Novel Corner-Reflector Array Application in Essential Infrastructure Monitoring

High-precision monitoring of infrastructure using artificial reflectors is possible with freely available Sentinel-1 data, but large reflectors are needed. We find that a triangular trihedral corner reflector should typically have at least 1-m inner leg length. As such large reflectors are often not feasible for use in urban areas for essential infrastructure monitoring, we designed a multiple corner-reflector array to replace a single corner reflector with an inner leg length of 1 m. In this case, we use four reflectors where each of them is a truncated triangular trihedral with an inner leg length of 0.33 m. We measured interferometric synthetic aperture radar (InSAR) amplitude, phase, and coherence of this reflector array with various configurations of alignments of the array. We find that as long as great care is taken in the relative positioning of the four corner reflectors, so that they constructively interfere, each horizontal or vertical configuration provides the expected amplitude, coherence, and phase stability. Applications of multiple small corner reflectors in urban areas range from essential infrastructure monitoring (e.g., bridges, overpasses, and tunnel constructions), through assessment of structural health of buildings, to monitoring highway and railway embankments. We show that the multiple corner array works when placed in a single InSAR resolution cell, but depending on the application, the number and projection of corner reflectors can be varied, as long as sufficient signal-to-clutter ratio is achieved in the area of interest.

methods have improved our capabilities to monitor large 36 areas with various techniques of different temporal and spatial 37 resolutions. 38 In particular, interferometric synthetic aperture radar 39 (InSAR) is being widely used for ground motion detec-40 tion for various applications ranging from worldwide natural 41 hazard monitoring (e.g., [1]) and early warning (e.g., [2], 42 [3]) through nationwide infrastructure and land observation 43 (e.g., [4], [5]) to small-scale studies of local deformations 44 (e.g., [6], [7]). The Sentinel-1 mission, part of the European 45 Commision's Copernicus program operated by the European 46 Space Agency (ESA), was launched in 2014 and has been 47 providing freely available SAR acquisitions globally ever since 48 (https://www.copernicus.eu/en, accessed on 4 Jun 2021). The 49 Sentinel 1A and 1B satellite pair provides an ascending and a 50 descending coverage at least once every six days over Europe. 51 This mission has furthered applications of InSAR remote 52 sensing due to its reliability, repeatability, and all-reaching 53 coverage. Sentinel-1 is a C-band mission (∼6 cm wavelength) 54 which provides moderate resolution InSAR data compared 55 with the commercial, high-resolution X-band satellite missions 56 (e.g., TerraSAR-X, COSMO-SkyMed). The C-band missions 57 are typically used for global mapping and monitoring and 58 detecting changes in areas with low to moderate penetration. 59 The X-band missions, on the other hand, are traditionally used 60 for urban monitoring and in areas with low vegetation levels. 61 At the C-band, Sentinel-1 InSAR acquisitions are often not 62 coherent enough over rural, vegetated areas to interpret ground 63 motions in these places. To enhance the InSAR amplitudes 64 and measurement accuracy, corner reflectors can be used in 65 these settings. Among the applications of corner reflectors are 66 landslide monitoring [8], [9], land management [10], ground 67 instability observations [11], or calibration of InSAR and other 68 geophysical observations [12]. Based on a literature and corner 69 reflector database review, the size of these corner reflectors can 70 range from a 0.35-m up to 3-m inner leg length depending on 71 the area of interest and the InSAR mission that it is targeted 72 toward. [Red line of Fig. 8(b) shows the measurement of the 73 inner leg length on a triangular trihedral corner reflector.] To 74 use a corner reflector with the Sentinel-1 InSAR mission, the 75 reflector needs to be quite large; Bozsó et al. [13] showed that 76 a triangular trihedral of 1-m inner leg length provides a robust 77 signal for Sentinel-1 [13]. 78 Large corner reflectors may not be suitable for urban 79 applications, as there are often limits on the size of objects 80 that can be attached to buildings or infrastructure such as 81 bridges. In particular, the projection of the reflector can 82 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ be a limiting factor. In this article, we show the results normalized by the area of the illuminated resolution cell [15] where the illuminated area on the ground is where p a and p r are the azimuth and slant range pixel 130 resolutions, respectively, and θ is the local incidence angle.

131
The theoretical RCS, often denoted as σ T , of a triangular 132 trihedral corner reflector that is significantly larger than the 133 SAR wavelength is a function of its size [16] 134 σ T = 4πa 4 3λ 2 (3) Fig. 1. SCR and the corresponding error in phase (blue solid line) and displacement (blue dashed line). The orange line shows the size of a trihedral corner reflector compared with the SCR it produces, assuming a 15.8-dB background clutter amplitude. The black arrows show the following example: to achieve mm-level precision in the displacement measurement, the SCR needs to be at least 10 dB, which corresponds to a trihedral corner reflector with a 1.2-m-long inner leg with the defined background clutter level.
where a is the inner leg of the trihedral corner reflector, and 136 λ is the wavelength of the acquisition.

137
The expected amplitude is calculated from the RCS as The ratio of the RCS of a corner reflector and the power 140 of its background clutter, the signal-to-clutter ratio (SCR), 141 is used to assess the InSAR phase variance [17] and absolute 142 positioning accuracy [18] of point targets, such as corner 143 reflectors [19]. This determines whether a corner reflector's 144 size is sufficient to be used in a certain setting with a particular 145 clutter level.

146
The phase and displacement errors can be theoretically 147 estimated using the SCR as [20], [21], [22] 148 Fig . 1 shows the displacement precision that can be achieved 151 with a certain size of corner reflector as a function of SCR 152 assuming a 15.8-dB background clutter level. This figure and 153 its calculations are based on the Sentinel-1 wavelength of 154 5.55 cm and is representative of the C-band SAR acquisitions; 155 the figure would look different for the X-band or L-band.

156
When designing an experiment with a corner reflector, it is 157 useful to know about the clutter level in the area of installation 158 ahead of planning. To have a large enough reflector to be 159 "visible" in the desired setting, one should achieve a certain 160 level of SCR, which will then give phase and displacement 161 precisions for the intended application. 163 We collected information about corner reflectors that 164 have been placed in various locations around the world and 165 categorized them in terms of their shape, size, and orientation. 166 Most are triangular trihedrals or truncated triangular trihedrals, 167 with the exception of the bar-pattern reflector in China. The were installed before the launch of the Sentinel-1 satellites; in 178 these cases, we processed the earliest available data. Others 179 were installed after 2015; in these cases, we aimed to process 180 the SAR data before and after the installation of the corner 181 reflectors and compared the change in amplitude and phase 182 at their locations. Table I shows the locations, sizes, shape 183 specifications, and references to these corner reflectors. For 184 this section, we relied on other studies that provided us the 185 lat/lon coordinates of the reflectors, and we assume they used 186 GNSS instruments to get the precise position of each reflector.

187
References to each of the study areas are shown in Table I. 188 We obtained the coordinates either from these publications,     These reflectors are too small to stand out from the background with Sentinel-1 with a trihedral inner leg measure of 0.4 m. Red dots mark pixels with one reflector, and blue dots mark pixels with two reflectors placed there. 1) the "stable" and "noisy" pixels and of and 2) the "stable" 224 and corner reflector pixels (Fig. 6. For a complete collection of 225 the phase figures, refer to the Appendix. We expect the latter 226 differential phase signal to be less noisy (i.e., smaller standard 227 deviation from the mean of the series) than that of the former. 228 In cases where corner reflectors were installed after the launch 229 of Sentinel-1, and their size is sufficiently large to be visibly 230 differentiable from the background on the amplitude analysis, 231 we can also observe the stabilization of the phase after the 232 reflector was installed (Fig. 6). 233 We find that a trihedral corner reflector with an inner leg 234 of at least 1 m is sufficiently large to give a stable phase 235 response, and one with an inner leg of up to 0.6 m appears to 236 be too small for the C-band Sentinel-1 acquisitions. We cannot 237 conclude a clear cut-off in size, as we do not have any InSAR 238 data processed for a corner reflector that is between 0.6 and 239 1 m. One example where smaller reflectors (0.35-m inner 240 leg triangular trihedrals) were installed after the launch of 241 the Sentinel-1 mission is a study on the Waterloo Bridge in 242    that these calculations assume the signals' sum constructively.

272
As we discuss later, this depends strongly on the various 273 aspects of the installation.

274
Following studies on the shape of a corner reflector [31],

275
[32], we choose to use triangular trihedral corners, as it proves To carry out various experiments with the four small reflec-283 tors, we attached them to a frame, where they can be placed 284 in a straight line, with an adjustable distance in between them. 285 Each reflector can be rotated and tilted in any direction. A pole 286 is attached to the frame, to which we attached a GNSS antenna 287 for monitoring any movement of the ground below the frame. 288 We took hour-long GNSS measurements during the morning 289 of each day when the Sentinel 1A or 1B satellites acquired 290 data over the area. 291 We also manufactured a large corner reflector with 1.5-m 292 inner leg which was placed on the same field for reference. 293 This was also a truncated trihedral with an actual inner leg 294 length of 1 m. This corner reflector was set up in an "ideal" 295 position facing the line of sight of the ascending satellite acqui-296 sition (a direction of 259 • from north and a tilt of 17.3 • from 297 horizontal). We also acquired hour-long GNSS measurements 298 at this reference reflector at the same time as at the frame 299 of the small reflector. We set up the reflectors on the 9th of 300 November 2020, at University of Leeds Farm, located between 301 Leeds and York in the U.K. (Fig. 9). The exact coordinates of 302 the reference reflector are 53.8658 N, 1.3337 W, and of the 303 four-corner array are 53.8658 N, 1.3322 W. Fig. 10 shows the 304 photographs of the installation of the corner reflectors.

305
The area of the farm is covered by two ascending Sentinel-306 1 tracks; we aimed the reflectors toward track 132. Using 307

310
We installed the reflector array in various configurations, 311 aligning them in range, azimuth, and an arbitrary direction in 312 horizontal setups, as well as aligning them vertically (Fig. 10). 313 We also experimented with a "shadowed" setup where within 314 a vertical setup we moved the four corner reflectors closer 315 to each other. In this case, the lower three reflectors do 316 not have a clear line-of-sight vision of the satellite for the 317 whole area of the reflector. A full list of the various setups 318 and the corresponding dates are shown in Table IV in the 319 Appendix. The alignments in azimuth and range of the frame 320 were obtained using both a compass and a GNSS reference 321 line. The individual corner reflector tilts were measured with 322 a digital inclinometer. During the time of the experiment, the 323 local magnetic declination according to the World Magnetic 324 Model [33] was between 0.35 • and 0.45 • (±0.4 • ) and was not 325 taken into account when orienting the corner reflector array. 326 Alignment requirements are further discussed in Section IV-A. 327 We processed the Sentinel-1 data using the GAMMA-based 328 LiCSAR package as described in Section II-C between July 329 2020 and May 2021. We did not apply any multilooking 330 to preserve the natural resolution of the acquisition. The 331 amplitudes of coregistered SLC images over the area of the 332 farm are shown in Fig. 11. The amplitude values are averaged 333 over the four months before the installation of the corner 334 reflectors (1st July 2020 to 5th November 2020) and during 335 the azimuthal alignment setup (29th November 2020 to 4th 336 January 2021). 337 We extracted the amplitude values for the duration of the 338 experiment from the coregistered SLC images corresponding 339 to the pixels where the reflector array and the reference 340 corner reflector were placed. To find the exact phase and 341 amplitude center of the experimental setup and of the ref-342 erence corner reflector, we oversampled a subset of the SLC 343 images 16 times. Oversampling gives better point density, 344 and therefore we could more accurately pinpoint the phase 345 center of the reflectors [34], [35]. For the reflector array, the 346 oversampled pixel position changes between different setups, 347 but stays the same within each individual setup. We also 348 selected a further two pixels for amplitude and phase analysis: 349 a reference pixel corresponding to a nearby cluster of buildings 350 and a background "field" pixel corresponding to the grassy 351 field between the location of the large corner and the reflector 352 array. Fig. 12 shows the amplitude time series before and 353 during the experiment for the selected four pixels: Reference 354 reflector (blue), four-corner reflector array (red), reference 355 building (yellow), and background field (purple).

356
The vertical lines on Fig. 12 separate the various setups 357 of the four-corner reflector array, while horizontal lines show 358 the expected amplitudes for different cases. We calculated the 359 large reference reflector to have a nominal RCS of 38.38 dB, 360 and the array of four corners 31.34 dB without any shadowing 361 and 28.8 dB with the setup where there is shadowing in 362 the vertical direction 3. We find that the large reflector has 363 an amplitude as expected, except for a dip on 22nd May 364 2021. This was due to water accumulation in the reflector; 365 we manufactured the reflector with a small hole in the middle 366 for drainage, but on this occasion the hole was filled with 367 debris and had to be manually removed. The amplitude of 368 the four-corner array exceeded our expectations both with and 369 without shadowing, perhaps due to the contributions from the 370 frame. 371 We processed the hour-long GNSS measurements with the 372 GAMIT/GLOBK GNSS processing package, using the closest 373   (Table IV). results are shown in Appendix C. 381 We carried out the phase analysis using the same four 382 pixels selected (reference corner, four-corner array, reference 383 building, and background field). Fig. 13 shows the phase 384 differences between these pixels before and during the time 385 of the experiment.

386
To quantify the phase noise, we analyzed the coherence 387 of each setup using the following equation (7) from (16) in 388 Pepe and Lanari [37]:  (Table IV).  Achieving constructive interference between the reflectors 415 is essential. One of the most important factors is spacing 416 between the reflectors, which matters when they are aligned 417 in the range direction, while it can be anything when aligned 418 in the azimuthal direction. Fig. 14 shows how distances can 419 be calculated depending on which configuration the reflectors 420 are placed. It is important to keep in mind that a small error in 421 tilt or orientation can significantly affect the optimal distance 422 between the reflectors. The distance between corner reflectors 423 refers to the distance between the reflecting centers rather 424 than the distance between the physical center of the reflectors. 425 We used sub-mm precision when setting the distance during 426 our experiments with the four-corner array.  Fig. 15).

478
In the course of six months of the experiment, and during 479 the various seasons, we observed that snow, debris, rain, 480 or bird droppings can accumulate in the corner reflectors and 481 can cause a loss of amplitude when not removed on time. 482 We found that the hole in the corner that we cut for drainage 483 is too small when debris accumulates and can cause rainwater 484 to accumulate. A larger hole could solve this problem, or a 485 cover on the corner reflector that would protect it from rain 486 and larger leaves and other debris falling in. This cover 487 would have to let the SAR waves through not to lose the 488 signal.

490
The horizontal alignment in azimuth is ideal in that the 491 spacing between reflectors does not matter, and an array can 492 therefore be produced with a fixed spacing that is suitable for 493 multiple applications. However, the spacing can also be fixed 494 with an alignment in range, with the spacing set for an average 495 incidence angle. The whole array can then be tilted to account 496 for the actual incidence angle at the installation location. 497 This will result in a nonideal orientation for each individual 498 reflector, but a tilt of a few degrees does not significantly affect 499 the RCS.

500
On the side of structures, such as bridges or tall buildings, 501 a vertical setup would be ideal, while on the top of structures 502 or along embankments a horizontal setup is more desirable. 503 Bespoke arrays can be designed for the sides of nonvertical 504 structures.

506
In this article, we present a novel corner reflector array 507 of four small reflectors that can replace a large one and 508 provide equivalent amplitude, phase, and coherence in InSAR 509 applications. It is especially useful in urban areas to monitor 510 essential infrastructure remotely. 511 We analyzed the Sentinel-1 InSAR data acquisitions over 512 corner reflectors of various sizes. We found that to observe a 513 distinct amplitude signal with the C-band Sentinel-1 InSAR 514 measurements, an inner leg of a triangular trihedral reflector 515 needs to be at least 1 m long. We observed that an inner leg 516 of 0.6 m is too small to give a consistently large amplitude 517 to stand out from the background and stable phase signal; but 518 have not established a clear cut-off in between, as we did not 519 process any data over corner reflectors that have an inner leg 520 length between 0.6 and 1 m. The theoretical considerations 521 discussed in Section II-A show that the sufficient size of the 522 corner reflector depends both on the wavelength of the SAR 523 acquisition and the background clutter level of the area of 524 interest. The corner reflector can be truncated as shown by [13] 525 and the 1-m inner leg can be reduced to 0.67 m while still 526 achieving similar amplitudes.

527
Due to its size, a corner reflector projecting 0.67 m may 528 still be too large to be routinely used in urban areas for 529 essential infrastructure monitoring. In some places, there are 530 restrictions on the projection and size of external fixtures (e.g., 531 30 cm on Waterloo Bridge in London), while in other places it 532 would just not be feasible to place such an object, or it would 533 attract too much unwanted attention. We propose to replace 534 one corner reflector with an array of smaller ones within the In this section, we refer to the corner reflectors in Table I. 582 We analyzed the coherence of the corner reflectors at various 583 locations using (7) from (16) in Pepe and Lanari [37].

588
For each corner reflector, we used ten acquisitions, as close 589 to the installation date as possible with the varying availability 590 of the Sentinel-1 measurements. In some cases when the 591 corner reflectors were installed years before the start of the 592 Sentinel mission and their size is not larger than an inner 593 leg length of 0.6 m, it is not possible to say whether we 594 chose the right pixel for the coherence analysis. This clearly 595 shows in the large spread of coherence values and no clear 596 increase with size that we see with the corner reflectors with 597 sizes between 0.3 and 0.6 m. The corner reflectors with a 1-598 m inner leg length (both trihedrals and truncated trihedrals) 599 show a coherence close to 1, with some outliers down to a 600 coherence of 0.6. We do not know whether there was any real 601 movement of the corner reflectors recorded during this time, 602 and therefore cannot subtract any such movement during the 603 coherence analysis. In conclusion, the coherence of the corner 604 reflectors with a 1-m inner leg length seems satisfactory for 605 further analysis. 606 Table III shows the standard deviation values for the phase 607 differences where acquisitions were available both before and 608 after the installation of corner reflectors.

611
In this section, we show the results from the GNSS measure-612 ments that we carried out every six days. These hour-long mea-613 surements took place on the days when the Sentinel-1 track 614 132 acquisitions were made. We processed the GNSS data 615 with the GAMIT/GLOBK GNSS processing package, using 616 the closest permanent GNSS station (LEED) as a reference 617 point [36].

618
Between the different setups, we occasionally repositioned 619 the antenna, to ensure it was not in the SAR line of sight. 620 Large movements on the antenna between setups are due to 621 this manual repositioning.

622
Within each setup (described in Table IV), we calculated the 623 difference between the position of the reference corner reflec-624 tor and the four-corner array. Between the setups, we moved 625 the array and adjusted the position of the GNSS antenna 626 depending on the horizontal or vertical setup; this can be 627 observed in the GNSS results shown in Fig. 33. However, 628 within a single setup we find that there was no movement 629 of the ground that would measure above the noise level of 630 the acquired GNSS data (∼1-2 mm), with the exception of 631 the north component within setup C. This seems to be an 632 outlier as we do not expect any ground motion occurring on 633 the farm, and it is probably due to an atmosphere related 634 error. We also did not measure any settlement of the cor-635 ner reflectors during the experiment and within the various 636 setups.  Tables III and IV. 641 Fig. 16. Average amplitudes of corner reflectors at the Pisciotta area 1, Italy, recorded by the 044A ascending track. Red dots mark pixels with a reflector placed there. Corner reflectors are 0.6-m trihedrals.                  The authors would like to thank the NERC BIGF for 648 providing the GNSS data of the LEED permanent GNSS 649 station. The authors would also like to thank colleagues at 650 the British Geological Survey (BGS) and at the University of 651 Naples for providing detailed information about the installa-652 tion locations and times of the various corner reflectors used 653 in this study, in particular Dr. Alessandro Novellino and 654 Dr. Diego DiMartire. The authors are grateful for the col-655 laboration at the Farm of the University of Leeds, which 656 allowed the placement and continuous monitoring of the corner 657 reflector experiment. Peru, and U.K. Her roles in industry included designing new structures on 864 mega-projects like the Crossrail trainline in London, assessment to upgrade 865 U.K. infrastructure assets, and working on sites to reconstruct housing 866 destroyed by earthquakes. She has also worked in industry research and 867 development roles for developing new solutions and technologies to change 868 the way infrastructure is designed, constructed, and maintained. She spent part 869 of her doctoral training as a Visiting Researcher with the German Aerospace 870 Center (DLR), Oberpfaffenhofen, Germany, in 2019. She is the Isaac Newton 871 Trust Fellow of engineering with the University of Cambridge. Her research 872 interests include integration of remote sensing with structural monitoring to 873 contribute toward sustainable and resilient cities.