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Article

Reconstruction of Coal Mining Subsidence Field by Fusion of SAR and UAV LiDAR Deformation Data

by
Bin Yang
1,
Weibing Du
1,2,*,
Youfeng Zou
1,
Hebing Zhang
1,
Huabin Chai
1,
Wei Wang
3,
Xiangyang Song
1 and
Wenzhi Zhang
1
1
School of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo 454003, China
2
Collaborative Innovation Center of Geo-Information Technology for Smart Central Plains, Zhengzhou 450000, China
3
Shendong Coal Branch, China Shenhua Energy Co., Ltd., Yulin 719000, China
*
Author to whom correspondence should be addressed.
Remote Sens. 2024, 16(18), 3383; https://doi.org/10.3390/rs16183383
Submission received: 10 August 2024 / Revised: 7 September 2024 / Accepted: 10 September 2024 / Published: 12 September 2024
(This article belongs to the Special Issue State-of-the-Art on Satellite and UAV Remote Sensing in Geoscience Research)
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Versions Notes

Abstract

:
The geological environment damage caused by coal mining subsidence has become an important factor affecting the sustainable development of mining areas. Reconstruction of the Coal Mining Subsidence Field (CMSF) is the key to preventing geological disasters, and the needs of CMSF reconstruction cannot be met by solely relying on a single remote sensing technology. The combination of Unmanned Aerial Vehicle (UAV) and Synthetic Aperture Radar (SAR) has complementary advantages; however, the data fusion strategy by refining the SAR deformation field through UAV still needs to be updated constantly. This paper proposed a Prior Weighting (PW) method based on Satellite Aerial (SA) heterogeneous remote sensing. The method can be used to fuse SAR and UAV Light Detection and Ranging (LiDAR) data for ground subsidence parameter inversion. Firstly, the subsidence boundary of Differential Interferometric SAR (DInSAR) combined with the large gradient subsidence of Pixel Offset Tracking (POT) was developed to initialize the SAR preliminary CMSF. Secondly, the SAR preliminary CMSF was refined by UAV LiDAR data; the weights of SAR and UAV LiDAR data are 0.4 and 0.6 iteratively. After the data fusion, the subsidence field was reconstructed. The results showed that the overall CMSF accuracy improved from ±144 mm to ±51 mm. The relative errors of the surface subsidence factor and main influence angle tangent calculated by the physical model and in situ measured data are 1.3% and 1.7%. It shows that the proposed SAR/UAV fusion method has significant advantages in the reconstruction of CMSF, and the PW method contributes to the prevention and control of mining subsidence.

1. Introduction

Coal mining is an important part of the energy security system, which is directly related to food security and ecological security [1,2]. The Coal Mining Subsidence Field (CMSF) is a world-concerned issue of sustainable development in coal mining [3,4]. Reconstruction of CMSF is beneficial not only for understanding the ecological environment evolution and risk in coal mining areas but also can provide scientific ways for land surface damage repair [5]. Parameter analysis of CMSF has a significant contribution to maintaining ecological balance and realizing sustainable development in mining areas [6]. By using the innovative SA remote sensing technology, both the rough data of mining areas at a large scale and accurate data of working faces at a small scale can be quickly obtained.
The SAR mentioned in this paper mainly includes DInSAR and POT. At a large scale, SAR is feasible for mine subsidence monitoring [7,8]. It has made considerable progress in seismic deformation [9,10], volcanic activity [11,12], glacier monitoring [13,14], urban surface subsidence, and landslides [15,16,17,18]. DInSAR is an extension of InSAR, mainly used to capture the centimeter level or smaller surface deformation along the Line of Sight (LOS) of satellite radar [19]. The Small Baseline Subset InSAR (SBAS InSAR) specializes in the intensity of satellite time series, and consequently it improves the accuracy of deformation monitoring in mining areas [20,21]. Permanent Scatter InSAR (PS InSAR) can select many permanent scatterers with high coherence, so the deformation rate and elevation error between PS points and the main reference point can be calculated, and the reliability of deformation data can be improved [22,23]. In early research, DInSAR and PS InSAR were applied to recognize slow subsidence in the Wieliczka Salt Mine, Poland. The Wieliczka Salt Mine DInSAR data obtained from ERS-1/2. It was data of the C band with 4 × 20 m spatial resolution and 1 day of temporal resolution [24]. The Multitemporal DInSAR was used to calculate mining subsidence characteristics and some pseudo parameters in the working face of Buertai Mine in Shendong Coalfield, China. The Buertai Mine DInSAR data were obtained from RADARSAT-2. It was data of the L band, with 5 m spatial resolution and 24 days of temporal resolution [22]. The coal mining subsidence usually has a large deformation in a short time; for example, it was observed in the mining area of Shendong Coalfield that 0.5 m formed in one day. For SAR satellites, their revisiting cycles are usually longer than one day; the coal mining subsidence value that can be monitored by SAR satellites is just at the centimeter level, even at the millimeter level. Therefore, DInSAR can obtain the boundary of CMSF very well.
Based on SAR intensity image pairs, POT can be used to monitor deformation with meter level accuracy, which has been applied in monitoring sea ice, alpine glaciers, and landslide movement [25,26,27]. POT has previously been applied to monitor coal mining subsidence at a large scale in the Bulianta and Shangwan Coal Mine, Shendong Coal Group, China. The POT data of Bulianta and Shangwan Coal Mine were ALOS-2, with L band, 5 m spatial resolution, and 14 days of temporal resolution [28]. The Corner Reflector is synchronously put on the ground with SAR satellite observation, which can achieve the accurate correction of POT image pairs [25,26]. If the POT image pairs are corrected by the external datum Digital Elevation Model (DEM), it can effectively compensate for the bias caused by terrain undulation [29]. However, the deformation accuracy obtained by POT is about 1/10~1/30 pixel values, heavily depending on the spatial resolution of SAR images [30]. In order to obtain an effective meter level deformation value, the coal mining subsidence value should be at least 1/3 of an image pixel value. Thus, considering that POT and DInSAR can be used to obtain deformation information at the meter level and at the centimeter level, respectively, the fusion of POT and DInSAR has an advantage in monitoring CMSF on a large scale [31].
In terms of coal mining working face with a small scale, multitemporal UAV LiDAR can be used to obtain the multitemporal DEMs. After difference processing, the coal mining subsidence information of the working face area can be obtained. The UAV LiDAR was applied to the coal mining subsidence rate in the working face of the No. 1 Coal Mine of Yangquan Coal Group, Shanxi Province, China [32]. The UAV LiDAR data of Yangquan Coal Group have approximately 2.5 × 108 points in a 4 km2 area, with an average point density of 62 pts/m2; this study indicated the subsidence rate was greater than 5 cm/month. The multitemporal DEMs were derived from UAV LiDAR to obtain a digital subsidence model and subsidence parameters in the Liangshuijing Coal Mine, northwest Shaanxi, China [33]. The UAV LiDAR data of Liangshuijing Coal Mine have 2.9 × 108 points in a 0.04 km2 area, with an average point density of 55 pts/m2; this study figured out the coal mining subsidence rate with the maximum subsidence value of 1.7 m and the subsidence boundary angle of about 63°. Increasing the SA fusion data sources of observations can better reconstruct the CMSF and can figure out relatively accurate subsidence parameters. The accuracy of UAV LiDAR can reach the centimeter level, which is not suitable for areas with small subsidence values, especially when the subsidence values are less than 10 cm [33].
In recent years, the SAR/UAV cooperative observation method has been used in many aspects of geological surveys. Researchers used SAR/UAV collaborative observation to study the landslide with a long runout debris flow in Gokseong County, South Korea, on 7 August 2020 [34]. The results show that the multi-source remote sensing SAR/UAV cooperative observation technology is effective in monitoring complex landslide events. At the same time, SAR/UAV collaborative observation technology has also been widely used in glacier monitoring, permafrost degradation, earthquake monitoring, and other fields [35,36,37]. Moreover, the fusion of multi-source SA heterogeneous remote sensing data has risen to be the key content of the reconstruction of CMSF [38,39]. Here, three SAR/UAV data fusion methods for the reconstruction of CMSF can be summarized as follows: (1) the oblique photogrammetry 3D model and the DInSAR deformation data were fused by the threshold segmentation method [40,41]; (2) the Digital Terrain Model (DTM) derived from UAV LiDAR was used as the datum DEM for DInSAR data processing to optimize CMSF [42]; and (3) the CMSF was reconstructed by using the UAV deformation field to refine the SAR deformation field. At present, the main methods for the reconstruction of CMSF are divided into phase fusion and subsidence information fusion [43,44]. Phase fusion starts by considering the principles and limitations of the SAR monitoring method. Then, the large gradient deformation detected by the UAV is converted into phase information to correct the phase cycle number. Finally, the phase is transformed into deformation information to refine the accuracy of the reconstructed CMSF. However, phase fusion ignores the establishment of a reliable deformation boundary, which leads to errors in the CMSF boundary area. Meanwhile, the process of the fusion method is complicated. Subsidence information fusion is to fuse the large gradient deformation information obtained by UAV with the small gradient deformation obtained by SAR to improve the accuracy of reconstructed CMSF. The process of subsidence information fusion is relatively simple. Most of the fusion based on subsidence information adopts the Prior Weighting (PW) method, but the PW method is widely used in the fusion of SAR deformation information [43]. At present, the application of this method in SAR/UAV data fusion is still lacking. The PW method has the advantages of high solving efficiency, strong compatibility with different deformation data, and high reliability, so it has a good application prospect in the reconstruction of CMSF [45,46].
The above analysis suggests that SAR and UAV LiDAR are highly complementary. SAR has the advantage of detecting the CMSF at a large scale in mining areas. However, the UAV LiDAR has the advantage of figuring out the coal mining subsidence parameters at a small scale on specific working faces. The UAV LiDAR has difficulty detecting small subsidence values, while the DInSAR can be used to detect the small deformation value and delimit the boundary of the subsidence field.
This paper reconstructs the CMSF Field by fusion of SAR and UAV LiDAR deformation data. Firstly, for the fusion of DInSAR and POT deformation data, the initial weight is determined by the PW method, and the weight range threshold is set by the deformation accuracy of DInSAR and POT. The preliminary CMSF is reconstructed by meter level subsidence field by POT and subsidence boundary by DInSAR. Secondly, the primary CMSF is refined by the PW method through the fusion of UAV LiDAR deformation data, and the higher precision CMSF is reconstructed. Finally, the accuracy of refined CMSF by the PW method is evaluated by the Global Navigation Satellite System (GNSS) in situ measured data, and the rationality and feasibility of this method are verified.

2. Study Area and Data

2.1. Overview of the Study Area

The geographical extent (Figure 1) of Shendong Coal Group is 38°52′~39°41′N, 109°51′~110°46′E. It is 38~90 km long from north to south and 35~55 km wide from east to west. It is located in the north region of Shenmu County, Yulin, Shaanxi province. It is a typical landform of the Loess Plateau with arid and semi-arid climate [47]. Shendong Coal Group is one of the largest mines in China and even in the world [48,49,50]. It has a coal mine cluster with an annual output of 10 Mt, with 14 underground coal mines such as Daliuta, Buertai, Bulianta, Haragou, Shangwan, and Shitai, and 5 open-pit coal mines such as Harusu and Hedaigou [22]. The long-term and high-intensity continuous mining activities have resulted in more than 170 km2 of surface ecological damage. The annual soil and water loss has increased by about 28 Mt. The Wulanmulun River has been tasked with transporting an additional 239 Mt of sediment in the past few years [51]. The Huojitu Mine Shaft, a part of the Daliuta Coal Mine, consists of 3 main coal seams and 3 panels. The topography of the Huojitu Mine Shaft is characterized by higher elevation in the west and lower elevation in the east. Its western part is predominantly characterized by landforms such as ridges, hillocks, and gullies, while the eastern part is predominantly characterized by wind-accumulated landforms [52]. This study focuses on the No. 8 working face of the Huojitu Mine Shaft. The strike length and dip length of the working face are 2525 m and 325 m, respectively, with an average coal seam thickness of 4.2 m (Figure 1e). The coal seam is horizontal with a dip angle of 0°. The roof lithology of the coal seam is primarily composed of fine siltstone and mudstone, while the floor lithology is dominated by siltstone, fine sandstone, and mudstone. The Huojitu Mine Shaft is a large modern mechanization mine. In 2003, the Huojitu Mine Shaft had a production capacity of 15.6 Mt/a. In 2006, the Huojitu Mine Shaft was approved, and its production capacity was 11 Mt/a. In 2024, it has 36 years left in service. Here, the No. 8 working face of Huojitu Mine Shaft is taken as the research area. The mining period of the No. 8 working face is from March to December 2023.

2.2. Satellite SAR Data Including DInSAR and POT Data at the Ming Area Scale

Sentinel-1A is the first satellite for the Copernicus Global Observation Project developed by the European Commission and the European Space Agency (ESA) [53]. It is mainly used for land surface deformation monitoring. It offers four working modes of the strip map, interferometric wide swath, extra wide swath, and wave [54]. The Sentinel-1A satellite image has a spatial resolution of 5 × 20 m and a temporal resolution of 12 days [55]. The phase image and the intensity image of the Single-Look Complex (SLC) product of Sentinel-1A were, respectively, used for DInSAR and POT processing. The acquisition ascending dates of the main image and the slave image were 5 March and 22 April 2023, respectively. The temporal baseline and spatial baseline between the two scene images are 48 days and 250 m, respectively
The Copernicus DEM is a terrain data product published by ESA. It has three versions of data with resolutions of 10 m, 30 m, and 90 m. It is generated following terrain correction and error removal [56,57]. Its accuracy is deemed reliable, with vertical accuracy exceeding 4 m and plane absolute accuracy surpassing 6 m [58]. The Copernicus DEM with a spatial resolution of 30 m is used to remove terrain phase information and SAR image co-registration in this study.

2.3. UAV LiDAR Data at Working Face Scale

The FEIMA D200 UAV equipped with the D-LiDAR2000 lidar remote sensing module was used to acquire point cloud data on the No. 8 working face, and the parameters of the UAV are shown in Table 1. The UAV LiDAR integrates inertial navigation, laser scanner, satellite positioning, and other sensor systems so that it can simultaneously obtain point cloud data, positioning, and attitude information. The UAV flight parameters were set as the relative flight height of 100 m, and the overlap rate of adjacent routes was 40%. The UAV LiDAR data of the No. 8 working face have approximately 1.9 × 108 points in 3 km2 area, with an average point density of 64 pts/m2. Two phases of point cloud data collection were carried out on 18 March and 14 April 2023, respectively. At the same time, we select 30 checkpoints by Real-Time Kinematic (RTK) measurement in the No. 8 working face. The UAV RTK checkpoints were a plan position that we designed in advance on the map and then measured in the field synchronously with the UAV LiDAR. The distribution of the 30 UAV RTK checkpoints is also shown in Figure 1e. These UAV RTK checkpoints were used to evaluate and verify the UAV LiDAR DEMs generated from the point cloud, and the plane position error is within ±2 cm.

2.4. No. 8 Working Face GNSS in Situ Measured Data

Compared to traditional surveying methods, GNSS has the characteristics of all-weather, high precision, and short time, and it can be used well in complex terrain surveys. In this paper, GNSS was selected to monitor the surface subsidence of the No. 8 working face and the position of the GNSS in situ measured points were fixed to the working face by pouring cement. Considering the complex surface environment of the mining area, 31 observation stations of Line H (strike observation line) and 15 observation stations of Line A (dip observation line) were obtained under the premise of maximum consideration of surface subsidence characteristics. Lines H and A were used as reference data for the PW method and accuracy evaluation of the reconstructed CMSF. A total of 14 periods of GNSS in situ measured data were obtained for the No. 8 working face from 31 March to 30 April 2023. The frequency of the GNSS in situ measured data was varied about 1 to 3 days.

2.5. Dataset Summaries

In this paper, we performed DInSAR and POT processing on Sentinel-1A data. The Copernicus DEM was used for SAR image co-registration and terrain phase removal. The UAV LiDAR point cloud data were used to generate the work surface DEM. UAV RTK checkpoints were used to check the UAV LiDAR DEM’s accuracy. GNSS in situ measured data were used as reference data for the PW method and accuracy evaluation of reconstructed CMSF. The data details are shown in Figure 2, and the data usage diagram is shown in Table 2.

3. Methodology

SAR has the advantage of detecting the CMSF at a large scale about hundreds of square kilometers of the mining area; however, the UAV LiDAR has the advantage of figuring out the CMSF parameters at a working face scale. The SAR and UAV LiDAR have a strong complementarity in terms of data fusion. This paper proposes a PW method based on multi-source heterogeneous remote sensing data. (1) For the fusion of DInSAR and POT deformation data, the initial weight is determined by the PW method, and the weight range threshold is set by the deformation accuracy of DInSAR and POT. The SAR primary CMSF is reconstructed by meter level subsidence field by POT and subsidence boundary by DInSAR. (2) The SAR preliminary CMSF is refined by the PW method through the fusion of UAV LiDAR CMSF, and the refined CMSF is reconstructed. (3) The accuracy of the refined CMSF by the PW method is evaluated by GNSS in situ measured data, and the rationality and feasibility of this method are verified. The specific process to reconstruct the CMSF is shown in Figure 3. The main methods related to this paper include five parts: Section 3.1—DInSAR Method, Section 3.2—POT Method, Section 3.3—UAV LiDAR Method, Section 3.4—PW Fusion Method, and Section 3.5—the CMSF Accuracy Evaluation Method.

3.1. DInSAR Method

DInSAR is mainly used to obtain the deformation information from the phase parameters of two SAR images [59,60]. Depending on the interference mode, DInSAR can be divided into two-track, three-track, and four-track differential interference. Because of the convenience of data acquisition, two-track DInSAR is used to monitor ground subsidence in mining areas. The basic principle of DInSAR is to generate an interferogram by conjugate multiplication of two SLC images and then extract deformation data from the differential interferogram [61]. Firstly, the external DEM is used to remove the terrain phase, co-registration, and define ground control points, which can provide relatively accurate deformation information from the interferogram. Secondly, multi-looking processing is used to reduce the effect of noise in the low coherence area with the multi-looking parameter set to 1 (azimuth looks) × 5 (range looks). In addition, in order to improve the detection capability of interferometric SAR, the atmospheric delay error is corrected by the Atmospheric Phase Screen (APS) model [62]. Furthermore, an adaptive Goldstein filter is used to reduce decorrelated noise caused by spatial or temporal baselines, while phase unwrapping is performed using the minimum cost flow method. Finally, terrain correction is performed. To make the deformation information easier to understand the deformation information, it is essential to convert the deformation information from a radar coordinate system to a geographic coordinate system.

3.2. POT Method

POT is generally divided into (1) coherence tracking and (2) intensity tracking. Coal mining areas are usually distributed in suburban areas, and the surface is often covered by vegetation. Coherence tracking is often affected by vegetation changes and large gradient deformation, so it is often ineffective in mining monitoring applications. However, intensity tracking does not require interference and phase unwrapping, so it is less affected by image coherence. This research chose POT based on intensity tracking to monitor the study area. POT, based on intensity tracking, is used to obtain the deformation in satellite azimuth and range distance, which are less affected by the spatiotemporal baseline. POT calculates the Normalized Cross-Correlation (NCC) of the selected Ground Control Points (GCPs) in the master and slave SAR images by Formula (1). The NCC schematic is shown in Figure 4. The mine deformation is calculated according to the offset of each GCP. The steps to obtain the images offset through the POT are as follows: (1) Focusing and multi-look processing. (2) Precise orbit determination. To eliminate the orbit error, the track state vector of the SLC products is updated with accurate orbit determination data. (3) Master and slave image co-registration. With the assistance of an external DEM, the slave image is co-registered with the master image. The accuracy reaches the sub-pixel level. (4) Offset tracking. For selected GCPs from the master and slave images, the NCC is calculated. (5) Data postprocessing. The median filter is used to filter the offset result. It eliminates the influence of noise.
N C C ( u , v ) = ∑ I m ( x , y ) ⋅ I s ( x + u , y + v ) ( ∑ I m ( x , y ) ⋅ I m ( x , y ) ) × ( ∑ I s ( x + u , y + v ) ⋅ I s ( x + u , y + v ) ) 1 / 2
In Equation (1), N C C ( u , y ) , is the normalized cross-correlation; u and v are the range and azimuth oriented offsets of the feature window, respectively; x , y are the row and column numbers in the image, respectively; I m ( x , y ) is all the pixels in the master image feature window in row x and column y ; I s ( x + u , y + v ) is all the pixels in the slave image feature window in row x + u and column y + v .
In this paper, according to the ratio relationship between the range and azimuth resolution of the Sentinel-1A image, the size of the matching window is set to 128 × 32 pixels. Under the given SNR threshold of 0.1, the smaller the window, the more discontinuous the offset results and the more noise. The larger the window, the coarser the offset details will be. In order to ensure the accuracy of the results, a 10 × 2 step size was used for calculation. Considering the need for large gradient deformation monitoring and search of surface feature information, the time interval of the SAR image is 48 days.

3.3. UAV LiDAR Method

The original UAV LiDAR point cloud data cannot directly construct the DEMs. Only after POS combination subsidence, data fusion, point cloud filtering, and other operations can we obtain high-precision point cloud data of ground 3D coordinate information can be obtained. The construction of the LiDAR DEMs can be affected by the vegetation and buildings on the No. 8 working face. In order to build high-precision LiDAR DEMs, it is necessary to denoise, register, and filter the original point cloud data. Firstly, the outlier point cloud data are eliminated by point cloud denoise operation. Secondly, due to a series of factors such as data acquisition time, location, and the attitude of the UAV, it is necessary to register and fuse two or more phases of LiDAR point cloud data to obtain an accurate 3D scene. Currently, commonly used filtering algorithms include cloth simulation filtering algorithms, morphological filtering algorithms, triangulation irregular-based filtering algorithms, etc [63,64]. Because the cloth simulation filtering algorithm has better adaptability than other filtering algorithms in desert areas, this algorithm is used for filtering processing in this paper. In the filtering process, the average spacing of the cloth grid is set to 2 m, the maximum number of iterations is set to 200, and the point cloud classification threshold is set to 0.5 m. Finally, the LiDAR DEMs of the No. 8 working face are constructed using inverse distance weight interpolation with a step size of 1 m.

3.4. PW Fusion Method

In this paper, the preliminary CMSF obtained by DInSAR, POT, and UAV LiDAR is fused based on the fusion weight determined by the GNSS in situ measured data, resulting in the reconstruction of a high-precision CMSF. For the area where the reliable CMSF ranges, this paper adopts Formula (2) to fuse the CMSF according to the GNSS in situ measured data based on the principle of prior error determining weight. By calculating the Root Mean Square Error (RMSE) of the CMSF and the in situ measured data in the fusion area, the CMSF information of the fusion area is obtained by weighted processing. It is important that the weighting range between DInSAR, POT, and UAV LiDAR be selected. For SAR preliminary CMSF fusion, the weight range was determined from the perspective of DInSAR and POT recognition accuracy, combined with GNSS in situ measured data (Section 4.1). When the SAR preliminary CMSF and UAV LiDAR CMSF are fused, the RMSE from two kinds of data and GNSS in situ measured data are used as the basis for the second determination of the weight range (Section 4.3). At the same time, spatial and temporal resolution is important for data fusion. In terms of spatial resolution, firstly, 5 m × 5 m grids were created, and the measured values of UAV and InSAR in the center of the grid were extracted, respectively. Secondly, all grid points were traversed, the grid points whose measurement values were not in the weighted range were deleted, and PW weighted fusion was performed on the remaining grid points. Finally, the inverse distance interpolation is applied to the null value region. In terms of temporal resolution, SAR data and UAV LiDAR data do not completely match at the acquisition time. In order to minimize the impact of temporal resolution on the result, this study selected the region whose subsidence has reached stability during the study period for data fusion and then carried out piecewise linear interpolation on it in the temporal domain. In this way, the temporal resolution of SAR data and UAV LiDAR data is unified.
D f u s i o n = P 1 = ∑ z = 1 n σ z 2 − σ 1 2 ∑ z = 1 n σ z 2 , P 2 = ∑ z = 1 n σ z 2 − σ 2 2 ∑ z = 1 n σ z 2 , … , P n = ∑ z = 1 n σ z 2 − σ n 2 ∑ z = 1 n σ z 2 D i , j 1 D i , j 2 ⋮ D i , j n ( 0 < σ 1 , σ 2 , … , σ n )
In Equation (2), D i , j 1 , D i , j 2 , …, D i , j n are the CMSF vertical deformation value obtained from different pixel data. σ 1 , σ 2 , …, σ n are the RMSE of the GNSS in situ measured data D i , j 1 , D i , j 2 , …, D i , j n , respectively; P 1 , P 2 , …, P n are the weights of D i , j 1 , D i , j 2 , …, D i , j n , respectively.
During data fusion, not all CMSF deformation values match the weighted range, so the CMSF deformation regions that can match the weighted range are called reliable regions, and the others are unreliable regions. Firstly, the reliable region is weighted, and for the unreliable region, the null value is generated. If there is a null value between the fused data, the inverse distance weighting method is used to determine the value of the vacant position; that is, the empty value is calculated from the distance d j = ( x i − x j ) 2 + ( y i − y j ) 2 between the monitoring point ( x i , y i ) and the monitoring point ( x j , y j ) .
W i = ∑ j = 1 n d j ∑ j = 1 n d j ⋅ W j
In Equation (3), i is the null value point; j is the monitoring point around the null point; and W i and W j are the deformation values of the corresponding points.

3.5. CMSF Accuracy Evaluation Method

In order to test the reliability of remote sensing data, it is necessary to evaluate the accuracy of the results. The remote sensing data and the measured data are taken as two experimental samples. The RMSE was used to analyze the relationship between the two groups of data, and the calculation method was shown in Formula (4).
R M S E = ∑ i = 1 n ( D r s − D i n   s i t u ) 2 n
In Equation (4), R M S E represents the root mean square error between the GNSS in situ measured data D i n   s i t u and the remote sensing data D r s ; and n represents the number of experimental samples.

4. Results and Analysis

4.1. The Preliminary CMSF Reconstructed by the SAR Method Including DInSAR and POT

Firstly, the No. 8 working face is a horizontal coal seam mining area, and the subsidence caused by it is mainly vertical subsidence. Secondly, according to the mining subsidence law, the surface subsidence caused by mining disturbance is mainly vertical subsidence. In addition, the GNSS in situ measured data also show that the horizontal displacement appeared at the end of April 2023. To sum up, the displacement in the horizontal direction is not considered in this paper. According to the SAR satellite imaging geometry, the deformation of the satellite LOS is converted to the deformation in the vertical direction [65]. DInSAR and POT results are shown in Figure 5. The DInSAR can be used to monitor the CMSF boundary. Due to the strong sudden collapse, the subsidence gradient is too large, resulting in a partial unwrapping error in the boundary deformation solution. According to the “Guidelines for Retaining and Mining Coal Pillars in Buildings, Water Bodies, Railways, and Main Well Tunnels”, −10 mm is the outermost boundary of the subsidence area [66,67]. In order to ensure the accuracy of the CMSF boundary monitoring results, the interference pair coherence coefficient greater than 0.7 and the subsidence value greater than 10 mm were used as a double threshold mask to extract a relatively accurate CMSF boundary. It will be used as the fusion basis of the SAR preliminary CMSF. As can be seen from Figure 5a, the red CMSF boundary obtained by DInSAR exactly surrounds the monitored subsidence center obtained by POT. The left CMSF boundary has obvious characteristics of surrounding the subsidence center, while the right CMSF boundary has a low fitting effect due to the influence of mining on the working face. The maximum subsidence value of DInSAR is only −124 mm in the study area. The Maximum Absolute Error (MAE) between DInSAR results and GNSS in situ measured data at the subsidence boundary is 54 mm, while the maximum error between DInSAR results and GNSS in situ measured data near the subsidence center is 3315 mm. This is obviously different from the actual situation in the mining area. As can be seen from Figure 5b, POT can obtain a relatively reliable CMSF center area, and the maximum subsidence value reached 3.2 m. The expression ability of POT at the CMSF boundary is weaker than that of DInSAR, and the MAE is 625 mm. Although POT can obtain large gradient subsidence, there is still an error of about 200 mm between POT and GNSS in situ measured data. It can not fully reflect the actual change in the subsidence center of the working face. In view of the above problems, DInSAR can be used to obtain the CMSF boundary of a large range by using SAR phase information, and POT can be used to obtain the meter level CMSF by using SAR intensity information. The monitoring advantages of the two technologies are complementary to establishing a SAR preliminary CMSF.
The Sentinel-1A radar image covering the No. 8 working surface has a wavelength of 5.6 cm. According to the basic conditions for the smooth implementation of interferometry given by Zebker et al. [68], the offset of ground objects corresponding to the unit pixel along the radar LOS during the imaging phase should not exceed half a wavelength. That is, the theoretical deformation value of the unwrapping unit pixel is 2.8 cm. However, in the actual phase unwrapping, for slow deformation, the deformation gradient of two adjacent pixels is less than λ / 4 , and the actual maximum deformation value that can be unwrapped is much larger than λ / 2 . Therefore, the deformation value less than 0.028 m (2.8 cm) is taken as the correct value obtained by DInSAR and the upper weighting threshold. POT monitoring accuracy ranges from 1/30 to 1/10 pixel resolution. In order to obtain the SAR preliminary CMSF, 0.66 m is used as the lower weighting threshold. According to the GNSS in situ measured data, the weights of DInSAR and POT are 0.455 and 0.545, respectively, in the range of [0.66 m, 0.028 m]. The range of the deformation value is weighted and fused. As shown in Figure 6, the subsidence center of the SAR preliminary CMSF is about 150 m away from the mining line, and the dip width is about 270 m. The CMSF boundary is improved after fusion interpolation. Due to the limitation of the spatial resolution of the Sentinel satellite, the central position of the subsidence basin, which is identified by POT, can not accurately reflect the large gradient subsidence above the working face. The subsidence position identified by the SAR preliminary CMSF is relatively accurate. There is still a large error between the subsidence center value identified by the SAR preliminary CMSF and the GNSS in situ measured data, and the error between the GNSS in situ measured data is about 100 to 200 mm. In this paper, the deformation information obtained by high-precision UAV LiDAR will be incorporated to further refine the SAR preliminary CMSF through the PW method.

4.2. The CMSF Reconstructed by the UAV LiDAR

When acquiring UAV LiDAR point cloud data, factors such as the instrument’s angle and the UAV’s flight attitude can affect the accuracy of the DEMs generated from the point cloud data. Therefore, it is necessary to verify the accuracy of the constructed UAV LiDAR DEMs. In this paper, the elevation of UAV RTK checkpoints collected is compared with the UAV LiDAR DEMs, and the partial results are shown in Table 3. The RMSE of the DEM in the first phase is 0.038 m (38 mm), and the Average Absolute Error (AAE) is 0.033 m (33 mm). The RMSE of the second phase DEM is 0.041 m (41 mm), and the AAE is 0.035 m (35 mm).
In order to obtain the vertical deformation on the working face scale, the CMSF of the No. 8 working face is obtained by using UAV LiDAR DEMs difference. The CMSF of the No. 8 working face is shown in Figure 7. The maximum deformation value of the working face is about −3.4 m. The subsidence area identified by UAV LiDAR DEMs difference is close to that monitored by SAR preliminary CMSF, which is distributed on the second and third mining areas, and the subsidence value is concentrated between −3.33~0 m. However, errors will inevitably occur during the generation of UAV LiDAR DEMs, and the different technologies used in this paper will result in error propagation. According to the error law, the errors in surface elevation changes are shown in Formula (5).
∂ Δ h = ± ∂ h 1 2 + ∂ h 2 2
In Equation (5), ∂ h 1 represents the RMSE of elevation before the subsidence event occurs, and ∂ h 2 represents the RMSE of elevation after the subsidence event occurs. Accordingly, it can be estimated that the RMSE of subsidence after the DEM difference is 0.055 m (55 mm), which is negligible for large gradient subsidence.
In this paper, a UAV LiDAR DEM with two phases working face scale is used for differential analysis to obtain the UAV LiDAR CMSF. Due to the mismatch between the time of UAV LiDAR acquisition and the time of GNSS in situ measured data and the influence of mining movement, the subsidence value of some points along the direction of mining advance is slightly higher than that of GNSS in situ measured data. The subsidence center of UAV LiDAR CMSF is about 140 m away from the mining line, and the dip width is about 280 m. As the UAV LiDAR DEMs constructed from the point cloud data have millimeter errors compared to the actual terrain, there is a significant error in the boundary area of the UAV LiDAR CMSF. Compared with the GNSS in situ measured data, it is found that the MAE in the CMSF boundary is 93 mm. Its ability to monitor boundary accuracy and monitoring range is weaker than that of SAR preliminary CMSF. However, for large gradient subsidence monitoring, the maximum subsidence obtained by UAV LiDAR CMSF is 3.4 m, which is consistent with the actual situation of the mining area.

4.3. The Refined CMSF Reconstructed by the PW Method

The No. 8 working face has typical characteristics of shallow burial depth and high-intensity coal mining. Its mining and subsidence speeds are fast. The traditional measurement and observation not only have high labor intensity, but also the observation data may have significant time asynchronism. In order to realize the real-time, high precision, and full-range surface subsidence monitoring of the No. 8 working face, the PW method is used for the reconstruction of CMSF. The specific methods are as follows: (1) GNSS in situ measured data are used to provide a unified spatiotemporal reference for SAR and UAV LiDAR data. (2) DInSAR and POT are used to realize space macro monitoring, and SAR preliminary CMSF is established. (3) The SAR preliminary CMSF is refined by the PW method through the fusion of UAV LiDAR CMSF, and the CMSF is reconstructed out. The schematic diagram is shown in Figure 8.
According to the results in Section 4.1 and Section 4.2, the RMSE of the SAR preliminary CMSF, UAV LiDAR CMSF, and GNSS in situ measured data are 144 mm and 98 mm, respectively. These two numerical indicators are used as the segmentation threshold of the weight range. We calculated the absolute error of the SAR preliminary CMSF and the UAV LiDAR CMSF with all GNSS in situ measured data. The error comparison is shown in Figure 9b. The subsidence values of SAR preliminary CMSF and UAV LiDAR CMSF with absolute error within the range of [98 mm, 144 mm] are mainly concentrated in the range of [0.2 m, 3 m]. Therefore, 0.2 m and 3 m are used as upper and lower upper weighting thresholds, respectively. When the subsidence is less than 0.2 m, the subsidence identified by the SAR preliminary CMSF is used for monitoring. For the subsidence larger than 0.2 m and smaller than 3 m, the SAR preliminary CMSF and UAV LiDAR CMSF are fused according to a certain weight by the PW method. Subsidence greater than 3 m is monitored by UAV LiDAR CMSF.
According to the GNSS in situ measured data, the weights of SAR preliminary CMSF and UAV LiDAR CMSF are 0.392 and 0.608, respectively, in the range of [0.2 m, 3 m]. Based on the above weights, the reconstructed CMSF is obtained by the PW method. In order to facilitate description and differentiation, the reconstructed CMSF optimized by UAV LiDAR CMSF is uniformly called refined CMSF (Figure 10). The refined CMSF comprehensively reflects the influence range of mining subsidence. The refined CMSF effectively eliminates the shortcomings of poor expression ability of UAV LiDAR CMSF at the subsidence boundary and obtains the subsidence center value that is more consistent with the GNSS in situ measured data. As can be seen from Figure 10, small gradient subsidence occurred at the subsidence boundary because there were a series of small faults near the mining process of the working face. With the continuous advancement of mining work, the overlying strata were disturbed, and small deformation was generated, which caused varying degrees of impact on the surrounding environment. This is consistent with the actual situation in the CMSF and the law of surface fracture development. As of 22 April 2023, the subsidence center of refined CMSF is located about 150 m away from the mining line. Its subsidence center shows a state of development along the mining direction, which is mainly due to the horizontal mining of the working face. Meanwhile, the maximum subsidence value of the refined CMSF monitored reaches 3.4 m. The average subsidence velocity is about 64 mm/d.

5. Discussion

In order to further verify the accuracy of the PW method, we extracted the refined CMSF, SAR preliminary CMSF, and UAV LiDAR CMSF results from 46 GNSS in situ observation points on the strike and dip line. Three CMSF results were compared and analyzed. The strike GNSS in situ measured points (H06~H25) and the dip GNSS in situ measured points (A13~A22) are divided into the subsidence center area, and the remaining points are divided into the subsidence boundary area. The layout of GNSS in situ measured points is shown in Figure 11.

5.1. Accuracy of the Preliminary CMSF by SAR

As can be seen from Figure 12a, the error between DInSAR results and GNSS in situ measured results is small before the H06 point; after that, due to the large subsidence amplitude, an incoherent phenomenon appeared in DInSAR. Near the center of the CMSF, the actual observed amount increases, but the subsidence amount monitored by DInSAR in this area is relatively small. The RMSE at the CMSF boundary and CMSF center is 25 mm and 1894 mm, respectively. Therefore, DInSAR cannot accurately extract the information of the whole CMSF, and the CMSF boundary monitoring results are relatively reliable. It can be seen in Figure 12a that large gradient subsidence can be obtained by the POT (RMSE: 289 mm). By comparing the subsidence value obtained by POT with GNSS in situ measured data, it is found that POT cannot obtain accurate boundary information of the CMSF (RMSE: 237 mm). It can be seen from Figure 12b,d that the SAR preliminary CMSF obtained by combining DInSAR and POT can not only obtain accurate information on the boundary of the CMSF but also effectively monitor a large gradient deformation near the subsidence center. The MAE, AAE, and RMSE between the SAR preliminary CMSF and GNSS in situ measured data are 400 mm, 96 mm, and 144 mm, respectively (Table 4). However, the maximum subsidence value of the SAR preliminary CMSF is only 3.2 m, which still has a 0.2 m error with the maximum subsidence value of 3.4 m detected by the GNSS in situ measured data.

5.2. Accuracy of the CMSF by UAV LiDAR

Because the UAV LiDAR data and the GNSS in situ measured data do not match completely in the data acquisition time, some points after H24 are slightly higher than the ground observation data (Figure 13 ). However, at the center of the CMSF, the MAE, AAE, and RMSE between the UAV LiDAR CMSF and GNSS in situ measured data are 264 mm, 84 mm, and 98 mm, respectively. It can be seen that UAV LiDAR CMSF (RMSE: 59 mm) is superior to SAR preliminary CMSF (RMSE: 114 mm) in identifying a large gradient subsidence. Due to the millimeter errors of UAV LiDAR DEMs themselves, the obtained UAV LiDAR CMSF have relatively large errors in the CMSF boundary, which has limitations in monitoring the small gradient subsidence of the CMSF boundary. Moreover, by comparing Table 4 and Table 5, it can be found that UAV LiDAR CMSF (RMSE: 178 mm) is weaker than SAR preliminary CMSF (RMSE: 21 mm) in small gradient subsidence monitoring.

5.3. Accuracy of the Refined CMSF

Compared with the results of SAR preliminary CMSF, a significant improvement was observed in the monitoring capability of the reconstruction CMSF at the subsidence center, with the RMSE increased from 178 mm to 62 mm. Although the approximate CMSF was also detected in the SAR preliminary CMSF, the detected central subsidence value was slightly different from the GNSS in situ measured data. Compared with the GNSS in situ measured data, the MAE reached 400 mm at the H12 point (Figure 14). The meter level value of SAR preliminary CMSF is obtained by POT, which is limited by the spatial resolution of the SAR image, and the surface vegetation and noise reduce the quality of the SAR image, resulting in the inability to detect the actual subsidence information at the CMSF. But, by comparing the monitoring accuracy of SAR preliminary CMSF and UAV LiDAR CMSF at the boundary, it can be found that SAR preliminary CMSF is slightly better than the UAV LiDAR CMSF.
By comparing the UAV LiDAR CMSF with the GNSS in situ measured data, the UAV LiDAR CMSF can monitor the maximum subsidence value. It fully reflects the influence range of CMSF, but the expression ability of the subsidence boundary is not perfect. By using the PW method, UAV LiDAR CMSF is used to optimize the SAR preliminary CMSF to obtain the final refined CMSF. It greatly improves both the monitoring accuracy of the subsidence boundary and subsidence center. The RMSE of the subsidence boundary is increased from 59 mm to 21 mm. The RMSE of the subsidence center is increased from 114 mm to 62 mm (Table 6). Firstly, the PW method can effectively compensate for the nonperfect accuracy of UAV LiDAR CMSF at the subsidence boundary. Secondly, it also makes up for the lack of expression of large gradient information in SAR preliminary CMSF.
From the perspective of parameter inversion, the average subsidence velocity of the goaf is about 64 mm/d, which is higher than that of other positions of the working face. Under the premise that the mining thickness is known to be 4.2 m, the subsidence coefficient calculated based on the refined CMSF is 0.81, which is slightly larger than that calculated from GNSS in situ measured data (0.80), and the relative error is 1.3%. The main influence angle tangent calculated based on the refined CMSF is 2.31, which is slightly smaller than that calculated from GNSS in situ measured data (2.35), and the relative error is 1.7%. This is mainly because the No. 8 working face is affected by repeated mining, resulting in a larger subsidence coefficient and surface subsidence influence area than that of the first mining, which is in accord with the general law of mining subsidence. Moreover, DInSAR based on phase information, is used to calculate the small gradient subsidence at the CMSF boundary in the PW method. It can obtain the boundary information of the CMSF more accurately. It is proved that the CMSF area obtained based on InSAR is larger. In summary, the overall error of the refined CMSF parameters obtained by the Probability Integral Method (PIM) is less than 3%, which has high reliability. The PW method provides data support for solving the predicted parameters of surface subsidence.
Judging from the total results, the PW method fusion with the advantages of SAR preliminary CMSF and UAV LiDAR CMSF can accurately detect the location, scope, and subsidence change trend of the CMSF. It can obtain the surface movement law and mining subsidence parameters of the CMSF accord with the mining area. Compared with the SAR preliminary CMSF or UAV LiDAR CMSF, the overall monitoring accuracy of the refined CMSF is improved compared with the former two CMSFs, whether it is at the subsidence boundary or the subsidence center. It is proved that the weighting thresholds between SAR preliminary CMSF and UAV LiDAR CMSF in this paper are reasonable. By comparing with the GNSS in situ measured data, it can be seen that the PW method can obtain the reconstruction CMSF, which is more consistent with the actual situation.

6. Conclusions

In this paper, firstly, for mining areas with large gradient variables, the SAR preliminary CMSF at the mining area scale is established by DInSAR and POT. Secondly, the RMSEs of SAR preliminary CMSF and UAV LiDAR are used to determine the threshold of the weight range. Finally, the refined CMSF of the working face area is reconstructed by the PW method. The main conclusions are as follows:
(1) In the refined CMSF by UAV LiDAR, the weights of SAR preliminary CMSF and UAV LiDAR CMSF are 0.392 and 0.608, respectively. Compared with the SAR preliminary CMSF, the accuracy of the refined CMSF is improved, which reveals that the deformation information obtained by the SAR and UAV LiDAR is complementary. Thus, it is very necessary to fuse the deformation information of SAR with UAV LiDAR.
(2) For mining areas at a large scale, the boundary of CMSF can be delineated effectively by phase information of DInSAR. The meter level deformation of the mining area can be obtained by intensity information of SAR. After detecting the SAR preliminary CMSF in a large-scale mining area, UAV LiDAR was used to refine the SAR preliminary CMSF. The RMSE was improved from ±144 mm of the preliminary CMSF to ±51 mm of the refined CMSF.
(3) PIM was used to calculate the key subsidence parameters of the refined CMSF. The average subsidence speed of the goaf is about 64 mm/d. In the case of mining thickness of 4.2 m, the subsidence factor and the main influence angle tangent are 0.81 and 2.31, respectively, which are close to the GNSS in situ measured data.
(4) This research can provide method references for data complementarity, multi-source data fusion, and disaster warning model construction. However, the PW method is largely based on GNSS in situ measured data, and it is difficult to obtain ideal fusion weights with little or no GNSS in situ measured data. Moreover, the PW method is just a linear model; as a result, the precision of the deformation field is still limited. Nonlinear deep learning models are expected to improve the accuracy and precision of data fusion in further research.

Author Contributions

Validation, formal analysis, data curation, writing—original draft, and writing—review and editing, B.Y.; methodology, formal analysis, investigation, resources, writing—review and editing, supervision, project administration, and funding acquisition, W.D.; project administration and funding acquisition, W.D. and Y.Z.; project administration, W.W. and W.Z.; writing—review and editing, H.Z., H.C. and X.S. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Natural Science Foundation of China under Grant Nos. U22A20620, U22A20620/003, and U21A20108. At the same time, the research was also funded by the PI project of the Collaborative Innovation Center of Geo-Information Technology for Smart Central Plains Grant No. 2023C003. We thank them for their support for this research.

Data Availability Statement

The data presented in this study are available on request from the corresponding author due to restrictions of data privacy.

Acknowledgments

The authors acknowledge all data contributors and platforms that provide data and express gratitude to anonymous reviewers for constructive comments and improving advice.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. (a) The location of Shendong Coal Group around the world; (b) optical image map of the Shendong Coal Group (acquired on 18 April 2023); (c) the red star represents approximate location of Huojitu Mine Shaft, 3D terrain generated by the Copernicus DEM (resolution is 30 m); (d) topographic map of Huojitu Mine Shaft; (e) location distribution of UAV RTK checkpoints.
Figure 1. (a) The location of Shendong Coal Group around the world; (b) optical image map of the Shendong Coal Group (acquired on 18 April 2023); (c) the red star represents approximate location of Huojitu Mine Shaft, 3D terrain generated by the Copernicus DEM (resolution is 30 m); (d) topographic map of Huojitu Mine Shaft; (e) location distribution of UAV RTK checkpoints.
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Figure 2. (a) Satellite SAR data of mining area scale; (b) UAV LiDAR data of working face scale.
Figure 2. (a) Satellite SAR data of mining area scale; (b) UAV LiDAR data of working face scale.
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Figure 3. Technical flow chart to reconstruct the CMSF.
Figure 3. Technical flow chart to reconstruct the CMSF.
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Figure 4. NCC schematic, the red box represents the search window.
Figure 4. NCC schematic, the red box represents the search window.
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Figure 5. (a) DInSAR results; (b) POT results; the red boundary represents the 10 mm CMSF boundary.
Figure 5. (a) DInSAR results; (b) POT results; the red boundary represents the 10 mm CMSF boundary.
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Figure 6. (a) The contour map of SAR preliminary CMSF; (b) the 3D map of SAR preliminary CMSF.
Figure 6. (a) The contour map of SAR preliminary CMSF; (b) the 3D map of SAR preliminary CMSF.
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Figure 7. The CMSF reconstructed by the UAV LiDAR.
Figure 7. The CMSF reconstructed by the UAV LiDAR.
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Figure 8. Multi-source remote sensing data mining area joint monitoring scheme.
Figure 8. Multi-source remote sensing data mining area joint monitoring scheme.
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Figure 9. (a) The deformation comparison between some GNSS in situ measured data and remote sensing data. (b) The error comparison between some GNSS in situ measured data and remote sensing data.
Figure 9. (a) The deformation comparison between some GNSS in situ measured data and remote sensing data. (b) The error comparison between some GNSS in situ measured data and remote sensing data.
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Figure 10. (a) The contour map of reconstruction CMSF; (b) the 3D map of reconstruction CMSF.
Figure 10. (a) The contour map of reconstruction CMSF; (b) the 3D map of reconstruction CMSF.
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Figure 11. (a) Mining area and point layout diagram. (b) Pouring cement of the GNSS in situ measured points. (c,d) Placement diagram of GNSS in situ measured points.
Figure 11. (a) Mining area and point layout diagram. (b) Pouring cement of the GNSS in situ measured points. (c,d) Placement diagram of GNSS in situ measured points.
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Figure 12. (a,d) The deformation comparison of the DInSAR, POT, and GNSS in situ measured data in Line H and Line A, respectively. (b,e) The deformation comparison of the SAR preliminary CMSF and GNSS in situ measured data in Line H and Line A, respectively. (c,f) The error between SAR preliminary CMSF and GNSS in situ measured data in Line H and Line A, respectively.
Figure 12. (a,d) The deformation comparison of the DInSAR, POT, and GNSS in situ measured data in Line H and Line A, respectively. (b,e) The deformation comparison of the SAR preliminary CMSF and GNSS in situ measured data in Line H and Line A, respectively. (c,f) The error between SAR preliminary CMSF and GNSS in situ measured data in Line H and Line A, respectively.
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Figure 13. (a,c) The deformation comparison of the UAV LiDAR CMSF and GNSS in situ measured data in Line H and Line A, respectively. (b,d) The error between UAV LiDAR CMSF and GNSS in situ measured data in Line H and Line A, respectively.
Figure 13. (a,c) The deformation comparison of the UAV LiDAR CMSF and GNSS in situ measured data in Line H and Line A, respectively. (b,d) The error between UAV LiDAR CMSF and GNSS in situ measured data in Line H and Line A, respectively.
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Figure 14. (a,d) The deformation comparison of the SAR preliminary CMSF, UAV LiDAR CMSF, and GNSS in situ measured data in Line H and Line A, respectively. (b,e) The deformation comparison of the refined CMSF and GNSS in situ measured data in Line H and Line A, respectively. (c,f) The error between refined CMSF and GNSS in situ measured data in Line H and Line A, respectively.
Figure 14. (a,d) The deformation comparison of the SAR preliminary CMSF, UAV LiDAR CMSF, and GNSS in situ measured data in Line H and Line A, respectively. (b,e) The deformation comparison of the refined CMSF and GNSS in situ measured data in Line H and Line A, respectively. (c,f) The error between refined CMSF and GNSS in situ measured data in Line H and Line A, respectively.
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Table 1. UAV parameters.
Table 1. UAV parameters.
TypeProductNote
UAVFEIMA D200Maximum flight time: 48 min
Cruising speed: 15 m/s
Takeoff weight: 7.5 kg
LiDARD-LiDAR2000 [32]Ranging:
190 m@10%Reflectivity@100 klx
450 m@80%Reflectivity@0 klx
Scanning frequency:240 kHz
Ranging accuracy: ±2 cm
Horizontal positioning accuracy: 2 cm
Table 2. Data usage table.
Table 2. Data usage table.
Dataset NamesData TimePurpose
Sentinel-1A5 March and 22 April 2023DInSAR and POT processed
Copernicus DEM2015SAR image co-registration and removal of terrain phase
UAV LiDAR point cloud data18 March and 14 April 2023Generate working surface UAV LiDAR DEMs
UAV RTK checkpoints18 March and 14 April 2023Check the UAV LiDAR DEM’s accuracy
GNSS in situ measured data31 March to 30 April 2023Reference data for the PW method and accuracy evaluation of reconstructed CMSF
Table 3. Partial elevation deviation between UAV LiDAR DEM and RTK in two phases.
Table 3. Partial elevation deviation between UAV LiDAR DEM and RTK in two phases.
First Phase Elevation AssessmentSecond Phase Elevation Assessment
IDRTK/mUAV LiDAR DEM/mDifference ValueIDRTK/mUAV LiDAR DEM/mDifference Value
11141.1721141.1700.00211141.2261141.250−0.024
21145.4111145.3800.03121145.4091145.3900.019
31154.6371154.640−0.00331154.6301154.5700.06
41188.5971188.630−0.03341188.6591188.6100.049
51163.5901163.5400.0551160.6551160.700−0.045
61169.9421169.960−0.01861169.8921169.8800.012
71165.6901165.6300.0671165.8321165.7800.052
81184.5921184.5500.04281184.4801184.510−0.03
91185.0651185.070−0.00591185.0401185.050−0.01
101178.6531178.6300.023101178.5681178.570−0.002
..………..………
RMSE:0.038 m AAE:0.033 mRMSE:0.041 m AAE:0.035 m
Table 4. Precision statistics of SAR preliminary CMSF.
Table 4. Precision statistics of SAR preliminary CMSF.
Observation LineMAE (mm)AAE (mm)RMSE (mm)
Boundary Center Boundary Center Boundary Center
Line H424001317118210
Line A4716019752782
Total result40096144
Table 5. Precision statistics of UAV LiDAR CMSF.
Table 5. Precision statistics of UAV LiDAR CMSF.
Observation LineMAE (mm)AAE (mm)RMSE (mm)
Boundary CenterBoundary Center BoundaryCenter
Line H932645710360122
Line A8113754915696
Total result2648498
Table 6. Accuracy comparison of the three CMSF.
Table 6. Accuracy comparison of the three CMSF.
AreaData SourceMAE (mm)AAE (mm)RMSE (mm)
Boundary deformationSAR preliminary CMSF471621
UAV LiDAR CMSF935659
Refined CMSF471621
Center deformationSAR preliminary CMSF400123178
UAV LiDAR CMSF26497114
Refined CMSF934862
Total resultSAR preliminary CMSF40096144
UAV LiDAR CMSF2648498
Refined CMSF933951
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MDPI and ACS Style

Yang, B.; Du, W.; Zou, Y.; Zhang, H.; Chai, H.; Wang, W.; Song, X.; Zhang, W. Reconstruction of Coal Mining Subsidence Field by Fusion of SAR and UAV LiDAR Deformation Data. Remote Sens. 2024, 16, 3383. https://doi.org/10.3390/rs16183383

AMA Style

Yang B, Du W, Zou Y, Zhang H, Chai H, Wang W, Song X, Zhang W. Reconstruction of Coal Mining Subsidence Field by Fusion of SAR and UAV LiDAR Deformation Data. Remote Sensing. 2024; 16(18):3383. https://doi.org/10.3390/rs16183383

Chicago/Turabian Style

Yang, Bin, Weibing Du, Youfeng Zou, Hebing Zhang, Huabin Chai, Wei Wang, Xiangyang Song, and Wenzhi Zhang. 2024. "Reconstruction of Coal Mining Subsidence Field by Fusion of SAR and UAV LiDAR Deformation Data" Remote Sensing 16, no. 18: 3383. https://doi.org/10.3390/rs16183383

APA Style

Yang, B., Du, W., Zou, Y., Zhang, H., Chai, H., Wang, W., Song, X., & Zhang, W. (2024). Reconstruction of Coal Mining Subsidence Field by Fusion of SAR and UAV LiDAR Deformation Data. Remote Sensing, 16(18), 3383. https://doi.org/10.3390/rs16183383

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