New Approaches to Processing Ground-Based SAR (GBSAR) Data for Deformation Monitoring

remote sensing

Article New Approaches to Processing Ground-Based SAR (GBSAR) Data for Deformation Monitoring

Sichun Long 1,2,3,*, Aixia Tong 2, Ying Yuan 2, Zhenhong Li 3,* , Wenhao Wu 1,2 and Chuanguang Zhu 1

1 Hunan Key Laboratory of Coal Resources Clean-Utilization and Mine Environment Protection, Hunan University of Science and Technology, Xiangtan 411201, China; [email protected] (W.W.); [email protected] (C.Z.) 2 School of Resource Environment and Safety Engineering, Hunan University of Science and Technology, Xiangtan 411201, China; [email protected] (A.T.); [email protected] (Y.Y.) 3 School of Engineering, Newcastle University, Newcastle upon Tyne NE1 7RU, UK * Correspondence: [email protected] (S.L.); [email protected] (Z.L.); Tel.: +86-13016178519 (S.L.); +44-779-089-0820 (Z.L.) Received: 29 October 2018; Accepted: 28 November 2018; Published: 1 December 2018

Abstract: In this paper, aiming at the limitation of persistence scatterers (PS) points selection, a new method for selecting PS points has been introduced based on the average coherence coefﬁcient, amplitude dispersion index, estimated signal-to-noise ratio and displacement standard deviation of multiple threshold optimization. The stability and quality of this method are better than that of a single model. In addition, an atmospheric correction model has also been proposed to estimate the atmospheric effects on Ground-based synthetic aperture radar (GBSAR) observations. After comparing the monitoring results before and after correction, we clearly found that the results are in good agreement with the actual observations after applying the proposed atmospheric correction approach.

Keywords: ground-based SAR; TS30; corner reﬂector (CR); deformation monitoring; PS point selection; atmospheric correction

1. Introduction Ground-based synthetic aperture radar (GBSAR) interferometry is a local area deformation monitoring technology that has been rapidly developed over the past two decades. Compared with traditional deformation monitoring methods such as GPS, total station, level, and laser monitoring, GBSAR has a greater observation distance, larger ﬁeld of view, can penetrate rain and fog, can provide continuous space coverage and real-time monitoring, offers a high spatial resolution, and provides up to sub-millimeter measurement accuracy. Compared with spaceborne SAR, GBSAR offers a portable solution with a millimeter accuracy for displacements in a localized area [1–3]. Moreover, the whole data collection and post-processing are simple and convenient, making GBSAR an effective supplement to spaceborne SAR and conventional geodetic monitoring instruments. At present, GBSAR is primarily used to monitor landslides [2,4–6], slopes [7], Volcanic activity [8], and glaciers [9], as well as the deformation of large buildings such as dams [9–12] and towers and bridges [7,13,14]. Antonello et al. employed the InGrID-Lisa GBSAR system to monitor the Stromboli Volcano and through the radar measurement it has been possible to assess the deformation ﬁeld over a large portion of the target area and to differentiate different processes [15]. Noferini et al. used a GBSAR system to monitor a landslide in northeastern Italy and proved that such a system can be used for glacial displacement monitoring [2]. Del Ventisette et al. used GBSAR to monitor the ruin on landslide in Italy for a period of one year and

Remote Sens. 2018, 10, 1936; doi:10.3390/rs10121936 www.mdpi.com/journal/remotesensing Remote Sens. 2018, 10, 1936 2 of 15 concluded that there was a close correlation between surface deformation and rainfall. This showed that such a system could act as an early warning for landslide disasters [16]. Serrano-Juan et al. used GBSAR in the construction of the Lazaglerra Railway Station in Brazil [17]. Inferred GBSAR has a high sensitivity to small displacements and can accurately acquire two-dimensional deformation fields, which can help in understanding the mechanisms underlying control structure deformations and quickly determine a vulnerable deformation disaster area. In China, Yang et al. compared GBSAR observations to conventional measurement techniques and empirically validated the effectiveness and feasibility of using GBSAR to monitor open pit mine slopes [7]. Xu et al. demonstrated the feasibility to use the IBIS-S system to monitor bridge stability [13]. Regarding the selection of the persistent scatter (PS) point, Ferretti et al. defined the ratio between the standard deviation of the amplitude information and the mean of the amplitude information of each pixel in the time series as the amplitude dispersion, and select the PS point according to the amplitude dispersion information of each pixel point [18]. Kampes et al. selected PS points using the amplitude information of the pixel in the SAR image [19]. Adam tried to estimate the signal-to-noise ratio of the target points first, and then used this information to select the PS point, but this method was not effective for some scenes [20]. Hooper et al. proposed a method for selecting PS points using target point phase information by using the spatial correlation features of the interference phase [21]. The principle of GBSAR deformation interferometry is essentially identical to that of Spaceborne SAR [22]. Hence, the approach to selecting PS points for both GBSAR and Spaceborne SAR should be similar [23]. On that basis, this work proposes a joint PS points selection solution based on the average coherence coefficient, amplitude deviation index, estimated signal-to-noise ratio, and displacement standard deviation optimization. To confirm the validity of this approach, the influence of atmospheric effects over water area on bridge deformation monitoring results are experimentally accounted for and corrected.

2. Problem Statement and Basic Theory

2.1. Principle of GBSAR for Deformation Monitoring GBSAR is an active microwave imaging radar, which obtains high-resolution two-dimensional images through the combination of linear frequency modulated continuous wave (FM-CW) technology and SAR processing technique. Using radar interference, the phase and amplitude information of the target back scattered signal can be obtained from the coherent radar image. GBSAR usually observes the target area at a ﬁxed location with a zero spatial baseline. The differential phase ϕm of each pixel can thus be decomposed into

ϕm = ϕdisp + ϕatm + ϕnoise (1) where ϕdisp represents the phase change in the radar line of sight (LOS), ϕatm is atmospheric phase delay, and ϕnoise is noise. The observed phase change in the radar LOS can be expressed as

4π 4π ϕ = d = ·d ·s (2) disp λ λ xyz where d is the displacement in the radar LOS, dxyz is the three-dimensional displacement, and s is the unit vector in the radar LOS.

2.2. PS Point Selection Rules Most of the commonly used PS points selection solutions, such as the amplitude deviation threshold method [18], the coherence coefficient threshold method [20], and the phase deviation threshold method [24] are limited in that they usually only consider one of the characteristics of Remote Sens. 2018, 10, 1936 3 of 15 the PS points. In order to set the thresholds of both the average coherence coefficient and the amplitude deviation index, one possible way is combining the phase deviation, the average coherence coefficient and the amplitude deviation methods and so on. Such that the initial PS points are screened through the mathematical methods (intersection or union) process [24], and then PS points stability is considered [21]. The persistent scatter control (PSC) is further selected from the primary PS points by estimating the signal-to-noise ratio and the displacement standard deviation for construction of network solution. The initial phase ambiguity estimation, the atmospheric influence, and the displacement solution are all determined spatially over time before all of the PS points are integrated into a solution for the overall deformation field [25]. In this paper, we study the average coherence coefficient and amplitude deviation threshold integration method to calculate the temporal coherence coefficient r of each pixel in the image and the average coherence coefficient γ of each pixel in the time series. The appropriate coherence coefficient threshold can then be set to eliminate all PS points with coherence coefficient values that are less than the threshold. At the same time, the mean value mA and the standard deviation σA of each pixel amplitude in the time series are calculated, and the amplitude deviation index DA = mA/σA of each pixel is obtained. Testing several times according to actual conditions by setting a reasonable threshold value Td, a cell with DA ≤ Td is initially selected as the primary PS points. From the primary PS points, other PS points are further selected using an estimated signal to noise ratio (SNR) threshold. The estimated signal-to-noise ratio in a GBSAR system can be calculated using the average amplitude of each pixel and the standard deviation of the amplitude, expressed as

m2 = A SNRA 2 (3) 2σA where mA represents the average amplitude value of each pixel in the actual design size window in the images and σA represents the standard deviation of the amplitude. For the selected PS points, SNRA ≥ SNR points are further selected by setting the estimated SNR threshold. Although the estimated signal-to-noise ratio threshold is higher, the selected points quality is better, but considering the density of the PS points, the threshold setting should not be too high, which should be determined according to the actual situation on site. The Ku-band radar electromagnetic wavelength used by GBSAR is 17.4 mm. If the standard ◦ deviation of phase is σϕdisp = 20 , the displacement standard deviation of monitoring is 0.5 mm. By setting the displacement standard deviation threshold σd, points less than the threshold are selected as PS points, and the speciﬁc displacement standard deviation expression can be expressed as

λ σ = σ (4) d 4π ϕdisp where σd is the standard deviation of displacement and σϕdisp is the standard deviation of phase. Although appropriately setting the PS point selection threshold improves the quality of the PS points, the PS point density needs to be sufﬁcient to ensure continuous data processing after interpolation. Thus, the threshold cannot be set too high and should be determined empirically based on the characteristics of the area being observed.

3. Case Studies

3.1. Case Study 1: Yuehu Bridge Movement Monitoring The Yuehu Bridge used in Case Study 1 is located at Yuehu District, Xiangtan City, Hunan, China. It is a landscape bridge across the artiﬁcial lake. The bridge spans about 70 m and is 11 m wide. The bridge mainly uses pedestrians and non-motor vehicles. The Yuehu Bridge is a reinforced concrete structure located on the lake. No motor vehicle passed over the bridge during the experiment and there was a clear LOS of GBSAR. That is, the emitted radar signal covered the entire Yuehu Remote Sens. 2018, 10, 1936 4 of 15

Bridge without any obstruction between the radar system and the bridge (Figure1). In order to assess the performance of GBSAR, a Leica TS30 total station (nominal distance standard uncertainly: 0.6 mm + 1 ppm) collected measurements prism position data simultaneously. Five corner reﬂectors were ﬁxed on the bridge with a prism being placed near to each CR, as shown in Figure1. GBSAR and Leica TS30 total station is about 170 m away from Yuehu Bridge. The basic parameters of GBSAR Remote Sens. 2018, 10, x FOR PEER REVIEW 4 of 15 during the detection are set as: Ku band, 17.2 GHz; bandwidth is 199.9 MHz; pulse repetition frequency isinterval 375.1 Hz;is 30 range s. The resolution Leica TS30 is 0.5total m; station azimuth measurement resolution is interval 4.5 mrad; is scan10 min interval each time. is 30 s.Finally, The Leica the TS30experiment total station collected measurement 30 sets of intervalLeica TS30 is 10 total min eachstation time. data Finally, and and the monitored experiment 350 collected GBSAR 30 setsimage of Leicascenes. TS30 total station data and and monitored 350 GBSAR image scenes.

Figure 1. 1. ExperimentExperiment site site of the of theYuehu Yuehu Bridge Bridge and associ and associatedated electromagnetic electromagnetic wave reflection wave reflection energy energydiagram. diagram. 3.1.1. PS Point Detection 3.1.1. PS Point Detection In order to reduce clutter interference from other ground objects outside the bridge area, PS points In order to reduce clutter interference from other ground objects outside the bridge area, PS were selected using the new solution described in Section 2.2. The PS points were selected based on points were selected using the new solution described in Section 2.2. The PS points were selected the amplitude, deviation threshold, and coherence coefficient thresholds, and only the Yuehu Bridge based on the amplitude, deviation threshold, and coherence coefficient thresholds, and only the was used for further data processing and analysis. The filter window was set to reduce the impacts of Yuehu Bridge was used for further data processing and analysis. The filter window was set to reduce noise and ensure the continuity of the phase so as to avoid phase unwrapping errors. the impacts of noise and ensure the continuity of the phase so as to avoid phase unwrapping errors. Error sources for GBSAR include observation platform instability, atmospheric delay, system Error sources for GBSAR include observation platform instability, atmospheric delay, system frequency deviation errors, and interference phase errors and so on, among which atmospheric delays frequency deviation errors, and interference phase errors and so on, among which atmospheric represent the largest error [26]. Using the combined optimal selection solution proposed in this delays represent the largest error [26]. Using the combined optimal selection solution proposed in work, PS points from the 350 scene images were extracted and collected. After several tests, different this work, PS points from the 350 scene images were extracted and collected. After several tests, thresholds were set for each of the four parameters: an amplitude deviation threshold of 0.4, an different thresholds were set for each of the four parameters: an amplitude deviation threshold of 0.4, average coherence coefficient threshold of 0.9, an estimated signal-to-noise threshold value of 15, and a an average coherence coefficient threshold of 0.9, an estimated signal-to-noise threshold value of 15, standard deviation of displacement of 0.4. A total of 538 PS points was obtained after the intersection and a standard deviation of displacement of 0.4. A total of 538 PS points was obtained after the extraction, as shown in Figure2, in which the x-axis represents the lateral distance for each PS point intersection extraction, as shown in Figure 2, in which the x-axis represents the lateral distance for to the monitoring instrument and the y-axis represents the longitudinal distance between each PS each PS point to the monitoring instrument and the y-axis represents the longitudinal distance point and the monitoring instrument. Since the actual area occupied by the bridge in the extracted between each PS point and the monitoring instrument. Since the actual area occupied by the bridge image was small, the size of the PSC search grid was set to 5 × 5 m2 and the threshold was set to 0.2. in the extracted image was small, the size of the PSC search grid was set to 5 × 5 m2 and the threshold As shown in Figure3, 12 PSC points were obtained for the bridge. was set to 0.2. As shown in Figure 3, 12 PSC points were obtained for the bridge.

Remote Sens. 2018, 10, x FOR PEER REVIEW 4 of 15 interval is 30 s. The Leica TS30 total station measurement interval is 10 min each time. Finally, the experiment collected 30 sets of Leica TS30 total station data and and monitored 350 GBSAR image scenes.

Figure 1. Experiment site of the Yuehu Bridge and associated electromagnetic wave reflection energy diagram.

3.1.1. PS Point Detection In order to reduce clutter interference from other ground objects outside the bridge area, PS points were selected using the new solution described in Section 2.2. The PS points were selected based on the amplitude, deviation threshold, and coherence coefficient thresholds, and only the Yuehu Bridge was used for further data processing and analysis. The filter window was set to reduce the impacts of noise and ensure the continuity of the phase so as to avoid phase unwrapping errors. Error sources for GBSAR include observation platform instability, atmospheric delay, system frequency deviation errors, and interference phase errors and so on, among which atmospheric delays represent the largest error [26]. Using the combined optimal selection solution proposed in this work, PS points from the 350 scene images were extracted and collected. After several tests, different thresholds were set for each of the four parameters: an amplitude deviation threshold of 0.4, an average coherence coefficient threshold of 0.9, an estimated signal-to-noise threshold value of 15, and a standard deviation of displacement of 0.4. A total of 538 PS points was obtained after the intersection extraction, as shown in Figure 2, in which the x-axis represents the lateral distance for each PS point to the monitoring instrument and the y-axis represents the longitudinal distance between each PS point and the monitoring instrument. Since the actual area occupied by the bridge inRemote the Sens.extracted2018, 10 image, 1936 was small, the size of the PSC search grid was set to 5 × 5 m2 and the threshold5 of 15 was set to 0.2. As shown in Figure 3, 12 PSC points were obtained for the bridge.

Remote Sens. 2018, 10, x FOR PEER REVIEW 5 of 15

Figure 2. Result of selected PS points.

Figure 3. ResultResult of of selected selected PSC representative points.

After image collection, the average coherence coeffi coefficientcient of each point was extracted, along with the amplitude deviation index, the the estimated signal signal to noise ratio, and the displacement standard deviation. As As shown shown in in Table Table 11,, eacheach PSCPSC pointpoint parameterparameter isis betterbetter thanthan thethe experimentalexperimental setset value,value, and the amplitude dispersion index is less than 0.2, indicating that the scattering characteristics of each PSC pointpoint obtainedobtained areare relatively relatively stable. stable. The The coherence coherence of of each each point point is alsois also at leastat least 0.917, 0.917, and and the themean mean value value is about is about 0.95, 0.95, which which indicates indicates that thethat correlation the correlation coefficient coefficient of these of these points points in the in PS the point PS pointset in theset in time the series time changesseries changes little with little time. with The time signal-to-noise. The signal-to-noise ratio is positivelyratio is positively correlated correlated with the withcoherence the coherence coefficient, coefficient, and most and of themmost areof them above are 25 above dB, which 25 dB, means which that means the that measurement the measurement process processis less affected is less affected by the external by the external environment environm and theent instrumentand the instrument itself. The itself. difference The difference in the standard in the standarddeviation deviation of displacement of displacement in the PSC in point the PSC set ispoint relatively set is relatively large, which large, is relatedwhich tois related the change to the of changethe area of of the each area PSC of pointeach PSC in the point measurement in the measurement process. One process. of the One maximum of the maximum displacement displacement standard standarddeviations deviations reaches 0.431 reaches mm. 0.431 The mm. analysis The basedanalysis on based the area on ofthe this area point of this may point be duemay to be the due process to the processof measurement, of measurement, it is affected it is byaffected the influence by the influence of pedestrians of pede andstrians vehicles, and butvehicles, it does but not it affectdoes not the affectdeformation the deformation analysis results analysis of theresults entire of area. the entire Overall, area. the Overall, four parameters the four ofparameters each PSC featureof each point PSC featurereach the point thresholds reach the which thresholds is necessary whichto is meetnecessary the extracted to meet the requirements extracted requirements of PS points. of PS points.

Table 1. PSC parameters.

Amplitude Average Coherence Signal to Noise Ratio Standard Deviation X(m) Y(m) Amplitude Average Signal to Noise Deviation Index Coefﬁcient (SNR) Estimate Standardof Displacement Deviation X(m) Y(m) Deviation Coherence Ratio (SNR) −42.1 181.3 0.167 0.935 24.35 of Displacement−0.184 −41.8 187.1Index 0.124 Coefficient 0.950 Estimate 23.69 −0.195 −42.1−39.1 181.3 172.2 0.167 0.091 0.935 0.994 24.35 24.82 −0.184 0.091 −41.8−37.8 187.1 170.4 0.124 0.088 0.950 0.928 23.69 23.19 −0.195 0.268 −37.12 185.42 0.185 0.917 19.54 −0.180 −39.1−36.4 172.2 172.8 0.091 0.037 0.994 0.989 24.82 26.55 − 0.0910.083 −37.8−27.4 170.4 179.5 0.088 0.037 0.928 0.992 23.19 27.68 0.268 0.431 −37.12−19.6 185.42 185.6 0.185 0.034 0.917 0.987 19.54 26.31 −0.180 0.085 −18.6 185.2 0.038 1 27.86 0.065 −36.4−0.5 172.8 187.1 0.037 0.124 0.989 0.950 26.55 23.69 −−0.0830.195 −27.43.3 179.5 182.1 0.037 0.045 0.992 1 27.68 29.89 − 0.4310.088 − −19.64.2 185.6 180.5 0.034 0.070 0.987 0.983 26.31 25.89 0.0850.079 −18.6 185.2 0.038 1 27.86 0.065 −0.5 187.1 0.124 0.950 23.69 −0.195 3.3 182.1 0.045 1 29.89 −0.088 4.2 180.5 0.070 0.983 25.89 −0.079

3.1.2. Atmospheric Effects The Leica TS30 total station and GBSAR observed the bridge simultaneously. TS30 collected one measurement every 10 min. It acquired 28 sets of distance measurements between TS30 and the five prisms. The offset of the five viewing prism positions is shown in Figure 4. Since the range of variation is in the range of 1 mm, the chart retains only its mm value. Each data of the results show that the distance fluctuation is within the range of the instrument nominal standard deviation of 0.6 mm, indicating that there was no deformation of the bridge. Remote Sens. 2018, 10, 1936 6 of 15

3.1.2. Atmospheric Effects The Leica TS30 total station and GBSAR observed the bridge simultaneously. TS30 collected one measurement every 10 min. It acquired 28 sets of distance measurements between TS30 and the five prisms. The offset of the five viewing prism positions is shown in Figure4. Since the range of variation is in the range of 1 mm, the chart retains only its mm value. Each data of the results show that the distance fluctuation is within the range of the instrument nominal standard deviation of 0.6 mm, Remote Sens. 2018, 10, x FOR PEER REVIEW 6 of 15 Remoteindicating Sens. 2018 that, 10 there, x FOR was PEER no REVIEW deformation of the bridge. 6 of 15

Figure 4. TheThe fluctuation fluctuation diagram of the slop slopee distance measurements of TS30. Figure 4. The fluctuation diagram of the slope distance measurements of TS30. For the five five Corner Reflectors, Reflectors, PS points were extracted from the GBSAR images. The time series For the five Corner Reflectors, PS points were extracted from the GBSAR images. The time series changing curves of deformations are shown in Figure 55.. ItIt cancan bebe clearlyclearly seenseen thatthat thethe deformationdeformation changing curves of deformations are shown in Figure 5. It can be clearly seen that the deformation time series curve of each point shows a tilt changechange trend, and the maximum point position has a time series curve of each point shows a tilt change trend, and the maximum point position has a variation ofof nearly nearly 2 mm,2 mm, but but actually actually the CRthe and CR the and above the monitoredabove monitored prism position prism wereposition stationary, were variation of nearly 2 mm, but actually the CR and the above monitored prism position were stationary,and there was and no there deformation, was no indicating deformation, that theindi radarcating measurement that the radar exhibited measurement atmospheric exhibited delays. stationary, and there was no deformation, indicating that the radar measurement exhibited atmosphericThe meaning delays. of cuw Thein the meaning Figure 5of is cuw Coordinate in the Figure UnWrapped. 5 is Coordinate UnWrapped. atmospheric delays. The meaning of cuw in the Figure 5 is Coordinate UnWrapped.

(a) (b) (a) (b) Figure 5. LOSLOS displacement displacement before before atmospheric atmospheric correction of the five representative PSs. (a) (a) indicates Figure 5. LOS displacement before atmospheric correction of the five representative PSs. (a) indicates points ((-41.1,−41.1, 169.1) 169.1) and ((-35.6,−35.6, 173.4); 173.4); (b) (b) indicate indicatess pointspoints ( −(-29.1,29.1, 178.2), ((-21.3,−21.3, 183.4) 183.4) and ((-14.1,−14.1, 189.1). 189.1). points (-41.1, 169.1) and (-35.6, 173.4); (b) indicates points (-29.1, 178.2), (-21.3, 183.4) and (-14.1, 189.1). Because of of the the short short distance distance observations, observations, no no sudden sudden change change of weather of weather occurred occurred during during the Because of the short distance observations, no sudden change of weather occurred during the observationthe observation period, period, and and we weassume assume that that the the experimental experimental area area was was in in a a uniform atmospheric observation period, and we assume that the experimental area was in a uniform atmospheric environment and atmospheric effects were only relatedrelated to the radar travel path. Thus, Thus, the the relationship relationship environment and atmospheric effects were only related to the radar travel path. Thus, the relationship can be expressed as: can be expressed as: 4π ϕatm = 4 ar (5) = 4λ (5) = (5) where = 7.76 10 +3.7310 [27] and r is the distance between the sensor and the target. where = 7.76 10 +3.7310 [27] and r is the distance between the sensor and the target. The 12 PSC points were then used to establish the atmospheric correction model: The 12 PSC points were then used to establish the atmospheric correction model: 4 = 4 (6) = (6) where m is the number of polynomials. where m is the number of polynomials. Through setting different values of i, according to the number of calibrations in Equation (6), we Through setting different values of i, according to the number of calibrations in Equation (6), we found that the best value for the polynomial number m to fit the data was 2. Figure 6 shows the results found that the best value for the polynomial number m to fit the data was 2. Figure 6 shows the results Remote Sens. 2018, 10, 1936 7 of 15

= × −5 P + × −1 e where a 7.76 10 T 3.73 10 T2 [27] and r is the distance between the sensor and the target. The 12 PSC points were then used to establish the atmospheric correction model:

m 4π i ϕatm = ∑ air (6) λ i=0

where m is the number of polynomials. Remote Sens. 2018, 10, x FOR PEER REVIEW 7 of 15 RemoteThrough Sens. 2018, setting10, x FOR different PEER REVIEW values of i, according to the number of calibrations in Equation (6),7 of we 15 found that the best value for the polynomial number m to fit the data was 2. Figure6 shows the results for the five PS points of the atmospheric phase diagram. It can be seen that the atmosphere phase has forfor the the five five PS PS points points of of the the atmospheric atmospheric phase phase diag diagram.ram. It It can can be be seen seen that that the the atmosphere atmosphere phase phase has has significant influence on the measurement results. According to the graph of atmospheric phase curve, significantsignificant influence influence on the the measur measurementement results. results. According According to to the the gr graphaph of of atmospheric atmospheric phase phase curve, curve, as the monitoring time extends the generated atmospheric impact also adds. asas the the monitoring monitoring time extends the generated atmospheric impact also adds.

(a) (b) (a) (b) Figure 6. Atmospheric phase changes of five representative PS points. (a) indicates points (-41.1, 169.1) FigureFigure 6. 6. AtmosphericAtmospheric phase phase changes changes of five of ﬁve representative representative PS points. PS points. (a) indicates (a) indicates points points (-41.1, ( −169.1)41.1, and (-35.6, 173.4); (b) indicates points (-29.1, 178.2), (-21.3, 183.4) and (-14.1, 189.1). and169.1) (-35.6, and (173.4);−35.6, (b) 173.4); indicates (b) indicates points (-29. points1, 178.2), (−29.1, (-21.3, 178.2), 183.4) (−21.3, and 183.4) (-14.1, and 189.1). (−14.1, 189.1). 3.1.3.3.1.3. Results Results 3.1.3. Results UsingUsing the the atmospheric atmospheric correction correction model model from from the the previous previous section, section, all all the the radar radar observations observations Using the atmospheric correction model from the previous section, all the radar observations werewere corrected, corrected, as as shown shown in in Figure Figure 77.. A comparison of the deformation curves before (Figure5 5)) andand were corrected, as shown in Figure 7. A comparison of the deformation curves before (Figure 5) and afterafter (Figure (Figure 77)) atmosphericatmospheric correction clearly illustrates that the deformation values of the target after (Figure 7) atmospheric correction clearly illustrates that the deformation values of the target pointspoints selected selected in in the the monitored monitored time time period period are are mostly −−0.50.5 to to 0.5 0.5 mm mm in in the the sight sight direction direction of of the the points selected in the monitored time period are mostly −0.5 to 0.5 mm in the sight direction of the radar.radar. That That is, is, the the changes changes in in displacement displacement are are within within 1 1 mm. mm. radar. That is, the changes in displacement are within 1 mm. Displacement [mm] Displacement Displacement [mm] Displacement

(a) (b) (a) (b) FigureFigure 7. 7. LOSLOS displacement displacement after after atmospheric atmospheric correction correction of the of thefive ﬁverepresentative representative PS points. PS points. (a) Figure 7. LOS displacement after atmospheric correction of the five representative PS points. (a) indicates(a) indicates points points (-41.1, (− 41.1,169.1) 169.1) and (-35.6, and (− 173.4);35.6, 173.4); (b) indicates (b) indicates points points (-29.1, ( −178.2),29.1, 178.2),(-21.3, (183.4)−21.3, and 183.4) (- indicates points (-41.1, 169.1) and (-35.6, 173.4); (b) indicates points (-29.1, 178.2), (-21.3, 183.4) and (- 14.1,and (189.1).−14.1, 189.1). 14.1, 189.1). Based on the monitoring results of the five PS points, the LOS deformation mean value and root Based on the monitoring results of the five PS points, the LOS deformation mean value and root mean square (RMS) error before and after atmospheric correction at each point were calculated, and mean square (RMS) error before and after atmospheric correction at each point were calculated, and the LOS direction deformation value comparison chart before and after atmospheric correction was the LOS direction deformation value comparison chart before and after atmospheric correction was obtained, as shown in Table 2. As can be seen from the figure, the average deformation before obtained, as shown in Table 2. As can be seen from the figure, the average deformation before correction is larger than that after correction, and the maximum correction for atmospheric can reach correction is larger than that after correction, and the maximum correction for atmospheric can reach 0.25 mm. At the same time, the RMS error of deformation after correction is smaller than that of 0.25 mm. At the same time, the RMS error of deformation after correction is smaller than that of deformation before correction. It can be seen that the monitoring results after atmospheric correction deformation before correction. It can be seen that the monitoring results after atmospheric correction are closer to the measured values. are closer to the measured values.

Remote Sens. 2018, 10, 1936 8 of 15

Based on the monitoring results of the ﬁve PS points, the LOS deformation mean value and root mean square (RMS) error before and after atmospheric correction at each point were calculated, and the LOS direction deformation value comparison chart before and after atmospheric correction was obtained, as shown in Table2. As can be seen from the ﬁgure, the average deformation before correction is larger than that after correction, and the maximum correction for atmospheric can reach 0.25 mm. At the same time, the RMS error of deformation after correction is smaller than that of

Remotedeformation Sens. 2018 before, 10, x FOR correction. PEER REVIEW It can be seen that the monitoring results after atmospheric correction8 of 15 are closer to the measured values. Table 2. Comparison of average displacements of five PS points before and after atmospheric Table 2. Comparison of average displacements of ﬁve PS points before and after atmospheric correction. correction. Before Correction Average After Correction Average Before CorrectionPoint Average Deformation Value After Correction Average Deformation Value Point Deformation Value (mm) Deformation Value (mm) (mm) (mm) P1 P10.3 0.3 0.05 0.05 P2 P20.29 0.29 0.17 0.17 P3 0.34 0.2 P3 0.34 0.2 P4 0.29 0.09 P4 0.29 0.09 P5 0.38 0.18 P5 0.38 0.18

AllAll the PSPS points points are are applied applied joint joint interpolation interpolat calculationion calculation before andbefore after and atmospheric after atmospheric correction, correction,and the deformation and the deformation results of results the Yuehu of the bridge Yuehu were bridge shown were as shown Figure as8. Figure Comparison 8. Comparison of the two of thegraphs two graphs shows that,shows before that, before correction, correction, the deformation the deformation was − was4 to − 34 mm, to 3 mm, while while the deformation the deformation after afteratmospheric atmospheric correction correction was was only only−1 − to1 to 1 1 mm, mm, indicating indicating that that thethe PSPS point atmospheric atmospheric correction correction solutionsolution can can reduce reduce atmospheric atmospheric delays. delays.

(a) (b)

FigureFigure 8. 8. DeformationDeformation ofof thethe Yuehu Yuehu bridge bridge before before and and after after atmospheric atmospheric correction. correction. (a) indicates (a) indicates before beforeatmospheric atmospheric correction; correction; (b) indicates (b) indicates after atmospheric after atmospheric correction. correction.

ForFor monitoring monitoring areas areas with with short short distances, distances, the the jo jointint PS PS point point atmospheric atmospheric correction correction solution solution can can reducereduce the the influence inﬂuence of of atmospheric atmospheric delay delay an andd improve improve deformation deformation monitoring monitoring accuracy. accuracy.

3.2.3.2. Case Case Study Study 2: 2: Earth Earth Wall Wall Scarp Scarp Deformation Deformation Monitoring Monitoring TheThe small small earth earth wall wall slope slope used used in in Case Case Study Study 2 2is is located located at at Yuehu Yuehu District, District, Xiangtan Xiangtan City, City, Hunan,Hunan, China. China. It Itis about is about 5 m 5 high m high and and 40 m 40 wide. m wide. The terrain The terrain is relatively is relatively flat in flatfront in of front the slope, of the predominantlyslope, predominantly vegetable vegetable fields, fields,with low with vegetati low vegetationon cover cover on the on theleft left side. side. A Acement cement concrete concrete foundationfoundation platform platform with with good good visibility visibility about about 70 70 m m away away from from the the earth earth wall wall slope slope was was selected selected as as thethe GBSAR GBSAR instrumentinstrument observationobservation position, position, due due to to its its stability, stability, and and four four corner corner reflectors reflectors were placedwere placedon the on slope the (Figureslope (Figure9). The 9). test The lasted test lasted about about 5 h, and 5 h, a and total a oftotal 510 of radar 510 radar images images were were collected. collected.

(a) Remote Sens. 2018, 10, x FOR PEER REVIEW 8 of 15

Table 2. Comparison of average displacements of five PS points before and after atmospheric correction.

Before Correction Average Deformation Value After Correction Average Deformation Value Point (mm) (mm) P1 0.3 0.05 P2 0.29 0.17 P3 0.34 0.2 P4 0.29 0.09 P5 0.38 0.18

All the PS points are applied joint interpolation calculation before and after atmospheric correction, and the deformation results of the Yuehu bridge were shown as Figure 8. Comparison of the two graphs shows that, before correction, the deformation was −4 to 3 mm, while the deformation after atmospheric correction was only −1 to 1 mm, indicating that the PS point atmospheric correction solution can reduce atmospheric delays.

(a) (b)

Figure 8. Deformation of the Yuehu bridge before and after atmospheric correction. (a) indicates before atmospheric correction; (b) indicates after atmospheric correction.

For monitoring areas with short distances, the joint PS point atmospheric correction solution can reduce the influence of atmospheric delay and improve deformation monitoring accuracy.

3.2. Case Study 2: Earth Wall Scarp Deformation Monitoring The small earth wall slope used in Case Study 2 is located at Yuehu District, Xiangtan City, Hunan, China. It is about 5 m high and 40 m wide. The terrain is relatively flat in front of the slope, predominantly vegetable fields, with low vegetation cover on the left side. A cement concrete foundation platform with good visibility about 70 m away from the earth wall slope was selected as Remotethe Sens. GBSAR2018, 10 instrument, 1936 observation position, due to its stability, and four corner reflectors were9 of 15 placed on the slope (Figure 9). The test lasted about 5 h, and a total of 510 radar images were collected.

Remote Sens. 2018, 10, x FOR PEER REVIEW (a) 9 of 15

Remote Sens. 2018, 10, x FOR PEER REVIEW 9 of 15

(b) Figure 9. Electromagnetic wave reflection energy diagram experiment site of the small slope with Figure 9. Electromagnetic wave reflection energy diagram experiment site of the small slope with adjustable CR. The picture on the left of part (a) shows the scene of the small earth wall slope adjustable CR. The picture on the left of part (a) shows the scene of the small earth wall slope monitoring. The positions of the four corner reflectors are marked in the figure, and the right picture monitoring.shows the The related positions electromagnetic of the four reflection corner reflectors energy ma arep. (b) marked is the inadjustable the figure, corner and reflector the right with picture showsmeasuring the related ruler. electromagnetic reflection energy(b) map. (b) is the adjustable corner reflector with Figuremeasuring 9. Electromagnetic ruler. wave reflection energy diagram experiment site of the small slope with adjustable3.2.1. PS Point CR. Detection The picture on the left of part (a) shows the scene of the small earth wall slope 3.2.1. PS Point Detection monitoring.PS point The extraction positions was of the performed four corner on reflectothe imagrs aree. After marked experimental in the figure, analysis, and the the right PS picture point showsPSamplitude point the extractiondeviationrelated electromagnetic threshold was performed was reflectionset to on0.4, thetheenergy av image.erage map. coherence After(b) is the experimental coefficient adjustable threshold corner analysis, reflector was the 0.7, with PS the point amplitudemeasuringestimated deviation SNR ruler. threshold threshold was 10, was and set the to standard 0.4, the de averageviation threshold coherence was coefficient 0.4. After the threshold intersection was 0.7, the estimatedextraction from SNR the threshold thresholds, was a total 10, of and 801 thePS points standard was obtained. deviation As threshold shown in Figure was 0.4. 10, where After the intersection3.2.1.the PS X-axis Point extraction representsDetection fromthe lateral the di thresholds,stance of each a totalPS point of 801from PS the pointsmonitoring was instrument, obtained. and As the shown Y- in axis represents the longitudinal distance of each PS point from the monitoring instrument. The size FigurePS 10 point, where extraction the X-axis was representsperformed the on lateralthe imag distancee. After of experimental each PS point analysis, from the the monitoring PS point of the PSC points search grid area was also set to 5 × 5 m2, and the threshold was set to 0.2, then a instrument, and the Y-axis represents the longitudinal distance of each PS point from the monitoring amplitudetotal of deviation five PSC representative threshold was points set to were 0.4, obtained, the average as shown coherence in Figure coefficient 11. threshold was 0.7, the instrument.estimated SNR The threshold size of the was PSC 10, points and the search standard grid area deviation was also threshold set to 5 ×was5 m 0.4.2, andAfter the the threshold intersection was setextraction to 0.2, thenfrom a the total thresholds, of five PSC a representativetotal of 801 PS pointspoints werewas obtained. obtained, As as shownshown inin FigureFigure 11 10,. where the X-axisThe average represents coherence the lateral coefficient, distance amplitude of each PS deviation point from index, the estimatedmonitoring signal-to-noise instrument, and ratio, the and Y- standardaxis represents deviation the oflongitudinal displacement distance of each of point each ofPS PSC point were from extracted. the monitoring As shown instrument. in Table3, theThe four size parametersof the PSC points of each search PSC feature grid area point was are also within set the to threshold5 × 5 m2, and range the to threshold meet theselection was set to requirements 0.2, then a oftotal PS of points. five PSC representative points were obtained, as shown in Figure 11.

Figure 10. Result of selected PS points.

Figure 11. Result of selected PSC representative points.

The average coherence coefficient, amplitude deviation index, estimated signal-to-noise ratio, and standard deviation of displacement of each point of PSC were extracted. As shown in Table 3, the four parameters of each PSC feature point are within the threshold range to meet the selection requirements of PS points.

Figure 11. Result of selected PSC representative points.

Remote Sens. 2018, 10, x FOR PEER REVIEW 9 of 15

(b) Figure 9. Electromagnetic wave reflection energy diagram experiment site of the small slope with adjustable CR. The picture on the left of part (a) shows the scene of the small earth wall slope monitoring. The positions of the four corner reflectors are marked in the figure, and the right picture shows the related electromagnetic reflection energy map. (b) is the adjustable corner reflector with measuring ruler.

3.2.1. PS Point Detection PS point extraction was performed on the image. After experimental analysis, the PS point amplitude deviation threshold was set to 0.4, the average coherence coefficient threshold was 0.7, the estimated SNR threshold was 10, and the standard deviation threshold was 0.4. After the intersection extraction from the thresholds, a total of 801 PS points was obtained. As shown in Figure 10, where the X-axis represents the lateral distance of each PS point from the monitoring instrument, and the Y- axis represents the longitudinal distance of each PS point from the monitoring instrument. The size of the PSC points search grid area was also set to 5 × 5 m2, and the threshold was set to 0.2, then a total of five PSC representative points were obtained, as shown in Figure 11.

Remote Sens. 2018, 10, 1936 10 of 15 Figure 10. Result of selected PS points.

Figure 11. Result of selected PSC representative points.

The average coherence coefficient,Table amplitude 3. Four parameters deviation of PSC. index, estimated signal-to-noise ratio, and standard deviation of displacementAmplitude of Averageeach po Coherenceint of PSC were extracted.Standard As shown Deviation in Table 3, X(m) Y(m) SNR the four parameters of eachDeviation PSC feature Index point Coefﬁcientare within the threshold rangeof to Displacement meet the selection requirements−18.52 of 63.28 PS points. 0.101 0.965 24.35 0.017 −2.67 69.41 0.134 0.932 23.19 −0.193 −0.18 69.96 0.053 1 29.33 0.034 0.18 70.47 0.069 1 28.45 0.209 8.66 71.45 0.101 0.985 25.87 −0.067

3.2.2. Atmospheric Effects To verify the accuracy of the test, an adjustable CR with measuring ruler was adjusted five times during the monitoring period, and set to 3 mm, 4 mm, 3 mm, 3 mm, and 3 mm, respectively. Four corner reflectors PS points (Figure 10) were extracted from the GBSAR images for verification. The time series curves of the deformation result are shown in Figure 12. It can be clearly seen from Figure 12 that the manual adjustment displacement of the adjustable CR with measuring ruler is clearly identified, as shown in Figure 12a,b. At the same time, the time curves of the four corner reflectors show a large tendency of system tilt change. The largest point has a variation of approximately 2 mm. During the monitoring period, the monitoring area was stable, and the CR was a fixed device on the earth wall slope, there was no deformation. It can be seen that the measurement results have the influence of noise errors such as atmospheric delay.

Figure 12. Cont. Remote Sens. 2018, 10, 1936 11 of 15

Figure 12. Displacement of sight line before atmospheric correction of the four representative PSs. (a) indicates points (−12.9, 69.8) and (4.9, 71.3); (b) is the box portion in (a), the corner reﬂector adjustment size has been marked in the ﬁgure, and (c) indicates the point (1.3, 71.5) with (−14.8, 65.3).

RemoteAs Sens. shown 2018, 10 in, x FigureFOR PEER 13 REVIEW, atmospheric delay for four PS points has been derived according 11 of to15 the atmospheric delay estimation method mentioned above. It can be clearly found out that the atmosphere delay has a great impactimpact onon thethe results,results, withwith maximummaximum valuevalue reachedreached 22 mm.mm. We alsoalso ﬁndfind thatthat withwith thethe longerlonger amountamount ofof monitoringmonitoring time,time, thethe cumulativecumulative impactimpact ofof atmosphericatmospheric effectseffects willwill increase.increase.

(a) (b)

Figure 13. Atmospheric phase phase of of the the four four representative representative PSs. PSs. (a) (a indicates) indicates poin pointsts (-12.9, (−12.9, 69.8) 69.8) and and (4.9,(4.9, 71.3);71.3); ((b)b) indicatesindicates thethe pointpoint (1.3,(1.3, 71.5)71.5) withWith ((-14.8,−14.8, 65.3). 65.3).

3.2.3. Results The atmosphericatmospheric phase phase delay delay correction correction was performedwas performed on each on PS pointeach toPS obtain point the to deformation obtain the resultdeformation after correction, result after as correction, shown in Figure as shown 14. Comparingin Figure 14. the Comparing deformation the curvesdeformation before curves and after before the atmosphericand after the phase atmospheric delay correction phase delay in Figures correction 12 and in Figures14, it can 12 be and clearly 14, it seen can that be clearly after the seen atmospheric that after phasethe atmospheric delay correction, phase delay the target correction, point the selected target in po theintmonitoring selected in the period monitoring is between period−0.5 is mmbetween and 0.5−0.5 mm mm in and the 0.5 radar mm sight in the line, radar which sight is the line, displacement which is the change displacement value. Itchange ﬂuctuates value. within It fluctuates 0.8 mm. Atwithin the same0.8mm. time, At the the deformation same time, valuesthe deformatio monitoredn byvalues the adjustablemonitored CR by with the measuringadjustable rulerCR with are 2.8measuring mm, 4 mm, ruler 3.1 are mm, 2.8 3mm, mm 4 andmm, 3.2 3.1 mm mm, respectively. 3 mm and 3.2 The mm monitoring respectively. results The are monitoring very close results to the resultsare very of close the manual to the results set change of the of manual measuring set change ruler, suggesting of measuring that rule thisr, solution suggesting of atmospheric that this solution delay correctionof atmospheric is effective. delay correction is effective.

(a) (b)

Figure 14. Displacement of sight line after atmospheric correction of the four representative PSs. (a) indicates points (-12.9, 69.8) and (4.9, 71.3); (b) indicates the point (1.3, 71.5) With (-14.8, 65.3).

The fusion processing results of other PS points on the earth wall slope before and after atmospheric phase delay correction are shown in Figure 15. It can be found that the deformation before correction is between −3 to 2 mm, and the deformation after correction is about −1 to 1 mm, and the actual deformation of the monitoring area shows that the PS points correction solution can weaken the effect of systematic errors such as atmospheric phase delay and improve the deformation monitoring accuracy. Remote Sens. 2018, 10, x FOR PEER REVIEW 11 of 15 atmosphere delay has a great impact on the results, with maximum value reached 2 mm. We also find that with the longer amount of monitoring time, the cumulative impact of atmospheric effects will increase.

(a) (b)

Figure 13. Atmospheric phase of the four representative PSs. (a) indicates points (-12.9, 69.8) and (4.9, 71.3); (b) indicates the point (1.3, 71.5) With (-14.8, 65.3).

3.2.3. Results The atmospheric phase delay correction was performed on each PS point to obtain the deformation result after correction, as shown in Figure 14. Comparing the deformation curves before and after the atmospheric phase delay correction in Figures 12 and 14, it can be clearly seen that after the atmospheric phase delay correction, the target point selected in the monitoring period is between −0.5 mm and 0.5 mm in the radar sight line, which is the displacement change value. It fluctuates within 0.8mm. At the same time, the deformation values monitored by the adjustable CR with measuring ruler are 2.8 mm, 4 mm, 3.1 mm, 3 mm and 3.2 mm respectively. The monitoring results areRemote very Sens. close2018 ,to10 the, 1936 results of the manual set change of measuring ruler, suggesting that this solution12 of 15 of atmospheric delay correction is effective.

(a) (b)

Figure 14. 14. DisplacementDisplacement of of sight sight line line after after atmospheric atmospheric correction correction of the of four the fourrepresentative representative PSs. (a) PSs. indicates(a) indicates points points (-12.9, (−12.9, 69.8) 69.8) and and(4.9, (4.9,71.3); 71.3); (b) indicates (b) indicates the point the point (1.3, (1.3,71.5) 71.5) With with (-14.8, (− 14.8,65.3). 65.3).

The fusion processing results of other PS poin pointsts on the earth wall slope before and after atmospheric phase delay correction are shown in Figure 1515.. It It can be found that the deformation before correction is between −33 to to 2 2 mm, mm, and and the deformation after correction is about −11 to to 1 1 mm, mm, and the actual deformation of the monitoring area shows that the PS points correction solution can weaken the effect of systematic errors such as atmospheric phase delay and improve the deformation monitoringRemote Sens. 2018 accuracy. , 10, x FOR PEER REVIEW 12 of 15

(a) (b)

Figure 15. Deformation results before and after atmospheric correct. (a) (a) indicates before atmospheric correction, and ((b)b) indicates after atmospheric correction.

4. Discussion In this paper, thethe selectionselection methodsmethods ofof GBSARGBSAR PS points and the establishmentestablishment of atmospheric correction model of PS points triangular network were put forward, in which the deformation of Yuehu Bridge and and the the small small slope slope were were monitored monitored respectively, respectively, taking taking the theatmospheric atmospheric influence inﬂuence into intoconsideration. consideration. Based Based on the on theabove above experimental experimental me methodsthods and and results, results, four four questions questions need need to to be discussed. Details are as follows. (1) In Yuehu BridgeBridge monitoringmonitoring tests,tests, thethe selectionselection of PS pointspoints waswas analyzed,analyzed, and atmospheric effect correction model was built. The adoption of PS points of atmospheric correction methods can effectively improveimprove thethe monitoring monitoring precision precision by by reducing reducing atmospheric atmospheric effects effects on on the the condition condition that that the monitoringthe monitoring ofthe of the surrounding surrounding environment environment is is stable, stable, and and the the target target is is in in a a short-rangeshort-range monitoring area. However, the atmosphere effect correction model needs further improvement for the complex terrain, weather, unstableunstable regionsregions ofof thethe application.application. (2) InIn the the small small earth earth wall wall slope slope monitoring monitoring tests, tests, the adjustable the adjustable CR with CR measuring with measuring ruler arranged ruler arearranged inadequate are inadequate in number in due number to the due limited to the test limi conditions.ted test conditions. Other PS Other points PS are points manually are manually selected asselected a complement as a complement to build to the build triangulation the triangulation atmospheric atmospheric correction correction model, whichmodel, can,which to acan, certain to a extent,certain improveextent, improve the precision the precision of the monitoring of the monitori results.ng results. But the But inﬂuence the infl ofuence the atmosphere of the atmosphere cannot cannot be completely eliminated, so there still exists some residual error. Therefore, more experiments are needed to test the effect of the atmospheric correction network with more CR reflectors. (3) In order to reduce the interference of clutter signals, only the image data of the Yuehu Bridge was selected for data processing. In the process of PS points selection, points that are less than the threshold are selected by setting the average correlation coefficient and amplitude deviation threshold integration methodology. The threshold should not be set too high, but set according to the actual situation, because the density of PS points needs to be considered from the perspective of data processing, although the threshold settings are adopted to improve the quality of PS points. (4) Errors affecting GBSAR include systematic frequency deviation error, observation platform instability error, and atmospheric delay effect, etc. In this paper, the interference of atmospheric effects on radar echo signal was studied. The monitoring experiment of the Yuehu Bridge and the small earth wall slope showed that selecting the appropriate atmospheric correction model can effectively improve the precision of GBSAR monitoring results. Under the condition of long-time observation, the effect of platform instability, etc. should also be considered.

5. Conclusions In this paper, a PS Optimization Selection Method was put forward that takes into account the average coherence coefficient, the amplitude deviation index, the estimated signal to noise ratio, and the displacement accuracy index. This method effectively improved the quality of the selected PS points. In addition, atmospheric delay correction method was proposed, in which the monitoring experiment of Yuehu Bridge and the small earth wall slope is carried out respectively. After comparing the Leica TS30 total station and the adjustable CR with measuring ruler, it is shown that the GBSAR system could achieve sub-millimeter high precision monitoring after atmospheric Remote Sens. 2018, 10, 1936 13 of 15 be completely eliminated, so there still exists some residual error. Therefore, more experiments are needed to test the effect of the atmospheric correction network with more CR reﬂectors. (3) In order to reduce the interference of clutter signals, only the image data of the Yuehu Bridge was selected for data processing. In the process of PS points selection, points that are less than the threshold are selected by setting the average correlation coefﬁcient and amplitude deviation threshold integration methodology. The threshold should not be set too high, but set according to the actual situation, because the density of PS points needs to be considered from the perspective of data processing, although the threshold settings are adopted to improve the quality of PS points. (4) Errors affecting GBSAR include systematic frequency deviation error, observation platform instability error, and atmospheric delay effect, etc. In this paper, the interference of atmospheric effects on radar echo signal was studied. The monitoring experiment of the Yuehu Bridge and the small earth wall slope showed that selecting the appropriate atmospheric correction model can effectively improve the precision of GBSAR monitoring results. Under the condition of long-time observation, the effect of platform instability, etc. should also be considered.

5. Conclusions In this paper, a PS Optimization Selection Method was put forward that takes into account the average coherence coefficient, the amplitude deviation index, the estimated signal to noise ratio, and the displacement accuracy index. This method effectively improved the quality of the selected PS points. In addition, atmospheric delay correction method was proposed, in which the monitoring experiment of Yuehu Bridge and the small earth wall slope is carried out respectively. After comparing the Leica TS30 total station and the adjustable CR with measuring ruler, it is shown that the GBSAR system could achieve sub-millimeter high precision monitoring after atmospheric correction for short-range deformation monitoring. More specifically, the results presented in the paper clearly highlight that: (1) In the Yuehu Bridge deformation monitoring test, the GBSAR system and the Leica TS30 total station were used for comparative analysis. Simultaneous monitoring of the same target was performed. After data processing and analysis, the monitoring results of the GBSAR system and the Leica TS30 total station values were identical with each other and consistent with the actual situation on site. (2) After expounding the conventional PS points selection methods, we put forward a GBSAR PS points selection method based on the average coherence coefficient, amplitude dispersion index, estimated signal-to-noise ratio and displacement accuracy index, and so on. An empirical study and analysis of Yuehu Bridge and small slope were carried out, and the PS points with higher quality than the single method were successfully selected. The atmospheric correction model constructed by PS point was used to correct the monitoring results of the Yuehu Bridge and the small earth wall slope. The comparative analysis of the deformation time series curves before and after the atmospheric correction shows that the use of PS points to construct the triangulation network for atmospheric correction has achieved good results. (3) In the small slope monitoring test, the collected data were processed by focusing, interference, unwrapping phase, etc., and the final displacement map was obtained. According to the actual situation analysis, it was concluded that the atmospheric effect is the main factor affecting the precision of the test results. By comparing the adjustment of the CR with measuring ruler and the GBSAR monitoring results, it was concluded that the GBSAR has sub-millimeter-level monitoring precision after atmospheric correction.

Author Contributions: S.L. conducted the algorithm design. S.L., Y.Y. and A.T. wrote the paper. S.L. and Z.L. revised the paper. Formal Analysis, S.L., Y.Y. and A.T.; Data Curation, Y.Y. and A.T.; Investigation, Y.Y., A.T., W.W., C.Z.; Resources, Y.Y. and A.T.; Supervision, S.L. and Z.L.; Project Administration, S.L.; Funding Acquisition, S.L. All authors have contributed signiﬁcantly and have participated sufﬁciently to take responsibility for this research. Remote Sens. 2018, 10, 1936 14 of 15

Funding: This work was supported by the National Natural Science Foundation of China (grant 41877283, 41474014), and the Study Abroad Fund of the Hunan Provincial Department of Education (2015212), and the Scientific Research Fund of Hunan Provincial Education Department (15A060). Acknowledgments: Thanks to Fast-GBSAR system for providing accurate test data, and thanked the company’s technical staff Li Chen and Zheng Wang in Newcastle University for their technical support. Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations The following abbreviations are used in this manuscript:

CR corner reﬂector FM-CW Frequency Modulated Continuous Wave GBSAR Ground-Based Synthetic Aperture Radar GPS Global Positioning System InSAR Interferometric Synthetic Aperture Radar LOS Line of sight PS Permanent Scatterers PSC Permanent Scatterers Candidates RMS Root Mean Square SNR Signal to Noise Ratio

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