TBM-MSE: A Multi-Engine State Estimation Based on Inertial Enhancement for Tunnel Boring Machines in Perceptually Degraded Roadways

Autonomous localization and operation of tunnel boring machines in perceptually degraded roadways is essential for intelligent upgrading of tunneling. Tunneling robots are far less intelligent than anticipated owing to the darkness, dust, vibration, and geometrically degraded roadways. We presented a multi-engine state estimation method for mapping and localizing tunnel boring machines (TBM-MSE). TBM-MSE designed a novel inertial enhancement model that maintains a global consistent posture in violent vibrations. TBM-MSE constructed lever arm error compensation terms for the total station and inertial component to improve the accuracy of position constraints. Meanwhile, the multi-engine framework of the TBM-MSE adaptively adjusts the weight of the multiple sensors in dusty environments. TBM-MSE was tested on dust-free and dusty roadways. The results demonstrate that TBM-MSE was more suitable for the state estimation of tunnel boring machines than LINS and RRR-MF. TBM-MSE estimation accuracy meets actual excavation requirements. In addition, the ablation experiments further confirm the effectiveness of inertial enhancement in handling perceptually degraded environments.


I. INTRODUCTION
Compared with coal mining, tunneling mechanization development in China is stagnant. Accurate state estimation of a tunnel boring machine (TBM) is essential for achieving intelligent tunneling. Mainstream posture estimation technologies for TBM include a laser pointer, machine vision, ultra-wideband (UWB), and simultaneous localization and mapping (SLAM). Researchers constructed an automatic laser navigation system using a machine body, laser, target prism, and earth coordinate system to calculate the yaw of a TBM [1]. Some researchers established a six-degreeof-freedom (6-DOF) detection model based on machine vision and laser targets [2]. A UWB pose detection system (UPDS) for TBM was designed, which realizes the remote The associate editor coordinating the review of this manuscript and approving it for publication was Halil Ersin Soken . posture measurement in a narrow and long enclosed roadway space [3]. The above studies should fully consider sensor posture perception accuracy. With the breakthrough of SLAM in robot pose estimation [4], [5], [6], multi-legged robots or unmanned aerial vehicles (UAVs) can deal with the underground environment without GPS. However, SLAM still faces many problems in TBM state estimation, such as the vibration noise of the oil pump motor and crawlertraveling devices during the inertial measurements; as well as the effects of roadway dust on LiDAR odometry.
The sensor errors are amplified by dust, darkness, and geometrically degraded rock walls. LiDAR odometry drifts during violent LiDAR motion; Darkness renders the camera ambiguous and tends to distort the global map; The confidence level of the inertial odometry decreases over the long-term work of the tunneling robot; Due to the excavation direction limitations of tunneling robots, loop closure methods are unable to deliver local optimization information for odometry. Therefore, improving the validity of sensor information in abnormal environments is an urgent problem to be solved [7]. Accurate sensor information is critical for state estimation. The primary methods for improving the performance of state estimation are two-sensor information complementation and multi-sensor fusion systems.
Researchers have used the complementary nature of sensors to improve LiDAR registration effectiveness. Motion prediction of inertial components ensures accurate convergence of LiDAR odometry [8], [9], even though the LiDAR is in motion. Fast-LIO [10] proposed a back-propagation process to compensate for the LiDAR distortion. Compensated feature primitives have rotational invariances, such as edges and surfaces [11]. Using curvature labels to extract these features can increase the validity of point cloud registration [12]. Based on the complementarity of sensor information, researchers have explored multisensor fusion models to integrate two or even more types of perception information. The fusion systems involving LIDAR and inertial components can be divided into loosely coupled and tightly coupled methods. Loosely coupled systems ignore high-order errors and linearization site selection during the independent state estimation of each sensor, which reduces the estimation accuracy. On the other hand, the feature fusion that fully considers the inherent relationship between sensors is referred to as tightly coupled [13], [14], [15]. The iterated extended Kalman filter (IEKF) methods [16], [17], [18] are commonly used for tightly coupled that correct linearization errors. The tightly coupled INS integration has achieved significant advancements in eliminating a tremendous amount of redundant computation in the prediction process [19], correcting sensitivity to measurement errors [20], and improving fusion performance [21].
To reduce the risk of loosely coupled or tightly coupled single-engine estimation, multi-sensor distribution fusion has increasingly drawn attention from researchers. The mainstream technical route of multi-sensor data fusion combines local decentralized fusion and optimal global fusion to improve the accuracy and reliability of integrated navigation systems [22], [23]. Recently, LiDAR has gradually become a primary sensor of posture perception. Multi-sensor data fusion combined with Lidar odometry has also become a popular research direction. Super Odometry [24] was the first to propose an estimation framework that considers both loosely coupled and tightly coupled methods. The inertial navigation estimation of Super Odometry was loosely coupled, while vision-inertial and LIDAR-inertial odometry components were tightly coupled methods. RRR-MF [25] adhered to the concept of multi-engine fusion. An error state Kalman filter (ESKF) fused the inertial component and total station data; the filtered result was treated as a factor and added to the factor graph along with the LiDAR odometry factor. The LiDAR-centric SLAM framework is a reliable localization method for autonomous robots in GNSS-denied environments [26]. However, dust roadway challenges the accuracy of LiDAR measurements. Inertial navigation estimation constitutes the primary means for removing LiDAR distortions. Therefore, inertial estimation needs to be robust and may even make a significant contribution to the results.
However, inertial components are typically regarded as auxiliary sensors with low-weight factors when information complementarity or multi-sensor fusion systems are utilized under complex conditions. Researchers have investigated the effects of complexity and instability of external vibration on inertial navigation estimation, enhanced the reliability of inertial measurement, and improved the weight of the fusion system. Currently, the primary methods of enhancing the effectiveness of inertial measurement include discrete wavelet threshold filtering (DWTF) and empirical mode decomposition (EMD). The researchers proposed the Wavelet Packet Transform-Chaos Particle Swarm Optimization-Back Propagation Neural Network (WPT-CLSPSO-BP) method to decompose the signal containing vibration noise and fully reconstruct the valuable information [27]. To remove the jitter and interference caused by the inertial measurement unit (IMU) at the speed over group and course over group, the researchers implemented the EMD noise reduction algorithm for trajectory reconstruction [28]. DFA-EMD combined detrended fluctuation analysis (DFA) and empirical mode decomposition (EMD) to reduce fiber optic gyroscope (FOG) random noise and drift [29]. A neural network (NN) prediction model and wavelet packet transform (WPT) technology were simultaneously incorporated into the EMD method to improve the denoising ability [30]. Although the aforementioned techniques effectively reduced drift errors, the vibration noise generated by oil pump motors and crawlertraveling devices posed a challenge to these methods. Therefore, this paper proposes a novel multi-engine estimation method with an inertial enhancement model to improve posture perception accuracy and attain globally consistent state estimation.
Motivated by the aforementioned discussion, this paper presents the development and implementation of an inertial enhancement-centric multi-engine estimation, which serves as a critical enabler for TBM localization in perceptually degraded environments. An overview of our framework is shown in Figure. 1. The primary contributions of TBM-MSE are as follows: 1. TBM-MSE creates an inertial enhancement model to reduce vibration and non-exchangeable errors from the oil pump motor and crawler-traveling devices.
2. TBM-MSE designs an INS/total station coupled filter with lever arm error compensation terms to enhance the independence and accuracy of the position constraint.
3. TBM-MSE proposes multi-engine estimation to ensure the validity of LiDAR registrations and the global consistency of the estimated state in perceptually degraded roadways.  For the purpose of enhancing the validity of state perception, there is a coherent relationship between these three contributions, forming a more robust and accurate TBM state estimation system. The inertial enhancement model primarily enhances the precision of attitude estimation (roll, pitch, yaw), and the error compensation of the lever arm focuses on the correction of position estimation (x, y, z). Together, they form an INS/total station coupled filter to deliver an improved 6-DOF state estimation of the TBM. Environmental characteristics markedly influence LiDAR, but LiDAR odometry can rectify the outcomes produced by the INS/total station coupled filter in favorable working conditions. Additionally, the multi-engine estimation can maximize the advantage of LiDAR without cumulative error, further enhancing the entire system's accuracy and reliability.
The remaining paper is organized as follows: We present the details of each key component in Section. II. The experimental results are presented in Section. III. We design the ablation experiment in Section. IV. The conclusions in Section. V.

II. METHODOLOGY A. INERTIAL ENHANCEMENT MODEL
TBM-MSE minimizes nonlinear and nonsmoothed vibration noise produced by oil pump motors and crawler traveling devices by an inertial enhancement that consists of inertial measurement pre-processing and inertial navigation system mechanization optimization.
Pre-processing techniques of the TBM-MSE include oil pump noise compensation and internal parameters recalibration. The time-domain and frequency-domain analyses of the TBM vibration characteristics reveal that static measurements are destroyed by oil pump noise, such as the fluctuations of X-axis specific force and X-axis angular velocity in Figure. 2.
TBM-MSE adopts a novel empirical mode decomposition to rapidly sift and reconstruct the intrinsic mode functions (IMFs) [31]. TBM-MSE converts raw measurements x(t) into IMF components and trend terms. Autonomously discriminates the boundary parameters M of IMFs by the Euclidean distance. The ∧ x(t) indicates the initial reconstruction result.
where N is the number of sampling points and t i is the sampling moment. Based on the TBM vibration noise characterization, TBM-MSE uses a soft threshold to optimize the signal. where The σ indicates the noise variance. After suppressing the vibration noise of the oil pump, TBM-MSE re-calibrates the Gaussian white noise b and random wandering noise w [32].
Assuming that the inertial system (i) coincides with the carrier coordinate system (b), T b i = I ; T i TS represents the relative transformation from total station prism (TS) to the inertial component (i), T i TS = T b TS ; T i L indicates external parameters of LiDAR and the inertial component (i), T i L = T b L . This paper adopts the North-East-Down (NED) coordinate system (n). The inertial navigation system mechanizations optimization contains two components: error compensation of crawler 55980 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.  traveling devices and static attitude correction. The state differential formula can be solved by the Peano-Baker approximation, which ignores the nonexchangeable error of the actual attitude change. Increasing the output frequency of dead reckoning can effectively avoid the cone error impact. After experimental testing and evaluation, the output frequency was raised to 475Hz.
The equivalent rotation vector φ k is created by the double sampling of the angular velocity vector ω ib (t) [33], θ k indicates the angular increment in [t k , t k+1 ]. Updating the direction cosine matrix C n b(k) in a discrete-time system, TBM-MSE ignores the transformation of navigation coordinate systems during the movement. φ k × represents the skewsymmetric matrix of φ k .
The influence of the paddle effect is reduced by double sampling both angular velocity vector ω ib (t) and specific force vector f (t), v k indicates the velocity increment in [t k , t k+1 ]. The position p n k update depends on the velocity v n k .
The motion characteristics of TBM increase the sensitivity of gyroscope measurements. Attitude update methods that rely on gyroscope measurements are unreliable. According to the TBM kinematics and sensors error characteristics, TBM-MSE modifies attitude by static acceleration value. We establish the attitude accelerometer correction term q ′ acc based on the orientation filter [34]. In this paper, the parameters of adaptive gain α in q ′ acc are optimized to match the actual accelerometer output of TBM. The α = L(e m ) adaptively adjusts state estimation weights of the accelerometer and gyroscope for different motion states of TBM.
e m = f + [0, 0, g p ] T − g p g p (14) where ∥∥ denotes the norm of the acceleration vector, g p = 9.81m/s 2 . When f changes dramatically, α is close to zero and q ′ acc approaches 1 0 0 0 T ; otherwise, α is almost equal VOLUME 11, 2023 to 1, q ′ acc corrects attitude q b(k−1) b(k) . The gain α = L(e m ) of TBM-MSE increases the smoothness of the output.

B. INS/TOTAL STATION COUPLED FILTER
Due to the complexity of roadway environments, this paper proposes a multi-engine coupling state estimator. TBM-MSE is composed of loosely coupled filters and tightly coupled filters. TBM-MSE considers the inertial error model and simplifies the observations, and compensates for lever arm errors between the prism and inertial component.

1) STATE DEFINITIONS
Based on operations ''⊞'' and ''⊟'' defined in [35], the relationships between the actual state X n true and error state δX n are as follows: where p n , v n , and C n b are outputs of inertial enhancement model; w b ib and f b are the actual measurements. The sensor error model includes bias b and Gaussian white noise w: where w g and w a are Gaussian white noise of the gyroscope and accelerometer. To overcome the effect of the roadway on the random bias error, accelerometer bias b a and gyroscope bias b g are considered first-order Markov processes in the time interval T : where w gb and w ab denote the driven white noise of the gyroscope and accelerometer, respectively.

2) ERROR STATE EQUATIONS
The differential formula of the error state δX is where ω n in represents the projection of the angular velocity vector under the navigation system, R M and R N are curvature radius of the meridian and prime vertical, angular velocity of earth rotation w e = 7.2921 × 10 −5 rad/s.

3) PROPAGATION EQUATIONS
The discrete propagation model and the covariance matrix of error state are as follows, Q w denotes system noise covariance that is computed off-line during recalibration:

5) UPDATE
The INS/total station coupled filter adjusts the weight of redundant errors between predictions and observations by K k . ins X n k indicates the output of inertial estimation and e X n k is the output of INS/total station coupled filter in the navigation coordinate system: VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.

C. ITERATED ERROR-STATE KALMAN FILTER 1) PROPAGATION EQUATIONS
The propagation equations of iterated Kalman filter are the same as INS/total station coupled filter.

2) LIDAR MOTION DISTORTION COMPENSATION
TBM-MSE inputs e X n k as an initial value into the iterated error-state filter. The oil pump motor and the crawler traveling devices cause TBM to shake violently, which exacerbates the LiDAR nonuniform motion. TBM-MSE compensates for movement distortion by e X n k . The t i is adjacent to the timestamps τ j and τ j+1 in e X n k . These corresponding b,i at t i [36].
The T n(k) b,end is the end posture of the k th LiDAR scan. Calculating T end i is the essence of eliminating motion distortion. Then the point k p i is projected into the NED, represented by k p n i .
TBM-MSE extract line and surface features by magnitude relationship between the eigenvalues. Assume x j (j = 1, 2····· ·, n) are the nearest point clouds to p i , S represents covariance matrix, where Y = y 1 . . . . . . y n , y j = x j − p i . The λ indicates the eigenvalue of S. The u is the corresponding eigenvector of S. are retained; when |λ 1 −λ 2 | |λ 2 −λ 3 | ≥ , p i belongs to F edge , λ 1 and u 1 are retained. The F edge and F plane are used to construct the local map map p i . According to the experimental results, γ = 0.37, = 2.1.

3) LiDAR MEASUREMENTS
TBM-MSE fuses LiDAR observation with the error state (δ ∨ X k , ∨ P k ). To obtain dense mapping results and efficient dynamic data updates, TBM-MSE maintains a map by ikd-Tree [17]. The k p n i can search for corresponding feature primitives in the local map map p i . TBM-MSE takes eigenvectors to construct distance residuals: The actual point cloud gt,k p n i contains LiDAR measurement noise n L . The corresponding residuals are represented as z(X n k , n L ). The following expression is obtained by approximating residual z(X n k , n L ) with first-order approximation at r X n op,k .
gt,k p n i = k p n i − n L (32) z(X n k , n L ) ≈ z( r X n op,k , 0) + r M k · (X n k ⊟ r X n op,k ) + u L (33) where r denotes the number of iterations, u L ∈ N (0, Q L ) comes from LiDAR measurement noise n L . r X n op,k is the optimal state in iteration, its initial state is e X n k . VOLUME 11, 2023 55983 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.

4) RESIDUAL COMPUTATION
Based on the initial state of the INS/total station coupled filter and observation residuals, TBM-MSE treats the error state update as an optimization problem. The following formula is constructed via Mahalanobis distance:

5) ITERATED UPDATE
Formula (36) can be solved by the following formulas, where the initial state of r P k is ∨ P k . If formula (36) converges, the error state r δX k and the optimal estimation state r+1 X n op,k stop updating. r+1 X n op,k = r X n op,k ⊞ r+1 δX k (42)

A. SYSTEM HARDWARE
The system hardware included a LiDAR (Velodyne), an inertial component (FOSN II), and a total station (TS60), as shown in Figure. 4. TBM-MSE was deployed on a tunnel boring machine (EBZ160M-2).

B. THE RESULT OF INERTIAL ENHANCEMENT
Static initialization results and dynamic measurement stability demonstrated the necessity of inertial enhancement. The vibration noise of the oil pump interferes with the accuracy of the static initialization, as shown in Table 1, the yaw error was about 0.4 • . After inertial enhancement, the error of the yaw initialization result was reduced by 81.57 %, as shown in Table 2. TBM-MSE recalibrates internal parameters. The results were, as shown in the equation at the bottom of the next page. With inertial enhancement, inertial measurements can resist external vibrations during the three motion states: continuous straight forward, turning, and intermittent backward. Taking specific force as an example, Figure. 5 displayed the change after inertial enhancement. Combining the static initialization results and dynamic inertial measurements, the inertial enhancement model improves the robustness of inertial estimation.

C. STATE ESTIMATION IN DUSTFREE ROADWAYS
Based on our previous work [25], TBM-MSE only uses independent position errors to solve the Z-axis drift problem. The TBM is set to move forward 4.70 m and then return to the starting position, as shown in Figure. 6. TBM-MSE was compared with LINS [16] and RRR-MF [25] in terms of trajectory estimation, as shown in Figure. 7.
By analyzing the trajectory curves of the three methods, we can accurately evaluate the posture initialization and real-time position estimation accuracy. The actual initial position in the carrier coordinate system was (0m, 0m, 1.5m). The trajectories of the TBM-MSE and RRR-MF differed by a few millimeters. LINS was the most significant Z-axis drift, with an error range of ±0.10 m. The Z-axis position estimation errors of the TBM-MSE and RRR-MF were nearly identical, which were 3/20 of LINS. At the same time, the average error in the Y-axis for LINS exceeded 0.25 m. In the dust-free roadway, the localization capabilities of TBM-MSE and RRR-MF were equivalent. RRR-MF is an optimization-based algorithm that relies on the accuracy of LiDAR odometry to ensure consistent global estimation.

D. STATE ESTIMATION IN DUST ROADWAYS
The dust weakens the accuracy of LiDAR odometry. We proposed a multi-engine coupling framework to lessen reliance on LiDAR odometry. We established a dust removal system, as shown in Figure. 8. TBM-MSE was compared with LINS and RRR-MF in terms of mapping, position estimation, and attitude estimation in dusty, as shown in Figure. 9, Figure 10, and Figure 11.
The significant estimation drift of RRR-MF led to mapping failure in the dust. The RRR-MF has no comparative value because of the significant estimation errors. The mapping results of TBM-MSE outperform LINS in terms of map accuracy and density. There were significant mistakes in LINS mapping, which marked objects at the same height in reality with different colors, as shown in Fig. 9(c). The LINS mapping only had 19 sub-maps and TBM-MSE's map consists of 940 submaps.   The average drift of the LINS Z-axis trajectory increased to 3.263m, indicating that the dust further amplified the state estimation error. However, there was no apparent drift in the TBM-MSE mapping or the position estimation. Compared with the TBM-MSE, the attitude angle of LINS fluctuated more than 50 • , as shown in Figure. 11. The bottom of the dust roadway was generally flat, so the roll and pitch estimated by LINS are unrealistic.   This paper quantifies the difference in localization between TBM-MSE and LINS in dust by absolute pose error (APE) and relative pose error (RPE), using the result of TBM-MSE as a reference, as shown in Figure. 12 and Figure. 13. The error indicators for LINS were illustrated in Table 3 and  Table 4.   Dust caused huge posture estimation errors in RRR-MF, while LINS was also impacted by dust, and its estimation results demonstrated more severe drift than the dust-free roadway. In conclusion, TBM-MSE is the most effective framework for real-time TBM state estimation in perceptually degraded roadways.

IV. ABLATION EXPERIMENT
The essence of the TBM-MSE is to make the inertial estimation more robust under challenging environments. TBM-MSE without an inertial enhancement model was distinguished by * to investigate the effect of inertial measurement pre-processing and inertial navigation system mechanization optimization in initialization, mapping, and localization. The results are shown in Figure. 14 and15.
The position estimation error of the TBM-MSE * led to ghosting in mapping, as shown in Figure. 14(a) and Figure. 15(a). TBM-MSE * had huge initialization errors. At the beginning of state estimation, there were significant fluctuations in the Z-axis position, roll, and pitch. TBM-MSE * was affected by the TBM vibration, so the pitch and roll amplitude changes were more dramatic. In summary, the localization of TBM benefits from the inertial enhancement model.

V. CONCLUSION
This paper introduces the TBM-MSE, a novel multi-engine estimation method that focuses on inertial enhancement for autonomous localization in coal mine roadways, specifically designed for applications on TBM. A robust inertial enhancement model has been developed and validated, improving the accuracy of posture perception. Ablation experiments have demonstrated that this model can suppress vibration noise caused by the oil pump motor and crawler traveling devices, reduce attitude initialization errors, and enhance the VOLUME 11, 2023 ability to constrain the Z-axis during dynamic estimation. The multi-sensor distribution fusion incorporates total station lever arm error compensation and adaptive adjustments to LiDAR odometry weights. Compared to the single-engine method, LINS and RRR-MF, TBM-MSE excels in state estimation across different coal mine scenarios. After ablation and comparative experiments, the multi-engine estimation framework of TBM-MSE is validated as the optimal choice for TBM localization. TBM-MSE is capable of achieving globally consistent state estimation, even when operating in dusty and vibration-prone environments.