Method for measuring relief using an antenna with a known gain profile

Abstract

Method for characterizing a reflective surface (4) subject to imaging by a vehicle at a distance from said reflective surface (4) and collecting during the echo of waves emitted by it towards said reflective surface (4), the emission and reception of the waves being carried out using a set of transmitting (1E) and receiving antennas having a known gain profile in emission. The method comprises a search in the measured intensities for at least one extremum and by identifying said at least one extremum at a local extremum of said gain profile of the set of antennas, a location of the corresponding point of the image. Abstract figure: 1B

Description

Title of the invention: Method for measuring relief using an antenna with a known gain profile

[0001] Technical background

[0002] The invention which is the subject of this document falls within the field of radar or sonar.

[0003] The receiving antenna (receiving array in English) can be a synthetic receiving antenna in which case we speak of synthetic aperture sonar or radar, or synthetic aperture sonar or radar (synthetic aperture sonar in English), but it can also be a real receiving antenna or natural antenna (real aperture sonar in English).

[0004] The transmitting and receiving antennas (transmitting and receiving arrays in English) considered can be carried on the side of a vehicle moving at a distance from a surface, in particular the surface of a seabed (seafloor in English) in the case of a sonar carried by a marine or underwater vehicle, or the emerged terrestrial surface in the case of a radar carried by an aerial vehicle. In this case, these are therefore side-looking antennas (typically the central axis of the antenna is inclined by approximately 15° downwards relative to the horizontal): this is called a side-scan sonar.

[0005] The invention aims to provide a simple means for assisting in determining the relative altitude of a bottom point with respect to the antennas for a point being imaged in the region close to the nadir (vertical downward direction) of the vehicle.

[0006] The location of imaged points is commonly carried out by interferometry. The principle of interferometry is to add at least one receiver offset on the vertical plane relative to the main antenna. While the antenna measures a first distance, the second receiver, by measuring a second distance, makes it possible to access a phase difference which is, to within an integer number of wavelengths, linked to the location of the imaged point. The integer number of wavelengths, initially unknown, is determined by the so-called Vernier method. But this method remains difficult to apply near the nadir of the vehicle and even in a wide cone around the nadir.

[0007] The present invention therefore seeks to improve the determination of the bottom relief in the nadir area, by using the fact that the antenna gain, counted for transmission and reception, exhibits fluctuations producing a fringe pattern. in the received image with typically an image that is “dark” where the gain is low and “bright” where the gain is high.

[0008] In general, we seek to reduce these fluctuations in order to obtain a uniform gain image. This can be achieved by various devices such as optimization of the antenna lobes or an adaptive gain calculation.

[0009] It is nevertheless proposed to use these undesirable variations to trace the difference in relative altitude between the bottom and the vehicle by appreciating that the location of the fringes is a function of the direction of the local extrema of the antenna lobe and of this relative altitude between the bottom and the vehicle that one seeks to determine. The monitoring of these fringes thus makes it possible to determine an estimate of the relief of the bottom which can be used as is, or possibly be involved in a subsequent or complementary interferometry process.

[0010] The invention can be used either upstream of the formation of synthetic image, or downstream, in order in this case to supplement the determination of bathymetry by interferometry.

[0011] In the field of sonar, knowledge of the relative altitude difference between the bottom and the vehicle also helps to determine the relief of the bottom, which makes it possible to construct a bathymetric map of the bottom by taking into account the depth of the vehicle carrying the sonar, known elsewhere, and compensating for tidal effects.

[0012] The accurate determination of the relative bottom-sonar altitude difference is therefore an important function of a sonar imaging system and it is important that it operates satisfactorily.

[0013] Technical problem and solution provided

[0014] To improve existing solutions, and in particular to improve the characterization of points close to the nadir, a method is proposed for characterizing a terrestrial or marine reflecting surface subject to imaging by collecting echoes of waves emitted towards said reflecting surface, for example by a vehicle moving at a distance from said reflecting surface and collecting during its movement the echo of waves emitted by it towards said reflecting surface from one of its sides.The transmission and reception of waves are carried out using a set of transmission and reception antennas, the set of antennas having a known angular gain profile in the vertical plane, which may be for example a main lobe and at least one secondary lobe - sidelobe in English (and often many secondary lobes), said main lobe and said at least one secondary lobe then being directed towards said reflecting surface, and the intensities of the reflected signal as a function of the ranges between the set of antennas and the reflecting surface being measured by the set of antennas for the purpose of constituting an image of the surface.

[0015] The method comprises, in an original manner, a search in the measured intensities for at least one local extremum (or even in certain cases global) and, by an identification of said at least one extremum with an extremum (local or global) of said known gain profile of the set of antennas (this extremum of the gain profile can be a zero of the antenna, or the top of a lobe, but this is not necessary), a location with respect to the vehicle, or at least with respect to the set of antennas, of a point of the image corresponding to said measured intensity extremum.

[0016] Account may be taken, where appropriate, optionally and advantageously, of a current roll angle value or a current altitude value of the vehicle (or at least of the set of antennas), or of these two values.

[0017] The invention is advantageous in particular in that it provides a means of locating the points of the image in the areas close to the nadir (y>45° typically, see figures 1 and 2), where interferometric methods are difficult to apply.

[0018] This method does not require additional hardware equipment, compared to conventional assembly.

[0019] The method can then be used in addition to an interferometric method, in particular to help initialize the reference phase difference of the signal. The location of the corresponding point of the image can in any case be done by providing an angle value, for example the site angle (or elevation angle) with respect to the set of antennas (or the vehicle), or a height value, such as the relief on the reflecting surface.

[0020] According to advantageous and optional characteristics: - the search may include searching for several gain extrema and creating a relief map of the reflective surface by interpolation between the corresponding points; - the transmitting antenna may have been chosen so that the lobes are in a chosen number, a large number often being advantageous, and which may be arbitrary; one can choose a high number of lobes and therefore of fringes, (in particular a dozen or more), on half of the transmitting antenna on the side of the reflecting surface; - the search for extrema can be carried out on data (measured intensities) before beamforming but after gain control or on data (still intensities) after beamforming, with beamforming having been carried out before or after gain control; - the data (intensities) can be subject to a preliminary low-pass filtering, along the axis of the ranges, in order to eliminate the dark areas due to the relief and not to the antenna gain diagram. This low-pass filter can be adaptive (i.e. have a different size depending on the position in the image) - the size can thus be variable or constant depending on the position in the image; - the antenna assembly may be carried by (attached to) a moving vehicle, for example on its side, successive acquisitions being carried out by the antenna assembly, and optionally but advantageously, low-pass filtering of the measured intensities is carried out along the axis of the acquisition numbers prior to the search for extremum, - the antenna assembly may include a synthetic antenna or a natural antenna for reception; - said location can be used in a subsequent process of location of the reflective surface by interferometry, as a reference or to remove ambiguities; - the waves may be sonar acoustic waves, the reflecting surface comprising a seabed; - the waves may be electromagnetic radar waves, the reflecting surface comprising an emerged terrestrial surface; - the set of transmitting and receiving antennas presents in the elevation transmission diagram, a plurality of local minima and maxima of amplitude sufficiently large to allow said search, but sufficiently small not to prevent the perception of objects located in the low gain level zones.

[0021] List of figures

[0022] [Fig.1A] presents principles of interferometry applied to the context of the side-looking antenna.

[0023] [Fig.lB] shows the principles of the invention.

[0024] Figures 2A and 2B show the geometry of the antenna lobes, which is used within the scope of the invention.

[0025] [Fig.3] shows a sonar image, highlighting the areas viewed by the lobes, as opposed to the areas between the lobes, which are darker.

[0026] [Fig.4] shows the gains of the imaging process, as a function of the vis- opposite the nadir, for two different depths.

[0027] [Fig.5] shows a sequence of steps implemented in a mode of realization of the invention.

[0028] Figures 6 and 7 show a transmitting antenna geometry as discussed for optimization purposes.

[0029] These figures are simple illustrations, and will be commented on in more detail here. Detailed description

[0030] [Fig. 1 A] Referring to Figure 1 A, which is a vertical section along the sonar trajectory along a horizontal axis with coordinates x, a first antenna 1 located at the abscissa y=0 and at the altitude z=H (above an arbitrarily taken altitude reference, with an altitude axis oriented upwards) is shown, as well as a second antenna 2 located at the abscissa y=B.sin(a) and z=H+B.cos(a) and a target 3 placed on the bottom of the ocean 4 and located at the abscissa y=Y and at an altitude z=h.

[0031] Antennas 1 and 2, for the purposes of FIG. 1, are considered to be receiving antennas.

[0032] For each receiver, there exists, in a given direction towards the ocean floor, a range r (in the figure rl or r2) to the ocean floor 4, which depends in addition to the height of the receiver, also on the variations in the relief of the ocean floor 4, which is not known in advance.

[0033] B is called the base, or "baseline" and is the distance between the two receivers. The angle a is the inclination of the antenna relative to the vertical axis 5, and integrates the roll angle. This angle is known, for example by using an attitude unit.

[0034] The path difference measured between the two antennas 1 and 2 - that is to say the difference between on the one hand the distance (or range) rl between the first antenna 1 and the target 3 and on the other hand the distance r2 (here also the range, but for the second antenna) between the second antenna 2 and the target 3 is:

[0035] _r} _^r2 + g2 + 2rlB.cos(y + a) -

[0036] where y is the angle of the line connecting the target and antenna 1 counted with respect to the horizontal direction (this angle would be the grazing angle - that is to say the angle between the tangent to the bottom and the line connecting the target and antenna 1, if the bottom were horizontal, or if the tangent to the bottom to the target were horizontal - it is defined at the center of the set of transmitting and receiving antennas, between the horizontal direction and the direction of the visualized point which returns the reflected wave), which is the quantity to be determined, because it allows (knowing a, B, H, rj, r 2), to determine h .hHr^iny

[0037] The measurement is nevertheless not directly r2-ri but a phase ¢, proportional to 2ir(r2-ri ) / X modulo 2ir where X is the wavelength of the carrier frequency of the sonar or radar:

[0038] —=^-(\lrj + B2 + 2rjB.cos(y + a) -fJ = 0 + IttN, N e N

[0039] .. .with N unknown. Therefore, several angles y are solutions of the previous equation,

[0040] indeed: / (r ,+# +^)^-52 \ y = acos ) - a

[0042] Only one value N = No of number of cycles is correct. The solution generally used to find this value No of N is phase unwrapping or phase unrolling. We assume that we observe a phase ¢1 for a first point, and that we know the correct value of Ni for this point. Then, if we observe the phase ¢2 of a point close to the first, such that we know with certainty that the phase difference 02-01 is such that -ir<02-01 en, then it is immediate to find the value N2 of the current point from that of the first point. It is then possible to propagate the value of the integer number of cycles from one to the next. In practice, we work on an image, so an observed point has up to eight neighbors, which makes it possible to constrain phase unwrapping with different approaches such as Markov fields or graph theory.

[0043] Moreover, several interferometric bases can be used to determine the number of cycles. Thus, K receiving antennas are used, superimposed on each other, K being greater than the number 2 shown in Figure 1. We then have Kl phase measurements. The diversity of measurements provides a system of equations for constraining the unknown numbers of cycles and for providing hypotheses for eliminating outliers. The phase unrolling process is essentially reproduced Kl times, while retaining the solutions that are simultaneously correct for the Kl equations thus obtained.

[0044] Frequency diversity can also be used. If it is possible, even for a base of K=2 receivers, as in Figure 1, to have several different phase measurements (for L different wavelengths XI to XL), we also obtain L phase hypotheses allowing us to constrain the phase unwrapping. This phase diversity is obtained by quickly emitting a wideband signal. We seek to take XI and X2 as primes between them (one is not close to an integer multiple of the other), so that the minimum distance at which the phases are identical is as large as possible - this is then the product XlxX2. We then reproduce the principle of the vemier (vemier phase unwrapping or Vernier phase unwrapping).

[0045] A limitation of the phase unwrapping method is that it is important to initialize the method with a correct value. It is also necessary that the phase variations are spatially slow enough compared to the spatial sampling step so that the phase unwrapping can be carried out correctly (the spatial sampling step must be smaller than the wavelength). Finally, the phase must not be too noisy.

[0046] These assumptions are not necessarily realized, in particular when the observation is close to nadir 5, namely for Y — 90 0 , and in a region where the angle Y is from 45° to 90°, approximately. For these reasons, the determination of the Y angle is not robust in these regions.

[0047] [Fig.IB] With reference to [Fig.IB], the lower part of which constitutes a section vertical, elements have been shown in relation to a single antenna 1E carried by a vehicle V (seen in the figure from the rear). Antenna 1E is considered to be a transmitting antenna, knowing that a receiving antenna is placed or several receiving antennas are placed in the immediate vicinity of antenna 1E, for example on either side - they are considered to be localized. The antenna assembly transmits and receives with a wide angular aperture, but the angular gain diagram is not constant, which will be exploited. The ocean floor 4 reflects the emitted waves and the travel times make it possible to determine the distances r. The sonar therefore has reflected signal intensity values ​​as a function of distance values ​​r.

[0048] The upper part of Figure 1B presents the curve which shows the measured amplitude A of the reflected signal, received on a channel, as a function of the distance r. The lower part of the figure shows alternative bottom profiles 4A, 4B, 4C, 4D, in dotted lines, which it is necessary to exclude to identify the true ocean bottom 4, represented in solid lines. The angle y is estimated by counting the fringes in the image received by the sonar. It defines the direction of a minimum of the antenna pattern with respect to, for example, the horizontal. In the curve of the upper part, the measured amplitude A has minima, corresponding to the dark fringes of the image (low intensity, at least before image processing), and to the minima of the angular antenna pattern, which will be used to advantage.By identifying, in this measured amplitude curve, a value Ao which is the minimum (local, or possibly global) of A, which is observed for a range r0, we deduce the distance between the sonar and the true ocean floor 4, and consequently the altitude (depth) of the floor in the direction of the angle y which corresponds to the minimum local gain in the angular gain diagram. The angle y being thus determined, we easily calculate the depth, by calculating the height difference A / z = rC).siny. .

[0049] Conversely, the alternative backgrounds 4A, 4B, 4C, 4D give range values ​​rA, rB, rc and rD which are translated on the amplitude curve A by high values, corresponding to light areas of the image. They are discarded.

[0050] [Fig.2A] With reference to [Fig.2A], which is again a vertical section, elements have been shown in relation to a single antenna 1E, which is considered to be a transmitting antenna, knowing that a receiving antenna is placed or several receiving antennas are placed in the immediate vicinity of the antenna 1E, for example on either side. The gain diagram shown in the figure corresponding to the sum (in dB) of the transmit and receive pattern. However, in one embodiment, it is the transmit antenna, by its design, which creates many lobes; the receive antenna creates fewer.

[0051] The figure represents for simplicity the case of a non-curved transmitting antenna in the vertical plane, that is to say flat, with a typically cardinal sinus transmitting diagram. In one embodiment the shape can be arbitrarily different in order to increase the number of lobes.

[0052] We note Ge(6) the gain of the antenna in transmission (in decibels dB) and Gr(0') 'c 8a'n dc the antenna in reception (still in dB) with 0 the angle of elevation counted in relation to the main axis 6 of the antenna 1E and with 0 the angle of elevation counted in relation to the main axis 6 of the reception antenna; considering that 0~ 0', the angle (ï being then omitted from [Fig.2A], for simplicity, we can consider the total gain (in dB):

[0053] G(3) =Ge(3')+Gr(e)

[0054] The geometry of the transmitting and receiving antennas is such that the function G(0) has a maximum at 0 = 0, in the main lobe 7 of the aperture antenna A0, and secondary maxima 8 generally distributed at intervals gradually decreasing on either side of the main lobe in secondary lobes. The lobes are apex angles of the antenna 1E, in which the gain increases regularly towards a maximum, then decreases globally regularly (in fact there are fluctuations) from this maximum, the graphical representation of the gain from the apex of the angle as a function of the angular position graphically forming a lobe.

[0055] There are, visible in the figure, three lobes on either side of the main lobe, but there may be more, or even many more. Between the lobes there are regions 9 where the gain tends towards " °° (in dB) at + g N- The points 10 and 11 of the seabed represented in the figure are respectively in the direction g + AS (first interlobe towards the seabed) and q + 222 (second inter-lobe towards the seabed). They will be commented on later. It is possible that the 3rd inter-lobe towards the seabed is beyond the nadir, but depending on the angle a which is the inclination of the antenna with respect to the vertical axis 5 or the horizontal axis (which is equal to the roll to within an additive constant and which is represented in two different arbitrary ways in figure 2), it may, as well as the following inter-lobes, in nevertheless limited number, be before the nadir.

[0056] The sonar image is the function I which, at a measured distance r and at an abscissa x from the sonar along its trajectory, associates an acoustic intensity 1 in dB corresponding to all the signals reflected by the targets at a distance r from the sonar. The function f is therefore p2 M p - that is to say that it associates two real values ​​with a single real value.

[0057] Under the generally well-verified hypothesis that for a given abscissa x and range r, there is only one target 3 which presents an index - ratio expressed in decibels of the energy returned to the incident energy (target strength in English) - significant compared to the others, then we can associate (x, v. r) with a single value of 0, the site angle of the target.

[0058] The measured intensity is then given in decibels by the sonar equation of the form:

[0059] l(x, r) = P + - 401og ( Qr + s(x, r, fl)+K

[0060] With:

[0061] p the transmission power, constant, known (the value is however not necessary for the calculations developed here);

[0062] G(0) the total gain (transmission and reception), assumed to be known at least to a factor additive near not depending on 0;

[0063] 401og r the term of dilution of the power by the distance, calculable, holding account of the geometric losses on the outward and return journey of the wave under the assumption of constant speed in the medium, knowing 1;

[0064] $(x, r, 0) the index of the target (unknown);

[0065] K represents various gain terms (processing gains, etc.).

[0066] [Fig.2B] In figure 2B, a transmission antenna diagram Ge(fl) is shown which is a curve of the gain (in logarithmic scale, as a function of the elevation angle 0, typical of a curved antenna (described later in figures 6 and 7). For d = 0 0 , the gain is zero, and is therefore 0 dB, whereas for positive or negative angles 0, the gain becomes negative, and experiences fluctuations. There are amplitude fluctuations of 3 to 5 dB, as shown in [Fig.2B] for example for a zone of positive elevation angles, in which the gain passes through a local minimum then through a local maximum which is greater than it by a gain noted A, of the order of 3 to 5 dB. In the example shown, the gain then decreases as the elevation angle increases, but then undergoes more significant fluctuations, which can be 10 to 15 dB. The diagram presented is given for illustrative purposes only and other diagrams are possible.One effect of the curvature of the transmitting antenna is in fact to create fluctuations as small as a few decibels. These fluctuations, although small, are exploited in certain embodiments by the invention, because they are visible in the image over many consecutive transmissions, and therefore it is possible to identify them and exploit them by an integration effect over time. Local minima of the gain diagram are therefore used. These local minima can be compensated in a posteriori processing for imaging purposes, but before such compensation, they are used to make the bathymetry calculations according to the invention.

[0067] [Fig.3] In relation to Figure 3, we discuss an image formed by the sonar during its trajectory, considered rectilinear, along the x axis, with in the figure r the range on the abscissa and x the trajectory on the ordinate. The gray level of the image at a point is, as indicated above, the acoustic intensity 1 in dB corresponding to the signals reflected by the targets at a distance r from the sonar, the light grays being associated with high intensities, and the dark grays, with low intensities. In the left part of the figure, for low ranges, less than the shortest distance between the antenna system and the reflecting surface, the intensity is low, in the absence of a reflecting surface for the range values ​​concerned. Then, moving towards the higher range values, a specular reflection is observed, corresponding to the surface of the underwater floor at the nadir.For increasing range values ​​from this first value, the observed ground consists of the areas crossed by a displacement from the ground to the nadir, in a direction perpendicular to the axis of movement of the vehicle or at least in the direction of sight of the antenna system, which is generally perpendicular to the displacement.

[0068] Under one of the two following hypotheses i) that the amplitude of the variations of the total gain G(0) with $ is large compared to that of the index of the observed elements s(xr 0( or ii) that the spatial extent of the strong variations of index S(x, r, 6)- is small compared to that of the variations of G^d^ we can consider that the measured intensity is written:

[0069] / (x, r) & G(6) + K'(r)' with a term almost exclusively a function of L

[0070] This approximation is particularly true near the nadir (left on the figure). Its implication is that the sonar image has dark fringes 20, 21 (and following, although it is possible that only two inter-lobes are present before the nadir in which case there are only two dark fringes), where G(0) is low, and that these dark fringes alternate with light fringes 23 and following where G(0) is high. In the example of Figures 2 and 3, points 10 and 11 are respectively, as stated, in the direction 0 + (first inter-lobe) and Jâ® (second inter-lobe) and their sonar images 100 and 110 are black, which thus reflects a very low received power. Conversely, point 3 is close to the direction of the main lobe and its image 30 therefore appears in a well-illuminated region.

[0071] There is a link between the angle 6, the angle Y and the height difference between the antenna 1E and the target 3. Indeed, the roll angle a being measured by an attitude unit, it is equivalent to determine the elevation angle 6 and to determine the angle Y, because y = a + 0 (this can be seen clearly in figure 2). We also have: [°°721 sin(y)=^ = #

[0073] If we know 0 and a then the relation — H -h — r.cos(a - 6) expresses the height difference between the antenna 1E and the target 3.

[0074] If we know, for a given range ', what the elevation angle 0 is, we can deduce the height difference Hh. However, spatially, the alternations of dark fringes 20, 21 and following and light fringes 23 and following are very visible and can be searched for by varying x, therefore by scrolling the sonar image. We can know to which dark fringe 20, 21 or following an angle 0 corresponding to a region 9 where the antenna gain is low corresponds. It is therefore possible to deduce the altitude difference FI-h.

[0075] [Fig.4] With reference to [Fig.4], which shows the shape of the gain function (in dB) (on the abscissa the range r in meters, from 0 to 150 m in the figure, and on the ordinate the gain from -150 dB to -60 dB) for two different heights H = 15 m and H = 20 m (therefore offset by 5 m from each other), the invention begins with a detection, in the image, of the dark fringes 20, 21 and following corresponding to the inter-lobe spaces 90 (the antenna nulls), or to a local minimum of the antenna diagram. It is specified that the antenna can have a rectangular aperture or be a curved antenna. The figure represents the case of a non-curved, flat antenna, with an emission diagram typically in cardinal sine.

[0076] This detection can be carried out at different stages of the sonar data processing, for example using the gain calculated at the automatic gain control stage, or in the formed channel image, or a combination of the two. This step makes it possible to provide, for each given position x of the sonar along its trajectory, corresponding to a transmission number (ping number in English) n, a collection of P ranges t^^, 1 < k < p where P is the number of dark fringes detected - [Fig.4] represents a case with p = 5 fringes.

[0077] This determination of the ranges is followed by a labeling process by the angles of the inter-lobe spaces or local minima. For this, for example, we start by identifying the position of the main lobe in the image, we identify the maximum 50 associated in the gain diagram, then we assign the angle j = 0O + to the minimum 200 closest to the maximum 50, the angle $ - 222 to the second minimum 210 the closer to the maximum 50, and so on, so that the same interlobe space starting from the main lobe and returning towards the weak ranges, is assigned to ranSle9^ = 9o+“'

[0078] The algorithm for determining local minima followed by the assignment of angles therefore provides an estimate of P range-site pairs, for example ( rn k ' k — $ + ) 1 < k < p- As, for r > Hn where Hn is the flight altitude of the sonar (height above the seabed at nadir) measured by a sounder on the date of emission of emission n, it is possible to link the distances to the abscissas of the point on the ground by the relation:

[0079] v -H2 YnJc n

[0080] we therefore also have the abscissa-elevation angle pairs / v 9 t = 6 V \ ' nJc nk o ~ / As, by the relationship already seen above, it is possible to go back to a difference in height:

[0081] — »• i sinGr i )

[0082] where gives the inclination of the sonar at emission n , we therefore have the abscissa-height difference pairs y^, Az^ .

[0083] Local maxima 51 and following can also be identified for the secondary lobes and they are associated with the ranges r'n.i r'2>2 and following.

[0084] These pairs y^, Az^ j can be filtered in order to incorporate an a priori provided by the dynamics of the vehicle (values ​​of Hn, a») or an a priori on the profile of the background coming from another sensor, from another implementation of the method presented at another stage of the data processing, etc., in order to eliminate aberrant data.

[0085] This filtering step can use existing conventional techniques such as optimal filtering, the Kalman filter, set membership filtering, or others.

[0086] We can finish by generating a height profile by interpolation (linear, spline, or other) of the measurement points thus obtained, for 0 < y < yj:

[0087] interpolation(y, {(0, Hn); (y^[f, (yn^v kz„^ ^zny)])

[0088] It is also possible to obtain a map of the angles y, which constitutes a central element of the objectives of the invention:

[0089] z Az(«,v) y(n,y) =acos-^==7

[0090] Alternatively, it is possible to provide the points [ z „ TT . . , . . . . z . , ] raw as p 0, Hn); (y^Az^p), (y^,, Az^); ...; (ynl, AznJ)| references that can be used to initialize a classical phase unwrapping algorithm, which, unlike interpolation, fills in missing data with real measurements.

[0091] Alternatively and ideally, it is possible to hybridize these two approaches: interpolation and phase unfolding constrained by measurements on the fringes.

[0092] [Fig.5] With reference to [Fig.5], which shows a typical block diagram of two approaches for determining the Az(n,y) profile, we now present several approaches, which can be implemented independently or in a complementary manner, and which are described below. In a successful implementation, these approaches are implemented sequentially in order to increase the performance of the process, but it is possible to use one without the other.

[0093] A first approach, or a first stage, consists of working on the data resulting from automatic gain control on the raw sensor signals, after pulse compression in distance (pulse compression) but before beam / forming in natural or synthetic antenna. This automatic gain control has the effect of equalizing the received intensities in order to bring them into the dynamics of the data storage file and also to facilitate the visualization of the data by the operator. Automatic gain control aims to completely eliminate local variations in intensity in the image due to the effects of antenna gain and attenuation by distance.

[0094] A typical, but not limiting, conventional implementation of gain control is as follows, and is shown in Figure 5. The details of the implementation are not essential. Let Nc be the number of sensors of the receiving antenna and n, r) the intensity received at transmission 11 for the distance 1 for the i-th sensor of the antenna (1 < i < Nc). Let 1 be the average intensity - the signal 410 - received at the distance r for all the sensors:

[0095] J \ E^aXw) WP.....iT......a-......

[0096] with ai a parameter (a real value close to 1) allowing to correct any inter-sensor calibration defects in intensity. Then we can estimate a function f(n, r) obtained by convolution on the distance axis of with a function B(r, Hn) of typically rectangular impulse response, whose typical length l(r) on the distance axis can vary (or not) as a function of 1 according to the constraints specific to the field of application of the sonar (in particular the altitude Hn of flight of the sonar at the n 'th emission), in order to carry out a low-pass filtering 420 (a low-pass filtering on the distance axis r), the result of this filtering 420 being f(n, r):

[0097] f (n, r) = î(n, r) * B(r, H)

[0098] The exact implementation of this filter h) is not essential, but it is desirable that the spatial support of this filter is such that the typical spatial length variations are smoothed out, small compared to those of the fringes (the width of the inter-lobes, approximately evaluated) of the transmitting-receiving antenna lobes. From f (n, r), one can also estimate a second function g(n, r) - after the filtering 420, this is of a second filtering 430, namely a low-pass filtering r) carried out on the axis of the emission numbers, at emission n; a non-limiting approach is for example by a first-order recursive filtering of the type:

[0099] g( 1, r) =f(l, r)

[0100] g(n,r) = (lP)g(n-lr)+pf(n,r)

[0101] with P a parameter between 0 and 1. Then, the multiplicative gain applied to the data from sensor i is / g(n, r) For values ​​r > H (and 1, for values ​​r < h), bringing (on average) the observed values ​​around 1 for sonar distances greater than the altitude, therefore where the ocean floor is imaged. Whatever the low-pass filter used, its design criterion is that the impulse response of the filter must have the longest possible support, while being small compared to the minimum spatial period L of variation of the position of the fringes (20, 21) on the axis of movementx of the vehicle. The value of L is taken empirically as a hypothesis. The digital implementation of the filter therefore involves the instantaneous speed of the vehicle, measured elsewhere, as well as Af the pulse repetition period. In the special case of an implementation by first-order recursive low-pass filter, we have fi = exp( - VM / L)-

[0102] We have seen above that, under one of the two following hypotheses i) that the amplitude of the variations of the total gain G(0) with 0 is large compared to that of the index of the observed elements r, 0), or ü) that the spatial extent of the strong variations of index S(x, r, O)- is small compared to that of the variations of G( / A we can affirm that:

[0103] i(n,r)«G(6)+K(r)

[0104] By design, the function g(n, r) has the following properties: it eliminates (by low-pass effect) the strong variations of r, 0) of small size compared to the spatial extent of G{6) and it performs a local integration of the image on the ping axis (cross-range axis in English); in other words, it increases the signal-to-noise ratio of the image of G(0) compared to that of r. 0)- If hypotheses i) and ii) are not always true for I(n, r ), they are on the other hand much more often true for r):

[0105] g(n, r) ~ G (6) + K'(r)

[0106] This image g(n, r) is then a good approximation of G ( 0) 4- K'(rX and appears as a function whose logarithmic representation has numerous notches 90 (visible in figure 4) where the gain tends towards " æ at the ranges falling in the inter-lobe zones 9 where the antenna gain is very low. The shape of this function is illustrated in figure 4 by taking the arbitrary values ​​a = 15 0 (typical, but not limiting, value of the sum of the roll, generally almost zero, and the antenna offset angle (array tilt angle in English) towards the bottom marine) and AO- 10 ° (typical non-limiting values ​​of the opening of the main lobe). The figure also illustrates the fact that the distance1 where the minima 200, 210 are located is a function of the bottom topography: in fact, in the case illustrated here, the bottom is assumed to be perfectly flat, at 15 and 20 meters respectively from the sonar, and the 90 notches are shifted towards the short ranges if the bottom is closer.

[0107] By a determination algorithm 440 for the determination of local maxima and minima (Determination of the range of the local minima and maxima of #(#,#)), it is possible to determine, at emission n, the range M of the minima 200, 210 which correspond to the points 100, 110 located at the centers of the inter-lobe spaces, as well as the range r'ni of the maxima 220, 230 which correspond to the points located at the changes of sign of the derivative of the intensities, lobe by lobe. This determination algorithm 440 constitutes a search in the measured ranges (r) of at least one gain extremum.

[0108] This determination of the ranges lnJi is followed by a labeling process 450 by the angles corresponding to the local minima and maxima of the emission-reception diagram (radiation pattern in English), in particular labeling of the ranges by the angles of the inter-lobe spaces. This involves the identification or association of the local extrema of measured intensity (for example Ao in [Fig.lB]) with local extrema of the angular gain profile.

[0109] To do this, we start by identifying the main lobe, corresponding to the maximum 50 of the gain function g(n, r)- Assuming for example that the inter-lobe spaces are equidistant by a value A0, we assign the angle + Aâ to the minimum 200 closest to the maximum 50, the angle 0n? = 0Q + — to the second minimum 210 closest to the maximum 50, and so on, so that the same interlobe space starting from the main lobe and returning towards the weak ranges, is assigned the angle 0^ = 0O + ( k - 4 ) A0- We do the same with the local maxima, assigning the angle 0^Q — 0$ to the first maximum 50, the angle 0n । = 0O 4- A0 at the second maximum 51, and so on, so that the same inter-lobe space starting from the main lobe and returning towards the weak ranges, is assigned to the angle 0^ ' = 00 + kAO.If the inter-lobe spaces are not equidistant or approximately equidistant from a value A0, the calculation is done by taking the exact values ​​known and tabulated beforehand.

[0110] For a less regular profile, like that presented in [Fig.2B], we can also easily recognize the local minima and maxima, by proceeding in order and searching for them one after the other.

[0111] The process of determining local minima and maxima followed by the assignment of angles which constitutes steps 440 and 450 in figure 5, therefore provides an estimate of 2p range-elevation angle couples for example (rn,k, 0n,k + I <k <p et (r^^'^+kao^ckk^p-l comme, pour r>Hn where Hn is the flight altitude (reference 452 in figure 5, also visible in figure 2) of the sonar (height at nadir) provided as data to the algorithm measured either by a sounder or by the sonar itself on the date of emission of the emission n, it is possible to link the distances 1k to the abscissas of the point on the ground by the relation:

[0112] „ / 2 H2

[0113] we therefore also have the abscissa-elevation angle pairs for example fv 0 v = 6 + 1 • As, by the relation already seen above, it is possible to go back to a height difference using the roll information an (reference 451 in figure 5, the roll angle being an element of the vehicle attitude and the receiver tilt angle a also being visible in figure 2), according to the expression

[0114] Az^ = r^sinfa» - 0^ )

[0115] where gives the inclination of the sonar at emission n, we can finally perform a calculation 460 of the abscissa-height difference pairs, or abscissa elevation ( y , Aznk ). This is a localization with respect to the vehicle of the points of the image corresponding to the local extrema (such as Ao) of intensity.

[0116] An interpolation 470 of linear, spline, or other type is carried out on the measurement points 460 thus obtained:

[0117] Az(n,y) = interpolation(y,{(0,Hn); (y^Az^p), (ynp_r Az^i); (ynl,AznJj{ )

[0118] This is an Interpolation of the profile Az(y) from the points y We can end with the generation of a 480 profile of height Ad / î, y) - This output may be sufficient, depending on the applications, or reused downstream.

[0119] In this first approach, we worked in the raw data before formation of pathways or in the absence of formation of pathways.

[0120] In a second approach, a shaped channel image (the image obtained after the channel formation process) is used. Depending on whether this shaped channel image is calculated before or after applying the gain control, the method is slightly different.

[0121] If the channel-formed image is calculated before gain control, the application of the gain control is according to a procedure similar to that described above in relation with the first approach, considering that I(n, r) here denotes the intensity observed at range r for the n-th channel formed. The generation of the height profile Az(n, y) follows the same procedure as described previously in the first approach. This solution has the advantage that the spatial resolution on the displacement axis x is greater than during the emission-to-emission work of the first approach, by a factor of typically up to 50 channels per emission, or even more. Furthermore, the raw data from the sensors present an averaging effect of the intensities received on the displacement axis x, which makes the detection of the notches 90 robust.

[0122] If, on the contrary, the shaped channel image is calculated after gain control, the determination of the position of the alternation of dark and light fringes in the image takes into account the fact that the gain control could have been set to suppress them to provide good visual quality of the image and exploit the small residual intensity variations which remain, with an amplitude of the order of + / - 1 dB. The determination of the position of the fringes in the image is possible via different image processing techniques. Here we note I(n, r ) the intensity measured at channel n for the range \ These image processing methods are for example and in a non-limiting manner the following approaches:

[0123] The application of a second stage of automatic gain control similar to that described in the first approach, but configured so as to isolate the dark and light fringes well;

[0124] Or, we can use hidden Markov chain segmentation methods, considering that the intensity I(n, r) can be of two classes "pixel of a dark fringe" and "pixel of a bright fringe" of which we know the intensity distribution a priori, and the conditional probability that a pixel of a channel n is of a given class given the class of pixels of channel n - L

[0125] Once the local minima and maxima have been detected, the generation of the height profile Az(y) follows the same procedure as described previously in the first approach.

[0126] Thus, the process can successively include the following processing of the received acoustic signal averaged for each transmission (ping) on ​​all the sensors, or, if there has been channel formation, for the signal of each channel of the sonar image after channel formation:

[0127] i) low-pass filtering on the distance axis configured to smooth variations of size smaller than the spatial spacing of the fringes;

[0128] ii) the result of the previous low-pass filtering, passing through a low-pass filtering on the ping axis recursively using the result of the same step, for the previous ping;

[0129] iii) the result of the two previous filterings, serving as an approximate measurement of the intersection of the transmission-reception diagram with the ground, being submitted to the algorithm for determining the scope of the local maxima and minima of said diagram;

[0130] iv) the ranges estimated in the previous step, as well as the a priori knowledge of the angles where the maxima and minima are located, making it possible to label a collection of pairs (range, elevation angles relative to the main emission axis);

[0131] v) this collection of pairs (range, elevation angles relative to the main transmission axis), associated with the measurement of the attitude of the vehicle at the current ping, in particular the roll, as well as the altitude of the vehicle at the date of transmission of the current ping, making it possible to locate the points of the image for example by finding a collection of pairs (reference ground abscissa, reference ground-vehicle height difference), where the ground abscissa is along the transverse axis of the vehicle, parallel to the ground;

[0132] vi) this collection of pairs (reference ground abscissa, reference ground-vehicle height difference) then serving as support for an interpolation for example of a function “ground-vehicle height difference as a function of the ground abscissa”.

[0133] It is also possible to carry out a combination of the antenna lobe estimation developed here with the interferometric measurements known elsewhere.

[0134] The profiles 480 of the first approach or of the second approach are used to initialize and constrain a phase unrolling algorithm using interferometric measurements. For example, the algorithm can unroll the phase by choosing, in the event of phase ambiguity, the altitude best corresponding to that estimated in the profile 480. The estimate of the local elevation of the ground relative to the sonar or radar antenna obtained by relying as taught above on the knowledge of the angular diagram of the antenna group, can thus serve as a reference for an algorithm for estimating the local elevation of the ground by interferometry using the unrolling of the phase (Vemier method or its derivatives), by removing the phase ambiguities by choosing the phase giving the elevation closest to that estimated by the method proposed here.

[0135] [Fig.6] With reference to [Fig.6] which is a three-quarter view, and also to the [Fig.7] which is a sectional view, an optimized mechanical design of the transmitting antenna allowing to forge the transmission pattern and therefore, the position of the antenna lobes can also be used.

[0136] [Fig.7] The shape of the transmitting antenna can influence the shape of the lobes antenna and on the alternation of light and dark fringes in the image.

[0137] It is possible to couple the use of the method of determining the position of the fringes in the image, with a deliberate design of the antenna, in order to maximize the presence and visibility of these fringes.

[0138] If the antenna 300 is considered as a three-dimensional shape resulting from an extrusion, over a length L in the longitudinal axis, of a part 301, the surface of the part 301 must be optimized, in particular the side 302 of this surface, which, after extrusion, forms the emission face 305.

[0139] The local radius of curvature 304 at a point 303 on the side 302 immediately influences the elevation angle emission pattern of the antenna.

[0140] The antenna is then designed by multi-criteria optimization, in order to optimize the following factors: - The position, width and amplitude of the main and secondary lobes - The angular position of the local minima between the lobes - The local radii of curvature 304, which cannot fall below a minimum value depending on the antenna manufacturing process.

[0141] The shape of the transmitting antenna is therefore, in these embodiments, subjected to a multi-criteria optimization method in order to optimize its shape, essentially on the transverse plane, in order to optimize the position of the local minima and maxima on the basis of the following criteria: multiplicity of said minima and maxima, relative amplitude of the minima and maxima, radius of curvature of the transmitting face of the antenna in the transverse plane.

[0142] In this embodiment, the main lobe is optimized to be as wide as possible in elevation, with a globally uniform gain, but presenting slight variations of the order of a few decibels. These slight variations, noted A in [Fig.2B], are artifacts of the design of the antenna during the multi-criteria optimization process, artifacts used advantageously for the invention. Indeed, these slight variations are too small to affect the link budget in a very harmful way (it is always possible to image a region on the ground with a sufficient energy budget to discern the scene there) but these local gain variations cause the appearance of dark fringes on the image which, compared to the invention, have the same effect as the alternation of gain minima caused by clear interlobe spaces (elements 90 of [Fig.4]) where the gain tends towards minus infinity, as would be observed with a planar antenna, where the elevation gain pattern is typically cardinal sine squared. Although the gain variation is smaller (a few decibels instead of several tens, which can be assimilated to an infinite variation), this variation is, crucially for the invention, sufficient to be detectable by one, the other or both of the image filtering approaches (blocks 420, 430 and 440 of [Fig.5]), in particular by the integration effect caused by the low-pass filtering on the ping axis (block 430).

[0143] The receiving antenna may also be designed to optimize the shape of the antenna lobes for its operation within the scope of the invention but, In an advantageous embodiment, only the transmitting antenna is curved and therefore causes the most fluctuations in the transmitting lobe. The receiving antenna has a smoother gain in the working area and its effect is little felt, but in a variant, the receiving antenna is also cut differently to amplify the effects.

[0144] The invention is applied to improving the robustness of the altimetry and bathymetry function of an underwater drone, for rapid environment assessment (REA) functions or for an application dedicated to bathymetry and mapping. It is also applied to the possibility of designing a lateral micro-antenna giving, by a specific design of the transmitting antenna, a low-cost local relief determination function (without interferometry, or with low-resolution interferometry with small antennas), this function allowing, for example, a recalibration of the vehicle with respect to an altimetric map previously acquired and recorded in the vehicle (by a TERCOM type method: TERrain COntour Matching or terrain relief matching, for example).The use of low-tech sensors is of interest for small vehicles manufactured in large series, such as drone packs, or intended to be lost, such as single-use drones or smart munitions.

[0145] The invention has been presented with a side-scan sonar or a side-scan antenna, on a moving vehicle, but it also applies to the case of a stationary antenna, for example with a formation of azimuth channels.

[0146] The invention is then used by representing the sonar image at the fixed point in B-scan representation: the horizontal axis is the distance axis and the vertical axis is the azimuth axis: x=r, y=azhnut. The y axis is then called the azimuthal axis. We find the representation of the geometry of the lateral sonar.

[0147] In B-scan representation the operations remain the same, and the determination of the bottom bathymetry is then done by an adaptation of the reprojection equations.

Claims

Claims

1. Method for characterizing a reflecting terrestrial or marine surface (4) subject to imaging by collecting echoes of waves emitted towards said reflecting surface (4), the emission and reception of the waves being carried out using a set of transmitting (1E) and receiving (1, 2) antennas, the set of antennas having an angular gain profile in the vertical plane which is known, intensities (410) as a function of the ranges (r) between the set of antennas (1E, 1, 2) and the reflecting surface (4) being measured by the set of antennas (1E, 1, 2) for the purpose of constituting an image of the surface, the method being characterized in that it comprises a search (440) in the measured intensities (410) of at least one local extremum (Ao) and, by an identification (450) of said at least one local extremum (Ao) to a local extremum of said angular gain profile,a location (460) with respect to the set of antennas of at least one point of the image corresponding to said measured local intensity extremum (Ao), the location of said corresponding point of the image being done by providing a site angle value, or a height value.,

2. Method for characterizing a reflective surface (4) according to claim 1, characterized in that the set of antennas (1E) is carried on its side by a vehicle (V) which moves, successive acquisitions being carried out by the set of antennas.

3. Method for characterizing a reflective surface (4) according to one of the preceding claims, characterized in that the search (440) comprises the search for several intensity extrema, and the method comprises their identification with several local extrema of the angular gain profile and the creation (470) of a relief map (480) of the reflective surface (4) by interpolation.

4. Method for characterizing a reflective surface (4) according to one of the preceding claims, characterized in that the search (440) for at least one extremum is carried out on intensities measured before formation of channels but after gain control or on intensities measured after formation of channels, the formation of channels having been carried out before or after gain control.

5. Method for characterizing a reflective surface (4) according to one of the preceding claims, characterized in that the measured intensities are subject to low-pass filtering (420), prior to said search (440), along the axis of said ranges, with a variable or constant template depending on the position in the image.

6. Method for characterizing a reflective surface (4) according to one of the preceding claims, characterized in that the set of antennas (1E, 1, 2) comprises, for reception, a synthetic antenna or a natural antenna.

7. Method for characterizing a reflective surface (4) according to one of the preceding claims, characterized in that said location is used in a subsequent process of locating the reflective surface (4) by interferometry, as a reference or to remove ambiguities.

8. Method for characterizing a reflective surface (4) according to one of the preceding claims, characterized in that the waves are sonar acoustic waves, the reflective surface (4) comprising a seabed, or the waves are radar electromagnetic waves, the reflective surface (4) comprising an emerged terrestrial surface.

9. Method for characterizing a reflective surface (4) according to one of the preceding claims, characterized in that the location is made taking into account a current value (451) of roll angle of the set of antennas, or a current value (452) of altitude of the set of antennas, or both.

10. Method for characterizing a reflective surface (4) according to one of the preceding claims, characterized in that the set of transmitting (1E) and receiving (1, 2) antennas presents in the elevation transmission diagram, a plurality of local minima and maxima of amplitude sufficiently large to allow said search (440), but sufficiently small not to prevent the perception of objects (10) located in the low gain level zones (20).

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