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ISSN 1063 7710, Acoustical Physics, 2011, Vol. 57, No. 2, pp. 168­179. © Pleiades Publishing, Ltd., 2011. Original Russian Text © V.A. Gordienko, N.V. Krasnopistsev, V.N. Nekrasov, V.N. Toropov, 2011, published in Akusticheskii Zhurnal, 2011, Vol. 57, No. 2, pp. 179­191.

OCEAN ACOUSTICS. HYDROACOUSTICS

Localization of Sources on a Ship Hull Using Combined Receiver and High Resolution Spectral Analysis
V. A. Gordienkoa, N. V. Krasnopistsevb, V. N. Nekrasovb, and V. N. Toropovb
b

Physical Faculty, Moscow State University, Moscow, 119991 Russia e mail: vgord@list.ru FSUE National Research Institute for Physical Technical and Radio Engineering Measurements, Mendeleevo, Moscow oblast, 141570 Russia
Received May 13, 2009

a

Abstract--The fundamental possibility of application of a single combined receiving system based on a three component vector receiver for solution of problems of estimation of direction and localization of individual sources on a ship hull, source membership selection, and more reliable estimation of source signal levels is demonstrated. It is proposed to use high frequency resolution methods of sonographic analysis (spectral­ time representation) of projections of the acoustic power flux vector for spatial resolution of sources that pro vide a higher signal to noise level at the output of the processing system. DOI: 10.1134/S1063771011020060

1. INTRODUCTION The problem of localization and measurement of levels of low frequency, low level signal sources at present is one of the topical problems of modern hydroacoustics. Usually either a "strip" of single hydrophones [1, 2] or antenna arrays of different designs [3] are used for this purpose. One class of these problems, localization of low power emission sources on a ship's hull, assumes the presence of good diag nostic tools for analysis of the noise source and estima tion of its location on the hull and emission level for providing noise reduction of a particular sea object. The problem of obtaining an acoustic image is extremely difficult, since the required spatial source resolution at low frequencies is usually several times smaller than the acoustic wavelength. This is to a large extent the reason why the application of extended multielement antennas based on hydrophones often possesses low efficiency, especially at low signal to noise ratios. As a result, a tendency toward growing interest in compact hydroacoustic systems, including acoustic pressure receivers and vector receivers [4, 5], has been observed recently in our country and abroad. Compact receiving systems in which a nondirectional hydrophone and vector receiver are combined in one frame and have one phase center are usually called combined receiving systems or combined receivers. Paper [6] presents results of testing capabilities of antenna array consisting of five vector receivers situ ated at a distance of 10 cm from each other in the ver tical direction in determination of the position and intensity of sources on the hull of a submarine at the SEAFAC stationary hydroacoustic testing area of the US Navy in Behm (Alaska, not far from the village of

Ketchikan). Localization of sources on a submarine hull was achieved by comparison of responses of dif ferent channels of separate vector receivers on the assumption that there exists only one source onboard in the frequency interval of interest. If several sources were present, narrow beam directional diagram was formed by corresponding choice of the weighting vec tor in the algorithm of beam multiplicative processing. In our opinion, this approach cannot be considered optimal for low frequencies. Therefore, in our studies we use a single combined receiving system or com bined receiver, or, which is better, two combined receiving systems at a rather large distance from each other and then use the triangulation method for increasing the source localization accuracy. High fre quency resolution methods of spectral­time repre sentation (sonographic analysis) of projections of acoustic power fluxes are used for spatial resolution of sources; these methods make it possible to increase the signal to noise ratio at the output of the processing system. 2. GOALS AND METHOD FOR SOURCE LOCALIZATION USING VECTOR RECEIVER The measurements were performed for experimen tal verification of the possibility of application of vec tor receivers for localization and more reliable estima tion of levels of separate sources due to statistical spa tial filtering of acoustic power flux vector in conditions of water areas of stationary sea test sites in the case of a motionless ship with operating mechanisms near the berth or the coastline of an industrial zone.

168


LOCALIZATION OF SOURCES ON A SHIP HULL USING COMBINED RECEIVER Horizontal plane 90° Sh1 180° Dock Vertical plane Sh1 Sea surface 20 m
Combined receiving system Combined receiving system

169

Sh2

270° Pier

Bottom

Fig. 1. Geometry of measurements in (upper) horizontal and (lower) vertical planes.

A combined receiving system containing a three component vector receiver with a working frequency range of 5­1000 Hz and an acoustic pressure receiver placed in a dome of special design was used in experi ments. The geometry of location of the combined receiving system and potential noise sources in the horizontal and vertical planes is shown in Fig. 1. The studied ship Sh1 with operating main mechanisms was anchored not far from a pier. Another ship (Sh2) was moored to this pier. The dock with operating mecha nisms was situated in the immediate neighborhood on the other side of the pier. The combined receiving sys tem was at a distance of about 25 m in the horizontal plane from the ship bow, 1 m from the water area bot tom at a depth of approximately 20 m. The horizontal axis of the ship was directed practically toward the combined receiving system (Fig. 1). Such suboptimal geometry of the mutual position of the receiving sys tem and the ship in the framework of the described experiment prevented distinguishing individual sources of the ship Sh1 in the azimuthal plane. In this case the possibility of separation of these sources was provided only in the vertical plane taking into account the difference of the submergence depth of the noise sources and the combined receiving system. In princi ple, for reliable source separation, it is necessary to place the combined receiving system in such a way that one of the ship boards is observed from the side, as described, for example, in [6]. The axis of one of the vector receiver channels was oriented in the vertical direction. The spatial orientation of horizontal chan nels of the vector receiver was matched by measure ment of the angle of signal arrival from a localized acoustic source; a motorboat tacking along the known
ACOUSTICAL PHYSICS Vol. 57 No. 2 2011

controlled trajectory near the combined receiving sys tem was used as this acoustic source. The acoustic power flux vector is usually deter mined by the averaged over the period (or the time multiple or much larger than the period) value of the Umov vector [4],


WR = I() = 1 I()d t 1 P ()V()d t . t t tt


0


0

Hereinafter, the symbol "... " means time averaging. The projection WRr of the vector WR on the direction r characterized by the projection of the oscillation velocity Vr(t) is determined as W Rr = 1 P ()V r ()d t tt 0 and for the narrow band (quasiharmonic) signal with the average frequency f as



W R r ( f ) = 1 P 0 V 0 r cos ( PV ) 2 = 1 1 Re ( P * V r ) = ( PV * + P * V r ) , r 4 2

where PV is the phase difference between the pres sure and projection of oscillation velocity with the amplitudes P0 and V0r, respectively, and the symbol "*" denotes a complex conjugate quantity. It has been noted earlier [4, 7] that a single com bined receiving system formally does not make it pos sible to calculate the spatial spectrum with the wave vector k(, r), but, at the same time, allows it to be estimated using measurements performed in a spatial region much smaller than the wavelength. The algo


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rithm of determination of the direction toward the source used in this study was described in detail in [4]. This algorithm is based on statistical analysis of spatial distribution of the acoustic power flux vector WR( f, t). This algorithm increases the noise resistance of the receiving system by 10...20 dB (determined mainly by statistical specific features due to the formation of acoustic power flux vector of the noise field and local sources in the sea area [8]) and uses well known rela tions between the values of projections of the vector WR( f, t) and the direction of arrival of the wave energy. It is known that, within a unit sample with the length 0 for each frequency subrange fi, the azimuthal i and polar i angles of signal arrival in the horizontal and vertical planes and the intensity Ii of this signal can be determined from the analyzed range f; the signal intensity represents the absolute value of acoustic power flux vector in the direction determined by the angles i and i,

chosen for some 0, for each frequency on the record length tsm Nsm = tsm/ counts of the angle and inten sity I ( ), i.e., a total of Nsmm values of I ( ), can be obtained. For reducing fluctuations, a histogram of I ( n ) distribution in the analyzed frequency band f averaged over Nsm counts in each of angular sectors is constructed based on the obtained data. In this case, common averaging matched, for example, with the length of the analyzed record fragment tsm can be used. However, if the number N of counts (samples) is not known a priori, or in the case of real time operation, or if a sonogram or 3D diagram is constructed at the output of the data processing system, it is optimal (according to recommendations of experts of the com pany Bruel and Kjaer [9, 10]) to consider the so called "logarithmic" averaging, which yields rapid conver gence to the final result even for the number of counts q = N < Nsm,

ta n i =

W W

Ryi Rxi

,

ta n i =
2 Rxi

W W
2 Ry i 2 Rxi

Rzi

+W

2 Ry i

, (1)

I ( n ) =

( N sm - 2) I

q -1

( n ) + 2I q ( n )
sm

N

.

(3)

I i (i ) = W I i (i , i ) = W

+W

,
2 Rz i

2 Rxi

2 + WRyi + W

.

The essence of the approach used below is as fol lows. The whole range of analyzed angles is separated into sectors, for example, for the planar case of the horizontal plane = 360/0, where 0 is the cho sen spatial resolution. For the given frequency band

f = i =1 f i consisting of the set of m discrete fre quency intervals with the band fi each (for example, the frequency resolution of fast Fourier transform or transmission band of the narrow band filter), the dis crete set of values (array) I(n) for the sample q is cal culated according to the algorithm
I q ( n ) =



m

Here, I ( n ) is the current averaged value of intensity in the angular interval for which n (n - 1)0 < n0 , I q ( n ) is the result of determi nation of the value of intensity for the sample with the number q using formula (2), I q -1 ( n ) is the result of averaging using formula (3) at the previous step. The value of Nsm is usually chosen from the conditions of "reasonable" stationary character for the time interval tsm. In order to increase the number of independent unit counts, narrow band spectral analysis is usually used (for example, by choosing the sample 0 for fast Fourier transform to be large as possible) and intensity is reduced to the given frequency­angular range by summing the intensities in neighboring frequency bands of the signal. However, in this case, for signals with a low signal to noise ratio at the input, problems can occur; these problems will be discussed below. If Nsmm M, distribution (3) at the step q Nsm can be considered as the quasi spatial spectrum of acoustic signal with respect to the acoustic power flux in the hor izontal plane for the time interval tsm. In the case of absence of high power localized sources in the water area and absence of high level background noise arriv ing along the vertical coordinate (this condition is most often satisfied), in the first approximation, it may be close to the spatial spectrum obtained using the horizontal linear antenna. If the oscillation velocity is expressed in terms of equivalent units of acoustic pres sure of a plane acoustic wave (i.e., cV is considered instead of V, where c is the wave resistance of the medium), the dimensionalities of I and 2 coincide,
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i =1

m

I qi f i ,(n -1) 0 i < n 0 ,

(2)

where n takes values from 1 to . The result can be reduced to a band of 1 Hz by division of the obtained values of Iq(n) by f if necessary (if it does not i =1 i contradict the formulated problem). The reduction of the results to the 1/3 octave band was performed by weighted summing using a specially developed code. Subsequently, the next sample (q + 1) is considered and the procedure is repeated, yielding the array of values of I q +1( n ) for a following time instant larger than the previous one by , which is usually several times smaller than the length of the analyzed fast Fou rier transform sample. If, for obtaining the values of acoustic power flux projections, for example, on X and Y axes a segment of signal record with the length tsm > 0 multiple to is



m


LOCALIZATION OF SOURCES ON A SHIP HULL USING COMBINED RECEIVER 1 Wy (a) Wy (b) (c)

171

W WN I 0 Wx
0

WS Wx 0 1/M 23 0 90 180

1 4 270 , deg

Fig. 2. On formation of spatial statistical distribution of acoustic power flux vector WR: (a) noise isotropic in horizontal plane; (b) possible angular positions in the horizontal plane of the total acoustic power flux vector W in the presence of a local source forming acoustic power flux WS in the direction 0 and isotropic noise WN (WN < WS) in the water area; (c) approximate depen dences of the distribution I() normalized to P2 for several typical cases: (1) isotropic noise without a local source, (2) local source in the absence of noise, (3) WS level is much higher than noise WN level; and (4) WS WN.

and their numerical values can be compared. In this case for the water layer with the impedance boundary, according to [4], the following condition should be satisfied:


n =1

M

I (n ) I

I

P 2.

(4)

At first sight it seems that the application of an acoustic power flux receiver formally makes it possible to obtain any spatial resolution. However, it should be taken into account that, unlike antenna arrays, deter mination of spatial distribution of intensity based on combined processing of the signals P(r, t) and V(r, t) assumes signal expansion in the spatial domain over the nonorthogonal basis [4]. It should also be noted that the histogram represents the result of statistical signal processing and reflects the real noise anisotropy in the water area only in the absence of high power angularly localized sources. In this case obtained results can be interpreted as the spatial noise spectrum in the water area. In the presence of a high power localized source in the water area, the spatial spectrum is distorted. This is due to the fact that the direction of "instantaneous" value of the vector W , the absolute value of which is determined by the value of I() intro duced above at each time instant is determined as the sum of relatively spatially stable vector WS generated by the localized source and the vector WN of the field of self noise of the water area distributed according to some random law (Fig. 2), I() = W = |WS + WN |.
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Indeed, let us consider the behavior of the acoustic power flux vector formed by the localized source in the presence of noise isotropic in the horizontal plane. The noise signal intensity in the angular sector in the absence of a localized source in the case of pro cessing according to the algorithm described above is determined by the value of P2/M (Fig. 2c, depen dence 1). If there exists a localized source only, it cre ates acoustic power flux at an observation point that is not zero on average and is concentrated in the angular interval determined by expressions (1) (Fig. 2c, dependence 2). Therefore, by observing the acoustic field at one point, the conclusion that there is a direc tion toward the source (which is the essence of the direction finding problem), rather than the spatial noise spectrum, can be drawn. In the general case (in the presence of noise and localized source), the prob ability density distribution of the acoustic power flux vector for the localized source at the background of isotropic noise is described using the MacDonalds function [11]. The true direction finding for the local ized source in this case can be solved by additional processing of the profile of the envelope I(). The approximate form of the distribution I() for finite signal to noise ratios is shown in Fig. 2c (depen dences 3 and 4). As the signal to noise ratio decreases, the direction finding variance increases and, finally, signal excess over background noise can become com parable with the fluctuation component of the histo gram. If other localized noise sources are present in the water area, the profile of the dependence I() is more complex.


172 I()/P 2, dB ­25 ­35 ­45 ­55 2 1

GORDIENKO et al.

I()/P 2, dB 0 ­10 ­20 ­30 ­40 ­50 1 2

0

250

500

750

t, s

Fig. 3. Spatial distribution I() normalized to P2 and averaged over the angle distribution I() of noise intensity in the Water sea area in a frequency range of 78...315 Hz obtained using (1) algorithm I and (2) algorithm II as functions of time.

There exists another (second) approach (let us call it algorithm II, unlike algorithm I described above), the main part of which is the same as that of the algo rithm described above. The difference is in the histo gram construction method. Namely, within a separate sample, each angular cell with the number n charac terized by the average value of the direction finding angle n contains intensities determined, for example, from the condition

algorithm II, unlike (4), the following inequality is
2 always satisfied: I II = I (n ) < P . Concerning n =1 algorithm I, it contains information on the ampli tude­spatial (with account of fluctuations) intensity distribution and depends on statistical characteristics of the studied noise field. Therefore, it was already indicated above that for this algorithm, due to the spe cific features of formation of the spatial distribution of the vector WR, the angular dependence I ( n ) does not necessarily coincide with that determined using the extended antenna array. Although, in principle, if there are not more than one or two localized sources in the water area, it can be reconstructed using relatively simple processing algorithms.



M

I ( n ) I (n ) = 1 2

â I ( n ) - I (180 ° + n ) + I ( n ) - I (1 80 ° + n ) . In this case the isotropic component of water area noise decreases rather fast already for small averaging times and only relatively stable (stationary) in space and time anisotropic components of noise sources are left. This algorithm can be efficiently used for separation of the source of weak signals on the background of water area noise on the condition that the frequency and angular characteristics of the separated source and sta tionary components of the noise field do not coincide. The best effect should be obtained if the water area noise is close to isotropic. In this case the noise resis tance of the receiver recording the acoustic power flux vector can essentially exceed 20 dB [8]. Obviously, I() levels obtained using algorithms I and II coincide only for localized signal sources sta tionary with respect to direction finding during pro cessing. Usually different levels are obtained for the field of distributed noise sources. Algorithm II deter mines the level of the anisotropic component of acoustic power flux taking into account fluctuations (depending on averaging time); therefore, if the aver aging time increases, it decreases to this level accord ing to classical rules. It can be easily shown that, for

{

()

}

The example of processing data of a full scale experiment in the horizontal plane for the White Sea area (depth of about 300 m) according to algorithms I and II in the absence of visible localized sources in the area is shown in Fig. 3. The angular distribution I() normalized to the integral value of P2 for = 360 (angular resolution of 1°) constructed according to algorithm I corresponds to the statistical spatial reso lution of the vector WR of the area noise at the place of location of the receiving system in the horizontal plane. For the normalized values of I() shown in the

I ( n) P = 1 is well satis n=1 fied, i.e., the integral intensity level is equal to P2.
figure, the condition The dependence I() constructed according to algorithm II reflects the spatial distribution of a rela tively stable in the horizontal plane anisotropic com ponent of acoustic power flux vector for the noise field the integral level for this region of which is lower than 2 by a = 13...15 dB. This means that, according to
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(
360

2

)


LOCALIZATION OF SOURCES ON A SHIP HULL USING COMBINED RECEIVER

173 (b) 3 4

formal criteria, a single combined receiving device can in principle determine the direction to relatively weak localized sources for which the signal to noise ratio in the pressure channel is much lower than unity on the background of moderately isotropic noise fields based on measurement of acoustic field characteristics at one point. However, upon estimation of potential capabilities of separation of weak signals on the background of the water area noise some problems arise. Thus, for exam ple, for the situation described above the deterministic source with the signal level at the output of a single non directional hydrophone equal to the noise level of the water area should exceed the level of acoustic power flux in the angular sector of interest by the value a = 13...15 dB. However, that is not so. Unlike the antenna array for which the value of a characterizes its noise resistance in the given angular sector, the value of I of excess of the localized source signal with respect to the water area noise level (Fig. 2c) depends on a number of factors. The main factor is the signal to noise ratio for the acoustic power flux. Unlike the antenna array, the angular spectrum of energy arrival from the localized source determined using the above algorithms is rather broad. This is connected with essential spatial and temporal fluctuations of the total registered vector WS + WN formed with participation of the localized source. Obviously, as was noted above, the direction finding variance essentially depends on the ratio |WS|/|WN|. The latter, of course, makes the dif ference of direction finding using the combined receiving system and the antenna array. Therefore, usually additional processing of the I() envelope is required for determination of the true direction toward the source with a given accuracy, as well as for determination of the true signal level of this source. HIGH RESOLUTION SPECTRAL ANALYSIS Further improvement of the signal to noise ratio is performed due to application of algorithms of high frequency resolution spectral analysis based on meth ods of time­frequency signal transformations described in [7, 12]. These algorithms, as a rule, pro vide spatial separation of sources of discrete compo nents of signals generated by different objects in the same frequency range. Indeed, if the band for spectral analysis decreases, the direction finding variance can be reduced (and therefore, the reliability of separation of the signal from the localized source on the background of ambi ent noise can be increased) due to increasing the ratio |WS|/|WN| (Fig. 4) and the fluctuation component can be reduced due to increasing statistics. However, in many practical cases, especially for moving objects, the averaging time often cannot be essentially increased. Therefore, practically the only way of simultaneous satisfaction of both conditions is the
ACOUSTICAL PHYSICS Vol. 57 No. 2 2011

I, dB () 90

, dB 0 ­10 0 0.5 1 2

80

1.0 f, Hz 1

70

2 3 4 60 75 90 deg

60 45

Fig. 4. Profiles of dependence I( ) (a) for nonfluctuating with respect to the frequency harmonic signal at different frequency resolution ((1) 1, (2) 0.1, (3) 0.06, (4) 0.03 Hz); (b) estimation of the value of of Imax( ) reduction with respect to registered non fluctuating harmonic signal for different signal frequency fluctuation ((1) 0.01, (2) 0.5, (3)1, (4) 3 Hz).

larger number of analyzed frequency bands, i.e., higher frequency resolution of spectral analysis. This method, in most practical cases, provides spatial sepa ration of two and more real broad band signal sources operating in intersecting frequency bands. The latter is usually connected with the possibility of separation of the discrete noise component from most sea objects, which always exist. However, high frequency resolution imposes cer tain constraints on the capabilities of separation of weak signals on the background of ambient noise of the water area. Two problems should be solved in this case. The first one is connected with the necessity of increasing the array of processed data in the case of narrow band analysis. It is known that if standard fast Fourier transform algorithms are used the width of the frequency band for analysis is inverse proportional to the sample length. This means that, while for opera tion in a frequency range of 0...1000 Hz for a fre quency resolution of 1 Hz, a sample with a volume of approximately 3000­4000 counts per each channel is required, in the case of a frequency resolution of 0.05 Hz, the sample volume can reach 80 000 counts. The second problem is the presence of frequency fluc tuations of the signal both due to unstable operation of emitting mechanisms of the object, signal propagation fluctuations, and the Doppler effect if the studied object moves. The first problem is solved in a simple way. For reducing the volume of the analyzed sample, so called digital quadrature and low frequency filtering with subsampling can be used. These are usually designated for preliminary signal processing necessary for realiza


174

GORDIENKO et al.

tion of high frequency resolution algorithms of spec tral and sonographic analysis. Quadrature signal filter ing (complex demodulation) is the method used in sig nal processing problems in which some spectral region of the signal inside the frequency interval {fc; fc + fn} is useful for the solved problem [13]. It is realized by multiplying the initial signal U (i t ) discretely digitized with the quantization frequency f d = 1/ t (t is the initial quantization time interval and i is the count number) by the complex exponential function exp( j 2f ci t ) . Here, fc is the lower frequency of the analyzed frequency interval, j = ­ 1 . As a result of multiplication of the signal U(it) by the complex exponential function, the neighborhood of its spec trum with the center determined by the frequency fc of the exponential function is shifted toward zero fre quency. Then the signal is filtered using the low fre quency filter with the cutoff frequency fn (boundary of nontransmission frequency of the low frequency fil ter); as a result, only the spectral segment of interest is preserved in the frequency interval {fc, fc + fn}. The thus formed complex signal is usually called the com plex envelope. Then, according to the width of the band of low frequency filtering (Nyquist condition), the new quantization frequency fD of the complex envelope is chosen, f D 2 f n . The choice of fD is real ized by subsampling of counts of quadrature compo nents of the signal at the outputs of low frequency fil ters. The result of quadrature filtering with subsam pling is a complex signal in which spectral characteristics of the original signal in the filtering interval {fc; fc + fn} realized in a frequency band from 0 to fn are preserved. Then high frequency resolution spectral analysis is performed based on methods of time­frequency signal transformations [12, 13]. Three algorithms of such transformations are con sidered most often: time­frequency representation based on the fast Fourier transform (F algorithm), time­frequency Wigner representation (W algo rithm), and time­frequency representation using the compensating function of signal frequency variation with linear frequency modulation (Q algorithm). Each of these signal representation types possesses positive and negative properties. This prevents making an unambiguous choice of one of them. The main parameter of high frequency resolution algorithms is the effective width of the weighting func tion h(t ) determining the effective width of the sliding time window used in spectral analysis for reducing side lobes [14]. The choice of effective width depends on the high frequency resolution algorithm and the ana lyzed signal. The time­frequency representation usually is the sequence of Fourier spectra calculated for the sequence of segments (as a rule, overlapping) of the signal U(t) with the sliding time window h(t ) of effec

tive width Teff . This representation possesses rather good noise stability. The noise level for this representa tion is known [15] to decrease inverse proportional to the effective width of the window Teff , while the intensity of the narrow band peak corresponding to the signal stays the same and, therefore, the signal to noise ratio increases. However, possible changes of frequencies of dis crete components on the window time interval result in spectrum distortion (smearing). In this case fre quency components of discrete component spectrum are manifested in several frequency bands that result in worsening of the signal to noise ratio at the output and makes further reduction of the interval for fre quency analysis inefficient. Figure 4 shows the results of a model experiment on determination of the histo gram I () (angular resolution of 1°) for the harmonic signal with a frequency of 230 Hz on the background of isotropic in the horizontal plane noise with a close to unity signal to noise ratio in the pressure channel. Spectral analysis with different frequency resolution f was used. The dependences in Fig. 4a correspond to a signal that does not fluctuate with respect to frequency for the frequency resolution f equal to 1 (curve 1), 0.1 (curve 2), 0.06 (curve 3), and 0.03 Hz (curve 4). Fig ure 4b shows the results of estimation of the value of characterizing the reduction of the value of I max () in the direction toward the signal source for different fre quency resolution f of standard fast Fourier trans form for different frequency fluctuation of the signal of localized source with respect to the value of I max () for a nonfluctuating signal. It can be seen that, for the fre quency unstable signal, as early as with a frequency analysis band of 0.1