High-Precision Positioning Method of Coal Shearer in underground environment based on Rail Kinematics Model (October 2021)

The high-precision positioning of the shearer is the key technology to realize the automation of longwall mining. Since mine is a Global Position System (GPS)-denied environment, highly autonomous Inertial Navigation System (INS)/odometer integrated navigation has been widely used. At present, the shearer positioning method based on INS/odometer has been difficult to meet the requirements of long-time and high-precision mining. Aiming at the high-precision navigation in the complex environment of mining, this paper constructs a comprehensive rail kinematics model of the shearer that does not rely on external sensors. By analyzing the kinematic characteristics of the shearer and the scraper conveyor during the long-wall mining process, a method of information fusion and navigation system fault diagnosis based on the assistance of the shearer rail kinematics model is proposed. According to the working principle of the shearer rails and hydraulic supports, the characteristics of the trajectory deviation caused by the sensor fault of the hydraulic support are analyzed. Combined with the engineering requirements of Shearer mining, the model fault identification was carried out by the fading probability ratio detection algorithm. The simulation results show that the proposed algorithm effectively improves the positioning of shearer accuracy in multiple cutting cycles, and at the same time avoids the influence of the rail deviation caused by the rail kinematics model fault on the positioning of shearer.


I. INTRODUCTION
Coal is the main fossil energy and plays an extremely important role in the world energy structure. Because the mine is a closed environment, explosive gas and dust can easily lead to coal mine safety accidents [1]. Since the U.S. Bureau of Mines proposed computer-aided coal mining technology in the 1980s, the high-precision autonomous positioning of underground shearers has become a major technical challenge in the process of automation [2].
Inertial navigation system (INS) is widely used for positioning of underground equipment due to its highly autonomous and reliable navigation performance. As early as the 1980s, Sammacro et al. [3] developed a navigation system based on gyroscopes, magnetic heading sensors and inclinometers to measure the attitude of underground mine equipment for autonomous mining operations. However, INS inevitably has error divergence when it calculates position and attitude through numerical product, which is the inherent limitation. Therefore, inertial error is usually corrected through external information. David C. Reid et al. [4] utilized the motion characteristics of the sharer, the accumulated errors of the INS are corrected by zero velocity update (ZUPT). Although the ZUPT is simple and easy to implement, but the shearer needs to be stopped periodically. Whenever the shearer starts moving, errors will continue to accumulate.
The long-term positioning accuracy of the odometer is better than INS, meanwhile, odometer has excellent autonomy and stability. Therefore, the integrated navigation of INS/odometer is the main method of coal shearer positioning. Shijia Wang et al. [5] utilized the position and 6 VOLUME XX, 2017 speed information to fuse through information filtering, which significantly improved the positioning accuracy of the shearer compared with the pure inertial positioning. Ralston J C et al. [6] put forward the conception of using wireless sensor network to locate underground mine mobile equipment earlier. Qigao Fan et al. [7] positioned the shearer by using time of arrival (TOA) positioning method through UWB base station installed on the hydraulic support and labels installed on the shearer, which effectively reduces the positioning error of INS. To solve the mixed line-of-sight and non-line-of-sight errors caused by the underground environmental barriers, Bo Cao et al. [8] proposed an interactive multi-model algorithm based on Gaussian mixture model, aiming to reduce the frequent switching between lineof-sight and non-line-of-sight scenes. However, it is difficult to install and calibrate the base station used for shearer positioning, and the label may not always receive the base station signal due to the occlusion in the positioning process.
In addition, researchers have also conducted extensive studies on visual perception method [9], infrared radiation method [10], Doppler velocimetry method [11] and other methods [12]. Active sensing sensors are usually affected obviously by the complex environment of shearer working face, and their availability and reliability are difficult to be guaranteed.
To meet the positioning requirements of GPS-denied environment, the Commonwealth Scientific and Industrial Research Organization (CSIRO) in Australia has proposed a closed path based reverse correction method [13]. On this basis, Wang Shibo et al. [14] established the rail kinematics model to assist positioning according to the motion characteristics of the shearer on the scraper conveyor and improved the navigation accuracy of the shearer through Kalman filtering theory without relying on external sensors. Due to the lack of further analysis on the mechanical structure of scraper conveyor in the mining process, the engineering value of the algorithm is affected.
The rest of this paper is organized as follows: Firstly, a Refinement model of shearer rail is constructed in section Ⅱ. The integration navigation strategy is presented in section III, which provide the analyses on the construction of system model, measurement model and federated filtering architecture in the work. A rail kinematics model fault detection method based on the fading sequential probability ratio detection algorithm is proposed in section IV. In section V, the algorithm is verified by experiment and simulation. Finally, the conclusion is summarized in section VI.

II. Refinement model of shearer rail
Comprehensive mechanized coal mining a process of coal mining using mechanized and automated equipment. Fully mechanized mining equipment mainly includes shearer, scraper conveyor and hydraulic support [15]. In the cutting process, the shearer breaks the coal along the horizontal direction of the working face firstly. After the coal seam falls off, the scraper conveyor transports the coal to the crusher. In the cutting process of the shearer, the hydraulic support will ensure that the top coal will not collapse and control the longitudinal mining depth of the working face in the next cycle. Usually, according to the actual situation of the coal seam, the hydraulic support will push the roof support system and scraper conveyor after the 0.8-1m thick coal body is cut down by the shearer. Scraper conveyor is not only used to transport coal and materials, but also the rail of the shearer, so the movement of the shearer is consistent with the track of the scraper conveyor. Circular cutting track and scraper conveyor structure are shown in Fig. 2. The longitudinal distance between each cutting surface (point A to B) can be measured by the displacement sensor of the shearer's hydraulic support. The horizontal plane of the rail kinematics model is controlled by many hydraulic supports, so a certain error exists between each chute, resulting in the included angle between chutes. Since each chute is a rigid body, the movement trajectory of the shearer should be a broken line that conforms to the movement characteristics of the scraper conveyor [16].

III. INS/odometer high-precision positioning algorithm assisted by rail kinematics model
According to the cutting process of the shearer, the current cutting trajectory can be predicted according to the rail kinematics model based on the trajectory of the last cutting, and the position measurement of the current shearer can be obtained. The constraint information of the rail kinematics model is fused with the traditional INS/odometer. The system model, measurement model and fusion framework are constructed as follows:

A. System Model Construction
This paper is based on the east-north-up (ENU) coordinate system. The coordinates and attitude angles are shown in Fig.  3, the specific structure is shown in the Fig. 4.
is the firstorder Markov process random noise of the 3-axis gyroscope.
Because the zero bias of the accelerometer is small and relatively stable, it can be calibrated through the turntable. In order to reduce the amount of calculation, the random constant of the accelerometer is not modeled.
is the first-order Markov process random noise of the 3-axis accelerometer. s is the scale factor error of the odometer. According to the error equation of navigation system [16], the state equation is obtained: Where, the subscripts k and 1 k − stands for the sampling

B. Measurement Model Const ruction
According to the movement characteristics of the shearer, there are multiple moments of static state in the cutting process of the shearer, and the cumulative error of the speed can be corrected periodically through zero speed correction.
The measurement equation is as follows: is the difference between the measurement information of zero velocity correction and the velocity information of the INS, The odometer is a kind of sensor which can provide the distance relative to the initial position and has better long-term accuracy compared with INS. According to the working principle of the shearer walking device, the equipped odometer can only provide the forward pulse of the body coordinate. The current position of shearer can be obtained through the scale factor of the odometer pulse and the attitude information provided by the INS. The measurement model is as follows:  According to the rail kinematics model, the trajectory position information of the current cutting shearer can be predicted. Different working conditions will lead to different speed of shearer in each cutting cycle, so when shearer moves over a fixed distance, the predicted point of rail kinematics model matches the estimated point of current position. The measurement model is constructed as follows: Where, ,, sin( )sin( ) ,, sin( )cos( ) Where, , ik r is the distance that the shearer moves in the chute,  is the angle between the chute and the horizontal cutting surface of the shearer, usually a random value less than 1°. i b is the noise measured by the displacement sensor [18]. The measurement equation is as follows: , , , Where, Federated filter is a two-stage data fusion structure, which consists of several sub-filters working in parallel to complete Kalman filter calculation. In this paper, two sub-filters based on INS/odometer as well as INS/rail kinematics models are designed. The INS/odometer sub-filter and the INS/rail kinematics model sub-filter are corrected by the odometer 6 VOLUME XX, 2017 output position and the rail kinematics model output position respectively, and the ZUPT is carried out when the cutting stops. The information fusion of inertial state recursion and measurement is carried out by EKF respectively [19]. Then, the local estimations and the corresponding covariances are fused by a global filter to obtain the global optimal estimation. The information fusion equation is as follows: Where g P is the covariance matrix of the estimated state, j P corresponds to the estimated error covariance matrix of each sub-filter, ˆg X is the global optimal estimation result, ˆj X is the state estimation of the sub-filter, N represents the number of sub-filters, j stands for the j -th sub-filter.
There are two sub-filters in this algorithm. The filtering process of the sub-filter can be referred to [20].

V. Fault diagnosis of rail kinematics model based on federated filter
The scraper conveyor of the shearer is usually controlled by nearly 200 hydraulic supports. If the sensors of hydraulic supports fail and the faults are not timely isolated, the accuracy of rail kinematics model will decrease. According to the mining regulations of shearer, the scraper conveyor needs to maintain the horizontal bending angle of each chute and the horizontal cutting trajectory deviation should be less than the index requirements of the scraper conveyor. In this paper, a fault detection algorithm of fading probability ratio based on federated filter is proposed.

A. Fading probability ratio fault detection model based on federated filter
The rail kinematics model caused by the fault of the hydraulic support measurement sensor is shown in Fig. 5.

FIGURE 5. Schematic diagram of rail kinematics model
The discrete measurement model of federated filter subfilter under fault is as follows: The innovation value of the sub-filter at time k can be obtained by the following formula: Where k  is the system disturbance, When the system is not disturbed, the continuous-time innovation sequence The variance of the sub-filter can be obtained by the following formula: Where / -1 kk P is the one-step prediction mean square error, k R is measurement noise.
In the fault analysis of integrated navigation system, binary hypothesis is usually made for the mean value of the innovation sequence v of the sub-filter: Where 0 H and 1 H represent system fault and fault free, respectively. According to the above formula, the prior probability under the binary fault hypothesis is as follows: According to the maximal posterior probability criterion, the likelihood ratio of the innovation sequence samples in continuous time is as follows: 6 VOLUME XX, 2017 It can be seen from the above formula that as k increases, the proportion of the mean value of the innovation sample k v becomes smaller and smaller. The sensitivity of the detection algorithm is constantly decreasing, so the weight of the historical sample mean is reduced by introducing a fading factor, thereby improving the sensitivity of the detection algorithm. The mean value of the innovation sample after introducing the fading factor is as follows [21][22]: Where, b is the fading factor.
The statistic is as follows:

A. Simulation verification
To verify the effectiveness of the algorithm proposed in this paper, a simulation experiment was carried out. According to the actual working conditions of the shearer, a 360m working face of the shearer is designed, and scraper conveyer is composed of 200 chutes. Whenever a cutting cycle is completed, the hydraulic support advances 1m toward the coal body. The whole process simulates 5 cutting cycles, and the total time is 6.4 hours. The influence of rail kinematics model on the positioning accuracy of shearer is compared. The simulation Settings of the main sensor performance parameters are as follows:   Fig. 6 shows the trajectory comparison between the positioning result with or without the assistance of the rail kinematics model and the real trajectory. Fig. 7 and 8 respectively show the east and north position errors with or without the rail kinematics model. The trajectory without the assistance of the rail kinematics model has divergence trend over time in multiple cutting cycles due to the scale factor error and heading angle error of the shearer. The maximum positioning error occurs at the end of each cutting cycle. As listed in Table 2, The Root Mean Square Error (RMSE) of the east direction is 0.886m, 0.964m, 0.939m, 0.98m, 1.041m, and the RMSE of the north direction is 0.853m, 1.002m, 0.851m, 0.923m, 0.970m, respectively. Because the longitudinal displacement of shearer cutting surface is constrained by the measurement of kinematic model, the distance in the first cutting process also restrains the continuous divergence of odometer position recursion as a measurement. Therefore, the divergence of the shearer can be significantly restrained. The RMSE of the east direction is 0.420m, 0.446m, 0.592m, 0.663m, 0.816m, and the RMSE of north direction is 0.18m, 0.239m, 0.208m, 0.226m, 0.214m, respectively. It can be seen from the comparison that the error of the traditional INS/odometer positioning method will continue to increase with the mining of the shearer. However, the proposed algorithm does not diverge significantly in five cutting cycles, and the positioning error in each cutting cycle is smaller than that of the traditional algorithm, which significantly improves the positioning accuracy of shearer. 214 To improve the reliability of the rail kinematics model and meet the engineering requirements of shearer cutting, the possible faults is simulated to verify the detection and isolation effects of the proposed algorithm on the rail kinematics model. According to the motion characteristics of the rail kinematics model, the simulation injected a measurement deviation with a horizontal angle of 1° for every two chutes from 2825s to 3131s. The length of each chute is 1.8m, and the fault formed is shown in Fig. 9. Two different chi-square detection algorithms are used to compare with the algorithm in this paper, namely residual chi-square detection [23] and dual-state chi-square detection [20], which are currently commonly used fault detection methods. North error comparison of residual chi-square detection, dual-state chi-square detection and fading sequential probability ratio detection It can be seen from Fig. 10 and Fig. 11 that the fault function detection value and detection result of the algorithm in this paper can accurately reflect the fault. After the threshold is exceeded, the faulty rail kinematics model is isolated in time. The residual chi-square detection and twostate chi-square detection is not sensitive to soft fault, and the fault rail kinematics model will affect the positioning accuracy of the navigation system. It can be seen from Fig.  12 that after the fault measurement is isolated, the north position error does not change significantly. In a relatively short period of time, the odometer can ensure a higher position accuracy of the shearer. Compared with the traditional residual chi-square detection algorithm and state chi-square detection algorithm, the proposed algorithm significantly improves the positioning accuracy of the shearer and ensures the reliability of the system.

B. Experimental validation
The validity of the algorithm for shearer positioning is further verified by the real data obtained from the unmanned vehicle. The scenario is shown in Fig. 13. The unmanned vehicle is the Apollo unmanned mobile platform, which is equipped with optical fiber INS, odometer and dual antenna RTK. The high precision optical fiber INS is installed in the middle of the unmanned vehicle and odometer was connected to the wheel of the mobile carrier. The dual antenna RTK is mounted on the top of the vehicle as a reference track. The parameters of each sensor are shown in Table 3. The unmanned vehicle first performed an initial alignment for 5 minutes and then carried out 5 cutting cycles along the straight line of the playground runway at a speed of about 0.2m/s, which took about 20 minutes.   Fig.  15 and Fig. 16 are respectively the comparison of the east and north position errors with or without the assistance of rail kinematics model. The errors in both the east and north directions diverge without the assistance of the rail kinematic model. The positioning error diverges faster in the east direction than in the north direction. The main reason is that there is no effective measurement in the cutting direction of shearer. The change of error conforms to the rule that the error of the INS/odometer integrated navigation system first increases and then decreases during the back-and-forth motion.
As shown in Table 3, the east position RMSE of the traditional INS/odometer integrated navigation is 0.30m, VOLUME XX, 2017 9 0.37m, 0.53m, 0.69m, 0.88m. and the RMSE of the north direction is 0.90m, 0.90m, 0.87m, 0.84m, 0.88m during the five cutting processes, respectively. Combined with Fig. 17, the positioning method based on the rail kinematics model can effectively suppress the divergence of the heading angle, thereby improving the positioning accuracy in the longitudinal direction between the cutting surfaces. The position RMSE of proposed algorithm based on the rail kinematics model is 0.29m, 0.28m, 0.26m, 0.27m, 0.26m in the east direction and 0.88m, 0.89m, 0.82m, 0.82m, 0.80m in the west direction respectively in the five cutting processes. The positioning accuracy of the proposed algorithm is significantly higher than that of the traditional INS/odometer integrated navigation. It is worth noting that since the movement of the shearer at the working face is well constrained by the odometer. Because of the round-trip motion, the odometer errors will be partially offset and therefore diverge slowly. Since the heading angle of the vehicle in the experiment is about 172°, the constraint in the north direction is not obvious in the ENU coordinate, while the constraint in the east direction is better. 80 According to the effect of the proposed algorithm on fault detection and isolation of the rail kinematics model in the actual environment, the reliability of the model is verified by the experiment. A segment of fault is added to the abovementioned rail kinematics model. The specific detection effect is shown in Fig. 18 and Fig. 19.  East error comparison of residual chi-square detection, dual-state chi-square detection and fading sequential probability ratio detection As can be seen from Fig. 20, after the fault is identified and isolated, the positioning accuracy is significantly improved. However, the traditional method is not completely isolated from faults, leading to obvious fluctuation of position errors. The proposed algorithm has better fault identification efficiency compared with traditional residual chi-square detection and two-state Chi-square detection. It can effectively avoid the wrong correction of shearer position caused by model fault and improve the safety of underground mining.

VII. CONCLUSION
Through the analysis of the movement characteristics between the shearer, the scraper conveyor and the hydraulic support in the longwall mining, a refined rail kinematics model is constructed. Combined with the INS and odometer information carried by the shearer, this paper proposes a high-precision positioning algorithm for the shearer based on the rail kinematics model. Aiming at the decrease in VOLUME XX, 2017 9 positioning accuracy caused by the fault of the rail kinematics model, a fault detection and isolation algorithm based on fading sequential probability ratio is proposed. Simulation and experimental results show that the multisource information fusion by a federated filter with fault detection function can significantly suppress the position divergence of multiple cutting cycles of the shearer without relying on external sensors. When a measurement fault occurs in the rail kinematics model, the fault can be identified and isolated in time, thereby ensuring the positioning accuracy and robustness of the shearer.