Vehicle Velocity Research Articles

Simulation Studies of Pollutant Emission from Passenger Cars

<div>The article presents the results of simulation studies of pollutant emissions from passenger cars. The characteristics of emissions were determined using the vehicle driving test procedures, in consideration of differentiated average velocities as well as model traffic conditions: urban traffic jam, urban traffic with no congestion, rural, motorways, and highways. This article also presented the possibility of determining the characteristics of pollutant emission based on a singular realization of the vehicle velocities processes, as well as the intensity of pollutant emission, with the use of the Monte Carlo method. The pollutant emission characteristics enable specification of pollutant emission intensity, which can be used for the inventory of pollutant emissions from road transport (COPERT software applied as standard) and can be useful in the assessment of a degree of environmental hazard by modeling pollutant dispersion. In this article, the results related to pollutant emission characteristics were obtained with the use of the software HBEFA INFRAS AG for the cumulative category of passenger cars, in terms of their representative structure in Europe in 2020. The simulation driving tests were carried out separately for cars with spark ignition engines and for those with compression ignition engines. It was concluded that using specialized software to simulate emissions from road vehicles is an effective way to determine the characteristics of emissions from road transport.</div>

A novel method for measuring center-axis velocity of unmanned aerial vehicles through synthetic motion blur images

Accurate velocity measurement of unmanned aerial vehicles (UAVs) is essential in various applications. Traditional vision-based methods rely heavily on visual features, which are often inadequate in low-light or feature-sparse environments. This study presents a novel approach to measure the axial velocity of UAVs using motion blur images captured by a UAV-mounted monocular camera. We introduce a motion blur model that synthesizes imaging from neighboring frames to enhance motion blur visibility. The synthesized blur frames are transformed into spectrograms using the Fast Fourier Transform (FFT) technique. We then apply a binarization process and the Radon transform to extract light-dark stripe spacing, which represents the motion blur length. This length is used to establish a model correlating motion blur with axial velocity, allowing precise velocity calculation. Field tests in a hydropower station penstock demonstrated an average velocity error of 0.048 m/s compared to ultra-wideband (UWB) measurements. The root-mean-square error was 0.025, with an average computational time of 42.3 ms and CPU load of 17%. These results confirm the stability and accuracy of our velocity estimation algorithm in challenging environments.

The Motion Estimation of Unmanned Aerial Vehicle Axial Velocity Using Blurred Images

This study proposes a novel method for estimating the axial velocity of unmanned aerial vehicles (UAVs) using motion blur images captured in environments where GPS signals are unavailable and lighting conditions are poor, such as underground tunnels and corridors. By correlating the length of motion blur observed in images with the UAV’s axial speed, the method addresses the limitations of traditional techniques in these challenging scenarios. We enhanced the accuracy by synthesizing motion blur images from neighboring frames, which is particularly effective at low speeds where single-frame blur is minimal. Six flight experiments conducted in the corridor of a hydropower station demonstrated the effectiveness of our approach, achieving a mean velocity error of 0.065 m/s compared to ultra-wideband (UWB) measurements and a root-mean-squared error within 0.3 m/s. The results highlight the stability and precision of the proposed velocity estimation algorithm in confined and low-light environments.

Safe speeds for a heavy articulated vehicle when passing a floating bridge tower under crosswind

This paper recommends safe speeds for a heavy articulated vehicle when passing by Bjørnafjorden floating bridge tower under two constant crosswind speeds (65 km/h and 100 km/h). The analysis is based on the tractor-semitrailer (TS) model with fifth-wheel (FW) coupling in roll and free in yaw. Comparison of safe speeds assessments has been made with two TS models differ in FW coupling. Aerodynamic forces and moments for TS models as function of their position relative to the bridge tower and time were computed using Computational Fluid Dynamics (CFD) simulations. For TS model coupled in roll and free in yaw, no rollover risk is noticeable for both crosswind excitations. For TS model free in roll and in yaw, roll-over risk is noticeable at lower vehicle velocities (at 36 km/h and 54 km/h). TS with rigid connection in FW stays in the traffic lane for every considered vehicle velocity. TS model which is roll and yaw moment free in the FW overestimates rollover risk assessment at lower vehicle velocities. TS model with rigid connection in the FW underestimates traffic lane departure assessment at higher vehicle velocity. Appropriate mathematical modelling of a heavy articulated vehicle that considers tractor and semitrailer units as two separate bodies coupled in roll and free in yaw is of importance for accurately assessing safe speeds when a vehicle passing by the bridge tower.

Proximal Policy Optimization for RIS-Assisted Full Duplex 6G-V2X Communications

In this work, we consider a novel reconfigurable intelligent surface (RIS)-assisted full-duplex (FD) sixth generation (6G)-vehicle-to-everything (V2X) communication network having a FD base station (BS) simultaneously communicating with a uplink (UL) and a downlink (DL) mobile vehicles with the aide of two RISs, one for each link. We provide an analytical framework to investigate the performance of this network and, consequently, formulate an optimization problem to jointly optimize the phase shift matrices at both the RISs that maximize the achievable sum-rate. Thereafter, due to the non-convex nature of the problem, we propose a low complexity proximal policy optimization (PPO)-based deep reinforcement learning (DRL) algorithm that solves the problem in continuous action spaces by reducing the overall training overhead and provides optimum values of phase-shift matrix at each RIS. Further, we extend the analysis considering multiple transmit and receive antennas at the BS that simultaneously serves multiple UL and DL vehicles. We present exhaustive simulations-based graphical results to validate the effectiveness and accuracy of the proposed algorithm compared to deep deterministic policy gradient (DDPG) and successive refinement (SR)-based solutions. Accordingly, we demonstrate the dominance of the considered FD system over its half-duplex (HD) counterpart. We also discuss the impact of the number of elements at each RIS, each vehicle's velocity and their distance from the RIS and the BS on the performance of the respective links. Moreover, we also highlight the impact of imperfect self-interference cancellation and discuss the trade-off between the UL and DL performances due to this imperfection. Additionally, it is shown that the proposed algorithm is approximately <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10 \times$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ 40 \times$</tex-math></inline-formula> faster than DDPG and SR, respectively. Finally, for the multiple vehicle case, we demonstrate the effect of co-channel interference on the DL rate and the impact of RIS elements, the number of UL and DL vehicles on the system performance.

Analyzing Vertical Earthquake Vibrations and Moving Vehicle Loads for Structural Health Monitoring and Vibration Suppression in Bridges

The design of bridges often overlooks the vertical component of earthquakes or considers it of secondary importance, despite compelling evidence indicating specific structural damage caused by primary earthquake waves. Conversely, during the operational phase, the combined influence of ground motion and moving loads from vehicles can significantly impact the structural health monitoring (SHM) of bridges. This study aims to evaluate the simultaneous effect of vertical earthquake vibrations and moving vehicle loads on simply supported bridges. The research employs a practical methodology based on the eigenfunction expansion method to analyze change of deflection due to the effect of these concurrent forces under seven different earthquake records. It is shown that within a realistic range of vehicle mass and velocity, the average of changing the maximum deflection at the mid-span of the main beam (denoted as M_n) reaches up to 163% under various scenarios. Subsequently, the seismic parameters influencing this phenomenon are identified through a statistical analysis of set of 100 different earthquake records with unique features. A linear regression equation is presented to predict the M_n based on the earthquake specific properties. Additionally, to control the vertical vibration of bridge systems, a novel vibration suppression system utilizing steel pipe dampers is introduced, and its reliability is examined across a broad spectrum of bridge flexural rigidity. The results indicate that the system's efficiency depends on M_n and the soil type of the bridge construction, enabling a reduction in structural sections (up to 27%) while achieving the same maximum target deflection in the initial state. This efficiency leads to a more economical design solution, emphasizing the potential benefits of the proposed system for practical application.

CORRELATION STUDIES OF PROCESSES: VEHICLE VELOCITY, POLLUTANT EMISSIONS, AND VEHICLE FUEL CONSUMPTION IN THE WORLD-WIDE LIGHT-DUTY TEST CYCLE

The article presents the worldwide harmonized light-duty test cycle results of a diesel engine passenger vehicle carried out on a chassis dynamometer. Pollutant emissions from exhaust and fuel consumption were measured. Vehicle velocity was treated as a variable determining pollutant emissions and fuel consumption because the engine operating states depend on engine velocity and load during engine operation, and these states in turn affect pollutant emissions and fuel consumption. Actions taken to reduce pollutant emissions and consumption of fuel are often in opposition to each other. Therefore, there is a need to optimize these activities. There is also a need to know the relationship between the effects of taking specific actions that serve to achieve individual goals in order to rationalize actions aimed at reducing pollutant emissions and fuel use. The originality of the article lies in the use of the correlation theory between pollutant emission and fuel consumption as well as the processes that determine them, primarily vehicle velocity, to rationalize these activities. Pearson's linear correlation theory was used to assess the relationships between individual variables. Significant differences were found in the correlation coefficients between individual variables, which confirmed the need to take integrated actions to reduce pollutant emissions and fuel consumption.

Optimal hybrid strategy in adaptive cruise control system for enhanced autonomous vehicle stability and safety

The adaptive cruise control system relies heavily on the vehicle's longitudinal control algorithm. Traditional longitudinal control algorithms typically depend on precise vehicle dynamic modeling or complex controller parameter calibrations. In the research, an optimal hybrid strategy for the control of basic adaptive cruise control system is proposed. The proposed hybrid strategy is the combination of both the Model Predictive Control (MPC) and Coati Optimization Algorithm (COA) and hence it is named as MPCCOA strategy. The fundamental goal of the proposed work is that a vehicle should maintain its current velocity when it approaches another vehicle that is driving at a steady velocity. The inputs for the proposed strategy are vehicle speed and acceleration. The inter-vehicle distance error, velocity error and acceleration are regulated based on the upper and lower limit of acceleration command with the help of proposed strategy. For accomplishing the required steadiness with the limitations in the given input and actual velocity with constant previous vehicle velocity, the proposed controller is utilized. The proposed controller is used to control the traction force of the host vehicle such that the vehicle speed follows the optimal speed trajectory as good as possible while ensuring constraints like distance to a preceding vehicle or speed limits. The performance of the proposed is implemented in the MATLAB platform and compared with existing approaches. The proposed technique demonstrates superior performance metrics, achieving the collision rate, rate of reaching maximum deceleration and ratio of exceeding comfortable deceleration or jerk are 1.27 %, 3.131 % and 9.052 %, respectively.

Application of a time-dependent performance-based resilience metric to establish the potential of coupled green-grey infrastructure in urban flood management

Urban flood resilience (UFR) and related facilities for its improvement, such as green and grey infrastructures and their coupled approach have attracted global stakeholders' attention due to successive flooding events worldwide. However, research on quantifying the potential of such measures in UFR enhancement based on system performance and surface inundation is lacking. How these measures act in different stages of system performance reflecting the state of urban functionality has not been addressed. This study investigated the potential of green and grey infrastructures and their coupled approach in enhancing UFR using a time-dependent performance-based metric in the Minzhi region, Shenzhen City. The metric considers water velocity and physical mechanisms of residents and vehicles keeping their stability. Suggestions for UFR enhancement were proposed. The results suggest that the coupled approach performs best. The adopted measures exhibit different impacts during different phases of system performance. Exploring the implementation methods of individual measures, discussing the synergistic integration of individual measures, and implementing targeted approaches to further enhance UFR in vulnerable regions are important. The coupled approach should be prioritized if the grey one is effective in UFR enhancement and preference should be given to the green infrastructure when deciding between green and grey infrastructures.

Protuberance placement mastery: Shock wave control integration with Coanda effect to thrust vectoring on a sonic jet

Thrust Vector Control (TVC) is a technique that allows precise control over the direction and velocity of an aerial vehicle. This paper presents a novel approach combining shock wave control and the Coanda effect to apply this technique in sonic flows. The objective is to achieve more eligible and operational control over the deviation angles of the thrust vector. The research is conducted through numerical simulations and experimental tests to investigate the impact of protuberance location (1, 3.5, and 5 mm), protuberance width (1.5, 2 mm), depth of penetration (2, 6, and 10%), and nozzle pressure ratio (ranging from 2.1 to 4) on the flow field, thrust vector angle, and thrust value of the nozzle. The system's behavior depends on the protuberance location, pressure ratio, and penetration depth. The location of the protuberance influences the shocks and flow separation from the Coanda flap. Increasing the penetration depth up to 10% enhances system stability and reduces the protuberance location's influence on flow deviation. The study highlights the significant effect of protuberance placement on thrust loss, with higher penetration depths resulting in a more significant decrease. The system's behavior in terms of flow deviation is more stable at specific penetration depths and pressure ratios. The results show that the proposed technique achieves a maximum deviation angle of 83° for a sonic jet. In addition, the findings contribute to understanding TVC using protuberances and the Coanda effect. The proposed technique offers advantages in simplicity, reliability, and control performance. It opens possibilities for efficient and maneuverable aerospace vehicles, with applications in UAVs, surveillance, and search and rescue missions.

Authority Allocation Approach for the Human-Machine Co-Driving System in Crosswinds

To improve driving safety and the stability of human-machine co-driving vehicles in crosswinds, a human-machine co-driving system to address the impact of crosswinds is developed. To reveal the relationship between crosswinds and tire cornering stiffness, the effect of tire load on cornering stiffness is analyzed based on the Magic Formula tire model. On this basis, the correction function of tire cornering stiffness is obtained. A human-machine co-driving system framework is introduced, which includes the driver model, controller, and authority allocation strategy. The controller is used to guarantee the stability of the system, which can remain robust to the uncertainty of tire cornering stiffness and vehicle velocity. The authority allocation strategy can adjust the authority level of the driver and controller according to the crosswind speed, working states of the vehicle, and driving feeling of drivers. The effectiveness of the proposed system is verified by simulation. The results show that the proposed system can improve the vehicle’s lane-keeping and obstacle-avoidance abilities in crosswinds. Further, the system can be compatible with drivers with different driving characteristics and achieve greater versatility. In addition, the impact of crosswinds on the trajectory tracking performance and driving stability of the vehicle, at different speeds and different tire cornering stiffnesses, can be weakened and the reliability of the system improved significantly.

A Vehicle Velocity Prediction Method with Kinematic Segment Recognition

Accurate vehicle velocity prediction is of great significance in vehicle energy distribution and road traffic management. In light of the high time variability of vehicle velocity itself and the limitation of single model prediction, a velocity prediction method based on K-means-QPSO-LSTM with kinematic segment recognition is proposed in this paper. Firstly, the K-means algorithm was used to cluster samples with similar characteristics together, extract kinematic fragment samples in typical driving conditions, calculate their feature parameters, and carry out principal component analysis on the feature parameters to achieve dimensionality reduction transformation of information. Then, the vehicle velocity prediction sub-neural network models based on long short-term memory (LSTM) with the QPSO algorithm optimized were trained under different driving condition datasets. Furthermore, the kinematic segment recognition and traditional vehicle velocity prediction were integrated to form an adaptive vehicle velocity prediction method based on driving condition identification. Finally, the current driving condition type was identified and updated in real-time during vehicle velocity prediction, and then the corresponding sub-LSTM model was used for vehicle velocity prediction. The simulation experiment demonstrated a significant enhancement in both the velocity and accuracy of prediction through the proposed method. The proposed hybrid method has the potential to improve the accuracy and reliability of vehicle velocity prediction, making it applicable in various fields such as autonomous driving, traffic management, and energy management strategies for hybrid electric vehicles.

Estimation of Crosswind Disturbances for a Vehicle by LPV‐MHE and its Application to Disturbance Cancellation

Crosswinds and transverse slopes of the road surface affect the motion of a ground vehicle as disturbances. The objective of this paper is to develop a method for estimating crosswind disturbances and lateral force disturbances caused by transverse slopes of the road surface under the variation of the vehicle speed. Firstly, a dynamical model of a vehicle is described as a Linear Parameter‐Varying (LPV) system in which the value of the coefficient matrices vary with the vehicle velocity. Then, an algorithm to estimate the disturbance is derived based on Moving Horizon Estimation (MHE) and applied to the derived LPV system. Furthermore, a simple control law which counteracts the effects of the disturbances on the lateral velocity and the yaw rate in steady‐state based on the estimates of the disturbances is presented. The effectiveness of the proposed method is demonstrated by a numerical example. © 2024 The Author(s). IEEJ Transactions on Electrical and Electronic Engineering published by Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Finite Element Analysis on the Behavior of Solidified Soil Embankments on Piled Foundations under Dynamic Traffic Loads

Most research conducted so far has primarily focused on pile-supported gravel embankments. The ability of solidified soil used as an embankment filling material has been verified, and a clear view on the performance of solidified soil embankments on piled foundations is rather limited. The three-dimensional unit cell models of pile-supported embankments are conducted to investigate the performance of solidified soil embankments in comparison to gravel embankments under static and dynamic loads. Then, a systematic parametric analysis is performed to investigate the effects of various factors, including the cohesion and friction of solidified soil, the velocity and wheel load of vehicles, the pile spacing, the height of embankments. The results show that, compared with the results of gravel embankments, the heights of the outer soil arch plane in solidified soil embankments reduces under static and dynamic loads, and the piles bear more load. In addition, the total settlements of solidified soil embankments decrease with increasing cohesions, and there is an economical cohesion of 25 kPa. The vehicle wheel load, pile spacing, and the height of embankment significantly influence the load transfer mechanism and total settlement of solidified soil embankment, while the friction angles and velocities have little effect on the total settlements and vertical stress. The relationship between the soil arch height and various parameters in solidified soil embankments is established by multiple regression analysis. This investigation highlights the advantage of solidified soil in reducing total settlement and provides an insightful understanding of the load transfer mechanism of solidified soil embankment on piled foundation.

Time-Optimal Trajectory Planning and Tracking for Autonomous Vehicles.

This article presents a hierarchical control framework for autonomous vehicle trajectory planning and tracking, addressing the challenge of accurately following high-speed, at-limit maneuvers. The proposed time-optimal trajectory planning and tracking (TOTPT) framework utilizes a hierarchical control structure, with an offline trajectory optimization (TRO) module and an online nonlinear model predictive control (NMPC) module. The TRO layer generates minimum-lap-time trajectories using a direct collocation method, which optimizes the vehicle's path, velocity, and control inputs to achieve the fastest possible lap time, while respecting the vehicle dynamics and track constraints. The NMPC layer is responsible for precisely tracking the reference trajectories generated by the TRO in real time. The NMPC also incorporates a preview algorithm that utilizes the predicted future travel distance to estimate the optimal reference speed and curvature for the next time step, thereby improving the overall tracking performance. Simulation results on the Catalunya circuit demonstrated the framework's capability to accurately follow the time-optimal raceline at an average speed of 116 km/h, with a maximum lateral error of 0.32 m. The NMPC module uses an acados solver with a real-time iteration (RTI) scheme, to achieve a millisecond-level computation time, making it possible to implement it in real time in autonomous vehicles.

Lexical Expressions of Motion in Physical Environments a Cognitive Linguistics Perspective

This study aims to delve into the interaction between motion verbs, manners, and paths in the Vietnamese language to look at the lexicalization of motion occurrences. Utilizing Talmy's lexicalization patterns for cognitive linguistics, the study seeks to understand how Vietnamese encodes and conceptualizes motion events in a variety of physical contexts, such as the air, water, and land. A mixed-methods approach is used in this work, integrating qualitative analysis of annotated textual data with quantitative frequency analysis. Vietnamese has a rich system of motion verbs that may be paired with manner and path expressions to produce complex and subtle descriptions of movement, according to the research. The language displays intricate differences when describing the direction, velocity, and kind of vehicle of motion, in addition to various linear, curved, vertical, circular, and multidirectional routes. The complex interplay between language, cognition, and the embodied experience of motion is highlighted by this linguistic variety, which is a reflection of Vietnamese speakers' astute observation and interpretation of the physical world. The work adds to our knowledge of how language organizes and expresses the basic idea of motion and provides insights into the cognitive and cultural bases of language expression.

Pulsed Propulsion of Unmanned Aerial Vehicles by Centrifugal Force Modulation—First-Order Theory and Practicability

A novel technique suitable for the propulsion of small unmanned aerial vehicles (UAV) is discussed in this paper. This approach utilizes the rotational energy of airborne gyro rotors and converts it into translational propulsion for the vehicle. The energy conversion is achieved by generating precisely directed centrifugal force pulses through short-duration rotor unbalances. The accurate control of the timing and magnitude of these unbalances is crucial for successful propulsion generation. Our first-order theory of controlled unbalance propulsion (CUP) predicts the potential for achieving high translational accelerations and vehicle velocities up to orbital levels. Power-saving levitation of UAVs can be attained. In this paper, we provide traceable evidence that pulsed centrifugal propulsion is based on well-established laws of physics and can be realized using state-of-the-art technologies.

A VISION-BASED SYSTEM DESIGN AND IMPLEMENTATION FOR ACCIDENT DETECTION AND ANALYSIS VIA TRAFFIC SURVEILLANCE VIDEO

This study aims to test the entire framework on an AI demo board and investigate the issue of automatically and effectively recognizing and analyzing traffic incidents captured by surveillance cameras. To begin, the motion interaction field (MIF) method, which is capable of detecting collisions in video, is used to locate damaged automobiles based on the interactions of various moving objects. Second, the location of the destroyed vehicles is determined using the YOLO v3 model. Using a hierarchical clustering method, the vehicle trajectories prior to the collision are recovered, and the related trajectories are reconstructed. Finally, a perspective transformation is used to project the trajectory into a vertical view to help traffic cops make better decisions. The unbiased finite impulse response (UFIR) method, which does not require statistical information about the external noise, is used to estimate the vehicle's velocity. The estimated velocity and impact angle from the vertical view can then be used to investigate the traffic accident. Finally, a Huawei AI demo board called HiKey970, which was used to code all of the aforementioned algorithms, is used in an experiment to show how useful and effective the proposed method is in practice. A few mishap observation recordings are sent onto the demo board. Mishaps are recognized and the proper vehicle directions are gathered.

A Predictive Energy Management Strategy for Heavy Hybrid Electric Vehicles Based on Adaptive Network-Based Fuzzy Inference System-Optimized Time Horizon

Energy management strategies play a crucial role in enhancing the fuel efficiency of hybrid electric vehicles (HEVs) and mitigating greenhouse gas emissions. For the current commonly used time horizon optimization methods that only target the trend curve of the optimal battery state of charge (SOC) trajectory obtained offline, which are only suitable for buses with known future driving conditions, this paper proposed an energy management strategy based on an adaptive network-based fuzzy inference system (ANFIS) that optimizes the time horizon length and enhances adaptability to driving conditions by integrating historical vehicle velocity, accelerations, and battery SOC trajectory. First, the vehicle velocity prediction model based on the radial basis function (RBF) neural network is used to predict the future velocity sequence. After that, ANFIS was used to optimize and update the length of the forecast time horizon based on the historical vehicle velocity sequence. Finally, compared with the fixed time horizon energy management strategy, which is based on model predictive control (MPC), the average calculation time of the energy management strategy is reduced by about 23.5%, and the fuel consumption per 100 km is reduced by about 6.12%.

FGO-MFI: factor graph optimization-based multi-sensor fusion and integration for reliable localization

Reliable and precise information pertaining to the position, velocity, and attitude is essential for automated driving. This paper proposes FGO-MFI, a cost-effective and robust multi-sensor fusion and integration localization framework that utilizes factor graph optimization. Firstly, a tightly coupled Global Navigation Satellite Systems (GNSS)/on-board sensor fusion localization framework is established to estimate vehicle states, including position, velocity, and attitude. To address the large drift rate of the Inertial Measurement Unit (IMU), this study introduces a novel IMU/Dynamics pre-integration method based on the vehicle dynamics model. We establish a two-degree-of-freedom vehicle dynamics model utilizing measurements from the wheel speed sensor and steering wheel angle sensor. The IMU/Dynamics factor is devised through a close integration of the model output and IMU pre-integration, enabling the construction of precise odometry with low-cost on-board sensors. Then, to address the issue of the non-Gaussian distribution of GNSS pseudorange error, this paper employs a Gaussian Mixture Model (GMM) to characterize the pseudorange noise, which is then applied to further sensor fusion. Given the time-varying nature of pseudorange noise, the expectation maximization algorithm is utilized to estimate GMM parameters online, leveraging the pseudorange residuals within a sliding window. Comprehensive experiments, inclusive of challenging scenarios such as urban canyons, tunnels, and wooded areas, have been carried out. They affirm the superior performance of the proposed method. Experiments have shown that our method demonstrates reliable localization across different statuses of GNSS signal, exhibiting a 39.4% improvement in the root mean square error of position error when compared to the state-of-the-art. Additionally, this FGO-MFI is a general sensor data fusion framework and is able to incorporate diverse sensor measurements, for example, from cameras and LiDARs to provide more reliable and accurate localization information.