a sensor sampled at the frequency fm with r integer between 1 and R. After sampling and Fourier transform, and after selecting the time / frequency box corresponding to the same frequency fo of the analysis band B for the different samplings, the received signal in m, r can be written as: x., = ae19- + w ,,, with lai 0, Ibmi _ 0 (equation 1) where: a, complex, represents the contribution of the wanted signal. If present, lai> 0, (pm ,, represents the interferometric phase shift of the index sensor (m, r) with respect to an unspecified sensor, for a plane wave (i.e. the signal useful), coming from a direction 20 (6), 40) bmeiw- represents the possible contribution of a parasite intervening only in m = m0 by spectral folding (with its interferometric phase shifts), w'r represents the thermal noise that the Suppose white in m and 25 in r, with E (IW ,,, 12) - 262 for all m and r. The model in Equation 1 involves a large number of parameters. This makes it difficult to optimize the detection of the useful signal and to determine the interference situation. Since we can not take into account all the parameters, we consider a statistical type of modeling where the measurements of the received signal are samples of a random variable.
    [0011] We choose not to build a detector adapted for each direction of the useful signal and for each direction of the possible parasite. We limit ourselves to good treatments on average with respect to the directions of arrival of the incident waves. Given the lattice factors involved in the interferometric phase shifts, it can be shown that this amounts to plunging the model of equation 1 into a family of models in which the phase shifts ç.retv. and equidistributed over the interval [0.274. This makes it possible to simplify the probability density of the measurements of equation 1.
    [0012] Despite this generalization, there are still many parameters, especially with regard to the density of parasitic sensors. For this reason, the treatment is limited to the 2nd order behavior of the model. This amounts to considering xmr as Gaussian. We have, therefore, under the conditions mentioned above for equation 1: E (xmr) = 0 for every m, r; ) = al 2 + 262 5 ', r' ,,,, if m # mo 2 + 1b12lsmorm r if m = m0 1 if m = m 'and r = r' Where = 0 if m # m 'or r # r The following notations will be used: jar = 20.2 = power of the wanted signal b! 2 = 20.12 = power of the possible parasite We are interested in the probability density of the xmr measurements for m = 1, 2, ... M and r = 1, 2, ... R in the case where the useful signal is present and the parasite present in mo.
    [0013] We set Xm = (xm, r) T vector of dimension R. For mOrno, the Xm are Gaussian, centered, complex, independent and of covariance 40'2 + 02) / where I is the unit matrix of dimension R.
    [0014] For m = m0, Xmo is Gaussian, centered, complex, independent of X and covariance 2 (cre2 + 0-2 + ___2 m, m * mo 1 C) Finally we have: 1 (27r) MR (0: 2 + a2) (M-oR (2 2 0-2) R O- + 0-1 + 2 (equation 2) y 1X.112 mmma 2 (o2 + 0-2) exp Xmo exp 2 (6'2 +61) +62) / We obtain the densities of the measurements when the signal is absent by taking 6 2 .0 in equation 2 or when the parasite is absent by taking 612 O. Thereafter, the density p (.) Will receive the names following: Signal present, parasite absent: / 9100 Signal present, parasite in mo: pumo Signal absent, parasite absent: p00 oimo Signal absent, parasite in mo: P To complete the model, we consider that the probability of occurrence of a parasite is 1-a This parameter can be estimated from the mean density of the signals In order to simplify the notations, we will adopt the following writings: Q = MR and ym2 = 11) (n2 2/262.
    [0015] We can also notice that: 1 1cri 2 (02 +61 + 0.2) 0. + 2 (2 + O_2) = 2- (a2 +6262 + O-12 + cy2) 1o-2 (O2 + 0.2) + 2 (62) = 2- (6102 + cr2) 11 cry 472 + O.2) 2 (62) = 2- (0_ 2 Xci. 12 + 0. 2) ± (equation 3) (equation 4) We try to define a detection test, that is to say to decide on the presence or the absence of a useful signal, for each frequency fo of the band B, at the step AF of the analysis in DFT. The detection test is established on the basis of the probability densities of the measurements in the two hypotheses H1 (presence of signal + possible parasite + noise) and Ho (absence of useful signal but presence of noise + parasite if any). These densities are mixtures of densities corresponding to simpler situations: signal + noise, signal + parasite for mo + noise sampling; noise alone, noise + parasite for mo sampling. In order to simplify the writing of the probability densities, densities will be used in relation to the noise-induced measurement alone. This amounts to considering probability densities divided by poo (.). This does not change the treatment that will follow. Moreover, in order not to complicate the notations unnecessarily, the old denomination of the densities presented in equation 3 will be retained. After calculation, the following four new expressions are obtained, with the notation y2m: 0 "Q 0- (equation 5) 2 (2 Pio (Y12, ..., Yi ^ d) = ^ 2 2 exp E.2 2 Ym2 0- + 0 "0- ± 0- m / e2 0-2Q," 2 Piimo (Yi , ..., Ym2) = exp 2 2 E y. + M (o., 2 +0.2 rR _ (equation 6) 25 Poo (Yi, ---,) 1 (equation 7) el 2 (equation 8 ) 0- 2R POlm '(Y12, - - -5) = R exp 2' '1 2 yn, 2 () (0_12 + 0.2) cr + a- In hypothesis H1, as in the hypothesis Ho, the probability density is a mixture of elementary densities, for H1 p10 (.) and P1% 0, for Ho: Poo 0 and Pol, O- The coefficients of the mixture are a, a (absence of parasite) and 1- (presence The likelihood ratio, which is the quotient of the probability density in H1 by the probability density in Ho, can be written as: 1-a M (equation 9 ) agio (Yi, - - Y m2) (Yi, .-, Y) L (Yi M ° 1- a a + M (Yi, -., Yiid) m0 = 1 ° 10 If all the parameters of the model: a, 0_e2 612 (62 will be assumed to be known) were known, the optimal test to distinguish the hypothesis H1 from the hypothesis Ho would be to compare L (y12 ym2) with a predetermined threshold value (L (y12 ym2)> or <threshold ). The following notations are made: 0.92; 8 = 61 (equation 10) el2e2 (612e2) = 6.2 +62 = t2 + 62at2 +612 + Given equations 5, 6, 8 and 10, the likelihood ratio of equation 9 can be write: Q 62 20 L (.) = [o- 12 2 exp [flE y, n2 + o-) am cr2 cr2 ^,) (equation 11) The different terms in square brackets in equation 11 are not not of the same order of magnitude, which allows simplifications. ## EQU1 ## 0.2 / 0_2 = 10 6i2 = CRI2 and R = 2. We thus have: y k: 1/20; 8;:, 1 and fl For ym = 0 whatever m is: 0_ + a 2 expw) _ 0,1 (1 JR «1 1 - a 0,9x 4 aM 6t2 + o-2 +62 1 2 R +62 4.2) = 0,1 (0.9 x 4 UO) "1 mexp Let y2 = Max y ', 2 R o_t2 + (7 2 (2 2 exp (yy 2) 1 - r 1 -a o- + o- 1) 2 Eexp (yy ', 2 aM o-'2 + a12 + 0- 0- 2 ± 612 + Gr This increase reaches the value 1 for 1-a aM y2 = 1 ln a / of 2 + 6, +62 - = ln + R 1-ay 0.2 + 62 201n + 20R 1n 2 = 44 + 14R 1-a o-2 R 1 - r o-2 2) exp4,27,) <exp4 2 _ 2. 2 2 a a1 ± 1 ± m This enhancement reaches the value 1 for 2 1 a R ((3-2 + a 2 y = ln + ln = 1n9 + R1n10 = 2,2 + 2,3R 8 1-a 8 o-2 However, this is not the case for the denominator.1-a From these two calculations we deduce that the probability that the term in ... in the numerator of equation 11 reaches 1 is almost zero. can thus write equation 11 in the simplified form: 15 2 Q 1 (equation 12) = exp [flE o-y2 + o-2 m R 1 + 1-a o-2 am U_2 0.2 lmp (g ex Two remarks can be made: 1) Since L (.) Will have to be compared to a threshold value to form the detection test, the constant (but unknown) factor ^ 6 will not affect t2 + 0-2 the probability of false alarm and the probability of detection, it can be removed without inconvenience (we will keep the notation L (.)) 2) The signal-to-noise ratio 0.'2 / it is typically greater than 10 dB (similarly for 0 -2 / 0-2), so that f3 1 and 8 1. a 612+ 62 is now considered as "optimal" becomes: (After this s simplifications, if we put 4 = 1- a a-2 R, the test that L (.) = expE y '., 1 1 (equation 13) r 1 + Eexpe2, mm After taking the logarithm of the equation 13 we obtain as test: 1 (.y yi; 4) = 1n L (y 1 (y, y, I2) = E ym2 - ln [l + E y ', 2> or <threshold (equation 14) The test of equation 14 depends only on the parameter, and can be optimized in Pd / Pfa (with Pd the probability of detection and Pfa the probability of false alarm) in the vicinity of a parasitic situation defined for a and 0-2 / 62: just replace 4 by its expression in a and 0-2 / 0-2.
    [0016] The test is a symmetric function of y2, (symmetry of interference situations). We can notice that in the case where the interference is absent, that is to say a = 1 which leads = -0, we find the quadratic detector.
    [0017] The detector of equation 14 is not very complicated; nevertheless for computational speeds, the presence of the functions ln (.) and exp (.) is penalizing. We will therefore approach the test of equation 14 by a simpler and independent function of (*) If y2 'small, that is y2' much less than 1 whatever m. In this case, like 0 and y, 2 '1, equation 14 can be written, after limited expansion of the exponential function and the logarithmic function, in the form:) E ym2 ym2 m M (equation 15) ym2 (*) If y2, is large (ie ym2> 1) whatever m with all y2, approximately equal. In this case, -Iexpy ', is preponderant before 1 in equation 14. m 1 Note this time y2 = - M Eexpy', 2 and ym2 = y2 ± Aym; (lAy.1 "1), so that E Aym2 = 0. With this approximation and this notation, equation 14 is written: ## EQU3 ## (Eym2) = Eym2 -1n-y2 -14-ME exP (AY). exponentially: 1 1 -m exp (Ay m2) m [m E y m2 Therefore, in the area considered here, we have: / (Yi2, -, Y / id (1 (equation 16) 1- j. Ly, n M (*) If y, n2 »y ', 2 for m mo (presence of a parasite for sam index sensors sampled at f', o), the term -Zexpy, n2o alone is M ', preponderant compared to 1 in equation 14, we can therefore approximate this equation by: (l (y,) /, ..., y,;, 1).' Z, 'Ey.2 -1n ---, expy, n0 1+ Eexp (y, n -y ,,, 20 rn * mo ym2 << Y '., 2 Ym0 As, y;, ..., y,;, f) k,' V y2 - Max y2 CMJ (equation 17) The formulas of equations 15, 16 and 17 are the approximations of / vv (12, - 22, ---, Ym2) on the main areas of the domain of ty12, y22, .. .ym2 = (91+ r corresponding to the following physical situations: 1) absence of useful signal and parasite, 2) presence of signal useful without parasites; 3) presence of a parasite. With these approximations, we will be able to simplify the test of equation 14. Let D = 1 (3/12, Y2, -.-, Ym2 ie, 91+, such that l (Y12, Y22, .., % 2)> s} and Dc its complement in (9I + r) D contains the zone (s) where at least one y, 2'0 is large (y ', 2> 1) that is say that we have the approximation of the test by equation 16 for y, 2, large, all about equal, and by equation 17 for y, n20 large among y, 2n, m # mo.
    [0018] M 1 By observing that -Ey ', 2 maxym2 when all ym2 are M m = 1 close, we see that we can propose: /' y (12, y22, ..., ym2 ym2 -Max, m2 m "Y m = 1 as a test function which approaches / (.) On the two most important zones of D. The other subdomains of D are very little loaded by the probability densities. is not taken into account, but it is negligible Moreover, adding the term lrg to the detectors of equations 16 and 17 is of no importance because the performance of a test does not depend on an additive term. therefore to use as a simplified test: Zym2 -Max y '<or> threshold (equation18) m = 1 Comparing equation 15 with equation 18, we find that the approximation is not perfect on the domain where all the ym 2 are small, 15 This approximation amounts to adding the term - Max y ', 2 to the detector of equation 15., which is small, and - Max y, 7.2, which is negative, do not pose On the other hand, term 1ig is positive and is not always negligible compared to E. The approximation is not perfect. m = 1 20 This is the price to pay for a simple and universal expression for the test. Simulations have shown that the sensitivity difference between the two detection methods is less than 2 dB. We are now interested in the multicase case where the received signals extend over a window composed of N time / frequency boxes indexed by n (with n integer between 1 and N) for the MR reception channels corresponding to the sampling of frequency fn, (with m integer varying from 1 to M) and the sensors r (with r integer varying from 1 to R) associated with each frequency sampling fm (as for the monocase case).
    [0019] The same general requirement to find a good detection test on average whatever the direction of the wanted signal and the parasite, is renewed. The novelty to be treated with respect to the monocase case is taking into account the fluctuating nature of the useful signal from one time / frequency box to another, or even the absence of the useful signal. If we take again the model of the received signal expressed in the equation 1, by adding the index of time / frequency box n, we have: 10 x = ae '' + + w inni n ',' mn, 'In this writing : - an is complex and represents the useful signal received in a reference sensor. - Yo ', are the expression of interferometric phase shifts. 15 - bmn is complex and for each index n, at most only one bmn is different from O. This models the fact that one can be parasitized only for a single sampling, which can change randomly according to n. - is the interferometric phase shift of the parasite.mrn 20 - wmrn is the noise on the sensor mr for box n. {w ',,,} forms a series of independent Gaussian random variables, centered and with the same 2o-2 variance. The useful signal an is modeled as follows: an = 0 with probability 25 (1-q), and an is a sample of a centered Gaussian random variable of variance 20 -'2 with probability q. The samples are independent in n. In order to obtain an average good detection test for all directions of arrival of the signal and the parasite, it is proposed to limit the statistics to the second order when the signal and / or the parasite are present. The probability is that the cell n is parasitized for some mo sampling by a parasite whose power will be noted 20-12.
    [0020] In the case where the signal is present as well as the parasite for the mo sampling, the probability density of the M vectors of dimension R representing the set of measurements of the box n is written as in the equation 2 of the monosource case (omitted here the index 5 complicate): 1 (2.1) v / R (6.2 + 62) (M_oR f 2 0 2 R - + 0-2 - - - 1) n for not ( Xmo 112 (equation 19) + 0-2 +62) 1 exp exp ((IX.2 2 (62 + 62 2 (a By reasoning, as in the monocase case, we show the probability densities p10 'e D11% OOP , POIMO and we divide all these densities by p00 (absent signal, absent parasite) so as to have simpler expressions.This amounts to taking the probability densities compared to the measurement induced by the pure noise model. Next, we will speak of P10, P11, 7,0, Pobno after division by p00. In the case where a useful signal is present, the probability density is: 1-a a.Pio .0 4 ° When the signal n is not present the densi probability tee becomes: a + 1-a, poim. We can deduce the density of (X1, X2, ..., XA, f) for a cell in the hypothesis H1: (1-a "a.1910 M ^ (a + 1- a z., Poimo +0. Q mo.1 pl (X,, X2, ..., Xm) q P 1 lm lilM0 = 1 (equation 20) We deduce pe1, X2, ..., Xm), the density of the measurements of the box n, taking q = 0 in equation 20: a "po (V1, X2, ..., X, 14) = - a + 1 - Epokno (equation 21) m0 = 1 The independence of n-signals, as well as the independence of interference situations, give for the probability densities measurements for all the cells, in the hypothesis H1 or the hypothesis Ho: N n = 1 (equation 22) N n = 1 (Equation 23) As can be seen from equation 19, the densities of equations 22 and 23 are expressed as a function of pC.112 / 262, which we will write y, 7.2n thereafter. is expressed as the density quotient / 9; / Po - If all the parameters 6'2, q, a, o-12 of the model were known, the Neyman-Pearson optimal test to decide the presence of the signal u tile would be to compare this likelihood ratio to a threshold value. In the absence of this knowledge, the terms of the likelihood ratio are evaluated to derive a substantially optimized test in the vicinity of the operating point of interest.
    [0021] With simplified notation we obtain: ln P; N = ln Pi Po n = 1 P (equation 24) Moreover, thanks to equations 20 and 21 we have: 1-a M aPio pilmo Pi = 1-q + q MO = 1 Poa + 1- a ME poim ° The likelihood ratio of the monocase problem, noted y22n ym2n or L ,, is recognized as abbreviated: Pi = 1_ q ± in Po The likelihood ratio test is therefore: Eln (1- q + qLn)> or <threshold (equation 25) n = 1 Recounting the same approximations as in the case of monocase: 6.2 / 62 »1.0.12» 1, we find the same expression as in [(, t the monocase case (see equation 14): Ln = exp Eyrn2 ,, -ln 1 + 22-Eexpy ',' m M m which, introduced in equation 25, provides what we can call the "optimal (2 R" test depending on the parameters = 1 aa C72o- 0 "2 and q. + 1 1 To go further in the simplification, we put Ln = exn (y 12n y m2 nYI il / We now study the behavior of (see equation 25): q + q exp / n) (Equation 26) We have: ln (1-q + qexp1nq + / if 1 -> + this 1n (1-q + qexp /), 'k,' ql if / ->. FIG. 2 represents a representative curve of the detector as well as its asymptotes in 1 = 0 and in +0.25. 10 is defined by: q.10 = 10 + lnq or 10 = 1-q If we have an idea of q, we can propose a simplification of the test of equation 25 by: Emin> or <threshold, by reducing equation 26 to its n = 1 asymptotic behaviors.
    [0022] The nonlinear function A (l) can then be defined by: TO / </ 0: A (/) = ql A (1) = 1 + 1nq The nonlinear function A (I) can be represented by an increasing monotonic function whose representative curve can be defined by its 10 asymptotes, a first asymptote in 1 = 0 having for equation y = ql and a second asymptote for 1 -> + 00 having for equation y = l + In (q) where q represents a The latter expressions can be further simplified if the I formulation found in the monocase case is used: ln = Iy''2 '-maxy, n2,7. By way of example, FIGS. 3 to 6 illustrate the possible steps of the detection method in the case where the received signal is sampled with as many different frequency values as there are sensors (M = P), ie sensor sampling frequency (R = 1). Figures 3 and 4 represent the case of a monocase detection and Figures 5 and 6 the case of multicase detection. In a first step, the signals received on each sensor of the receiver are sampled, over an acquisition time AT, with frequencies fm of different value depending on the reception channels and not satisfying the Shannon criterion. According to one embodiment, the sampling of the signals received on each sensor is carried out during each time interval ln q [k -AT, (- k + 1) AT with k integer. Of course, this mode of implementation 2 2 is in no way limiting and other time intervals of duration AT can be chosen as for example, [k. AT, (k + 1) AT]. A discrete Fourier transform is then performed on the sampled signals. As seen previously, the pairs (Nm, fm) where fm is the sampling frequency, and Nm the number of sample points, are chosen such that Nni.Tm = AT. AF = 1 / AT is then the common spectral resolution for all samplings. The reception channels are therefore synchronous with the period 1 / AF and have the same channel width. This gives a time / frequency representation of the signals. The next step consists in calculating, in each time / frequency box of said discrete representation corresponding to a frequency tested fo, the power normalized in each quadratic summation sampling of the powers of all the reception channels sharing the same sampling frequency. fm. This power can be computed using formula 2 Elx.1 lx.11 r yzn = o-2 = r = 12 (72 view 2 above where R is an integer representing the number of channels sampled at the frequency In our example, R = 1. The calculation of the quadratic sum of the powers calculated on all the samplings in each time-frequency box is then made taking into account the power of a possible parasite.The power of the possible parasite may be taken into account in different ways.
    [0023] FIG. 3 illustrates the optimal test of the detection method in the case where the signals are only received on a time / frequency box. In this case, the influence of the parasitic signal is taken care of by subtracting the term [ln 1+ E expy ', 2 as previously seen especially with equation 14. M', in this expression, translates the possible presence of a parasite on a 1-a (0-2 R 30 of the samplings and = = The parameter u2 is a a21 + 62. assumed to be known (it can be obtained by calibration), the parameter a is computable from the density of signals to be intercepted, and the parameter 0-2 is set to the minimum power of the parasites to be protected, assumed to be of the same order of magnitude as the minimum power of the signals of interest. each time / frequency box using a predetermined threshold value This threshold value is determined so as to respect a given probability of false alarm.
    [0024] Figure 4 shows a simplified version of the test. In this version, the detection algorithm assumes that the highest value power corresponds to the power of a spurious signal. Among the calculated power values the highest is sought to exclude it. The quadratic sum of the powers is thus carried out with the remaining M-1 values. This simplified detection method systematically deletes a sampling channel, even if the signal power is low on all channels.
    [0025] In a different way, the optimal method illustrated in FIG. 3 has a behavior which adapts to the power of the received signal, going from the deletion of the sampling channel having the strongest power, if this one is very predominantly predominant. relative to the others, to a behavior close to the quadratic detector on all the channels, if the power received on all the channels is substantially similar. The simplified detection method has the advantage of offering greater ease of implantation and of being independent with respect to unknown parameters, at the cost of a moderate degradation of performance.
    [0026] FIG. 5 represents possible steps of the optimal detection method in the case where the signal is received over several time / frequency boxes. It is considered that the signal is received on a window of N time / frequency cells. As in the case of the optimal monocase method, the optimal multicase method calculates the normalized power in each sampling channel and in each time / frequency box, then the quadratic sum of the powers on all the samplings in each time / frequency box and subtracts a term reflecting the power of the parasite. It then applies a nonlinear function A in each time / frequency box and then sum the results on the N time / frequency boxes of the window. The process ends with a thresholding step using a predetermined threshold value. This threshold value can be determined so as to respect a given false alarm probability.
    [0027] Figure 6 illustrates the simplified version of the test of the detection method in the multicase case. In this configuration, the quadratic sum is computed by excluding the highest power value among the sampling channels.
    [0028] As before, a nonlinear function A is then applied in each time / frequency box and then the result is summed over the N time / frequency boxes of the window on which the signals are analyzed. The process ends with a thresholding step using a predetermined threshold value. Advantageously, the sub Shannon sampling method according to the invention makes it possible to have a complete and instantaneous vision of the whole band of the signals. The detection test is robust to the presence of parasites, that is to say, one can, for a probability of false alarm fixed, find for this test a threshold value independent of the power of the parasite. Compared to the optimal detector in the absence of folding which is the conventional quadratic detector, the equation of the detector according to the invention contains an additional term. In the presence of a high power parasite, the detector behaves like a quadratic detector on all samplings, the parasitic sampling being excluded.
    [0029] The present invention also relates to a passive or receiver detection device. This device comprises at least one receiving module and a calculation module configured to implement the method described above. The receiving module is configured to receive surrounding electromagnetic signals and transmit them to the computing module for processing. The receiving module may comprise at least one antenna, or an array of interferometric antennas. The antenna comprises at least one sensor. The receiving module is configured to continuously receive electromagnetic signals over the entire analysis frequency band. The computation module is configured to at least be able to perform sub Shannon sampling on several bits. The computing module may be one or more microprocessors, processors, computers or any other equivalent means programmed in a timely manner.
    权利要求:
    Claims (8)
    [0001]
    REVENDICATIONS1. A method for passive detection of electromagnetic signals implemented by a device comprising at least one antenna, said antenna comprising at least one sensor and said method being characterized in that it comprises: a step of sampling the signals received on each sensor, during a common acquisition time AT, using M different sampling frequency values fn, not satisfying the Shannon criterion, the signals sampled at the same frequency forming a sampling channel, M representing an integer greater than or equal to 2 and m the index of the sampling frequency between 1 and M, at least two samplings being made with sampling frequencies fn, and numbers of sampling points Nm different, the pair ( Nm, fm) being chosen such that the ratio AT = Nm / f, 'remains constant whatever the index A stage of transformation of the sampled signals in the domain Frequency ine by discrete Fourier transform on the Nn, sampling points of the received signal, sampled at fm over the common time interval AT, the common spectral resolution for all the samplings being AF = 1 / AT, the signals being presented in a discrete time / frequency representation, the method furthermore comprises, for each time / frequency box of said discrete representation, a step of calculating the normalized power in each sampling channel, a step of calculating the quadratic sum powers calculated taking into account the power of a possible parasite, - a step of thresholding said quadratic sum with a predetermined threshold value.
    [0002]
    2. Method according to the preceding claim according to which the calculation of the quadratic sum S of the powers is carried out using the formula S = E y, 2 '-1n 1+ k ± exp y', 2 m = 1 Ad m = 1 Where yll, 2 represents the normalized power in the frequency sampling channel fm indicates the possible presence of a parasite on one of the samplings with = 1-a 0-2 R a a2 ± 62 1 2612 represents the power of the possible parasite, 262 represents the power of the noise, a represents the probability of absence of parasite, and R represents the number of channels sampled at the frequency fm
    [0003]
    The method of claim 1 wherein the method further comprises a step of searching for the highest power value among the sampling channels, the quadratic sum being calculated excluding said highest value power and summing the (M-1) remaining powers, said highest value power being considered as the power of a spurious signal.
    [0004]
    4. Method according to one of the preceding claims wherein the signals are received on N time frequency boxes with N integer strictly greater than 1, the method further comprising the application of a non-linear function in each time / frequency box and a step summation of the result obtained on the N time / frequency boxes.
    [0005]
    5. Method according to the preceding claim wherein the nonlinear function is an increasing monotonic function whose representative curve is defined by its asymptotes, a first asymptote in 1 = 0 having for equation y = ql and a second asymptote for 1 --- > + .0 having the equation y = l + In (q) where q represents a real between 0 and 1.
    [0006]
    6. Method according to one of the preceding claims wherein the threshold value is defined to ensure a predetermined false alarm probability.
    [0007]
    7. passive detection device characterized in that it comprises a receiving module comprising at least one antenna and a calculation module configured to implement the method according to one of the preceding claims, said receiving module being configured to receive signals surrounding electromagnetic fields and transmit them to the computing module for processing.
    [0008]
    8. Device according to the preceding claim wherein the receiving module comprises an array of interferometric antennas.
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    同族专利:
    公开号 | 公开日
    WO2015158615A1|2015-10-22|
    EP3132358A1|2017-02-22|
    FR3020157B1|2016-05-27|
    US20170033822A1|2017-02-02|
    US9991919B2|2018-06-05|
    引用文献:
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    FR3073627A1|2017-11-16|2019-05-17|Thales|INTERFEROMETER AND ASSOCIATED PLATFORM|
    EP3671250A1|2018-12-21|2020-06-24|Thales|Digital interferometer with sub-sampling|US5627546A|1995-09-05|1997-05-06|Crow; Robert P.|Combined ground and satellite system for global aircraft surveillance guidance and navigation|
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    CN105974375B|2016-04-27|2019-01-18|山东省科学院自动化研究所|A method of for inhibiting time jitter in ultra-broadband wall-through radar|
    EP3812787A1|2019-10-25|2021-04-28|Tata Consultancy Services Limited|Method and system for field agnostic source localization|
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    优先权:
    申请号 | 申请日 | 专利标题
    FR1400935A|FR3020157B1|2014-04-18|2014-04-18|DIGITAL DETECTION METHOD|FR1400935A| FR3020157B1|2014-04-18|2014-04-18|DIGITAL DETECTION METHOD|
    PCT/EP2015/057807| WO2015158615A1|2014-04-18|2015-04-10|Digital detection method|
    US15/303,723| US9991919B2|2014-04-18|2015-04-10|Digital detection method|
    EP15717447.5A| EP3132358A1|2014-04-18|2015-04-10|Digital detection method|
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