Drift Error Research Articles

Nonlinearity Harmonic Error Compensation Method Based on Intelligent Identification for Rate Integrating Resonator Gyroscope

This paper presents an improved intelligent optimizing algorithm based on parameter identification and drift compensation for the rate-integrating resonator gyroscope (RIRG). Besides damping and frequency imperfections, the RIRG measurement accuracy still suffers from limitations due to nonlinear error. Therefore, the dynamic nonlinear error model for RIRG has been established to reveal the relationship between the pattern angle and harmonic drifts. Based on this, a dynamic analysis of the gyroscope operating state is carried out using nonlinear motion equations. The optimal harmonic error parameters are then identified by a particle swarm optimization (PSO) algorithm for the drift error compensation. To further improve the measurement accuracy, chaotic technology is integrated with PSO, leading to more precise identification. Subsequently, the harmonic parameters of the bias drifts are efficiently compensated. Experimental results demonstrate that the bias drift is reduced by over 90% after harmonic error compensation, demonstrating the validity of the proposed method in enhancing the measurement accuracy of RIRGs.

Maximum Mixture Correntropy Criterion-Based Variational Bayesian Adaptive Kalman Filter for INS/UWB/GNSS-RTK Integrated Positioning

The safe operation of unmanned ground vehicles (UGVs) demands fundamental and essential requirements for continuous and reliable positioning performance. Traditional coupled navigation systems, combining the global navigation satellite system (GNSS) with an inertial navigation system (INS), provide continuous, drift-free position estimation. However, challenges like GNSS signal interference and blockage in complex scenarios can significantly degrade system performance. Moreover, ultra-wideband (UWB) technology, known for its high precision, is increasingly used as a complementary system to the GNSS. To tackle these challenges, this paper proposes a novel tightly coupled INS/UWB/GNSS-RTK integrated positioning system framework, leveraging a variational Bayesian adaptive Kalman filter based on the maximum mixture correntropy criterion. This framework is introduced to provide a high-precision and robust navigation solution. By incorporating the maximum mixture correntropy criterion, the system effectively mitigates interference from anomalous measurements. Simultaneously, variational Bayesian estimation is employed to adaptively adjust noise statistical characteristics, thereby enhancing the robustness and accuracy of the integrated system’s state estimation. Furthermore, sensor measurements are tightly integrated with the inertial measurement unit (IMU), facilitating precise positioning even in the presence of interference from multiple signal sources. A series of real-world and simulation experiments were carried out on a UGV to assess the proposed approach’s performance. Experimental results demonstrate that the approach provides superior accuracy and stability in integrated system state estimation, significantly mitigating position drift error caused by uncertainty-induced disturbances. In the presence of non-Gaussian noise disturbances introduced by anomalous measurements, the proposed approach effectively implements error control, demonstrating substantial advantages in positioning accuracy and robustness.

Main factors affecting polaraxis offset characteristics of intact spherical superconducting rotor

Superconducting rotor has great potential applications in the field of precision measurement due to its unique physical properties. The superconducting rotor magnetic levitation device can be used to fabricate high-precision angular velocity sensors. Under the action of external interference torque, the pole-axis deviation from the initial position is the cause of the superconducting rotor pole-axis drift error, in which the spherical surface error and the earth’s rotation belong to the main sources of error, and compensating for the pole-axis drift speed caused by the spherical surface error of the superconducting rotor is a key step in realizing the high-precision superconducting rotor magnetic levitation device. Based on this, the factors affecting the spherical surface error of a complete spherical superconducting rotor and the rotation of the earth on the pole-axis offset characteristics of a superconducting rotor are investigated. First, the magnetic support structure of the superconducting rotor is modeled based on the vector magnetic potential equation, the magnetic field strength distribution on the surface of the superconducting rotor in the ideal state (i.e. suspended in the center of the spherical cavity) is analyzed, and the magnetic support force characteristics are investigated. Then the magnetic support interference moment of the superconducting rotor caused by the spherical surface error is analyzed, and a superconducting rotor dynamics model is established based on the superconducting rotor dynamics equations, and the distribution law of the superconducting rotor pole-axis drift error under different rotor structural parameters is given. Finally, the influence of the earth’s rotation on the superconducting rotor drift test is investigated. The results provide a reference for subsequently improving rotor drift accuracy, optimizing rotor structure design and improving drift test methods.

Long-distance SLAM scanning of mine tunnel - testing of precision and accuracy of Emesent Hovermap ST-X

This paper presents a detailed analysis of the Emesent Hovermap ST-X LiDAR scanner's precision in long-distance scanning of underground environments, specifically within the Josef mine's main gallery. The experiment aimed to evaluate the simultaneous localization and mapping (SLAM) capabilities of the Hovermap ST-X over a 750-meter straight tunnel section where conventional geodetic reference points are unavailable. To validate the scanner's accuracy, reference measurements were obtained using a Leica ScanStation P40 terrestrial laser scanner and a Leica MS60 total station, establishing a millimeter-level geodetic network with spherical control targets. The SLAM-based Hovermap ST-X scanner captured point clouds in both single (1P) and double (2P) pass modes, which were then analyzed for systematic errors in transverse (X), longitudinal (Y), and vertical (Z) directions using RMSE metrics. The study finds that while the Hovermap ST-X provides high-precision point clouds within shorter sections, cumulative errors arise over the entire 750-meter distance, particularly in the longitudinal axis, leading to slight compressions that necessitate scale corrections. In the transverse direction, the deviations reach up to tens of centimetres. The study also highlights that double-pass scans effectively reduce transverse deviation errors compared to single-pass measurements, yet significant systematic errors persist in both vertical and horizontal planes. These findings suggest that while SLAM scanning offers rapid data acquisition and adequate accuracy for various applications, its precision for geodetic surveys over extended distances could be improved by integrating scaling transformations and optimized pathing strategies. This work demonstrates the SLAM scanner's utility in challenging underground conditions and provides a framework for future precision assessments in mine surveying. The results suggest practical considerations for enhancing SLAM-based mapping accuracy in geodetic applications, emphasizing the need for periodic control points to minimize cumulative drift errors.

Real-Time Drivable Region Mapping Using an RGB-D Sensor with Loop Closure Refinement and 3D Semantic Map-Merging

Drivable region maps, created using a visual sensor, are essential for autonomous navigation because off-the-shelf maps do not reflect contemporary real-world conditions. This study presents a large-scale drivable region mapping system that is capable of capturing large-scale environments in real-time, using a single RGB-D sensor. Whereas existing semantic simultaneous localization and mapping (SLAM) methods consider only accurate pose estimation and the registration of semantic information, when loop closure is detected, contemporaneous large-scale spatial semantic maps are generated by refining 3D point clouds and semantic information. When loop closure occurs, our method finds the corresponding keyframe for each semantically labeled point cloud and transforms the point cloud into adjusted positions. Additionally, a map-merging algorithm for semantic maps is proposed to address large-scale environments. Experiments were conducted on the Complex Urban dataset and our custom dataset, which are publicly available, and real-world datasets using a vehicle-mounted sensor. Our method alleviates the drift errors that frequently occur when the agents navigate in large areas. Compared with satellite images, the resulting semantic maps are well aligned and have proven validity in terms of timeliness and accuracy.

Enhancing Intelligent Shoes with Gait Analysis: A Review on the Spatiotemporal Estimation Techniques

The continuous, automated monitoring of sensor-based data for walking capacity and mobility has expanded gait analysis applications beyond controlled laboratory settings to real-world, everyday environments facilitated by the development of portable, cost-efficient wearable sensors. In particular, the integration of Inertial Measurement Units (IMUs) into smart shoes has proven effective for capturing detailed foot movements and spatiotemporal gait characteristics. While IMUs enable accurate foot trajectory estimation through the double integration of acceleration data, challenges such as drift errors necessitate robust correction techniques to ensure reliable performance. This review analyzes current literature on shoe-based systems utilizing IMUs to estimate spatiotemporal gait parameters and foot trajectory characteristics, including foot–ground clearance. We explore the challenges and advancements in achieving accurate 3D foot trajectory estimation using IMUs in smart shoes and the application of advanced techniques like zero-velocity updates and error correction methods. These developments present significant opportunities for achieving reliable and efficient real-time gait assessment in everyday environments.

Multi-Camera Rig and Spherical Camera Assessment for Indoor Surveys in Complex Spaces

This study compares the photogrammetric performance of three multi-camera systems—two spherical cameras (INSTA 360 Pro2 and MG1) and one multi-camera rig (ANT3D)—to evaluate their accuracy and precision in confined environments. These systems are particularly suited for indoor surveys, such as narrow spaces, where traditional methods face limitations. The instruments were tested for the survey of a narrow spiral staircase within Milan Cathedral and the results were analyzed based on different processing strategies, including different relative constraints between sensors, various calibration sets for distortion parameters, interior orientation (IO), and relative orientation (RO), as well as two different ground control solutions. This study also included a repeatability test. The findings showed that, with appropriate ground control, all systems achieved the target accuracy of 1 cm. In partially unconstrained scenarios, the drift errors ranged between 5 and 10 cm. Performance varied depending on the processing pipelines; however, the results suggest that imposing a multi-camera constraint between sensors and estimating both IO and RO parameters during the Bundle Block Adjustment yields the best outcomes. In less stable environments, it might be preferable to pre-calibrate and fix the IO parameters.

Numerical-analytical optimization of orientation algorithms on a spherical model of angular motion of a rigid body

The problem of numerical-analytical optimization of three algorithms for determining orientation quaternions due to refinement of coefficients in the structure of algorithms is considered. Of them, two algorithms use the orientation vector as an "intermediate parameter". The coefficients are refined on the basis of computer modeling and the minimization of the error of the accumulated computational drift using the analytical reference model of the spherical motion of a rigid body as a model rotational motion in a sequence of Krylov angles that change over time according to a linear law. For this, the test motion model is supplemented by modeling ideal information from the outputs of the angular velocity sensors in the form of quasi-coordinates using analytical formulas for the apparent rotation vector. It is shown that the accumulated error of computational drift on the proposed reference model of rotary motion has a linear law of growth with time for all algorithms under consideration. As a result of the numerical experiment, new values ​​of the coefficients in the structures of the algorithms were obtained, which minimize the error of the accumulated drift and improve the characteristics of the trend of this error. The carried out optimization leads to a decrease by an order of magnitude of the maximum error value and a change in the linearly growing nature of the dependence of the calculation drift error on time to an oscillatory one. The results of the computational experiment are given.

Comparison of Middlewares in Edge-to-Edge and Edge-to-Cloud Communication for Distributed ROS 2 Systems

The increased data transmission and number of devices involved in communications among distributed systems make it challenging yet significantly necessary to have an efficient and reliable networking middleware. In robotics and autonomous systems, the wide application of ROS 2 brings the possibility of utilizing various networking middlewares together with DDS in ROS 2 for better communication among edge devices or between edge devices and the cloud. However, there is a lack of comprehensive communication performance comparison of integrating these networking middlewares with ROS 2. In this study, we provide a quantitative analysis for the communication performance of utilized networking middlewares including MQTT and Zenoh alongside DDS in ROS 2 among a multiple host system. For a complete and reliable comparison, we calculate the latency and throughput of these middlewares by sending distinct amounts and types of data through different network setups including Ethernet, Wi-Fi, and 4G. To further extend the evaluation to real-world application scenarios, we assess the drift error (the position changes) over time caused by these networking middlewares with the robot moving in an identical square-shaped path. Our results show that CycloneDDS performs better under Ethernet while Zenoh performs better under Wi-Fi and 4G. In the actual robot test, the robot moving trajectory drift error over time (96 s) via Zenoh is the smallest. It is worth noting we have a discussion of the CPU utilization of these networking middlewares and the perfosrmance impact caused by enabling the security feature in ROS 2 at the end of the paper.

Trajectory shaping guidance for impact angle control of planetary hopping robots.

This paper presents a novel optimal trajectory-shaping control concept for a planetary hopping robot. The hopping robot suffers from uncontrolled in-flight and undesired after-landing motions, leading to a position drift at landing. The proposed concept thrives on the Generalized Vector Explicit (GENEX) guidance, which can generate and shape the optimal trajectory and satisfy the end-point constraints like the impact angle of the velocity vector. The proposed concept is used for a thruster-based hopping robot, which achieves a range of impact angles, reduces the position drift at landing due to the undesired in-flight and after-landing motions, and handles the error in initial hopping angles. The proposed approach's conceptual realization is illustrated by lateral acceleration generated using thruster orientation control. Extensive simulations are carried out on horizontal and sloped surfaces with different initial and impact angle conditions to demonstrate the effect of impact angle on the position drift error and the viability of the proposed approach.

Differential Positioning with Bluetooth Low Energy (BLE) Beacons for UAS Indoor Operations: Analysis and Results.

Localization of unmanned aircraft systems (UASs) in indoor scenarios and GNSS-denied environments is a difficult problem, particularly in dynamic scenarios where traditional on-board equipment (such as LiDAR, radar, sonar, camera) may fail. In the framework of autonomous UAS missions, precise feedback on real-time aircraft position is very important, and several technologies alternative to GNSS-based approaches for UAS positioning in indoor navigation have been recently explored. In this paper, we propose a low-cost IPS for UAVs, based on Bluetooth low energy (BLE) beacons, which exploits the RSSI (received signal strength indicator) for distance estimation and positioning. Distance information from measured RSSI values can be degraded by multipath, reflection, and fading that cause unpredictable variability of the RSSI and may lead to poor-quality measurements. To enhance the accuracy of the position estimation, this work applies a differential distance correction (DDC) technique, similar to differential GNSS (DGNSS) and real-time kinematic (RTK) positioning. The method uses differential information from a reference station positioned at known coordinates to correct the position of the rover station. A mathematical model was established to analyze the relation between the RSSI and the distance from Bluetooth devices (Eddystone BLE beacons) placed in the indoor operation field. The master reference station was a Raspberry Pi 4 model B, and the rover (unknown target) was an Arduino Nano 33 BLE microcontroller, which was mounted on-board a UAV. Position estimation was achieved by trilateration, and the extended Kalman filter (EKF) was applied, considering the nonlinear propriety of beacon signals to correct data from noise, drift, and bias errors. Experimental results and system performance analysis show the feasibility of this methodology, as well as the reduction of position uncertainty obtained by the DCC technique.

Real-Time LiDAR–Inertial Simultaneous Localization and Mesh Reconstruction

In this paper, a novel LiDAR–inertial-based Simultaneous Localization and Mesh Reconstruction (LI-SLAMesh) system is proposed, which can achieve fast and robust pose tracking and online mesh reconstruction in an outdoor environment. The LI-SLAMesh system consists of two components, including LiDAR–inertial odometry and a Truncated Signed Distance Field (TSDF) free online reconstruction module. Firstly, to reduce the odometry drift errors we use scan-to-map matching, and inter-frame inertial information is used to generate prior relative pose estimation for later LiDAR-dominated optimization. Then, based on the motivation that the unevenly distributed residual terms tend to degrade the nonlinear optimizer, a novel residual density-driven Gauss–Newton method is proposed to obtain the optimal pose estimation. Secondly, to achieve fast and accurate 3D reconstruction, compared with TSDF-based mapping mechanism, a more compact map representation is proposed, which only maintains the occupied voxels and computes the vertices’ SDF values of each occupied voxels using an iterative Implicit Moving Least Squares (IMLS) algorithm. Then, marching cube is performed on the voxels and a dense mesh map is generated online. Extensive experiments are conducted on public datasets. The experimental results demonstrate that our method can achieve significant localization and online reconstruction performance improvements. The source code will be made public for the benefit of the robotic community.

Adaptive IMU error correction algorithm for dual-antenna GNSS/IMU integrated vehicle attitude determination

Abstract The attitude of a vehicle can be largely determined by integrating the global navigation satellite system (GNSS) and inertial measurement unit (IMU) in land-based applications. However, traditional dual-antenna GNSS/IMU integrated systems are susceptible to signal reflection, diffraction, and even interruption, leading to reduced accuracy and reliability in challenging environments. To address this issue, this paper proposes an adaptive IMU error correction algorithm for dual-antenna GNSS/IMU integrated vehicle attitude determination. First, we propose an IMU-aided baseline length constraint model to support the ambiguity resolution (AR) process. This model incorporates accurate prior information from the IMU, improving the success rate of AR within the dual-antenna GNSS/IMU integrated system. Second, we present an adaptive IMU error correction mechanism based on long short-term memory (LSTM) and particle swarm optimization (PSO) to assist in vehicle attitude determination and mitigate attitude error drift of the lMU during GNSS outages. Field test results verified that, compared to two other candidate algorithms, the proposed algorithm improves accuracy in roll, pitch, and yaw by 19.23%, 30.56%, and 67.12%, respectively, and by 12.50%, 10.71%, and 38.39% respectively. Moreover, in two distinct scenarios where GNSS is blocked for 120 seconds, the proposed algorithm still provides accurate and stable attitude information for vehicle navigation, with the accuracy of roll, pitch, and yaw kept within 0.08 degrees.

Adaptive temperature compensation for [formula omitted] humidity sensor in complex environments using ISSA-BP neural network

High-precision humidity detection in complex environments is essential across various fields. In this study, a high-performance MoS2 humidity sensor with a dynamic response time of less than 3 s was developed using molten salt-assisted chemical vapor deposition. To address the challenges posed by dynamic ambient temperature changes on sensor accuracy, an improved sparrow search algorithm-back propagation (ISSA-BP) neural network was constructed to mitigate temperature drift and correct nonlinear errors in the sensor output. The ISSA-BP neural network utilizes a global optimization strategy with adaptive learning, significantly enhancing accuracy and efficiency by optimizing the initialization and iterative update processes of traditional algorithms. Experimental results indicate that the proposed ISSA-BP achieves an average relative error of just 0.75% in humidity sensors across various environmental conditions, representing a 5.8-fold improvement in accuracy compared to traditional methods. Additionally, the algorithm demonstrated high robustness and accuracy across different environments, sensors, and datasets, confirming its applicability in complex and variable scenarios.

Accelerometer-assisted computer vision data fusion framework for structural dynamic displacement reconstruction

Accurate displacement measurement provides crucial information for evaluating the structural health condition. It is important to note that both direct and indirect displacement measurement methods have their own limitations, which can be remedied by leveraging each other’s strengths. In this study, a novel accelerometer-assisted computer vision data fusion framework is developed for accurately reconstructing structural dynamic displacement. The framework does not require a specific mathematical model or prior knowledge about the data’s characteristics, allowing it to be applied more broadly across different applications without the constraints of model assumptions. The core of this framework is to integrate successive variational mode decomposition (SVMD) and Bayesian optimization approaches to adaptively determine the weight factors of the fusion components. Importantly, an enhanced optical flow approach is presented for converting pixel movement to structural displacement from natural targets. This approach can effectively reduce the selection of mis-matched points within the ROI (Region of Interest), thereby reducing drift errors. The developed framework is verified via shaking table tests of a reinforced concrete frame structure under seismic excitation. Results indicate that the developed framework excels in accurately estimating structural dynamic displacement. Compared to single-vision displacement identification results, the proposed framework demonstrates lower peak error (< 1.65 mm) and normalized root mean square error (< 0.30). Meanwhile, the reconstructed displacement, by introducing dynamic displacement component from acceleration measurement, presents a wider frequency range than the vision-based displacement.

Usage of Machine Learning Techniques to Classify and Predict the Performance of Force Sensing Resistors

Recently, there has been a huge increase in the different ways to manufacture polymer-based sensors. Methods like additive manufacturing, microfluidic preparation, and brush painting are just a few examples of new approaches designed to improve sensor features like self-healing, higher sensitivity, reduced drift over time, and lower hysteresis. That being said, we believe there is still a lot of potential to boost the performance of current sensors by applying modeling, classification, and machine learning techniques. With this approach, final sensor users may benefit from inexpensive computational methods instead of dealing with the already mentioned manufacturing routes. In this study, a total of 96 specimens of two commercial brands of Force Sensing Resistors (FSRs) were characterized under the error metrics of drift and hysteresis; the characterization was performed at multiple input voltages in a tailored test bench. It was found that the output voltage at null force (Vo_null) of a given specimen is inversely correlated with its drift error, and, consequently, it is possible to predict the sensor’s performance by performing inexpensive electrical measurements on the sensor before deploying it to the final application. Hysteresis error was also studied in regard to Vo_null readings; nonetheless, a relationship between Vo_null and hysteresis was not found. However, a classification rule base on k-means clustering method was implemented; the clustering allowed us to distinguish in advance between sensors with high and low hysteresis by relying solely on Vo_null readings; the method was successfully implemented on Peratech SP200 sensors, but it could be applied to Interlink FSR402 sensors. With the aim of providing a comprehensive insight of the experimental data, the theoretical foundations of FSRs are also presented and correlated with the introduced modeling/classification techniques.

Thermal calibration for triaxial gyroscope of MEMS-IMU based on segmented systematic method

With the progress of micro electromechanical system (MEMS) technology, the performance of MEMS inertial measurement unit (IMU) composed of gyroscopes and accelerometers has been improved. Among the inertial sensors, MEMS triaxial gyroscope plays an important role in attitude estimation, navigation and positioning of intelligent mobile terminals such as unmanned aerial vehicles and unmanned vehicles. However, the measured values of low and medium cost MEMS triaxial gyroscopes are mainly affected by temperature (or thermal effect) and random errors. As results, the drift errors correlated with temperature will reduce application accuracy of MEMS triaxial gyroscope. The traditional calibration method for thermal drift errors relies on the expensive equipment, such as turntable and the temperature control system, which increases the cost of calibration. Therefore, an effective thermal calibration method that is available when using low- or high-cost tools for MEMS triaxial gyroscope will be meaningful for majority users. Hence, this paper analyzed and established the thermal drift model of MEMS triaxial gyroscope, and proposed a segmented systematic calibration method based on 24 states according to this model. Simulation shows that the proposed method can obtain the results approaching the real parameter thermal drift curves. Calibration experiments and parameters test show that the max errors of attitude calculation are reduced to 10% of the results using the original parameters, which indicates that the effectiveness of the proposed method.

A clinical investigation of force plate drift error on predicted joint kinetics during gait

Inverse dynamic analysis is a technique used during gait analysis to estimate intersegmental forces and net joint moments. Inverse dynamic calculations are susceptible to various forms of error. One such error is force plate drift, often produced by humidity condensing within the input connectors and electronics, causing an undesired change in output over time. This can be particularly concerning for movement laboratories where inverse dynamics are considered in clinical decision-making processes. Manufacturers will provide tolerance levels for drift. However, levels of acceptable drift are rarely considered from a clinical perspective. Therefore, this study aims to establish clinically acceptable limits of force plate drift error, induced by applying systematic errors to force plate channels, on predicted lower limb joint moments during gait. Gait data of 10 children with typical development were analysed and induced errors of 0.5 N, 1 N, 1.5 N, 3 N, 6 N and 12 N were incrementally applied to the horizontal and vertical force channels. Data were recalculated for each increment and mean profiles compared to an error free mean (±1SD) band. Error was deemed clinically significant when moments fell outside the mean (±1SD) band. Induced error at 6 N and above was sufficient to cause a clinically significant change. Sagittal and coronal plane moments at the hip were most affected, followed by the knee and then the ankle. While manufacturer guidelines for acceptable drift are usually well below 6 N, care is needed when using force plates over several minutes or more as drift may eventually exceed clinically acceptable limits.

An enhanced stochastic error modeling using multi-Gauss–Markov processes for GNSS/INS integration system

Angular random walk (ARW), rate random walk (RRW), and bias instability (BI) are the main noise types in inertial measurement units (IMUs) and thus determine the navigation performance of IMUs. BI is the flicker noise, which determines the noise level of an inertial sensor. The traditional error modeling approach involves modeling the ARW and BI processes as RRW or Gauss–Markov (GM) processes, and this approach is applied as a suboptimal filter in the global navigation satellite system (GNSS)/inertial navigation system (INS) extended Kalman filter (EKF). In this paper, the random error identification processes for white noise and colored noise for inertial sensors are separated using the Allan variance and power spectral density methods and the equivalence of the stochastic process differential equations of bias instability and a combination of multiple first-order GM processes are derived. A colored noise compensation method is proposed based on the enhanced EKF model. Experimental results demonstrate that, compared to traditional error models, our proposed model reduces positional drift error in dynamic testing from 195 to 49 m, enhancing positional accuracy by 40.2%. These findings confirm the potential and superiority of our method in complex navigation environments.

Hybrid Visual Odometry Algorithm Using a Downward-Facing Monocular Camera

The increasing interest in developing robots capable of navigating autonomously has led to the necessity of developing robust methods that enable these robots to operate in challenging and dynamic environments. Visual odometry (VO) has emerged in this context as a key technique, offering the possibility of estimating the position of a robot using sequences of onboard cameras. In this paper, a VO algorithm is proposed that achieves sub-pixel precision by combining optical flow and direct methods. This approach uses only a downward-facing, monocular camera, eliminating the need for additional sensors. The experimental results demonstrate the robustness of the developed method across various surfaces, achieving minimal drift errors in calculation.