# Longwall Retreat and Creep Measurement Based on UWB Radar Imaging Method

Authors: Shijia Wang; Shibo Wang; Wanli Liu
Journal: Mathematical Problems in Engineering
 (2020)

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## Abstract

The measurement of longwall retreat and creep displacements is of great significance for the safety production of a coal mine. In order to reliably and accurately obtain the longwall retreat and creep displacements, this paper proposes an ultrawideband (UWB) radar imaging method. The bolt plates fixed in the roadway coal wall are imaged as the target points. First, a signal model is built, and a modified nonlinear chirp scaling (NLCS) imaging algorithm is designed to obtain the high-resolution image. Then, the retreat and creep displacements are estimated based on the imaging results. Finally, simulation and experiment are performed. The simulation results show that the radar imaging method is theoretically feasible to measure the retreat and creep displacements. The measurement errors in the experiment are 0.058 m and 0.040 m, respectively. In the experiment, the radar velocity fluctuation and signal attenuation cause the target azimuth and range errors in the imaging results, which makes the measurement errors in the experiment larger than that in the simulation. This method requires no additional roadway information except for the bolt plates fixed in the coal wall. In addition, the signal propagation of UWB radar is rarely affected by the dust and moisture in the harsh environment.


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## Body

## 1. Introduction

Longwall mining is a primary method for extracting coal from underground mine, as it can protect worker safety and improve mining productivity. The typical plane view of a longwall mining panel is shown in Figure1(a). Two long roadways are excavated to form the boundaries of the longwall panel [1, 2]. At the end of the roadway, a shearer, an armored face conveyor (AFC), and a roof support system are installed across the back of the panel, creating the longwall face. The shearer moves back and forth along a rail associated with the AFC to cut the coal seam, while the roof support system supports the coal seam roof. As the shearer travels, the AFC is pushed along the retreat direction by the larger hydraulic push arms attached to the roof support system for the next cutting cycle [3, 4]. A cutting cycle refers to the process in which the shearer moves the whole length of the longwall face. The longwall retreat displacement is the difference of AFC position along the retreat direction between the adjacent cutting cycles shown in Figure 2. Due to the interaction between the coal seam and equipment during the mining progress, different sections of the longwall face may have different retreat distances, causing deviations in the longwall face profile. Gradually, one part of the longwall face will lag behind the whole advancing progress, potentially causing the roof to fail. In addition, the interaction between the coal seam and equipment in variation pressures also leads to the sideway slippage of equipment across the longwall face, called the longwall creep. This prevents the retreat of longwall face. The longwall creep displacement refers to the difference of AFC position along the moving direction between the adjacent cutting cycles shown in Figure 2. Therefore, it is necessary to monitor the longwall retreat and creep displacements. Recently, researchers have proposed three methods, including a laser radar [5], an Endress-Hauser FMR 250 radar [6–8], and the ultrawideband (UWB) positioning technology [9, 10], to determine those two displacements.Figure 1
Typical plane view of (a) a longwall mining panel and (b) mining equipment [11].Figure 2
Diagram of the longwall retreat and creep displacements.Reid et al. [5] installed the laser radar on the roadway conveyor structure linked to the AFC to scan the roadway. Two sets of scanning results were obtained before and after the AFC movement, and a scan-matching algorithm was used to obtain the longwall retreat and creep information. However, the laser propagation is greatly affected by the dust and moisture in the underground mine, so the measurement accuracy is not guaranteed. Hargrave et al. [6–8] used the Endress-Hauser FMR 250 radar to identify the bolt plates in the roadway coal wall to measure the longwall retreat and creep displacements in the Australian Beltana mine. Longwall creep displacement was measured by the distance variance between the radar and the coal wall of the roadway. In the Beltana mine, the number of bolt plates in the coal wall is a known environment mining parameter, and the radar identified the bolt plates to estimate the longwall retreat distance. However, this parameter may be unknown or inaccurate in most mines, which means this method is not widely applied. Tian et al. [9, 10] proposed the ultrawideband (UWB) positioning technology to determine the longwall retreat and creep displacements. Reference nodes were placed on the roadway with known coordinates, and a target node was installed on the shearer. When the shearer moved to the end of the longwall face, the position coordinate of target node was determined through the reference nodes with the time of arrival (TOA) or time difference of arrival (TDOA) algorithms. The longwall retreat and creep displacements were the coordinate variation of the target node between the adjacent cutting cycles. However, the communication between the reference nodes and the target node may be blocked by the coal seam, shearer body, roof support system, and so on, which can cause the range error. This makes the measured displacements of longwall retreat and creep unreliable.In order to measure the longwall retreat and creep information reliably and accurately, an UWB radar imaging method is proposed in this study. Figure3(a) shows the UWB radar imaging device. The two-direction guide rail is installed in the head of AFC, which moves with the advancing of longwall face. The two-direction guide rail enables the radar to move along the horizontal axis at different heights. The bolt plates (Figure 3(b)) in the coal wall of roadway are the targets to be imaged. Before the advancing of longwall face, the radar images bolt plates in a certain area of the roadway. After the advancing, the rotation table changes the direction of the radar beam, and the radar scans the same area of the roadway. According to the coordinate relationship of the targets in these two images, the longwall retreat and creep displacements are obtained. This radar imaging method makes use of the bolt plates fixed in the coal wall as the target points and requires no additional environment information. In addition, the UWB signal can propagate nearly without the influence of the dust and moisture. Based on this idea, this study designs the algorithm to image the targets and proposes the method to obtain the target three-dimensional (3D) coordinates and longwall retreat and creep displacements. The simulation and experiment results are performed to validate the feasibility of the radar imaging method for measuring the retreat and creep displacements.Figure 3
The diagram of (a) UWB radar imaging device and (b) the bolt plates in the coal wall of roadway [7].
(a)
(b)The remainder of this paper is organized as follows. The radar imaging algorithm is described in Section2. Section 3 gives the method to obtain the longwall retreat and creep displacements according to the imaging results. The simulation and experiment are performed in Section 4 to validate the proposed method. Finally, the conclusion is summarized in Section 5.


## 2. Imaging Algorithm

For high-resolution squinted synthetic aperture radar (SAR) imaging, various algorithms have been proposed in recent years, including range-Doppler (RD) algorithm [12–14], chirp scaling (CS) algorithm [15–21], omega-K algorithm [22, 23], and backprojection (BP) algorithm [24, 25]. Because of the high efficiency and precise error compensation, CS algorithm has been widely applied to process the squinted SAR data compared with other algorithms. In the range focusing, Sun et al. [15] used the squint-minimized function to reduce the range cell migration (RCM). Wu et al. [16] and Sun et al. [17] eliminated the RCM with the keystone transform (KT) in the bistatic and monostatic SAR, respectively. Zhong et al. [18] utilized the linear range walk correction (LRWC) and bulk RCM correction (BRCMC) to remove the RCM. In the azimuth focusing, [19–21] proposed the nonlinear CS (NLCS) algorithm to equalize the azimuth-dependent frequency modulation (FM) rate. The RCM and azimuth-dependent FM rate make it difficult to obtain the high-resolution image. In this study, an algorithm is proposed to solve these two problems.


### 2.1. Signal Model

The geometric model of squinted SAR imaging is shown in Figure4. The roadway coordinate system is defined as OXYZ, and the radar coordinate system is OrXrYrZr. The radar moves along the direction parallel to Xr-axis with a constant velocity v. Os is the center of synthetic aperture length at radar height h where the azimuth time ta is equal to zero. The synthetic aperture length is the distance of radar movement. θs is the radar squint angle. The imaging scene is located on OXZ plane. The point T is the scene center, and M is an arbitrary point. r0 = GM is the slant range from the target M to the radar movement trajectory along the radar squint angle θs. When the radar is at azimuth time ta which meets vta = OsH, the instantaneous slant range of target M is given by R = HM. The target M is located at the azimuth time tn along the radar squint angle, which satisfies vtn = OsG = TM.Figure 4
Geometric model of SAR imaging.The expression of the instantaneous rangeR is given by(1)Rta,r0=v2ta−tn2+r02−2vr0ta−tnsinθs≈r0+∑i=14kita−tni,where ki is the coefficient of the Taylor polynomial.It is assumed a Gaussian pulse is transmitted by the radar, and the demodulated echo signalS0(tr, ta) from target M is given by(2)S0tr,ta=wrtr−2Rta,r0cwataptr−2Rta,r0cexp−j4πfccRta,r0,where tr is the fast time, ta is the slow time, wrtr is the range time envelope, wata is the azimuth time envelope, c is the speed of light, p(tr) is the Gaussian pulse, and fc is the carrier frequency.


### 2.2. Imaging Algorithm

The imaging algorithm contains the range focusing and azimuth focusing. In the range, the spatial-variant RCM is eliminated by the extended nonlinear CS (ENLCS) algorithm proposed in [26] and the secondary range compression (SRC). In the azimuth focusing, this algorithm adds an azimuth compensation factor to overcome the azimuth distortion compared with [19–21].


#### 2.2.1. Range Focusing

The echo signal (2) is transformed into the range-Doppler domain and yields(3)S1fr,ta=WrfrwataPfrexp−j4πfc+frcr0exp−j4πfc+frck1ta−tnexp−j4πfc+frck2ta−tn2+k3ta−tn3+k4ta−tn4,where fr is the range frequency, Wr(fr) is the range frequency envelope, and P(fr) is the frequency response of the Gaussian pulse.The linear range walk correction (LRWC) is firstly used to remove the liner component of RCM, and LRWC function is given as follows:(4)H1fr,ta=exp−j4πfc+frcvsinθqta,where θq is the squint angle of the reference point in the scene center. After LRWC, r0 becomes rLRCM=r0+vsinθqtn, and the coefficient k1 of LRCM becomes k1res=−vsinθs−−vsinθq. In this study, k1res is expressed as(5)k1res=k10+∂k1res∂tntn=k10+k11tn,where k10 is the azimuth-invariant term and k11 is the first-order coefficient of the azimuth-variant term. Then, ENLCS function [26] is used to eliminate the azimuth-dependent RCM as follows:(6)H2fr,ta=expj4πfc+frcp2ta2,where p2 = k11/2 is the coefficient of the ENLCS function. After ENLCS, transforming the result into the 2D frequency domain yields(7)S2fr,fa=WrfrWafaPfrexpjφfr,faexp−j2πfatn,where Wa(fa) is the azimuth frequency envelope and φ(fr, fa) is expanded as a series of fr as :(8)φfr,fa=φ0faφ1fafr+φ2fafr2+∑n=3∞φnfafrn,where φ0(fa) is the azimuth modulation term and φi(fa) (i = 1, 2, …) are the coefficients of the i-th range-dependent terms. Then, SRC is applied to remove the range-dependent RCM. Finally, range compression (RC) is operated to accomplish the range focusing. SRC and RC functions are as follows:(9)H3fr,fa=exp−jφfr,fa−φ0faexp−j4πrLRCMcfr,(10)H4fr=Pfr¯.Multiplying (9) and (10) with (7) and transforming the result into the range time and azimuth frequency domain yield(11)S3tr,fa=WafasincBrtr−2rLRCMcexpjφ0faexp−j2πfatn,where sinc(·) is the sampling function and Br is the signal bandwidth.


#### 2.2.2. Azimuth Focusing

Expandingφ0(fa) into a series of fa yields(12)φ0fa≈πη0+πη1fa+πη2fa2+πη3fa3+πη4fa4,where η0 is the azimuth-independent term and η1∼η4 are the coefficients of the azimuth-dependent terms. Firstly, an azimuth compensation factor is applied to compensate the azimuth distortion as follows:(13)H5fa=exp−jπη1fa.DefineKa = −1/2η2, and expand Ka as a series of tn as follows:(14)Ka=Ka0+Ks1tn+Ks2tn2,where Ka0 is the azimuth-independent term of Ka and KS1 and KS2 are the first-order and second-order coefficients of azimuth-dependent terms of Ka. Then, NLCS is utilized to eliminate the high-order Doppler phase and equalize the FM rate by multiplying a filter function in the range-Doppler domain and a scaling function in the 2D time domain. The filter and scaling functions are given as follows:(15)H6fa=expjπY3fa3+jπY4fa4,H7ta=expjπq2ta2+jπq3ta3+jπq4ta4,where the coefficients Y3, Y4, q2, q3, and q4 can be found in [21]. After the azimuth compensation and NLCS, the signal in the range-Doppler domain becomes(16)S4tr,fa=Wafa−q2tnKa+q2sincBrtr−2rLRCMcexp−j2πfatn2αexp−jπ1Ka0+q2fa2+jπY3Ka03+q3Ka0+q23fa3+jπY4Ka04+q4Ka0+q24fa4,where α is the scaling factor. Finally, azimuth compression (AC) is operated to realize the azimuth focusing. AC function is given as(17)H8fa=expjπ1Ka0+q2fa2−jπY3Ka03+q3Ka0+q23fa3−jπY4Ka04+q4Ka0+q24fa4.After AC, the result is transformed into the range time and azimuth time domain as follows:(18)S5tr,ta=sincBrtr−2rLRCMcsincBata−tn2α,where Ba is the Doppler bandwidth. The target is focused at (tn/2α, rLRCM), which needs to be corrected by geometry correction to obtain the real position by (18).(19)tnc=tn2α2α1rLC=rLRCM−tn2αsinθq.


## 2.1. Signal Model

The geometric model of squinted SAR imaging is shown in Figure4. The roadway coordinate system is defined as OXYZ, and the radar coordinate system is OrXrYrZr. The radar moves along the direction parallel to Xr-axis with a constant velocity v. Os is the center of synthetic aperture length at radar height h where the azimuth time ta is equal to zero. The synthetic aperture length is the distance of radar movement. θs is the radar squint angle. The imaging scene is located on OXZ plane. The point T is the scene center, and M is an arbitrary point. r0 = GM is the slant range from the target M to the radar movement trajectory along the radar squint angle θs. When the radar is at azimuth time ta which meets vta = OsH, the instantaneous slant range of target M is given by R = HM. The target M is located at the azimuth time tn along the radar squint angle, which satisfies vtn = OsG = TM.Figure 4
Geometric model of SAR imaging.The expression of the instantaneous rangeR is given by(1)Rta,r0=v2ta−tn2+r02−2vr0ta−tnsinθs≈r0+∑i=14kita−tni,where ki is the coefficient of the Taylor polynomial.It is assumed a Gaussian pulse is transmitted by the radar, and the demodulated echo signalS0(tr, ta) from target M is given by(2)S0tr,ta=wrtr−2Rta,r0cwataptr−2Rta,r0cexp−j4πfccRta,r0,where tr is the fast time, ta is the slow time, wrtr is the range time envelope, wata is the azimuth time envelope, c is the speed of light, p(tr) is the Gaussian pulse, and fc is the carrier frequency.


## 2.2. Imaging Algorithm

The imaging algorithm contains the range focusing and azimuth focusing. In the range, the spatial-variant RCM is eliminated by the extended nonlinear CS (ENLCS) algorithm proposed in [26] and the secondary range compression (SRC). In the azimuth focusing, this algorithm adds an azimuth compensation factor to overcome the azimuth distortion compared with [19–21].


### 2.2.1. Range Focusing

The echo signal (2) is transformed into the range-Doppler domain and yields(3)S1fr,ta=WrfrwataPfrexp−j4πfc+frcr0exp−j4πfc+frck1ta−tnexp−j4πfc+frck2ta−tn2+k3ta−tn3+k4ta−tn4,where fr is the range frequency, Wr(fr) is the range frequency envelope, and P(fr) is the frequency response of the Gaussian pulse.The linear range walk correction (LRWC) is firstly used to remove the liner component of RCM, and LRWC function is given as follows:(4)H1fr,ta=exp−j4πfc+frcvsinθqta,where θq is the squint angle of the reference point in the scene center. After LRWC, r0 becomes rLRCM=r0+vsinθqtn, and the coefficient k1 of LRCM becomes k1res=−vsinθs−−vsinθq. In this study, k1res is expressed as(5)k1res=k10+∂k1res∂tntn=k10+k11tn,where k10 is the azimuth-invariant term and k11 is the first-order coefficient of the azimuth-variant term. Then, ENLCS function [26] is used to eliminate the azimuth-dependent RCM as follows:(6)H2fr,ta=expj4πfc+frcp2ta2,where p2 = k11/2 is the coefficient of the ENLCS function. After ENLCS, transforming the result into the 2D frequency domain yields(7)S2fr,fa=WrfrWafaPfrexpjφfr,faexp−j2πfatn,where Wa(fa) is the azimuth frequency envelope and φ(fr, fa) is expanded as a series of fr as :(8)φfr,fa=φ0faφ1fafr+φ2fafr2+∑n=3∞φnfafrn,where φ0(fa) is the azimuth modulation term and φi(fa) (i = 1, 2, …) are the coefficients of the i-th range-dependent terms. Then, SRC is applied to remove the range-dependent RCM. Finally, range compression (RC) is operated to accomplish the range focusing. SRC and RC functions are as follows:(9)H3fr,fa=exp−jφfr,fa−φ0faexp−j4πrLRCMcfr,(10)H4fr=Pfr¯.Multiplying (9) and (10) with (7) and transforming the result into the range time and azimuth frequency domain yield(11)S3tr,fa=WafasincBrtr−2rLRCMcexpjφ0faexp−j2πfatn,where sinc(·) is the sampling function and Br is the signal bandwidth.


### 2.2.2. Azimuth Focusing

Expandingφ0(fa) into a series of fa yields(12)φ0fa≈πη0+πη1fa+πη2fa2+πη3fa3+πη4fa4,where η0 is the azimuth-independent term and η1∼η4 are the coefficients of the azimuth-dependent terms. Firstly, an azimuth compensation factor is applied to compensate the azimuth distortion as follows:(13)H5fa=exp−jπη1fa.DefineKa = −1/2η2, and expand Ka as a series of tn as follows:(14)Ka=Ka0+Ks1tn+Ks2tn2,where Ka0 is the azimuth-independent term of Ka and KS1 and KS2 are the first-order and second-order coefficients of azimuth-dependent terms of Ka. Then, NLCS is utilized to eliminate the high-order Doppler phase and equalize the FM rate by multiplying a filter function in the range-Doppler domain and a scaling function in the 2D time domain. The filter and scaling functions are given as follows:(15)H6fa=expjπY3fa3+jπY4fa4,H7ta=expjπq2ta2+jπq3ta3+jπq4ta4,where the coefficients Y3, Y4, q2, q3, and q4 can be found in [21]. After the azimuth compensation and NLCS, the signal in the range-Doppler domain becomes(16)S4tr,fa=Wafa−q2tnKa+q2sincBrtr−2rLRCMcexp−j2πfatn2αexp−jπ1Ka0+q2fa2+jπY3Ka03+q3Ka0+q23fa3+jπY4Ka04+q4Ka0+q24fa4,where α is the scaling factor. Finally, azimuth compression (AC) is operated to realize the azimuth focusing. AC function is given as(17)H8fa=expjπ1Ka0+q2fa2−jπY3Ka03+q3Ka0+q23fa3−jπY4Ka04+q4Ka0+q24fa4.After AC, the result is transformed into the range time and azimuth time domain as follows:(18)S5tr,ta=sincBrtr−2rLRCMcsincBata−tn2α,where Ba is the Doppler bandwidth. The target is focused at (tn/2α, rLRCM), which needs to be corrected by geometry correction to obtain the real position by (18).(19)tnc=tn2α2α1rLC=rLRCM−tn2αsinθq.


## 2.2.1. Range Focusing

The echo signal (2) is transformed into the range-Doppler domain and yields(3)S1fr,ta=WrfrwataPfrexp−j4πfc+frcr0exp−j4πfc+frck1ta−tnexp−j4πfc+frck2ta−tn2+k3ta−tn3+k4ta−tn4,where fr is the range frequency, Wr(fr) is the range frequency envelope, and P(fr) is the frequency response of the Gaussian pulse.The linear range walk correction (LRWC) is firstly used to remove the liner component of RCM, and LRWC function is given as follows:(4)H1fr,ta=exp−j4πfc+frcvsinθqta,where θq is the squint angle of the reference point in the scene center. After LRWC, r0 becomes rLRCM=r0+vsinθqtn, and the coefficient k1 of LRCM becomes k1res=−vsinθs−−vsinθq. In this study, k1res is expressed as(5)k1res=k10+∂k1res∂tntn=k10+k11tn,where k10 is the azimuth-invariant term and k11 is the first-order coefficient of the azimuth-variant term. Then, ENLCS function [26] is used to eliminate the azimuth-dependent RCM as follows:(6)H2fr,ta=expj4πfc+frcp2ta2,where p2 = k11/2 is the coefficient of the ENLCS function. After ENLCS, transforming the result into the 2D frequency domain yields(7)S2fr,fa=WrfrWafaPfrexpjφfr,faexp−j2πfatn,where Wa(fa) is the azimuth frequency envelope and φ(fr, fa) is expanded as a series of fr as :(8)φfr,fa=φ0faφ1fafr+φ2fafr2+∑n=3∞φnfafrn,where φ0(fa) is the azimuth modulation term and φi(fa) (i = 1, 2, …) are the coefficients of the i-th range-dependent terms. Then, SRC is applied to remove the range-dependent RCM. Finally, range compression (RC) is operated to accomplish the range focusing. SRC and RC functions are as follows:(9)H3fr,fa=exp−jφfr,fa−φ0faexp−j4πrLRCMcfr,(10)H4fr=Pfr¯.Multiplying (9) and (10) with (7) and transforming the result into the range time and azimuth frequency domain yield(11)S3tr,fa=WafasincBrtr−2rLRCMcexpjφ0faexp−j2πfatn,where sinc(·) is the sampling function and Br is the signal bandwidth.


## 2.2.2. Azimuth Focusing

Expandingφ0(fa) into a series of fa yields(12)φ0fa≈πη0+πη1fa+πη2fa2+πη3fa3+πη4fa4,where η0 is the azimuth-independent term and η1∼η4 are the coefficients of the azimuth-dependent terms. Firstly, an azimuth compensation factor is applied to compensate the azimuth distortion as follows:(13)H5fa=exp−jπη1fa.DefineKa = −1/2η2, and expand Ka as a series of tn as follows:(14)Ka=Ka0+Ks1tn+Ks2tn2,where Ka0 is the azimuth-independent term of Ka and KS1 and KS2 are the first-order and second-order coefficients of azimuth-dependent terms of Ka. Then, NLCS is utilized to eliminate the high-order Doppler phase and equalize the FM rate by multiplying a filter function in the range-Doppler domain and a scaling function in the 2D time domain. The filter and scaling functions are given as follows:(15)H6fa=expjπY3fa3+jπY4fa4,H7ta=expjπq2ta2+jπq3ta3+jπq4ta4,where the coefficients Y3, Y4, q2, q3, and q4 can be found in [21]. After the azimuth compensation and NLCS, the signal in the range-Doppler domain becomes(16)S4tr,fa=Wafa−q2tnKa+q2sincBrtr−2rLRCMcexp−j2πfatn2αexp−jπ1Ka0+q2fa2+jπY3Ka03+q3Ka0+q23fa3+jπY4Ka04+q4Ka0+q24fa4,where α is the scaling factor. Finally, azimuth compression (AC) is operated to realize the azimuth focusing. AC function is given as(17)H8fa=expjπ1Ka0+q2fa2−jπY3Ka03+q3Ka0+q23fa3−jπY4Ka04+q4Ka0+q24fa4.After AC, the result is transformed into the range time and azimuth time domain as follows:(18)S5tr,ta=sincBrtr−2rLRCMcsincBata−tn2α,where Ba is the Doppler bandwidth. The target is focused at (tn/2α, rLRCM), which needs to be corrected by geometry correction to obtain the real position by (18).(19)tnc=tn2α2α1rLC=rLRCM−tn2αsinθq.


## 3. Longwall Retreat and Creep Displacement Estimation

The imaging result contains the target position information, including the slant rangerLC and azimuth time tnc. In order to obtain the target 3D coordinate information, the radar needs to scan the target at different heights. Figure 5 shows the geometrical relationship of radar movement at h1 and h2 heights. rLC1 and rLC2 are the slant ranges of target M when the radar moves at h1 and h2 heights, respectively. l is the difference between h1 and h2, which is called the base line. With the cosine theorem, the relationship in the triangle h1Mh2 satisfies as follows:(20)rLC22=rLC12+l2+2rLC1lcosβ.Figure 5
The geometrical relationship of radar movement ath1 and h2 heights.According to (20), β is obtained as (21). Then, the height of target M is given as (22).(21)β=cos−1rLC12+l2−rLC22−2rLC1l,(22)hp=h1−rLC1cosβ.Through the above analysis, the 3D position coordinate of targetM in the OrXrYrZr is obtained as(23)Pvtnc+rLC1sinβsinθq,rLC1sinβcosθq,hp.Similarly, after the advancing of longwall face, the coordinateP′ of the target M is also obtained. Therefore, the advancing displacement is ΔP = −(P′−P). The longwall retreat and creep displacements are the components of the advancing displacement in the X-axis and Y-axis, respectively.


## 4. Simulation and Experiment

### 4.1. Simulation

To verify the effectiveness of the proposed method, a simulation with parameters in Table1 was performed using MATLAB. Suppose that the longwall advancing displacement ΔP was [0.80 m, 0.10 m, 0.00 m]; that is, the longwall retreat and creep information were 0.80 m and 0.10 m, respectively. There were three targets A∼C in the imaging scene. The coordinates of A∼C in the roadway coordinate system were A(0.786 m, 0.000 m, 0.300 m), B(1.386 m, 0.000 m, 0.300 m), and C(1.986 m, 0.000 m, 0.300 m), and the distribution of these targets was shown in Figure 6. The target B was chosen as the reference point. Before the advancing of longwall face, X-axis and Xr-axis were coincident, and other two axes in the OXYZ and OrXrYrZr were parallel, respectively. The radar traveled at two heights h1 = 0.15 m and h2 = 0.30 m before and after the advancing of longwall face. The radar squint angle was 30° before the advancing. After the advancing, the radar squint angle was changed to 13.18° to make the reference point B imaged in the middle of the imaging result. It needed special explanation that all imaging results were obtained without any processing of the weighting function or side-lobe control.Table 1
Parameters in the first simulation.
Parameters
Values
Parameters
Values
Signal carrier frequency
4.3 GHz
Signal bandwidth
1.7 GHz
Sampling frequency
20 Hz
Radar moving velocity
0.15 m/s
Synthetic aperture length
2 m
Radar height
0.15/0.30 m
Roadway width
2.4 m
Advancing displacement
[0.80, 0.10, 0.00] m
Radar squint angle
30°/13.18°Figure 6
The distribution of targets A∼C.Figure7 shows the radar imaging results at 0.15 m and 0.30 m heights before and after the advancing of longwall face. It was seen that three targets were clearly imaged. Because of the range shift caused by LRWC process, the targets A and C were not imaged in the same range cell as target B in the final imaging results. Target B had no the shift along the range direction because target B was selected as the reference point. The range shift was related with the target azimuth time and radar squint angle. The farther away the target is from the reference point in the azimuth direction, the greater the range shift is. When the azimuth time of target was less than that of reference point, the target had the shift along the range negative direction. When the azimuth time of target was larger than that of reference point, the target had the shift along the range positive direction. In addition, the range shift increased with the radar squint angle, which explained that the range shift of A and C relative to B in Figures 7(a) and 7(b) was greater than that in Figures 7(c) and 7(d). The imaging results contained the targets azimuth and range information. Because the distances between the targets and the radar did not vary much when the radar scanned at 0.15 m and 0.30 m heights, there were no obvious changes for the target position between Figures 7(a) and 7(b), as well as Figures 7(c) and 7(d). Table 2 shows the target azimuth and range errors before and after the advancing in the simulation. Table 3 shows the target positions and its errors in the radar coordinate system before and after the advancing, and the advancing displacements according to the target positions. Whether before or after the advancing of longwall face, the position errors of A∼C in Zr-axis were larger than the Xr-axis and Yr-axis. Actually, the radar moving at different heights was equivalent to form the synthetic aperture along Zr-axis. Because there were only two sampling data along Zr-axis, the Zr-axis position error was larger. If the radar moved at more heights, the Zr-axis position error would be reduced. Theoretically, as long as there was one target, the advancing displacement could be obtained. Three targets were imaged in the simulation to improve the measuring accuracy of advancing displacement with average operation. In Table 3, three displacements were obtained by targets A, B, and C, respectively, which were (0.786 m, 0.088 m, 0.047 m), (0.783 m, 0.097 m, −0.069 m), and (0.811 m, 0.100 m, 0.098 m). The advancing displacement with average operation was 0.794 m along X-axis, 0.095 m along Y-axis, and 0.025 m along Z-axis, whose errors were −0.006 m, −0.005 m, and 0.025 m, respectively. The advancing displacement error in Z-axis was larger than the other two axes because the target position error in Zr-axis was larger than the Xr-axis and Yr-axis.Figure 7
The radar imaging results at 0.15 m and 0.30 m heights before and after the advancing of longwall face. (a) 0.15 m before the advancing, (b) 0.30 m before the advancing, (c) 0.15 m after the advancing, and (d) 0.30 m after the advancing.
(a)
(b)
(c)
(d)Table 2
The target azimuth and range errors before and after the advancing in the first simulation.
Height (m)
Azimuth (m)
Range (m)
A
B
C
A
B
C
Before
0.15
0.024
0.004
0.010
0.022
0.002
0.009
0.30
0.024
0.008
0.022
0.021
0.001
0.006
After
0.15
0.002
0.014
0.004
0.005
0.004
0.003
0.30
0.004
0.010
0.008
0.006
0.001
0.004Table 3
Target positions and its errors in the radar coordinate system before and after the advancing, and the advancing displacements according to the target positions in the first simulation.
Targets
Real position (m)
Calculated position (m)
Error (m)
A
Before
(0.786, −2.400, 0.300)
(0.772, −2.418, 0.324)
(−0.014, 0.018, 0.024)
After
(−0.014, −2.500, 0.300)
(−0.014, −2.506, 0.277)
(0.001, −0.006, −0.023)
Displacement
(0.800, 0.100, 0.000)
(0.786, 0.088, 0.047)
(−0.014, −0.012, 0.047)
B
Before
(1.386, −2.400, 0.300)
(1.380, −2.401, 0.307)
(−0.005, −0.001, 0.007)
After
(0.586, −2.500, 0.300)
(0.597, −2.498, 0.376)
(0.012, 0.002, 0.076)
Displacement
(0.800, 0.100, 0.000)
(0.783, 0.097, −0.069)
(−0.017, −0.003, −0.069)
C
Before
(1.986, −2.400, 0.300)
(2.004, −2.404, 0.369)
(0.018, −0.004, 0.069)
After
(1.186, −2.500, 0.300)
(1.193, −2.504, 0.271)
(0.007, −0.004, −0.029)
Displacement
(0.800, 0.100, 0.000)
(0.811, 0.100, 0.098)
(0.011, 0.001, 0.098)Another simulation was performed according to the simulation parameters listed in Table4. Except for the signal carrier frequency, bandwidth, and sampling frequency, other parameters were changed compared with the first simulation. Three targets D∼F were imaged in this simulation, whose coordinates in the roadway coordinate system were D(1.678 m, 0.000 m, 0.400 m), E(1.678 m, 0.000 m, 1.200 m), and F(1.678 m, 0.000 m, 1.600 m) (Figure 8). The target E was selected as the reference point. It was supposed that, before the advancing of longwall face, X-axis and Xr-axis were coincident, and other two axes in the OXYZ and OrXrYrZr are parallel, respectively.Table 4
Parameters in the second simulation.
Parameters
Values
Parameters
Values
Signal carrier frequency
4.3 GHz
Signal bandwidth
1.7 GHz
Sampling frequency
20 Hz
Radar moving velocity
0.2 m/s
Synthetic aperture length
1.8 m
Radar height
0.05/0.25 m
Roadway width
2.0 m
Advancing displacement
[0.70, −0.10, 0.00] m
Radar squint angle
40°/27.24°Figure 8
The distribution of targets D∼F.Figure9 shows the radar imaging results at 0.05 m and 0.25 m heights before and after the advancing of longwall face. The target azimuth and range errors in the imaging results are listed in Table 5. Table 6 shows the target positions and its errors in the radar coordinate system before and after the advancing, and the advancing displacements according to the target positions. According to the calculated coordinates of targets D∼F before and after the advancing, three values of advancing displacement were obtained, which were (0.697 m, −0.100 m, 0.027 m), (0.691 m, −0.096 m, 0.019 m), and (0.699 m, −0.118 m, −0.033 m), respectively. The average value of advancing displacement was 0.696 m along X-axis, −0.105 m along Y-axis, and 0.004 m along Z-axis, and its errors were 0.004 m, 0.005 m, and 0.004 m, respectively. In the above two simulations, the advancing displacement errors in X-axis and Y-axis were at millimeter lever.Figure 9
The radar imaging results at 0.05 m and 0.25 m heights before and after the advancing of longwall face. (a) 0.05 m before the advancing, (b) 0.25 m before the advancing, (c) 0.05 m after the advancing, and (d) 0.25 m after the advancing.
(a)
(b)
(c)
(d)Table 5
The target azimuth and range errors before and after the advancing in the second simulation.
Height (m)
Azimuth (m)
Range (m)
D
E
F
D
E
F
Before
0.05
0.008
0.004
0.001
0.005
0.001
0.001
0.25
0.008
0.008
0.004
0.005
0.001
0.001
After
0.05
0.008
0.004
0.016
0.009
0.001
0.001
0.25
0.004
0.001
0.012
0.007
0.001
0.001Table 6
Target positions and its errors in the radar coordinate system before and after the advancing, and the advancing displacements according to the target positions in the second simulation.
Targets
Real position (m)
Calculated position (m)
Error (m)
D
Before
(1.678, −2.000, 0.400)
(1.667, −1.996, 0.404)
(−0.012, 0.004, 0.004)
After
(0.978, −1.900, 0.400)
(0.970, −1.896, 0.377)
(−0.008, 0.005, −0.023)
Displacement
(0.700, −0.100, 0.000)
(0.697, −0.100, 0.027)
(−0.003, 0.001, 0.027)
E
Before
(1.678, −2.000, 1.200)
(1.669, −1.991, 1.230)
(−0.010, 0.009, 0.030)
After
(0.978, −1.900, 1.200)
(0.978, −1.895, 1.211)
(0.001, 0.005, 0.011)
Displacement
(0.700, −0.100, 0.000)
(0.691, −0.096, 0.019)
(−0.009, 0.004, 0.019)
F
Before
(1.678, −2.000, 1.600)
(1.685, −2.006, 1.586)
(0.007, −0.006, −0.015)
After
(0.978, −1.900, 1.600)
(0.986, −1.888, 1.619)
(0.008, 0.012, 0.019)
Displacement
(0.700, −0.100, 0.000)
(0.699, −0.118, −0.033)
(−0.001, −0.018, −0.033)


### 4.2. Experiment

An experiment was conducted according to the parameters of the first simulation listed in Table1. Figure 10 shows the diagram of the experiment site and imaging device. The roadway coordinate system OXYZ was established as shown in Figure 10(a). The radar coordinate system OrXrYrZr was built in Figure 10(b), where Or is the center point of the horizontal axis of the two-direction guide rail. Three corner reflectors were used as the imaging targets, which had the strong scattering intensity. In the imaging device, the UWB module was connected to the data processing system by USB. The diagram of UWB module was shown in Figure 11, and the parameters of UWB module are listed in Table 7. The UWB module and the antenna were connected through a radio frequency line. The antenna was a pyramidal horn antenna, whose frequency was 3.1∼4.8 GHz, gain was 10 dB, and stationary wave was less than 1.5. The antenna was installed in the rotation table, and the rotation table was installed in the two-direction guide rail. The rotation table could adjust the direction of the radar beam. The two-direction guide rail not only makes the antenna move along the horizontal axis, but also changes the antenna height along the vertical axis. The two-direction guide rail was placed in a mobile robot.Figure 10
The diagram of the experiment site and device. (a) Experiment site and (b) imaging device.
(a)
(b)Figure 11
The diagram of the UWB module.Table 7
The parameters of the UWB module.
Parameters
Value
Dimension
89 × 56 mm
Input power
5.0 V
Average transmit power
50 uW
Radio frequency
3.1∼4.8 GHz
Center frequency
4.3 GHz
Sample frequency
20 Hz
Max data throughput
19.2 kbps to 612 kbpsThe coordinates of three corner reflectors in the roadway coordinate system were A(0.786 m, 0.000 m, 0.300 m), B(1.386 m, 0.000 m, 0.300 m), and C(1.986 m, 0.000 m, 0.300 m). The target B was chosen as the reference point. The horizontal distance between the corner reflectors and the antenna was 2.4 m. A tapeline and a laser range finder were used to repeatedly determine the positions of the mobile robot, antenna, and the corner reflectors, which made the mean error of each position less than 0.005 m and the standard deviation less than 0.005 m. Before the robot movement,X-axis and Xr-axis were coincident, and other two axes in the OXYZ and OrXrYrZr were parallel, respectively. The velocity of radar moving was 0.15 m/s. The synthetic aperture length was 2 m. The antenna aperture length was 0.14 m. The radar scanned the corner reflectors at 0.15 m and 0.30 m height, respectively. It was supposed that the mobile robot moved 0.80 m along X-axis, 0.10 m along Y-axis, and 0.00 m along Z-axis. The radar squint angle was adjusted from 30° before the robot movement to 13.18° after the movement so that the reference point B was imaged in the center of the imaging result.The detailed steps in the experiment are shown as follows:Step 1: the mobile robot was located at (0.000 m, 2.400 m, 0.000 m) in the roadway coordinate system, and the radar squint angle was 30°. The two-direction slipway made the radar antenna move along the horizontal axis at 0.15 m and 0.30 m heights, respectively.Step 2: the mobile robot moved to (0.800 m, 2.500 m, 0.000 m), and the radar squint angle was adjusted to 13.18° by the rotation table.Step 3: the radar antenna moved along the horizontal axis at 0.15 m and 0.30 m heights again.Figure12 shows the radar imaging results at 0.15 m and 0.30 m heights before and after the robot movement. The target B was clearly imaged. Because the target B was the reference point, its RCM and azimuth-dependent FM rate had the precise compensation. The targets A and C were far from the reference point along the azimuth direction, whose RCMs and azimuth-dependent FM rates could not be fully compensated. Therefore, the targets A and C had the defocus to some extent. Table 8 shows the target azimuth and range errors before and after the robot movement in the experiment. The bandwidth of radar signal was 1.7 GHz, so the range resolution was 0.088 m. The azimuth resolution was 0.07 m, which was half of the antenna aperture length. In the radar imaging result at 0.30 m height after the robot movement, the azimuth error of target A (0.103 m) was larger than the azimuth resolution, which might be caused by the fluctuation of radar moving velocity. Except for this, the azimuth and range errors of other targets were within the resolution. Table 9 shows the target positions and its errors in the radar coordinate system before and after the robot movement, and the movement displacements according to the target positions. Except for the target A before the movement, the Z-axis position errors of other targets were larger than the X-axis and Y-axis, which was explained in the simulation. According to the calculated position coordinates of A∼C in the radar coordinate system before and after the movement, three movement displacements were (0.759 m, 0.174 m, 0.281 m), (0.742 m, 0.110 m, −0.146 m), and (0.730 m, 0.137 m, 0.720 m), respectively. The average value of movement displacement was obtained, which were 0.742 m along X-axis, 0.140 m along Y-axis, and -0.285 m along Z-axis. The errors of movement displacement were 0.058 m, 0.040 m, and 0.285 m, respectively. The movement displacement error in Z-axis was larger than X-axis and Y-axis. If the radar moved at more heights, the Z-axis error would decrease.Figure 12
The radar imaging results at 0.15 m and 0.30 m heights before and after the robot movement. (a) 0.15 m before the movement, (b) 0.30 m before the movement, (c) 0.15 m after the movement, and (d) 0.30 m after the movement.
(a)
(b)
(c)
(d)Table 8
The target azimuth and range errors before and after the robot movement in the experiment.
Height (m)
Azimuth (m)
Range (m)
A
B
C
A
B
C
Before
0.15
0.052
0.015
0.042
0.041
0.071
0.007
0.30
0.045
0.036
0.045
0.038
0.083
0.044
After
0.15
0.042
0.058
0.038
0.044
0.023
0.082
0.30
0.103
0.051
0.009
0.063
0.045
0.080Table 9
Target positions and its errors in the radar coordinate system before and after the robot movement, and the movement displacements according to the target positions.
Targets
Real position (m)
Calculated position (m)
Error (m)
A
Before
(0.786, −2.400, 0.300)
(0.724, −2.367, 0.248)
(−0.068, −0.033, −0.052)
After
(−0.014, −2.500, 0.300)
(−0.035, −2.541, −0.033)
(−0.021, −0.041, −0.333)
Displacement
(0.800, 0.100, 0.000)
(0.759, 0.174, 0.281)
(−0.041, 0.074, 0.281)
B
Before
(1.386, −2.400, 0.300)
(1.366, −2.321, 0.515)
(−0.020, −0.079, 0.215)
After
(0.586, −2.500, 0.300)
(0.624, −2.431, 0.661)
(0.038, 0.069, 0.361)
Displacement
(0.800, 0.100, 0.000)
(0.742, 0.110, −0.146)
(−0.058, 0.010, −0.146)
C
Before
(1.986, −2.400, 0.300)
(1.921, −2.285, 0.987)
(−0.065, −0.115, 0.687)
After
(1.186, −2.500, 0.300)
(1.191, −2.422, 0.267)
(0.005, −0.078, −0.033)
Displacement
(0.800, 0.100, 0.000)
(0.730, 0.137, 0.720)
(−0.070, 0.037, 0.720)UWB radar imaging result is shown in different colors according to the scattering intensity of the object. Because the corner reflector has stronger scattering intensity than other objects in the experiment, three corner reflectors were clearly imaged. In the experiment, the tripods and other objects in the room had weaker scattering intensity than the corner reflectors, which explained that only three corner reflectors are clearly imaged in Figure12. Therefore, the tripods and others in the room environment little affected the imaging result. As mentioned above, the position errors of the imaging device and corner reflectors were corrected with the tapeline and laser range finder. In the experiment, the radar velocity fluctuation and the signal attenuation caused the target azimuth and range errors (Table 8), respectively, which were larger than that in the simulation (Tables 2 and 5). UWB pulse shape also had the influence on the image resolution. In [27], Oloumi et al. showed the Gaussian pulse provided better image resolution compared with the chirp pulse. Therefore, the Gaussian pulse proposed in [28] was used in this paper. In the next, increasing the signal transmitting power and bandwidth will be operated to improve the imaging quality. Other imaging algorithms including the back-projection algorithm and omega-k algorithm will be modified to reduce the measurement errors.


## 4.1. Simulation

To verify the effectiveness of the proposed method, a simulation with parameters in Table1 was performed using MATLAB. Suppose that the longwall advancing displacement ΔP was [0.80 m, 0.10 m, 0.00 m]; that is, the longwall retreat and creep information were 0.80 m and 0.10 m, respectively. There were three targets A∼C in the imaging scene. The coordinates of A∼C in the roadway coordinate system were A(0.786 m, 0.000 m, 0.300 m), B(1.386 m, 0.000 m, 0.300 m), and C(1.986 m, 0.000 m, 0.300 m), and the distribution of these targets was shown in Figure 6. The target B was chosen as the reference point. Before the advancing of longwall face, X-axis and Xr-axis were coincident, and other two axes in the OXYZ and OrXrYrZr were parallel, respectively. The radar traveled at two heights h1 = 0.15 m and h2 = 0.30 m before and after the advancing of longwall face. The radar squint angle was 30° before the advancing. After the advancing, the radar squint angle was changed to 13.18° to make the reference point B imaged in the middle of the imaging result. It needed special explanation that all imaging results were obtained without any processing of the weighting function or side-lobe control.Table 1
Parameters in the first simulation.
Parameters
Values
Parameters
Values
Signal carrier frequency
4.3 GHz
Signal bandwidth
1.7 GHz
Sampling frequency
20 Hz
Radar moving velocity
0.15 m/s
Synthetic aperture length
2 m
Radar height
0.15/0.30 m
Roadway width
2.4 m
Advancing displacement
[0.80, 0.10, 0.00] m
Radar squint angle
30°/13.18°Figure 6
The distribution of targets A∼C.Figure7 shows the radar imaging results at 0.15 m and 0.30 m heights before and after the advancing of longwall face. It was seen that three targets were clearly imaged. Because of the range shift caused by LRWC process, the targets A and C were not imaged in the same range cell as target B in the final imaging results. Target B had no the shift along the range direction because target B was selected as the reference point. The range shift was related with the target azimuth time and radar squint angle. The farther away the target is from the reference point in the azimuth direction, the greater the range shift is. When the azimuth time of target was less than that of reference point, the target had the shift along the range negative direction. When the azimuth time of target was larger than that of reference point, the target had the shift along the range positive direction. In addition, the range shift increased with the radar squint angle, which explained that the range shift of A and C relative to B in Figures 7(a) and 7(b) was greater than that in Figures 7(c) and 7(d). The imaging results contained the targets azimuth and range information. Because the distances between the targets and the radar did not vary much when the radar scanned at 0.15 m and 0.30 m heights, there were no obvious changes for the target position between Figures 7(a) and 7(b), as well as Figures 7(c) and 7(d). Table 2 shows the target azimuth and range errors before and after the advancing in the simulation. Table 3 shows the target positions and its errors in the radar coordinate system before and after the advancing, and the advancing displacements according to the target positions. Whether before or after the advancing of longwall face, the position errors of A∼C in Zr-axis were larger than the Xr-axis and Yr-axis. Actually, the radar moving at different heights was equivalent to form the synthetic aperture along Zr-axis. Because there were only two sampling data along Zr-axis, the Zr-axis position error was larger. If the radar moved at more heights, the Zr-axis position error would be reduced. Theoretically, as long as there was one target, the advancing displacement could be obtained. Three targets were imaged in the simulation to improve the measuring accuracy of advancing displacement with average operation. In Table 3, three displacements were obtained by targets A, B, and C, respectively, which were (0.786 m, 0.088 m, 0.047 m), (0.783 m, 0.097 m, −0.069 m), and (0.811 m, 0.100 m, 0.098 m). The advancing displacement with average operation was 0.794 m along X-axis, 0.095 m along Y-axis, and 0.025 m along Z-axis, whose errors were −0.006 m, −0.005 m, and 0.025 m, respectively. The advancing displacement error in Z-axis was larger than the other two axes because the target position error in Zr-axis was larger than the Xr-axis and Yr-axis.Figure 7
The radar imaging results at 0.15 m and 0.30 m heights before and after the advancing of longwall face. (a) 0.15 m before the advancing, (b) 0.30 m before the advancing, (c) 0.15 m after the advancing, and (d) 0.30 m after the advancing.
(a)
(b)
(c)
(d)Table 2
The target azimuth and range errors before and after the advancing in the first simulation.
Height (m)
Azimuth (m)
Range (m)
A
B
C
A
B
C
Before
0.15
0.024
0.004
0.010
0.022
0.002
0.009
0.30
0.024
0.008
0.022
0.021
0.001
0.006
After
0.15
0.002
0.014
0.004
0.005
0.004
0.003
0.30
0.004
0.010
0.008
0.006
0.001
0.004Table 3
Target positions and its errors in the radar coordinate system before and after the advancing, and the advancing displacements according to the target positions in the first simulation.
Targets
Real position (m)
Calculated position (m)
Error (m)
A
Before
(0.786, −2.400, 0.300)
(0.772, −2.418, 0.324)
(−0.014, 0.018, 0.024)
After
(−0.014, −2.500, 0.300)
(−0.014, −2.506, 0.277)
(0.001, −0.006, −0.023)
Displacement
(0.800, 0.100, 0.000)
(0.786, 0.088, 0.047)
(−0.014, −0.012, 0.047)
B
Before
(1.386, −2.400, 0.300)
(1.380, −2.401, 0.307)
(−0.005, −0.001, 0.007)
After
(0.586, −2.500, 0.300)
(0.597, −2.498, 0.376)
(0.012, 0.002, 0.076)
Displacement
(0.800, 0.100, 0.000)
(0.783, 0.097, −0.069)
(−0.017, −0.003, −0.069)
C
Before
(1.986, −2.400, 0.300)
(2.004, −2.404, 0.369)
(0.018, −0.004, 0.069)
After
(1.186, −2.500, 0.300)
(1.193, −2.504, 0.271)
(0.007, −0.004, −0.029)
Displacement
(0.800, 0.100, 0.000)
(0.811, 0.100, 0.098)
(0.011, 0.001, 0.098)Another simulation was performed according to the simulation parameters listed in Table4. Except for the signal carrier frequency, bandwidth, and sampling frequency, other parameters were changed compared with the first simulation. Three targets D∼F were imaged in this simulation, whose coordinates in the roadway coordinate system were D(1.678 m, 0.000 m, 0.400 m), E(1.678 m, 0.000 m, 1.200 m), and F(1.678 m, 0.000 m, 1.600 m) (Figure 8). The target E was selected as the reference point. It was supposed that, before the advancing of longwall face, X-axis and Xr-axis were coincident, and other two axes in the OXYZ and OrXrYrZr are parallel, respectively.Table 4
Parameters in the second simulation.
Parameters
Values
Parameters
Values
Signal carrier frequency
4.3 GHz
Signal bandwidth
1.7 GHz
Sampling frequency
20 Hz
Radar moving velocity
0.2 m/s
Synthetic aperture length
1.8 m
Radar height
0.05/0.25 m
Roadway width
2.0 m
Advancing displacement
[0.70, −0.10, 0.00] m
Radar squint angle
40°/27.24°Figure 8
The distribution of targets D∼F.Figure9 shows the radar imaging results at 0.05 m and 0.25 m heights before and after the advancing of longwall face. The target azimuth and range errors in the imaging results are listed in Table 5. Table 6 shows the target positions and its errors in the radar coordinate system before and after the advancing, and the advancing displacements according to the target positions. According to the calculated coordinates of targets D∼F before and after the advancing, three values of advancing displacement were obtained, which were (0.697 m, −0.100 m, 0.027 m), (0.691 m, −0.096 m, 0.019 m), and (0.699 m, −0.118 m, −0.033 m), respectively. The average value of advancing displacement was 0.696 m along X-axis, −0.105 m along Y-axis, and 0.004 m along Z-axis, and its errors were 0.004 m, 0.005 m, and 0.004 m, respectively. In the above two simulations, the advancing displacement errors in X-axis and Y-axis were at millimeter lever.Figure 9
The radar imaging results at 0.05 m and 0.25 m heights before and after the advancing of longwall face. (a) 0.05 m before the advancing, (b) 0.25 m before the advancing, (c) 0.05 m after the advancing, and (d) 0.25 m after the advancing.
(a)
(b)
(c)
(d)Table 5
The target azimuth and range errors before and after the advancing in the second simulation.
Height (m)
Azimuth (m)
Range (m)
D
E
F
D
E
F
Before
0.05
0.008
0.004
0.001
0.005
0.001
0.001
0.25
0.008
0.008
0.004
0.005
0.001
0.001
After
0.05
0.008
0.004
0.016
0.009
0.001
0.001
0.25
0.004
0.001
0.012
0.007
0.001
0.001Table 6
Target positions and its errors in the radar coordinate system before and after the advancing, and the advancing displacements according to the target positions in the second simulation.
Targets
Real position (m)
Calculated position (m)
Error (m)
D
Before
(1.678, −2.000, 0.400)
(1.667, −1.996, 0.404)
(−0.012, 0.004, 0.004)
After
(0.978, −1.900, 0.400)
(0.970, −1.896, 0.377)
(−0.008, 0.005, −0.023)
Displacement
(0.700, −0.100, 0.000)
(0.697, −0.100, 0.027)
(−0.003, 0.001, 0.027)
E
Before
(1.678, −2.000, 1.200)
(1.669, −1.991, 1.230)
(−0.010, 0.009, 0.030)
After
(0.978, −1.900, 1.200)
(0.978, −1.895, 1.211)
(0.001, 0.005, 0.011)
Displacement
(0.700, −0.100, 0.000)
(0.691, −0.096, 0.019)
(−0.009, 0.004, 0.019)
F
Before
(1.678, −2.000, 1.600)
(1.685, −2.006, 1.586)
(0.007, −0.006, −0.015)
After
(0.978, −1.900, 1.600)
(0.986, −1.888, 1.619)
(0.008, 0.012, 0.019)
Displacement
(0.700, −0.100, 0.000)
(0.699, −0.118, −0.033)
(−0.001, −0.018, −0.033)


## 4.2. Experiment

An experiment was conducted according to the parameters of the first simulation listed in Table1. Figure 10 shows the diagram of the experiment site and imaging device. The roadway coordinate system OXYZ was established as shown in Figure 10(a). The radar coordinate system OrXrYrZr was built in Figure 10(b), where Or is the center point of the horizontal axis of the two-direction guide rail. Three corner reflectors were used as the imaging targets, which had the strong scattering intensity. In the imaging device, the UWB module was connected to the data processing system by USB. The diagram of UWB module was shown in Figure 11, and the parameters of UWB module are listed in Table 7. The UWB module and the antenna were connected through a radio frequency line. The antenna was a pyramidal horn antenna, whose frequency was 3.1∼4.8 GHz, gain was 10 dB, and stationary wave was less than 1.5. The antenna was installed in the rotation table, and the rotation table was installed in the two-direction guide rail. The rotation table could adjust the direction of the radar beam. The two-direction guide rail not only makes the antenna move along the horizontal axis, but also changes the antenna height along the vertical axis. The two-direction guide rail was placed in a mobile robot.Figure 10
The diagram of the experiment site and device. (a) Experiment site and (b) imaging device.
(a)
(b)Figure 11
The diagram of the UWB module.Table 7
The parameters of the UWB module.
Parameters
Value
Dimension
89 × 56 mm
Input power
5.0 V
Average transmit power
50 uW
Radio frequency
3.1∼4.8 GHz
Center frequency
4.3 GHz
Sample frequency
20 Hz
Max data throughput
19.2 kbps to 612 kbpsThe coordinates of three corner reflectors in the roadway coordinate system were A(0.786 m, 0.000 m, 0.300 m), B(1.386 m, 0.000 m, 0.300 m), and C(1.986 m, 0.000 m, 0.300 m). The target B was chosen as the reference point. The horizontal distance between the corner reflectors and the antenna was 2.4 m. A tapeline and a laser range finder were used to repeatedly determine the positions of the mobile robot, antenna, and the corner reflectors, which made the mean error of each position less than 0.005 m and the standard deviation less than 0.005 m. Before the robot movement,X-axis and Xr-axis were coincident, and other two axes in the OXYZ and OrXrYrZr were parallel, respectively. The velocity of radar moving was 0.15 m/s. The synthetic aperture length was 2 m. The antenna aperture length was 0.14 m. The radar scanned the corner reflectors at 0.15 m and 0.30 m height, respectively. It was supposed that the mobile robot moved 0.80 m along X-axis, 0.10 m along Y-axis, and 0.00 m along Z-axis. The radar squint angle was adjusted from 30° before the robot movement to 13.18° after the movement so that the reference point B was imaged in the center of the imaging result.The detailed steps in the experiment are shown as follows:Step 1: the mobile robot was located at (0.000 m, 2.400 m, 0.000 m) in the roadway coordinate system, and the radar squint angle was 30°. The two-direction slipway made the radar antenna move along the horizontal axis at 0.15 m and 0.30 m heights, respectively.Step 2: the mobile robot moved to (0.800 m, 2.500 m, 0.000 m), and the radar squint angle was adjusted to 13.18° by the rotation table.Step 3: the radar antenna moved along the horizontal axis at 0.15 m and 0.30 m heights again.Figure12 shows the radar imaging results at 0.15 m and 0.30 m heights before and after the robot movement. The target B was clearly imaged. Because the target B was the reference point, its RCM and azimuth-dependent FM rate had the precise compensation. The targets A and C were far from the reference point along the azimuth direction, whose RCMs and azimuth-dependent FM rates could not be fully compensated. Therefore, the targets A and C had the defocus to some extent. Table 8 shows the target azimuth and range errors before and after the robot movement in the experiment. The bandwidth of radar signal was 1.7 GHz, so the range resolution was 0.088 m. The azimuth resolution was 0.07 m, which was half of the antenna aperture length. In the radar imaging result at 0.30 m height after the robot movement, the azimuth error of target A (0.103 m) was larger than the azimuth resolution, which might be caused by the fluctuation of radar moving velocity. Except for this, the azimuth and range errors of other targets were within the resolution. Table 9 shows the target positions and its errors in the radar coordinate system before and after the robot movement, and the movement displacements according to the target positions. Except for the target A before the movement, the Z-axis position errors of other targets were larger than the X-axis and Y-axis, which was explained in the simulation. According to the calculated position coordinates of A∼C in the radar coordinate system before and after the movement, three movement displacements were (0.759 m, 0.174 m, 0.281 m), (0.742 m, 0.110 m, −0.146 m), and (0.730 m, 0.137 m, 0.720 m), respectively. The average value of movement displacement was obtained, which were 0.742 m along X-axis, 0.140 m along Y-axis, and -0.285 m along Z-axis. The errors of movement displacement were 0.058 m, 0.040 m, and 0.285 m, respectively. The movement displacement error in Z-axis was larger than X-axis and Y-axis. If the radar moved at more heights, the Z-axis error would decrease.Figure 12
The radar imaging results at 0.15 m and 0.30 m heights before and after the robot movement. (a) 0.15 m before the movement, (b) 0.30 m before the movement, (c) 0.15 m after the movement, and (d) 0.30 m after the movement.
(a)
(b)
(c)
(d)Table 8
The target azimuth and range errors before and after the robot movement in the experiment.
Height (m)
Azimuth (m)
Range (m)
A
B
C
A
B
C
Before
0.15
0.052
0.015
0.042
0.041
0.071
0.007
0.30
0.045
0.036
0.045
0.038
0.083
0.044
After
0.15
0.042
0.058
0.038
0.044
0.023
0.082
0.30
0.103
0.051
0.009
0.063
0.045
0.080Table 9
Target positions and its errors in the radar coordinate system before and after the robot movement, and the movement displacements according to the target positions.
Targets
Real position (m)
Calculated position (m)
Error (m)
A
Before
(0.786, −2.400, 0.300)
(0.724, −2.367, 0.248)
(−0.068, −0.033, −0.052)
After
(−0.014, −2.500, 0.300)
(−0.035, −2.541, −0.033)
(−0.021, −0.041, −0.333)
Displacement
(0.800, 0.100, 0.000)
(0.759, 0.174, 0.281)
(−0.041, 0.074, 0.281)
B
Before
(1.386, −2.400, 0.300)
(1.366, −2.321, 0.515)
(−0.020, −0.079, 0.215)
After
(0.586, −2.500, 0.300)
(0.624, −2.431, 0.661)
(0.038, 0.069, 0.361)
Displacement
(0.800, 0.100, 0.000)
(0.742, 0.110, −0.146)
(−0.058, 0.010, −0.146)
C
Before
(1.986, −2.400, 0.300)
(1.921, −2.285, 0.987)
(−0.065, −0.115, 0.687)
After
(1.186, −2.500, 0.300)
(1.191, −2.422, 0.267)
(0.005, −0.078, −0.033)
Displacement
(0.800, 0.100, 0.000)
(0.730, 0.137, 0.720)
(−0.070, 0.037, 0.720)UWB radar imaging result is shown in different colors according to the scattering intensity of the object. Because the corner reflector has stronger scattering intensity than other objects in the experiment, three corner reflectors were clearly imaged. In the experiment, the tripods and other objects in the room had weaker scattering intensity than the corner reflectors, which explained that only three corner reflectors are clearly imaged in Figure12. Therefore, the tripods and others in the room environment little affected the imaging result. As mentioned above, the position errors of the imaging device and corner reflectors were corrected with the tapeline and laser range finder. In the experiment, the radar velocity fluctuation and the signal attenuation caused the target azimuth and range errors (Table 8), respectively, which were larger than that in the simulation (Tables 2 and 5). UWB pulse shape also had the influence on the image resolution. In [27], Oloumi et al. showed the Gaussian pulse provided better image resolution compared with the chirp pulse. Therefore, the Gaussian pulse proposed in [28] was used in this paper. In the next, increasing the signal transmitting power and bandwidth will be operated to improve the imaging quality. Other imaging algorithms including the back-projection algorithm and omega-k algorithm will be modified to reduce the measurement errors.


## 5. Conclusion

This study proposes an UWB radar imaging method to determine the longwall retreat and creep displacements. The SAR imaging algorithm including the range focusing and azimuth focusing is designed to image the targets. According to the radar imaging results at different heights, the target 3D coordinates and the longwall retreat and creep displacements are obtained. In two simulations, the retreat and creep displacement errors are 0.006 m, 0.005 m and 0.004 m, 0.005 m, respectively. In the experiment, the retreat and creep displacement errors are 0.058 m and 0.040 m, respectively. The radar velocity fluctuation and the signal attenuation cause the target azimuth and range errors, respectively. Next, we will improve SNR and signal bandwidth to reduce the measurement error. In addition, modified back-projection algorithm and omega-k algorithm will be operated to obtain high-resolution image.



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*Source: 4056246-2020-05-11.xml*