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On the Use of Transponders as Coherent Radar Targets for SAR Interferometry Pooja S. Mahapatra, Student Member, IEEE, Sami Samiei-Esfahany, Student Member, IEEE, Hans van der Marel, and Ramon F. Hanssen, Member, IEEE

Abstract— Monitoring ground deformation using SAR interferometry (InSAR) sometimes requires the introduction of coherent radar targets, especially in vegetated nonurbanized areas. Passive devices such as corner reflectors were used in such areas in the past. However, they suffer from drawbacks related to their large size and weight, conspicuousness, and loss of reliability because of geometric variations as well as material and maintenance-related degradation over several years of deployment. The viability of smaller, lighter, and less conspicuous radar transponders as an alternative is demonstrated via two field experiments: validation tests in a controlled environment, and operational performance for monitoring landslides in a heavily vegetated area. Comparison of 113 transponder-InSAR observations with independent validation measurements such as leveling and the global positioning system yields an empirical precision range of 1.8–4.6 mm, after outlier removal, for double-difference (spatial and temporal) transponder phase measurements in the radar line of sight, for Envisat and ERS-2. Index Terms— Corner reflector, geodesy, interferometry, measurement errors, persistent scatterer, phase measurement, quality control, synthetic aperture radar, transponder.

I. I NTRODUCTION

S

AR interferometry (InSAR) has emerged over the last decade as a technique capable of precise (subcentrimetric) measurements of ground deformation from space. The measurement points are radar scatterers that are phasecoherent over a period of time [1], such as buildings, roads, or stable rock outcrops, which we call persistent scatterers (PS). Although this technique has found wide application over several regions globally, there are still some limitations. PS form a geodetic network of opportunity, meaning that the exact location of PS measurement benchmarks is not under our control. This makes it difficult to determine a priori, i.e., before acquiring ∼20 SAR images, whether a particular area, for instance a vegetated landslide-prone hillside, can be monitored. Furthermore, ground deformation phenomena can occur in nonurbanized areas with few stable point targets, leading to low PS density. Therefore, for reliably and effectively monitoring of such areas using InSAR, measurements at opportunistic PS points alone may be insufficient.

Manuscript received December 6, 2012; revised March 4, 2013; accepted March 22, 2013. The authors are with the Department of Geoscience and Remote Sensing, Delft University of Technology, Delft 2628 CN, The Netherlands (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TGRS.2013.2255881

There are two possible approaches toward increasing InSAR measurement density. First, algorithmic improvements can be made to extract information not only from stable point-like targets, but also from resolution cells that are subject to temporal and geometrical decorrelation, referred as distributed scatterers (DS) [2]. DS may be desert areas or cultivated lands with short vegetation, for instance. Examples of such algorithms are given in [2]–[6]. These algorithms will be aided by upcoming satellite missions with shorter repeat cycles and narrower orbital tubes, which would further limit the temporal and geometrical decorrelation between acquisitions. Even so, coherent DS are not guaranteed to be present everywhere; there may still be areas that heavily decorrelate between SAR acquisitions, such as forests, from which no coherence information can be extracted. This points us toward the second approach, in which amplitude- and phase-stable radar scatterers are deliberately installed in such highly decorrelating areas. By doing so, one can additionally have some design control over the location of measurement points. Our paper focuses on the use of active radar transponders in this second approach. There has been some research in the recent years toward developing transponders for deformation monitoring [7]–[11], but experiments such as [12] and [13] have shown poor or partial agreement between transponder-InSAR and validation measurements. In this paper, we will demonstrate the applicability of a low-cost radar transponder for monitoring deformation and derive an estimate for the measurement precision (standard deviation). This paper is structured as follows. Section II compares and contrasts the utility of corner reflectors and active transponders, and details the characteristics of a transponder designed for deformation monitoring. It then discuss two field experiments performed to validate transponder use. Section III describes the methodology used in these experiments. The first experiment was conducted in a controlled environment in Delft, the Netherlands, where transponder-InSAR deformation measurements are compared with those using corner reflectors. Optical leveling is used for validation. The second experiment is performed in a vegetated landslide-prone area in the Slovenian Alps. Here, InSAR deformation measurements using transponders from an operational viewpoint are compared with those using collocated global positioning system (GPS) receivers. We discuss the results of both the experiments in Section IV, and conclude with an overall analysis in Sections V and VI.

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II. BACKGROUND A. Corner Reflectors The precision and reliability of corner reflectors were validated via many experiments conducted in the past [14]–[18]. Some of their advantages are that they are conceptually simple and can be constructed quite economically. They do not require a source of power, and do not possess electronic components whose performance could decay or drift over time. Corner reflectors suffer from a few drawbacks. They are large and heavy (particularly for longer wavelengths such as C-band), making them cumbersome to deploy especially in poorly accessible areas. Their autonomous motion (settling effect due to their weight) may contribute to the deformation signal being measured. For long-term deployment spanning several years, these large structures can be disturbed or geometrically altered by weather or thermal conditions, fauna, or even by vandalism or theft. They require protection from the accumulation of snow, rain and general debris, and/or need periodic maintenance. Additionally, only ascending or descending satellite passes can be used with a fixed reflector setup. Corner reflectors need to be relatively large to return sufficient power back to the satellite. Active devices such as radar transponders, however, can be more compact to achieve the same radar cross-section (RCS); a transponder can be of the size of a shoe box for the same RCS as a trihedral corner reflector with a side of around 1 m [19].

Transponders have several advantages over corner reflectors. They can be compact, lightweight (< 4 kg), and inconspicuous. They may be sealed, function autonomously and over a wide temperature range with internal power for more than a year, and are less susceptible to environmental impact such as strong winds, precipitation, and debris accumulation. Hence they require little or no maintenance; visits would only be required to change/charge the battery, check for clock drift, or upload a new SAR acquisition schedule, if needed. Moreover, since a transponder is transmitter-specific and only turned on at the time of the satellite overpass, it offers little interference to other radar or radio targets. Transponders can be used for both ascending and descending satellite modes in a single fixed setup, providing two components of motion vector as well as doubling the frequency of measurements. Since the signal frequency can be preprogrammed, they can be used for various C-band SAR sensors in a single setup. A limitation of current transponders is battery maintenance: the battery needs to be recharged once in several months, and may eventually need replacement if deployed over several years. This may be circumvented by the use of external power sources such as small solar panels. Also, the operational use of transponders may require transmission licenses, which vary across national boundaries [29]. Despite these limitations, transponders can be a more practical alternative for InSAR to corner reflectors, as long as phase stability is ensured.

B. Active Radar Transponders

C. Transponder Hardware

Radar transponders were used extensively in the past for SAR external calibration, both radiometric [20]–[24] and geometric [25], [26], but calibration transponders are expensive (of the order of several hundred thousand euros [27]) because of the power stability needed for calibration. For example, Sentinel-1 specifications are power accurate up to 1 dB, and therefore the calibration should be accurate to around 0.1 dB (equal to 3 σ ), with an RCS of around 70 dBm2 [27]. However, if there is a less stringent requirement on amplitude precision or stability, transponder cost can be lowered dramatically, down to a thousand euros, or even less if produced in large quantities [28]. A transponder designed for deformation monitoring operates as follows. It wakes up from sleep mode according to a preprogrammed schedule. When it is illuminated by the radar satellite, it receives the signal on a receiver antenna, and instantaneously retransmits a band-pass filtered and amplified version of the received signal on the transmit antenna. After the satellite overpass, the transponder enters sleep mode again. Being active devices, transponders face the undesirable possibility of their electronic component performance drifting/decaying over time. Therefore, the use of transponders for geodetic applications heavily depends on their short- and longterm phase stability (reliability) and precision in the relevant operating and environmental conditions. In other words, it is important that the transponder transmits a signal with the same frequency and a constant phase relationship with the received signal from the satellite, for all overpasses.

The prototype transponder used in this study consists of receiving and transmitting antennas, a phase-stable amplification chain designed for providing around 40 dB of gain (equivalent to an RCS of around 29 dBm2 ) and the means to power and control the unit. It has four C-band microstrip transmit and receive antenna arrays, and radio frequency (RF) switches control the received and transmitted signals from the satellite during overpass. The switching is programmed for signal throughput in vertical or horizontal polarization for the west- and east-pointing antennas. Similar switches also control the selection of switched bandpass filters designed to be compatible with Envisat/ERS or Sentinel-1/Radarsat-2. DC power is provided via a rechargeable deep discharge lead acid battery, and alternative options with solar panels may also be implemented. Transponder design addresses two key technical issues [28]: 1) maintenance of phase stability in all circumstances; and 2) isolation between receive and transmit channels. Phase stability implies that the phase relationship between received and transmitted radar signals remains constant over successive satellite acquisitions, irrespective of operating temperature or other changing ambient conditions. This is implemented by two means: selection of phase-stable components in the amplification chain, and calibration of residual variations (for example, with temperature). To avoid cross-coupling between the receive and transmit channels, over 70 dB of isolation is required between the receive and transmit antennas. Again, designing to avoid RF propagation and specific mitigation

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Fig. 2. On-site arrangement of devices on a Google Earth map. Triangles: corner reflectors. Rectangles: transponders. Red lines: leveling loops.

the corner reflector, which gives us an indicative transponder RCS of 32 dBm2 . This is equivalent to a corner reflector of L = 1 m. As mentioned before, it is of paramount importance in geodetic applications to ensure the phase stability of transponders. We will now describe the methodology followed in two field experiments performed toward this objective. Fig. 1. Example signals measured in the laboratory, from a corner reflector of L = 44 cm (black line), and from a transponder in Envisat/ERS (red line) and Sentinel-1/Radarsat-2 (blue line) bands.

III. M ETHODOLOGY A. Transponder Setup

steps prevent the feedback that otherwise disturbs phase stability. Transponders may need to be left unattended for extended periods, which requires a protective housing: it is currently designed for operation between −10 and +40 °C. Low power consumption is achieved by turning the units on for short windows around satellite overpasses, requiring a local clock to be synchronized versus satellite overpasses. The transponder microcontroller reads both user-programmed calendar and real-time clock information to synchronize with satellite overpasses, and maintains synchronization by means of a commercial quartz oscillator. The 3-dB beamwidth of the transponder in azimuth and elevation directions is around 20° and 40°, respectively. For comparison, a trihedral corner reflector has a 3-dB beamwidth of around 40° in both directions [30], and is therefore less sensitive to azimuth pointing errors than a transponder. D. Laboratory Tests Laboratory tests are performed on the transponder to measure its RCS. Transmitter and receiver horn antennas were aligned with respect to the transponder within its beamwidth, at a distance of 8.7 m. A continuous-wave signal sweep between 5.1 and 5.7 GHz at −18 dBm was emitted from the transmitter-horn to simulate a satellite signal. The signal received from the transponder at the receiver-horn is corrected for the background signal, noise-filtered and visualized. The same setup and procedure is used with a trihedral corner reflector made of three isosceles right triangles, of isosceles side length L = 44 cm. Fig. 1 shows the received power from the corner reflector and the transponder (in its two bands of operation). The maximum RCS of a trihedral corner reflector is given by [30] 4π L 4 (1) σmax = 3λ2 where λ is the radar wavelength. The maximum RCS of the corner reflector is therefore calculated to be around 17 dBm2 . From Fig. 1, the transponder is around 15 dB stronger than

1) Delft–Controlled Validation Experiment: A field experiment comprising three transponders (T1, T2, and T3) and two corner reflectors (C1 and C2) was set up in a pasture used for dairy farming in Delft, as shown in Fig. 2. The area is chosen because of the flatness of the ground (to exclude topographic phase contribution), low background clutter, and some amount of surface dynamism (swelling and shrinkage of peat), in addition to logistical convenience. The experiment involved capturing the relative motion between transpondercorner reflector pairs with both InSAR and leveling, to check whether InSAR measures the same deformation signal as leveling does, and if so, to what precision. Device pairs were identified as T1-C2, T2-C1, and T3-C1. Leveling between these pairs (Fig. 2) was performed shortly before or after the ERS-2 satellite overpasses, usually within 24 h. One of the transponders (T3) was subjected to an intentional displacement, to validate the ability of InSAR to capture this motion. 2) Slovenia–Validation of Operational Performance: To validate transponder operation in a practical case of deformation monitoring, a landslide site was chosen in a heavily vegetated area in the Slovenian Alps (Figs. 3 and 4). The landslide is known to have produced historical debris flows, with the potential for future slides presenting a risk to the village in the valley [31]. One reference and two landslide points were selected for this experiment, with a further location across the Sava fault chosen for tectonic application (Fig. 3). At each of these locations, a transponder and a GPS receiver mounted on a common baseplate is installed, as shown in the inset of Fig. 3. This ensured that the InSAR and GPS observations are collocated, i.e., that the two independent techniques are measuring the same deformation signal. B. InSAR Measurements Interferograms are created, in both experiments, using pairs of available SAR images. The phase value φims of a pixel i in an interferogram is an interferometric phase difference

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Fig. 4. Fig. 3. Potoška Planina site near the village of Koroška Bela, Slovenia, showing the approximate boundaries of the slipping area (translucent white polygon) and the terrain type on a Google Earth map. Measurement (red dots) and reference (blue dot) locations are marked. Inset: transponder and GPS receiver on a common baseplate, to ensure collocated measurements.

between the corresponding pixels at master time m and slave time s. However, this phase value is wrapped, and therefore meaningless. The first interpretable phase observation is the double difference (in time between m and s, and in space between i and j ). Therefore, InSAR observations require both a temporal and a spatial reference [32], [33], and we denote this interferometric double-difference phase as φijs , where s = 1, 2, . . . , (K − 1) and K is the number of SAR acquisitions. Thus ⎡ m⎤ φi ⎢   φis ⎥ ⎥ φijs = 1 −1 −1 1 ⎢ (2) ⎣ φ mj ⎦ . s φj Including its wrapped nature, this double-difference phase φijs can be quantified as [33] Bi⊥ 4π s 4π Hij + φisjatmo dij − λ λ Rim sin θim

 4π Bi⊥ + f φsorbit ξijm , ηijm + ηm m λ Ri tan θim ij

m 2π m s f DC,i − f DC,i ξij + n sij + (3) v where aijs is the integer ambiguity between points i and j , dijs is the radar line-of-sight deformation between points i and j and times m and s, Bi⊥ , Rim , θim are the perpendicular baseline, Range, and incidence angle, respectively, for point i , Hij is the (residual) topographic height between points i and j , φisjatmo is the atmospheric signal, f φsorbit is the (residual) orbital trend, m s f DC,i , fDC,i are the Doppler centroid frequencies of master and slave acquisitions, respectively, v the satellite velocity, ξijm , ηijm the subpixel positions in azimuth and range respectively, and n sij includes measurement noise and processinginduced errors. φijs = −2πaijs −

Elevation contour map of the Potoška Planina site shown in Fig. 3.

1) Delft Experiment: The experiment spanned the duration of the ERS-2 Ice-Phase Mission (before satellite decommissioning, Apr–Jul 2011), where SAR images were acquired with a three-day repeat cycle. Single-master interferograms are generated for 19 SAR images for which the corresponding leveling is performed. The master (13 May 2011) is chosen based on maximal stack coherence, which is a function of perpendicular and temporal baselines and Doppler centroid frequency [34]. InSAR double differences are computed for transponder-corner reflector pairs using (2), with 13 May 2011 as the time reference. In (3), aijs is solved using a testing procedure, described in Section III-E; Hij is estimated from leveling; φisjatmo is regarded to be less than 1–2 mm, due to the short device distances (< 100 m) [35]; f φsorbit is rendered negligible for the same reason; ξijm , ηijm are determined by oversampling by a factor of 32; and n sij is assumed zero-mean. The only unknown, deformation dijs , can therefore be estimated. 2) Slovenia Experiment: Envisat ASAR images were acquired in two tracks (108 and 381) in the periods Feb 2011–Mar 2012 (14 images) and Mar 2011–Dec 2011 (nine images), respectively. This data set was acquired after the orbital maneuver of Oct 2010, which implied drifting perpendicular baselines at the Slovenian latitude [36], as visible in the baseline plots of Fig. 5. Small baseline (SBAS) interferograms are therefore created for both Envisat tracks, and time-series InSAR processing is performed [3], [4]. The topographic phase is removed using an SRTM 3-arcsecond DEM. InSAR double differences are computed for transponder pairs using (2), with time reference to 01 August 2011 (Track 108) and 21 July 2011 (Track 381). Therefore, aijs is solved by InSAR phase unwrapping and the testing procedure described in Section III-E; Hij, φisjatmo , and f φsorbit are estimated during the SBAS InSAR processing; and n sij is assumed zero-mean. ξijm , ηijm are not estimated because of the short perpendicular baselines chosen and the stability of the Envisat Doppler centroid (unlike ERS-2 in the Delft case, which was operating in its zero-gyro mode [37]).

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transponder-InSAR double differences, as ⎡ m⎤ ρi ⎢   ρ mj ⎥ ms ⎥ = 1 −1 −1 1 ⎢ dij,GPS ⎣ ρs ⎦ i ρ sj

Fig. 5. Baseline plots of the available Envisat ASAR data and small baseline combinations for Track 108 (left) and Track 381 (right) over Slovenia. The SAR acquisitions are marked with red circles, and the green lines denote the small baseline combinations.

C. Validation Measurements 1) Leveling in Delft: Optical leveling was performed using a Leica NA3003 instrument shortly before or after most satellite overpasses, usually within 12 h. For comparison with InSAR double differences, leveling double differences in radar line of sight are derived from leveling height difference measurements h ij as s dimj ,lev

= cos θinc



    h m ij 1 −1  h sij

(4)

where m  and s  are the leveling measurement epochs closest to the InSAR master and slave times, respectively, i and j are the two leveling points (in this case, a bolt on the transponder platform and the apex of the corner reflector, respectively), and θinc is the radar incidence angle. The leveling double differences are thus converted into the radar line of sight assuming no horizontal deformation; a valid assumption since the reflectors and transponders were dug 20–50 cm into the ground with no cause for horizontal deformation over three-day intervals. Additionally, the meadow chosen was a secure site, meaning that extraneous sources of (horizontal) deformation could be ruled out. Campaign GPS measurements also confirmed this assumption. Based on the closing errors of the leveling loops, the standard deviation is estimated to be 1.4 mm for a single height difference measurement converted to radar line of sight, which propagates to a precision of 2 mm for double differences. This includes observational inaccuracies that may have crept in during the surveys due to, for example, windy or rainy conditions. The higher closing errors on such days are accounted for in the evaluation, see Section III-E. 2) GPS in Slovenia: For the four installed GPS receivers (collocated with transponders), station coordinates are estimated in ITRF2008/IGS08 on a daily basis. The daily NorthEast-up solutions are converted into double differences in the radar line of sight for comparison with the corresponding

(5)

where m and s are the GPS measurement dates corresponding to the InSAR master and slave dates, respectively, i and j are the two GPS receivers, and ρ is the North-East-up solutions converted into radar line of sight. The formal standard deviations are estimated during daily processing to be below 0.5 mm in north and east directions, and 1.5–2 mm in the up direction. These standard deviations are on the optimistic side because they only represent the internal accuracy during the processing. In particular, they ignore the effect of long periodic and systematic errors. Instead of the formal standard deviations, the daily station repeatability (root mean square error of the daily station coordinates after fitting a linear trend) can be considered as an indicator of the quality of the GPS solution. Compared with the formal errors, which tend to be too optimistic, the repeatabilities are overbounding the GPS errors and are on the pessimistic side. For the installed receivers in Slovenia, the repeatability for the north and east is 2–3 mm, and 5–7 mm for up. A moving average block filter of fortnightly length is applied to the GPS double differences converted to the radar line-of-sight, in order to reduce the noise (due to carrierphase multipath, different horizon masks, and so on) in the GPS time series that is not averaged out on a daily basis. Based on the conservative formal standard deviations and the pessimistic station repeatabilities, we estimate the standard deviation of the GPS measurements to be around 3 mm in the radar line-of-sight direction, which translates to a doubledifference standard deviation of 4.3 mm. D. Estimation of A Priori Transponder Precision InSAR measurement precision depends on the physical properties of the radar scatterer, uncertainties in identifying the phase centers, and interference due to surrounding clutter. Therefore, it is difficult to estimate the stochastic model of InSAR observations a priori. However, assuming stationary stochastic behavior of transponder surroundings, the signalto-clutter ratio (SCR) can be computed, which is related to the phase variance of a single SAR observation, σφ2 , by [33] σφ2 =

1 . 2 × SCR

(6)

The transponder SCR is estimated by taking the clutter to be the average intensity of four quadrant areas around the transponder that are not affected by the transponder sinc sidelobes in range and azimuth directions, and the signal to be the integration of the transponder intensity sinc pattern (in both range and azimuth) corrected for clutter [38], [39]. The average transponder SCR is calculated to be 14.3 dB. From this, the phase standard deviation for a single SAR observation

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is estimated as 0.14 rad, which corresponds to a doubledifference line-of-sight measurement standard deviation of 1.2 mm. We take this to be the a priori transponder precision. E. Estimation of A Posteriori Transponder Precision The a priori transponder double-difference phase precision, derived from its SCR, can be further refined by comparing the transponder-InSAR deformation measurements with the corresponding validation measurements for both the experiments. Therefore, the a posteriori transponder precision is estimated by using independent external validation measurements, leveling in the Delft case, and GPS in the Slovenia case. 1) Functional and Stochastic Models: If the stochastic vector y of p observations bears a known linear relationship with the vector x of q unknown parameters, we may write a model of observation equations as E{y} = Ax; D{y} = Q y

(7)

where A is the p × q design matrix, Q y is the p × p variancecovariance (VC) matrix of the observations, and E and D are the expectation and dispersion operators, respectively. We assume the null hypothesis that InSAR and the validation techniques (leveling or GPS) measure the same deformation signal dijms , with a possible offset b between their time series owing to the bias introduced by the InSAR and validation measurement uncertainties at reference time. Therefore, the functional and stochastic models of our observations can be written as    ms   ms  d ij, InSAR dij I 1 = H0 : ms d ij, val I 0 b   Q y,InSAR 0 Qy = (8) 0 Q y,val where H0 is the null hypothesis, I is the identity matrix, ms d ms ij,InSAR and d ij,val are the InSAR and validation double differences, respectively, Q y is the overall VC matrix of all the observations, and Q y,InSAR and Q y,val are, respectively, the a priori VC matrices of InSAR and validation measurements separately. Q y,InSAR is derived from the a priori transponderInSAR double-difference precision, and Q y,val is derived from the estimated line-of-sight-converted leveling and GPS double-difference precisions of 2 and 4.3 mm, respectively. Q y,InSAR and Q y,val also take into account the spatio-temporal covariances between observations. Additionally, in case of leveling, measurements with a higher closing error are given proportionally lower weights. The best linear unbiased estimate (BLUE) of y is given by [40] −1 T −1 yˆ = A(A T Q −1 (9) y A) A Q y y. 2) Hypothesis Testing: We use the overall model test (OMT) [41] to determine whether the null hypothesis is accepted. The OMT test statistic is given by TOMT =

ˆ eˆ T Q −1 y e p−q

(10)

where eˆ is the vector of residuals y − yˆ , and the difference between the number of observations and unknowns, p − q,

Fig. 6. Comparison between InSAR and leveling double differences in the radar line of sight. From top to bottom: device pairs T1-C2, T2-C1, and T3-C1.

Fig. 7. Comparison between T1-C1 and C2-C1 double differences over an arc length of around 450 m.

is the redundancy. TOMT should be close to 1 for H0 to be accepted. Rejection of H0 in the OMT can be due to the presence of large errors, anomalies or disturbances, or because the models (either functional or stochastic) fail to represent the measurements. In Slovenia, the GPS receiver was located on the same baseplate as the transponder, and collocated InSAR and GPS measurements were made at the time of satellite overpass. In the Delft case, leveling was usually performed within 12 h before or after the satellite overpass (which was at midnight). It can therefore be assumed that in both cases, InSAR and

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Fig. 8. Comparison between InSAR and GPS double differences in radar line of sight for Envisat track 108 (left) and track 381 (right). From top to bottom: device pairs T1-Ref, T2-Ref, and T3-Ref. TABLE I E MPIRICAL A P Location Slovenia Slovenia Delft

  P RECISION (σ ) OF T RANSPONDER-I N SAR D OUBLE D IFFERENCE P HASE M EASUREMENTS IN R ADAR L O S

Satellite Envisat (track 108) Envisat (track 381) ERS-2

Device Pairs Transponder-transponder Transponder-transponder Transponder-corner reflector

#InSAR observations 34 25 57

validation techniques are measuring the same deformation signal. Hence, our functional model is correct, and failure of the OMT can only be attributed to the presence of outliers and/or an incorrect stochastic model. 3) Ambiguity Resolution, Outlier Detection, and Variance Component Estimation: We use the w-test [41] data snooping technique to check each observation for a large error (outlier). Since the w-test statistic is normally distributed with zeromean and standard deviation equal to 1, we define an outlier to be an observation that yields a w-test statistic value larger than 2. The term aijs in (3) is also solved using the w-test; the value of aijs that gives φijs ± 2πaijs the minimum w-test statistic is chosen to be the integer ambiguity. If a large number of outliers are detected, we do not remove them, but estimate a new value of InSAR standard deviation using the technique of least-squares variance component estimation (VCE) [42], [43]. We then check again for outliers using the new

σall observations [mm] 4.9 4.6 6.7

#outliers 1 0 2

σafter outlier removal [mm] 1.8 4.6 3.9

value of InSAR standard deviation, and remove these outliers, if any. The final a posteriori InSAR double-difference standard deviation is determined by applying VCE again on the subset of observations after outlier removal. The following section summarizes the results obtained from both the experiments by applying the above methodology. IV. R ESULTS A. Delft Experiment The comparison between leveling and InSAR double differences in the radar line-of-sight for the three device pairs is shown in Fig. 6. 1) A Posteriori Transponder Precision: For ERS-2 data, the transponder-InSAR double-difference standard deviation in the radar line of sight estimated by applying VCE on all the 57 observations is 6.7 mm, After detecting and removing two outliers, the estimate drops to 3.9 mm.

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Fig. 9. Scatter plot of 113 transponder-InSAR and validation (leveling or GPS) measurements from the Delft and Slovenia experiments. The overall correlation coefficient is 0.62.

2) Long-Arc Comparison: As can be seen in Fig. 2, transponder T1 and reflector C2 are of comparable distances from reflector C1 (∼450 m). Assuming that the deformation in the vicinity of T1 and C2 was spatially correlated, i.e., T1 and C2 moved in the same way compared with C1, if the double differences between the transponder-reflector and reflector-reflector pairs match, we can infer that the transponder behaves like the corner reflector, though the converse may not necessarily be true. Fig. 7 shows this comparison. It is observed that the transponder-reflector and reflectorreflector double differences follow similar trends. The standard deviation of the difference between the T1-C1 and C2-C1 measurements is 5.0 mm. Assuming that the corner reflector and transponder have comparable precision levels, the transponder double-difference standard deviation is then 3.5 mm or better, since the difference also includes the relative motion between T1 and C2. B. Slovenia Experiment The comparison between InSAR and GPS time series for the two InSAR tracks and three unit combinations is summarized in Fig. 9. 1) A Posteriori Transponder Precision: Images from two Envisat tracks (108 and 381) were used in Slovenia, and hence the a posteriori transponder double-difference precision is estimated separately for the two different line of sight directions. VCE gives an estimate of 4.9 mm from 34 observations in track 108 and 4.6 mm from 25 observations in track 381. After detecting and removing one outlier in track 108, the transponder-InSAR double-difference precision estimate drops to 1.8 mm. C. Overall Analysis Considering the Delft and Slovenia experiments together, we have 113 transponder InSAR measurements (between two transponders or between a transponder and a corner reflector) which have a corresponding validation measurement either by leveling or by GPS.

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Fig. 8 shows a scatter plot of all the InSAR and validation measurements. The overall correlation coefficient between InSAR and validation double differences is 0.62; this value would be higher if larger deformation signals were being measured, i.e., if the InSAR and validation measurements had higher SNR. The empirical transponder-InSAR double-difference phase measurement precisions are summarized in Table I. The different precision estimates from tracks 108 and 381 of Envisat under very similar conditions can be explained by the different number of SAR images available per track. Owing to large device distances and changes in elevation, the SBAS InSAR processing methodology (including atmospheric and topographic phase estimation) was applied in Slovenia. Track 108 with 14 images therefore yielded better-constrained results than track 381 with only nine images. V. D ISCUSSION In the previous section, we have estimated the a posteriori transponder precision by comparing transponder-InSAR measurements with ground truth validation measurements, i.e., leveling and GPS. It is noteworthy that one cannot discriminate unambiguously between inaccuracies of the transponder and those in the validation measurements, owing to the precision limit of the latter. Additionally, in case of the Delft experiment, leveling was performed within 12 h of the actual satellite overpass, which was around midnight. From Fig. 6, there can be a variability of up to 10 mm over a 3-day period, possibly due to the swelling or shrinking of peat soil in the meadow. This means that the difference in InSAR and leveling measurement times may have contributed to an InSAR-leveling difference of up to 1–2 mm. Additionally, atmospheric delay differences may amount up to a millimeter or two, even for short (100 m) arcs. In the Slovenia trial, errors related to snow or frost on the GPS antenna during the winter months may have crept in. Moreover, the use of radar data from ERS-2 in its zero-gyro mode, Envisat with drifting baselines after orbital manoeuvre in 2010, and relatively few images in each track (therefore lower number of observations for statistical analysis) may also have worsened the transponder precision estimate. Even so, the estimated transponder double-difference phase precision of 1.8–4.6 mm in the radar line of sight is in the similar ballpark as the corresponding corner reflector precision of 1.5–2.6 mm estimated in [15]. The latter used large corner reflectors with approximately three times the SCR of the transponders, and double the number of SAR images, under similar field conditions. It also compares well with other studies that have estimated PS precision to be 5 mm [44], [45] up to 7 mm [46]. To judge the level of significance of the estimated transponder double-difference phase precision, it can be compared with the maximum standard deviation of double-differences of distributed scatterers. This standard deviation follows from the uniform distribution of distributed scatterer phases in the interval [−π, π) [47]  2 λ 1 2 (11) σDS = 48 cos θinc

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where λ denotes the wavelength and θinc the incidence angle of the radar signal. For ERS/Envisat, this standard deviation is ∼9 mm. The estimated transponder double-difference precisions are much lower than this maximum, which shows that these values could not have occurred from a uniformly random distribution. The values presented in Table I can be interpreted as the upper limit of transponder precision estimates, given the information that was available via the two field experiments. A repeated experiment with more precise validation measurements and a longer time-series of data from Radarsat-2 or the upcoming Sentinel mission could provide a more conservative estimate of transponder precision. VI. C ONCLUSION The applicability of active radar transponders for deformation monitoring was demonstrated, both under controlled conditions (a quiet meadow in Delft) as well as in an operational setting (monitoring a landslide area in Slovenia). The Delft experiment (InSAR and leveling) and the Slovenia monitoring case (InSAR and GPS) showed that the empirical standard deviation of transponder double difference phase measurements in the radar line of sight for Envisat and ERS-2 was 1.8–4.6 mm after outlier removal, making a transponder a compact and lightweight alternative to a corner reflector. ACKNOWLEDGMENT This research was performed under the framework of the I2GPS EU project (FP7-GALILEO-2008-GSA-1) and CATO2 (CO2 Capture, Transport and Storage in the Netherlands). The transponders used in this study were kindly made available by SEA Ltd., UK. The authors would like to thank A. Fromberg and C. Prior for their support with transponder operation and troubleshooting. They would also like to thank R. Holley of Fugro NPA, U.K., for designing the transponder/GPS network in Slovenia, and M. Komac, B. Milanic, and their colleagues at the Geological Survey of Slovenia for all the in situ work of device installation and maintenance. Sincere thanks are further due to P. Dheenathayalan, J. Martins, J.M. Delgado Blasco, L. Chang, A. Oyen, M. Arıkan, M. Caro Cuenca, P. Buist, S. Abdikan, S. Liu, A. Hooper, R. van Bree and others from the Delft University of Technology, for their valuable help with setting up the Delft experiment and the frequent leveling campaigns. The contribution of P. Aubry of the electromagnetics laboratory at EWI, TU Delft, is also appreciated. Finally, they thank ESA for providing the ERS-2 Ice-Phase Mission and Envisat ASAR data. R EFERENCES [1] A. Ferretti, C. Prati, and F. Rocca, “Permanent scatterers in SAR interferometry,” IEEE Trans. Geosci. Remote Sens., vol. 39, no. 1, pp. 8–20, Jan. 2001. [2] A. Ferretti, A. Fumagalli, F. Novali, C. Prati, F. Rocca, and A. Rucci, “A new algorithm for processing interferometric data-stacks: SqueeSAR,” IEEE Trans. Geosci. Remote Sens., vol. 49, no. 9, pp. 3460–3470, Sep. 2011.

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[3] P. Berardino, G. Fornaro, R. Lanari, and E. Sansosti, “A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms,” IEEE Trans. Geosci. Remote Sens., vol. 40, no. 11, pp. 2375–2383, Nov. 2002. [4] A. Hooper, “A multi-temporal InSAR method incorporating both persistent scatterer and small baseline approaches,” Geophys. Res. Lett., vol. 35, no. 16, p. L16302, Aug. 2008. [5] F. Rocca, “Modeling interferogram stacks,” IEEE Trans. Geosci. Remote Sens., vol. 45, no. 10, pp. 3289–3299, Oct. 2007. [6] A. Guarnieri and S. Tebaldini, “On the exploitation of target statistics for SAR interferometry applications,” IEEE Trans. Geosci. Remote Sens., vol. 46, no. 11, pp. 3436–3443, Nov. 2008. [7] M. Haynes, S. Smart, and A. Smith, “Compact active transponders for operational SAR interferometry applications,” in Proc. Envisat ERS Symp., 2004, pp. 1–4. [8] P. Russo, A. Rosa, A. D’ippolito, “Transponder having high phase stability, particularly for synthetic aperture radar, or SAR, systems,” U.S. Patent 6 861 971, Mar. 1, 2005. [9] D. Hounam, H. Zwick, and B. Rabus, “A permanent response SAR transponder for monitoring ground targets and features,” in Proc. 7th Eur. Conf. Synth. Aperture Radar. 2008, pp. 1–4. [10] C. Duffell, M. Willis, M. Haynes, and D. Rudrum, “Ground motion detection in rural areas using satellite interferometry,” in Proc. Amer. Soc. Civil Eng., 2006, pp. 1–6. [11] M. Riedmann and M. Haynes, “Developments in synthetic aperture radar interferometry for monitoring geohazards,” Geol. Soc., London, Special Publications, vol. 283, no. 1, pp. 45–51, 2007. [12] M. Willis, “CATinSAR trial-M1 Strelley: Report on trial findings,” Dept. Highways Agency Evaluation, Univ. Texas, USA, Tech. Rep. 4, 2007. [13] J. Hole, R. Holley, G. Giunta, G. Lorenzo, and A. Thomas, “InSAR assessment of pipeline stability using compact active transponders,” in Proc. FRINGE Workshop, 2011, pp. 1–2. [14] A. Ferretti, G. Savio, R. Barzaghi, A. Borghi, S. Musazzi, F. Novali, C. Prati, and F. Rocca, “Submillimeter accuracy of InSAR time series: Experimental validation,” IEEE Trans. Geosci. Remote Sens., vol. 45, no. 5, pp. 1142–1153, May 2007. [15] P. Marinkovic, G. Ketelaar, F. van Leijen, and R. Hanssen, “InSAR quality control: Analysis of five years of corner reflector time series,” in Proc. 5th Int. Workshop ERS/Envisat SAR Interferometry, 2008, pp. 1–25. [16] X. Ye, H. Kaufmann, and X. Guo, “Landslide monitoring in the Three Gorges area using D-InSAR and corner reflectors,” Photogram. Eng. Remote Sens., vol. 70, no. 10, pp. 1167–1172, 2004. [17] Y. Xia, H. Kaufmann, and X. Guo, “Differential SAR interferometry using corner reflectors,” in Proc. Geosci. Remote Sens. Symp., vol. 2, 2002, pp. 1243–1246. [18] C. Froese, V. Poncos, R. Skirrow, M. Mansour, and D. Martin, “Characterizing complex deep seated landslide deformation using corner reflector InSAR (CR-INSAR): Little Smoky Landslide, Alberta,” in Proc. 4th Can. Conf. Geohazards, 2008, pp. 1–4. [19] J. Merryman Boncori, “Error modelling for SAR interferometry and signal processing issues related to the use of an encoding SAR transponder,” Ph.D. dissertation, Dept. Electromag. Syst., Tech. Univ., Lyngby, Denmark, 2009. [20] D. Brunfeldt and F. Ulaby, “Active reflector for radar calibration,” IEEE Trans. Geosci. Remote Sens., vol. 22, no. 2, pp. 165–169, Mar. 1984. [21] A. Woode, Y. Desnos, and H. Jackson, “The development and first results from the ESTEC ERS-1 active radar calibration unit,” IEEE Trans. Geosci. Remote Sens., vol. 30, no. 6, pp. 1122–1130, Nov. 1992. [22] R. Hawkins, L. Teany, S. Srivastava, and S. Tam, “RADARSAT precision transponder,” Adv. Space Res., vol. 19, no. 9, pp. 1455–1465, 1997. [23] H. Jackson, I. Sinclair, and S. Tam, “Envisat/ASAR precision transponders,” in Proc. SAR Workshop: CEOS Committee Earth Observat. Satellites, vol. 450. 2000, p. 311. [24] R. Lenz, K. Schuler, M. Younis, and W. Wiesbeck, “TerraSAR-X active radar ground calibrator system,” IEEE Aerosp. Electron. Syst. Mag., vol. 21, no. 5, pp. 30–33, Apr. 2006. [25] J. Mohr and S. Madsen, “Geometric calibration of ERS satellite SAR images,” IEEE Trans. Geosci. Remote Sens., vol. 39, no. 4, pp. 842–850, Apr. 2001.

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 10

[26] D. Small, B. Rosich, E. Meier, and D. Nüesch, “Geometric calibration and validation of ASAR imagery,” in Proc. CEOS SAR Workshop, 2004, pp. 27–28. [27] P. Snoeij, European Space Agency (ESTEC), private communication, May 7, 2012. [28] A. Fromberg, SEA, private communication, 30 May 2012. [29] (Apr. 2013). International Telecommunication Union, The Radio Regulations, Edition of 2012 [Online]. Available: http://www.itu.int/pub/RREG-RR-2012 [30] D. Michelson, “Radar cross section enhancement for radar navigation and remote sensing,” Ph.D. dissertation, Dept. Electr. Comput. Eng., Univ. British Columbia, MO, USA, 1994. [31] J. Jez, M. Mikos, M. Trajanova, S. Kumelj, and M. Bavec, “Vrsaj Koroska Bela-Rezultat katastroficnih pobocnih dogodkov Koroska Bela alluvial fan-the result of catastrophic slope events,” Geologija, vol. 51, no. 2, pp. 219–227, 2008. [32] R. Hanssen, “Stochastic modeling of time series radar interferometry,” in Proc. Int. Geosci. Remote Sens. Symp., Sep. 2004, pp. 2607–2610. [33] V. B. H. Ketelaar, “Monitoring surface deformation induced by hydrocarbon production using satellite radar interferometry,” Ph.D. dissertation, Dept. Mater. Sci., Delft Univ. Technol., Delft, The Netherlands, Sep. 2008. [34] B. M. Kampes, “Displacement parameter estimation using permanent scatterer interferometry,” Ph.D. dissertation, Dept. Mater. Sci., Delft Delft Univ. Technol., The Netherlands, Sep. 2005. [35] R. F. Hanssen, Radar Interferometry: Data Interpretation and Error Analysis. Boston, MA, USA: Kluwer Academic Publishers, 2001. [36] N. Miranda, B. Duesmann, M. Pinol, D. Giudici, and D. D’Aria, “Impact of the Envisat mission extension on SAR data,” Eur. Space Agency, Paris, France, Tech. Rep. 1, 2010. [37] U. Wegmuller, M. Santoro, C. Werner, T. Strozzi, A. Wiesmann, and W. Lengert, “ERS-2 zero-gyro-mode data application showcases,” in Proc. FRINGE Workshop, vol. 26, 2007, p. 30. [38] A. Freeman, “SAR calibration: An overview,” IEEE Trans. Geosci. Remote Sens., vol. 30, no. 6, pp. 1107–1121, Nov. 1992. [39] A. Gray, P. Vachon, C. Livingstone, and T. Lukowski, “Synthetic aperture radar calibration using reference reflectors,” IEEE Trans. Geosci. Remote Sens., vol. 28, no. 3, pp. 374–383, May 1990. [40] P. J. G. Teunissen, Adjustment Theory; an Introduction, 1st ed. Delft, USA: Delft Univ. Press, 2000. [41] P. J. G. Teunissen, D. G. Simons, and C. C. J. M. Tiberius, Probability and Observation Theory. Dept. Delft Inst. Earth Observat. Space Syst., Delft Univ. Technol., The Netherlands, 2005. [42] A. Amiri-Simkooei, “Least-squares variance component estimation: Theory and GPS applications,” Ph.D. dissertation, Dept. TU Delft, Univ. Technol., The Netherlands, 2007. [43] P. J. G. Teunissen and A. R. Amiri-Simkooei, “Least-squares variance component estimation,” J. Geodesy, vol. 82, no. 2, pp. 65–82, 2008. [44] A. Ferretti, A. Tamburini, F. Novali, A. Fumagalli, G. Falorni, and A. Rucci, “Impact of high resolution radar imagery on reservoir monitoring,” Energy Procedia, vol. 4, pp. 3465–3471, Jan. 2011. [45] A. Pigorini, M. Ricci, A. Sciotti, C. Giannico, and A. Tamburini, “Satellite remote-sensing PSInSAR technique applied to design and construction of railway infrastructures,” in Proc. Ingegneria Ferroviaria, 2010, pp. 1–3. [46] P. González and J. Fernández, “Error estimation in multitemporal InSAR deformation time series, with application to Lanzarote, Canary Islands,” J. Geophys. Res., vol. 116, no. B10, p. B10404, 2011. [47] G. Ketelaar, P. Marinkovic, and R. Hanssen, “Validation of point scatterer phase statistics in multi-pass InSAR,” in Proc. CEOS SAR Workshop, 2004, pp. 27–28.

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Pooja S. Mahapatra (S’06) received the B.E. degree in electronics and communication engineering in 2007, and double M.Sc. degrees in space technology and instrumentation from the Luleå University of Technology, Luleå, Sweden, and Université Paul Sabatier III Toulouse, Toulouse, France, in 2009. She is currently pursuing the Ph.D. degree with the Delft University of Technology, Delft, The Netherlands. She was with the European Space Agency in 2009 for her Master’s thesis work, and before that for internships at the Fraunhofer Ernst-Mach-Institut, Freiburg, Germany, and the Indian Institute of Science, India. Her current research interests include space applications, remote sensing, signal/image processing and geodesy, monitoring ground deformation using satellite radar interferometry, and GPS. Sami Samiei-Esfahany (S’12) was born in Tehran, Iran, in 1982. He received the B.Sc. degree in civilsurveying engineering from the Amirkabir University of Technology, Tehran, Iran, in 2004, and the M.Sc. degree in geomatics engineering from the Delft University of Technology (TU Delft), Delft, The Netherlands, in 2007. He is currently pursuing the Ph.D. degree with the Department of Mathematical Geodesy and Positioning (currently reorganized in Department of Geoscience and Remote Sensing), TU Delft. His studies regard new algorithms in timeseries InSAR processing and optimal estimation of surface displacement induced by gas extraction/injection using satellite radar interferometry, with main focus on stochastic aspects of observations. His current research interests include estimation theory and mathematical geodesy with applications to SAR interferometry and deformation monitoring. Hans van der Marel received the M.Sc. degree in geodetic engineering and the Ph.D. (cum laude) degree from the Delft University of Technology, Delft, The Netherlands, in 1983 and 1988, respectively. He is an Assistant Professor with the Department of Geoscience and Remote Sensing, Delft University of Technology, Delft, The Netherlands. From September 1983 until July 1987, he was a Research Fellow with the Netherlands Organisation for Scientific Research and worked on the scientific data reduction for the astronomical satellite Hipparcos. From 1987 until 1989, he was a Research Fellow with the Netherlands Academy of Sciences. In 1989, he became an Assistant Professor with the Delft University of Technology in Global Navigation Satellite Systems (GNSS), with a specific interest in high-precision scientific and meteorological applications of GNSS. Ramon F. Hanssen (M’04) received the M.Sc. degree in geodetic engineering and the Ph.D. (cum laude) degree from the Delft University of Technology, Delft, The Netherlands, in 1993 and 2001, respectively. He was with the International Institute for Aerospace Survey and Earth Science (ITC), Stuttgart University, Stuttgart, Germany; the German Aerospace Center (DLR); Stanford University, Stanford, CA, USA (Fulbright Fellow); and the Scripps Institution of Oceanography in microwave remote sensing, radar interferometry, signal processing, and geophysical application development. Since 2008, he has been an Antoni van Leeuwenhoek Professor in earth observation with the Delft University of Technology, where, since 2009, he has been leading the research group on mathematical geodesy and positioning. He has authored a textbook on radar interferometry.