Method for monitoring the stability of an excavation front using radar interferometry

Abstract

A method for filtering an interferometric radar acquisition, said method comprising the step of prearrangement of a radar system for carrying out acquisitions of images of a scenario by means of SAR interferometry, the radar system comprising at least one radar sensor arranged to emit and receive a radar signal, a control unit configured to analyse said signal received by said radar sensor by means of interferometric technique, a screen arranged to show to a user said images of said scenario.

Claims

1. A method for filtering an interferometric radar acquisition, said method comprising the steps of: prearrangement of a radar system for carrying out acquisitions of images of a scenario by means of SAR interferometry, said radar system comprising: at least one radar sensor arranged to emit and receive a radar signal; a control unit configured to analyse said signal received by said radar sensor by means of interferometric technique; a screen arranged to show to a user said images of said scenario; by means of said radar system, periodic acquisition of images S.sub.i of said scenario for a number n.sub.c of cycles, with i=1,2, . . . , n.sub.c, each image S.sub.i comprising a number n.sub.p of pixels P.sub.ij having spatial coordinates defined with respect to a predetermined reference system, where P.sub.ij is the j-th pixel of the i-th image acquired at the i-th cycle, with j=1,2, . . . , n.sub.p; said method characterized in that, at each i-th cycle and for each pixel P.sub.ij, it is provided an iteration of the steps of: calculation of a coherence value γ.sub.ij arranged to represent the quality of the phase information supplied by a j-th pixel at the i-th cycle; comparison of said coherence value γ.sub.ij with a predetermined minimum coherence value γ.sub.min; interferometric calculation of a displacement value d.sub.ij of said pixel P.sub.ij, said displacement value d.sub.ij being zero in case that in case that γ.sub.ij<γ.sub.min; calculation of a cumulative displacement value D.sub.ij as the sum of the displacement values d.sub.ij in the N cycles preceding said i-th cycle, said cumulative displacement value D.sub.ij being calculated according to the equation D.sub.ij=Σ.sub.k=i-N.sup.i(d.sub.kj).

2. A method for filtering an interferometric radar acquisition, according to claim 1, wherein each pixel is associated with: a mask coefficient M.sub.ij arranged to assume a value M.sub.ij=NaN or a value M.sub.ij=1, and wherein when M.sub.ij=NaN said pixel P.sub.ij is not shown on said screen and when M.sub.ij=1 said pixel P.sub.ij is shown on said screen; a coherence coefficient m.sub.ij arranged to assume a value m.sub.ij=0 in case that γ.sub.ij<γ.sub.min or a value m.sub.ij=1 in case that γ.sub.ij≥γ.sub.min.

3. A method for filtering an interferometric radar acquisition, according to claim 2, wherein, at each i-th cycle and for each pixel P.sub.ij, the steps are provided of: evaluation of said value of coherence coefficient m.sub.ij in the N cycles preceding said i-th cycle; calculation of an over threshold fraction value f.sub.ij as the sum of the values of the coherence coefficient m.sub.ij in the N cycles preceding said i-th cycle divided the number of cycles N, said over threshold fraction value f.sub.ij being calculated according to the equation f.sub.ij=Σ.sub.k=i-N.sup.i(m.sub.kj/N); comparison of said over threshold fraction value f.sub.ij with a predetermined minimum over threshold fraction value f.sub.min; in case that f.sub.ij<f.sub.min, assignment to said pixel P.sub.ij of a dynamic mask coefficient M.sub.ij.sup.D=M.sub.ij=NaN.

4. A method for filtering an interferometric radar acquisition, according to claim 3, wherein: if M.sub.ij.sup.S=NaN and M.sub.ij.sup.D=NaN then M.sub.ij=NaN; if M.sub.ij.sup.S=NaN and M.sub.ij.sup.D=1 then M.sub.ij=NaN; if M.sub.ij.sup.S=1 and M.sub.ij.sup.D=NaN then M.sub.ij=NaN; if M.sub.ij.sup.S=1 and M.sub.ij.sup.D=1 then M.sub.ij=1.

5. A method for filtering an interferometric radar acquisition, according to claim 2, where the steps are provided of: calculation of a power value W.sub.ij for each pixel P.sub.ij of a predetermined image S.sub.i; comparison, for each pixel P.sub.ij, of said power value W.sub.ij with a predetermined minimum power value W.sub.min; in case that W.sub.ij<W.sub.min, assignment to said pixel P.sub.ij of a static mask coefficient M.sub.ij.sup.S=M.sub.ij=NaN; in case that W.sub.ij≥W.sub.min, assignment to said pixel P.sub.ij of a static coefficient of mask M.sub.ij.sup.S=1.

6. A method for filtering an interferometric radar acquisition, according to claim 2, wherein a step is provided of calculation of the number q of pixels P.sub.ij having mask coefficient M.sub.ij=NaN and wherein said radar system is adapted to emit an alarm in case that the ratio q/n.sub.p exceeds a predetermined threshold.

7. A method for filtering an interferometric radar acquisition, according to claim 2, wherein, said displacement value d.sub.ij is calculated according to the equation $d_{ij}=-\frac{\lambda }{4\pi }{m}_{ij}*\arg \left[I_{ij}\right],$ where λ is the wavelength of the signal emitted by said radar system.

8. A method for filtering an interferometric radar acquisition, according to claim 1, wherein steps are provided of: laser scanning with obtaining a three-dimensional map of said scenario; projection of each cumulative displacement value D.sub.ij on said three-dimensional map of said scenario obtained by said step of laser scanning.

9. A method for filtering an interferometric radar acquisition, according to claim 1, wherein said radar system is adapted to emit an alarm in case that a cumulative displacement value D.sub.ij exceeds a predetermined threshold D.sub.max.

10. A method for filtering an interferometric radar acquisition, according to claim 1, wherein, at each i-th cycle and for each pixel P.sub.ij, the steps are provided of: calculation of an interferogram I.sub.ij of said pixel P.sub.ij according to the equation I.sub.ij=s.sub.ij*s.sub.(i-1)j.sup.*, where s.sub.ij is the complex number representing the focused radar data of the j-th pixel of the i-th image and s.sub.ij.sup.* is the complex conjugate of s.sub.ij; interferometric calculation of said displacement value d.sub.ij as a function of arg[I.sub.ij], wherein arg[I.sub.ij] is the argument of the complex number I.sub.ij.

11. A method for filtering an interferometric radar acquisition, according to claim 1, wherein said coherence value γ.sub.ij is a spatial coherence value and it is calculated by the equation: ${\gamma }_{ij}=\frac{{.Math.s_{ij}*s_{\left(i-1\right)j}^{*}.Math.}_{spat}}{\sqrt{{.Math.s_{\left(i-1\right)j}*s_{\left(i-1\right)j}^{*}.Math.}_{spat}{.Math.s_{ij}*s_{ij}^{*}.Math.}_{spat}}}$ where .sub.spat is a spatial media mathematical operator operating in a neighbourhood of the j-th pixel, and where s.sub.ij is the complex number representing the focused radar data of the j-th pixel of the i-th image and s.sub.ij.sup.* is the complex conjugate of s.sub.ij.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Further characteristic and/or advantages of the present invention are more bright with the following description of an exemplary embodiment thereof, exemplifying but not limitative, with reference to the attached drawings in which:

(2) FIG. 1A schematically shows a radar system during the monitoring of an excavation face;

(3) FIG. 1B shows in detail the screen arranged to show the images of the scenario;

(4) FIG. 2A shows an optical image of a scenario inside a tunnel in which excavation operations are carried out;

(5) FIG. 2B shows by variation of color intensity a representation of the coherence value of the pixels corresponding to the interferometric image relating to the scenario of FIG. 2A;

(6) FIG. 3 shows by variation of color intensity a representation of the pixel displacement value projected on a three-dimensional map obtained by laser scanning;

(7) FIG. 4 shows a flow diagram of a possible embodiment of the method according to the present invention;

(8) FIG. 5 shows a flow diagram of a possible variant embodiment of the method according to the present invention.

DESCRIPTION OF SOME PREFERRED EMBODIMENTS

(9) With reference to FIGS. 1 and 4, in a possible embodiment of the present invention, the method for filtering an interferometric radar acquisition comprises a first step of prearranging a radar system arranged to provide acquisitions of images of the scenario by means of SAR interferometry. In particular, the radar system comprises at least one radar sensor 110 arranged to emit and receive a radar signal and a screen 120 arranged to show the images of the scenario. The radar system also comprises a control unit 115 configured to analyse the received signal by the radar sensor 110 by means of interferometric technique and to send images to the screen 120.

(10) The method then provides a step, by means of the radar system, of periodic acquisition of images S.sub.i of the scenario for a number n.sub.c of cycles, with i=1,2, . . . , n.sub.c. Each image S.sub.i comprises a number n.sub.p of pixels P.sub.ij having spatial coordinates defined with respect to a predetermined reference system, where P.sub.ij is the j-th pixel of the i-th image acquired at the i-th cycle, with j=1,2, . . . , n.sub.p.

(11) The method then provides a processing, by means of the control unit, of the acquired images by carrying out an iteration of the following steps at each i-th cycle and for each pixel P.sub.ij.

(12) There is a first step of calculation of the interferogram of a relative pixel P.sub.ij according to the equation:
I.sub.ij=s.sub.ij*s.sub.(i-1)j.sup.*

(13) where s.sub.ij is the complex number representing the focused radar data of the j-th pixel of the i-th image and s.sub.ij.sup.* is the complex conjugate of s.sub.ij.

(14) There is then a step of calculation of a coherence value γ.sub.ij arranged to represent the quality of the phase information supplied by the j-th pixel at the i-th cycle. In particular, the coherence value γ.sub.ij is arranged to represent the degree of correlation of the phase information provided by a j-th pixel at the i-th cycle with the phase information provided by the same pixel in the previous cycle.

(15) In one embodiment of the invention, the coherence value can be a spatial coherence value calculated considering the cycle i-th and the previous cycle by the equation:

(16) ${\gamma }_{ij}=\frac{{.Math.s_{ij}*s_{\left(i-1\right)j}^{*}.Math.}_{spat}}{\sqrt{{.Math.s_{\left(i-1\right)j}*s_{\left(i-1\right)j}^{*}.Math.}_{spat}{.Math.s_{ij}*s_{ij}^{*}.Math.}_{spat}}}$

(17) where .sub.spat is the spatial media mathematical operator operating in a neighbourhood of the j-th pixel. For example, it can be considered a neighbourhood of 5×5 pixel.

(18) In a subsequent step, the calculated spatial coherence value γ.sub.ij is compared with a predetermined minimum spatial coherence value γ.sub.min. Each pixel P.sub.ij is also associated with a coherence coefficient m.sub.ij which can assume a value m.sub.ij=0 or a value m.sub.ij=1.

(19) In case that γ.sub.ij<γ.sub.min, a coherence coefficient value m.sub.ij=0 is assigned to said pixel P.sub.ij, whereas, in case that γ.sub.ij≥γ.sub.min, a coherence coefficient value m.sub.ij=1 is assigned to said pixel P.sub.ij.

(20) There is then a step of interferometric calculation of a displacement value d.sub.ij of each pixel P.sub.ij according to the equation:

(21) $d_{ij}=-\frac{\lambda }{4\pi }{m}_{ij}*\arg \left[I_{ij}\right]$

(22) where λ is the wavelength of the emitted signal by the radar system and arg[I.sub.ij] the argument of the complex number I.sub.ij.

(23) As verifiable by the previous equation, displacement value d.sub.ij is zero in case that m.sub.ij=0.

(24) Finally, there is a step of calculation of a cumulative displacement value D.sub.ij as the sum of the displacement values d.sub.ij in the N cycles preceding the i-th cycle, i.e. according to the equation:

(25) $D_{ij}=\underset{k=i-N}{\overset{i}{.Math.}}\left(d_{kj}\right)$

(26) The method claimed in the present invention, therefore, by assigning a unitary or null value to the coherence coefficient m.sub.ij associated with each pixel P.sub.ij, allows to exclude from the calculation of the cumulative displacement D.sub.ij the pixels that do not have sufficient coherence, i.e. not reliable due to movements of objects with low coherence within the scenario.

(27) For example, the machinery 200 shown in FIGS. 1 and 2A, when turned on, result in objects with low coherence as they vibrate and move very fast with respect to the dimensions of the radar pixels and the scanning time, while the excavation face, for example a tunnel, moves slowly and consistently, and therefore is a highly coherent object. In FIG. 2B it is possible to verify that the zone A, corresponding to the presence of machinery 200 in FIG. 2A, has pixels with low coherence (darker color) as opposed to the pixels of the surrounding zone.

(28) With reference even at FIG. 5, in a variant embodiment of the method according to the present invention, there is also provided an association to each pixel P.sub.ij of a mask coefficient M.sub.ij arranged to assume a value M.sub.ij=NaN or a value M.sub.ij=1, in such a way that the pixel P.sub.ij is not shown on the screen 120 when M.sub.ij=NaN and is instead shown when M.sub.ij=1.

(29) Such mask coefficient value M.sub.ij can therefore determine the non-display of a pixel from the screen, for example, in the event that this pixel has insufficient power (static mask) or has a coherence coefficient value lower than the predetermined threshold for too long (dynamic mask).

(30) In particular, in this variant embodiment, the method provides a static mask filter implemented by means of a first step of calculation of a power value W.sub.ij for each pixel P.sub.ij of a predetermined image S.sub.i, a step of comparison of this power value W.sub.ij with a predetermined minimum power value W.sub.min and, in case that W.sub.ij<W.sub.min, an assignment to the pixel P.sub.ij of a static mask coefficient M.sub.ij.sup.S=NaN.

(31) This filter in the display of the pixels on the screen 120 is defined as a “static” mask filter, since the aforesaid steps are not iterated at each cycle, but are carried out only when required on a specific image. For example, the static mask filter can be realized both on the first acquired image of the scenario and on the following images, and it has an effect on all subsequent images, as long as a new calculation of the signal power is not made, if necessary.

(32) This calculation is carried out using an image acquired in the complete absence of machinery, in order to measure the signal strength at the excavation face. The static mask filter allows not to show the pixels with too low signal strength, which could give false positives, that is to report displacements that in reality are not taking place but which seem to take place due to a high background noise.

(33) Still with reference to FIG. 5, in this embodiment variant, the method also comprises a dynamic mask filter implemented by an iteration at each i-th cycle and for each pixel P.sub.ij of a first step of evaluation of coherence coefficient value m.sub.ij in the N cycles preceding the i-th cycle. Then follows a step of calculation of an over threshold fraction value f.sub.ij as the sum of the values of coherence coefficient m.sub.ij in the N cycles preceding the i-th cycle divided by the number of cycles N, i.e. by means of the equation:

(34) $f_{ij}=\underset{k=i-N}{\overset{i}{.Math.}}\left(m_{kj}\text{/}N\right)$

(35) There is therefore a step of comparison of the over threshold fraction value f.sub.ij with a predetermined minimum over threshold fraction value f.sub.min and, in case that f.sub.ij<f.sub.min, an assignment to the pixel P.sub.ij of a dynamic mask coefficient M.sub.ij.sup.D=NaN.

(36) This filter in the display of the pixels on the screen 120 is defined as a “dynamic” mask filter, since the aforesaid steps are iterated at each cycle, preventing the display of pixels considered as unreliable as they have had insufficient spatial coherence for several consecutive cycles.

(37) This allows to exclude from the image pixels that could give false negatives, that is to report that no movements are taking place, when in reality they are happening.

(38) As schematized in FIG. 5, if one of the conditions M.sub.ij.sup.S=NaN or M.sub.ij.sup.D=NaN is present, there is a mask coefficient M.sub.ij=NaN and therefore the corresponding pixel are not shown on the screen 120.

(39) The static and dynamic mask filters therefore allow to view on the screen 120 only the truly reliable pixels, providing the operator with an immediate understanding of the reliability of the image. In FIG. 3 it is possible to see a representation on the screen of the pixel displacement value projected on a three-dimensional map obtained by laser scanning of the scenario. In particular, zone A corresponds to a zone in which the pixels have low coherence and therefore are not displayed on the map, while zone B shows pixels that are having a high displacement. The pixels of zone B have high coherence, therefore it can be excluded that it is a false positive and the measurement of the displacement is reliable.

(40) The foregoing description some exemplary specific embodiments will so fully reveal the invention according to the conceptual point of view, so that others, by applying current knowledge, will be able to modify and/or adapt in various applications the specific exemplary embodiments without further research and without parting from the invention, and, accordingly, it is meant that such adaptations and modifications will have to be considered as equivalent to the specific embodiments. The means and the materials to realise the different functions described herein could have a different nature without, for this reason, departing from the field of the invention. it is to be understood that the phraseology or terminology that is employed herein is for the purpose of description and not of limitation.