Road Slope Research Articles

Reservoir water level decline accelerates ground subsidence: InSAR monitoring and machine learning prediction of surface deformation in the Three Gorges Reservoir area

IntroductionSurface deformation in the Three Gorges Reservoir area poses significant threats to infrastructure and safety due to complex geological and hydrological factors. Despite existing studies, systematic exploration of long-term deformation characteristics and their driving mechanisms remains limited. This study combines SBAS-InSAR technology and machine learning to analyze and predict surface deformation in Fengjie County, Chongqing, China, between 2020 and 2022, focusing on riverside urban ground, riverside road slopes, and ancient landslides in the reservoir area.MethodsSBAS-InSAR technology was applied to 36 Sentinel-1A images to monitor surface deformation, complemented by hydrological and meteorological data. Machine learning models—Random Forest (RF), Extremely Randomized Trees (ERT), Gradient Boosting Decision Tree (GBDT), Support Vector Regression (SVR), and Long Short-Term Memory (LSTM)—were evaluated using six metrics, including RMSE, R2, and SMAPE, to assess their predictive performance across diverse geological settings.ResultsDeformation rates for riverside urban ground, road slopes, and ancient landslides were −3.48 ± 2.91 mm/yr, −5.19 ± 3.62 mm/yr, and −6.02 ± 4.55 mm/yr, respectively, with ancient landslides exhibiting the most pronounced deformation. A negative correlation was observed between reservoir water level decline and subsidence, highlighting the influence of seasonal hydrological adjustments. Urbanization and infrastructure development further exacerbated deformation processes. Among the models, LSTM demonstrated superior predictive accuracy but showed overestimation trends in ancient landslide areas.DiscussionReservoir water level adjustments emerged as a critical driver of subsidence, with rapid water level declines leading to increased pore pressure and soil compression. Seasonal effects were particularly evident, with higher subsidence rates during and after the rainy season. Human activities, including urbanization and road construction, significantly intensified deformation, disrupting natural geological conditions. Progressive slope failure linked to road expansion underscored the long-term impacts of engineering activities. For ancient landslides, accelerated deformation patterns were linked to prolonged drought and reservoir-induced hydrological changes. While LSTM models showed high accuracy, their limitations in complex geological settings highlight the need for hybrid approaches combining machine learning with physical models. Future research should emphasize developing integrated frameworks for long-term risk assessment and mitigation strategies in reservoir environments.ConclusionsThis study provides new insights into the complex surface dynamics in the Three Gorges Reservoir area, emphasizing the interplay of hydrological, geological, and anthropogenic factors. The findings highlight the need for adaptive management strategies and improved predictive models to mitigate subsidence risks.

Research on the Correlation Mechanism Between Complex Slopes of Mountain City Roads and the Real Driving Emission of Heavy-Duty Diesel Vehicles

This research proposed the method of using cumulative positive and negative elevation increment indicators based on road segment to identify the slope characteristics of mountain city roads. Furthermore, it proposed the adoption of these indicators, combined with driving dynamics and emission theory, to analyze the correlation mechanism between the road slope and the actual driving fuel consumption and emissions. Three routes with different slope characteristics were selected in the mountain city of Chongqing, and six road driving tests were conducted using a Class N2 heavy-duty diesel vehicle. Finally, a comprehensive and in-depth study on fuel consumption and emission characteristics was carried out. The results show that the cumulative positive and negative elevation increment indicators based on road segment can correctly identify the complex slope characteristics of mountain city roads. Moreover, using the above indicators, the research method based on the theory of driving dynamics and emission successfully revealed the correlation mechanism between the slope of mountain city roads and the fuel consumption and emissions. Overall, the changes in fuel consumption factor and pollutants CO, NOX, and PN are positively correlated with the change in slope. The increase in slope leads to a rise in load, thereby increasing the required power, fuel consumption, and rich combustion conditions, ultimately leading to an increase in pollutants. It should be noted that driving dynamics also affect fuel consumption and emissions, leading to the specific rate of change between slope and fuel consumption not being consistent and a significant increase in the PN (Particulate Number) on some road sections. In addition, exhaust gas temperature may have a certain impact on emissions.

Development of Deep Learning-Based Algorithm for Extracting Abnormal Deceleration Patterns

A smart regenerative braking system for EVs can reduce unnecessary brake operations by assisting in the braking of a vehicle according to the driving situation, road slope, and driver’s preference. Since the strength of regenerative braking is generally determined based on calibration data determined during the vehicle development process, some drivers could encounter inconveniences when the regenerative braking is activated differently from their driving habits. In order to solve this problem, various deep learning-based algorithms have been developed to provide driving stability by learning the driving data. Among those artificial intelligence algorithms, anomaly detection algorithms can successfully separate the deceleration data in abnormal driving situations, and the resulting refined deceleration data can be used to train the regression model to achieve better driving stability. This study evaluates the performance of a personalized driving assistance system by applying driver characteristic data, obtained through an anomaly detection algorithm, to vehicle control.

Studying the performance of pavement defects at different road slopes using the vibration-based method and deep machine learning

Road networks are the backbone of urban life and significantly impact the sustainability of any country's infrastructure sector. Therefore, it is necessary to maintain the condition of roads and pavements through continuous monitoring and periodic maintenance in order to achieve the highest levels of service for road users and the sustainability of their use. Pavement is the main component of road networks, providing the highest degree of comfort to drivers and roadway users when it is appropriately designed and free from defects and cracks. More clearly, defects are one of the most important factors that reduce the operational life of roads and cause economic losses to road users by causing damage to their vehicles; moreover, the damaged pavement needs frequent and long maintenance that may also drain the resources of government institutions and transport agencies. Therefore, there is a crucial need for a monitoring and follow-up system for the condition of the roads in order to identify and treat defects quickly. This study used a vibration-based system to monitor pavement conditions on several roads with different gradients. A fully electric car was used to determine the vibration values, which indicate the degree of driving comfort, to determine the spread and behaviour of defects on the pavement at multiple locations on roads with different gradients. Also, a machine learning model was applied using a "decision tree" model to identify, classify and predict defects on the pavements. The results of this study indicated that pavement defects were more prevalent in the first and last quadrants of the high-slope roads compared to the low-slope roads. The prediction model achieved accuracy in predicting the performance of defects with a rate of 94% for roads with low gradients and 90% and 86% for roads with medium and high gradients, respectively.

Influence of the driving environment on the dynamic characteristics of a DCT vehicle starting considering the longitudinal and vertical coupling model

The most significant external excitation affecting the dynamic characteristics of a vehicle is its driving environment. This type of excitation leads to issues such as slow initial response during starting, significant vibrations in the transmission system, and overall performance instability. A longitudinal–vertical coupled dynamics model has been developed to analyse the impact of driving conditions on the dynamic characteristics of vehicles with Dual-Clutch Transmission (DCT) during starting. This model takes into account factors such as the engine’s harmonic torque, the time-varying meshing stiffness of the gear system, the nonlinear torsional behaviour of the dual-mass flywheel, the deformation and torsion of the powertrain mounts, tire deformation, and random road excitations. Utilizing the established coupled model for DCT vehicle transmission systems, the impact of varying road roughness, adhesion coefficients, and road slope on the dynamic performance of DCT vehicles. To verify the accuracy of the simulation results of the influence of the driving environment on the dynamic characteristics of the DCT vehicle starting process, the experimental and simulation results of the influence of the driving environment on the vehicle dynamic characteristics of flat road surfaces, B-level uneven road surfaces, wet road surfaces, and 10% road slopes were compared. The overall trend of the simulation results of the clutch master and slave end speeds, vehicle longitudinal and vertical impact degrees, etc., was in good agreement with the experimental results, confirming the accuracy of the established DCT vehicle transmission system coupling dynamic model.

Trajectory Tracking Control for Self-driving Vehicle Considering Road Slope and Adhesion Condition

Trajectory Tracking Control for Self-driving Vehicle Considering Road Slope and Adhesion Condition

Experimental Study Unraveling Flow Allocation Patterns at Crossroad Intersections During Urban Flooding

Urban roads can effectively handle peak flows during extreme storms by serving as surface flood passages, provided the flow remains within safety thresholds for vehicles and pedestrians. However, studies on flow allocation at crossroad intersections are limited. Previous research has overlooked important factors: road transverse slope and turning radius. This study built a “two in, two out” laboratory crossroad intersection to examine flow allocation patterns. Experiments explored the effects of road longitudinal slope, boundary conditions, and the combined influence of turning radius and side slope. The results indicated that at flatter slopes, flow allocation is more influenced by road slope, while at steeper slopes, the inflow Froude number ratio becomes more significant. The combined effect of the turning radius and side slope results in a flow allocation that differs by 44.3% compared to rectangular orthogonal channel intersections. A straightforward formula is proposed to calculate the flow allocation ratio based on experimental results and inflow power ratio. These findings could improve road intersection designs for better flood mitigation, offering a practical tool for planning flood-resilient road networks.

Multi-objective optimization shift strategy for vehicle based on adaptive linear weighted sum method

The shift strategy plays a pivotal role in influencing the power and economy performance of vehicles. In order to improve the adaptability of shift to dynamic driving conditions, this paper proposes a comprehensive shift strategy. This study employs the FMRLS algorithm to establish a model for identifying vehicle mass and road slope and presents a model for altitude identification based on SVM. The comprehensive shift strategy is formulated by using the NSGA-II algorithm to calculate the Pareto front of the shift speeds and determine the power and economy weights for different driving conditions based on the linear weighted sum method in an adaptive manner. The simulation results show that the energy consumption of the comprehensive shift strategy is close to the economy shift strategy under the CHTC-HT condition. Significantly, the maximum difference is 2.97% in acceleration time between the comprehensive and the power shift strategy under plateau condition. Additionally, the comprehensive shift strategy can eliminate cyclic shift on upslope and provide braking force in response to the driver intention to decelerate on downslope, improving vehicle safety, and dynamic adaptability.

Rare and Abundant phoD‐Harboring Bacteria Mediate the Mineralization of Organic Phosphorus Fractions in Soil Aggregates During Cut Slope Restoration

ABSTRACTPhosphorus (P) is the key nutritional element in the soil of cut road slopes undergoing ecological restoration, and the transformation of organic P (Po) is a crucial part of the P cycle. However, the role of phoD‐harboring bacteria in driving the mineralization of Po fractions in road slope soil aggregates is unclear. This study analyzed road slope soils that had undergone 7, 11, and 14 years of restoration in the western Sichuan Plateau of China. We examined the differences and associations between the Po fraction content, alkaline phosphatase (ALP) activity, and community composition of rare and abundant phoD‐harboring bacteria in soil aggregates of four particle sizes (0.053–0.25, 0.25–2, 0.053–0.25, and, > 2 mm). The results showed that NaHCO3‐extracted Po (NaHCO3‐Po) content in soil aggregates increased with restoration years, while NaOH‐extracted Po (NaOH‐Po) content decreased. ALP activity in soil aggregates increased with restoration years, but there was no significant relationship between ALP activity with the phoD‐harboring bacterial community. There were significant differences in the composition of rare and abundant phoD‐harboring bacterial communities during slope restoration. Soil moisture, pH, organic carbon, and the C:P ratio in soil aggregates were the primary factors affecting the distribution of the Po fractions and the phoD‐harboring bacterial community. NaHCO3‐Po and NaOH‐Po in soil aggregates were likely the main substrates for ALP‐mediated Po mineralization. More genera were involved in Po mineralization in slope soils restored for 14 years than in soils restored for 7 and 11 years, and rare phoD‐harboring genera were more actively involved in Po mineralization than abundant phoD‐harboring genera. This study provides some theoretical basis for P effectiveness enhancement and P management during slope soil restoration.

Permanent deformation and particle crushability of calcareous sands under cyclic traffic-induced loadings through simple shear apparatus

This study focuses on investigating permanent deformations, encompassing normal and shear strains, of calcareous sandy soils subjected to drained cyclic traffic-induced loadings. The investigation utilizes a Simple Shear (SS) apparatus allowing for variations in both normal and shear stress components over each cycle and incorporates Principal Stress Rotation (PSR), a feature not replicable in conventional cyclic uniaxial triaxial tests which is the key aspect of this research. The study also accounts for the harmonically changing the effective horizontal stress resulting from cyclic variations of effective vertical stress, conducted under a horizontally constrained boundary condition with zero lateral strain. A series of drained cyclic simple shear experiments is carried out, implementing a heart-shaped stress path, encompassing up to 1000 cycles. The objective of the study is to analyze permanent normal and shear deformations, along with associated total particle crushing, using both sieving analyses and 2D image processing of particles. The study also evaluates the impact of an initial static shear stress originating from the longitudinal slope of roads. The findings highlight the influences of induced cyclic amplitudes of stress components, principal stress and strain rate rotation, and initial static shear stress on the development of permanent strains. Furthermore, the research characterizes particle crushability in terms of total crushability over such loading, examining its dependency on relative density and variations in both shear and normal stress components.

The Effects of Strata Orientation and Water Presence on the Stability of Engineered Slopes Using DIPS and FLACSlope: A Case Study of Tubatse and Fetakgomo Engineered Road Slopes

This paper combines empirical observations, kinematic analysis, and numerical simulation to investigate slope failure susceptibility, with practical implications for regional infrastructure projects. Six slopes along the R37 road were analyzed to assess the impact of strata orientation and water presence on slope stability. The results indicate that various factors interact to destabilize the mechanical integrity of both rock and soil materials. Dry slopes were found to be less vulnerable to failure, although geological conditions remained influential. Numerical modeling using FLACSlope (version 8.1) revealed that the factor of safety (FoS) decreases as the water presence increases, highlighting the critical need for effective drainage solutions. Kinematic analysis, incorporating DIPS modeling and toppling charts, identified toppling as the most likely failure mode, with a 90% susceptibility rate, followed by planar and wedge failures at 6% and less than 5%, respectively. These findings are validated by the observed slope conditions and empirical data. Planar failures were often remnants of both sliding and toppling failures. Given the significant risk posed to road infrastructure, particularly where FoS hovers just above the stability threshold, this study emphasizes the importance of proactive, long-term slope monitoring and early mitigation strategies to prevent catastrophic failures. The results can guide infrastructure design and maintenance, ensuring safer and more resilient roadways in regions prone to slope instability. Nonetheless, the use of sophisticated slope stability modeling techniques is recommended for a thorough understanding of the mechanical dynamics of the slope material, and for catering to the shortfalls of the techniques applied in this paper.

Assessing energy consumption in scalable semi-autonomous destination-based E-platoons: A multiplayer approach

Recent developments in connected and automated vehicle technologies have opened up new possibilities but also posed enduring challenges. One of the primary challenges is the efficient coordination of vehicles in urban environments, specifically through scalable and destination-based platooning. While considerable research has focused on platooning with a limited number of vehicles demonstrating seamless connectivity and coordination on highways, there remains a significant gap in understanding and implementing scalable platoons in more dynamic urban settings. This paper bridges these gaps by developing a novel extension to the 3DCoAutosim simulation platform. Our model introduces ’Scalable Semi-autonomous Destination-based Multiplayer E-Platoons’, accommodating different automation levels and simulation characteristics of vehicles in five distinct platoons. We employed seven electric vehicles to create these platoons, each consisting of an autonomous lead vehicle, followers that are either autonomous or semi-autonomous (accompanied by drivers), customised according to the specific requirements of each platoon. Utilising Time Series Analysis, Multiple Linear Regression and a comprehensive, comparative scenario-based analysis, we assessed and validated our developed model’s impact on battery energy consumption under varying road slopes and car-following models. Our assessment employs real-world trip data from Upper Austria, with results indicating a potential reduction in total battery energy consumption when operating in platoon mode.

Electric vehicle ramp recognition based on fusion of vehicle mass estimation

Road slope is the necessary environmental information for intelligent electric vehicles. The accuracy of slope recognition directly determines the control quality of vehicles on the hill. Aiming at the problems that the existing ramp recognition algorithms have poor adaptability to the conditions and are unable to To satisfy the application requirements of mass production vehicles, this paper proposes an electric vehicle slope recognition method based on vehicle mass estimation. Firstly, the vehicle longitudinal dynamics model is established, and the signal characteristics of the acceleration sensor under the actual vehicle conditions are analyzed. The least square vehicle mass estimation strategy with forgetting factor is constructed to obtain the vehicle mass directly under the starting condition. Ramp recognition algorithms are designed for static parking and dynamic driving scenarios. In the static scenario, the filter latch strategy is used to deal with the interference factors such as activities in the vehicle. In the dynamic scenario, the Kalman filter algorithm based on measurement noise adaptation is designed to realize the fusion estimation of dynamic observation and kinematic observation for the slope. The effectiveness of the method is verified by Simulink -CarSim joint simulation. Finally, the real vehicle test is completed on Chery new energy's mass production electric vehicle platform and domain controller. road test results show that the mass estimation error is less than ±10 kg; the static estimation error of the slope is less than 0.001 rad, and the dynamic error is within 0.005 rad. The estimation accuracy and stability are greatly improved, which ensures the environmental adaptability of the intelligent electric vehicles.

Research on trajectory tracking control method for agricultural robot permanent magnet synchronous motor servo system based on improved EMD threshold wavelet filtering

In agricultural robots, trajectory tracking can be affected by disturbances such as road slopes or bumps, leading to sudden changes in path curvature and reduced control accuracy. To address this issue, we propose a servo motor drive control method based on an improved Empirical Mode Decomposition (EMD) threshold. A mathematical model integrating the drive and control of the servo motor is established, and the driving performance of the servo motor is analyzed. By detecting the speed and position of the servo motor, the specified three-phase current values for motor drive control are derived. The actual current of the motor is collected using Hall current sensors and denoised with an improved EMD threshold wavelet filtering method. Within the servo motor drive control model, the system calculates the difference between the given three-phase current values and the actual motor current, and this difference is then used to adjust the motor control via an input linear amplifier, ensuring integrated drive control. Simulation and experimental results show that the proposed trajectory tracking control method for the agricultural robot’s permanent magnet synchronous motor servo system exhibits high control accuracy, strong anti-interference ability, and good performance, making it more suitable for practical applications.

Designing of Ecological Model Predictive Control Algorithm for Electric Trucks Platoons with Optimal Energy Consumption

Abstract In response to the problem of motor vehicle exhaust emissions pollution, the development of new energy in China’s truck industry will be an inevitable trend. At present, the penetration rate and market share of pure electric trucks are constantly increasing. The research on electric truck platoons has strong practical significance. This article focuses on the ecological control strategy of pure electric truck platoons. Firstly, a platoon model of four electric trucks is established in Trucksim. The leading vehicle designs an ecological optimal speed dynamic programming algorithm, and in terms of following vehicle tracking control, the battery SOC state motor speed is considered to be improved, Designed an ecological model predictive control algorithm for electric truck platoon with optimal energy consumption. Using real road slope data in the mining area, a Trucksim/Matlab/Simulink joint simulation was conducted. The simulation results showed that compared with traditional constant speed cruise control, the proposed ecological predictive cruise control algorithm for pure electric commercial vehicle platoons saved 9.2577% of the overall battery SOC.

Energy management of fuel cell hybrid electric bus in mountainous regions: A deep reinforcement learning approach considering terrain characteristics

Environmental characteristics, particularly in mountainous regions with significant slopes, substantially impact vehicle power demand and fuel consumption, thereby influencing both fuel economy and vehicle lifespan. However, existing research lacks energy management strategies specifically designed for these challenging terrains. This study presents an innovative energy management strategy (EMS) for fuel cell hybrid electric buses (FCHEB) utilizing a deep reinforcement learning algorithm considering terrain characteristics. A comprehensive model that incorporates road fluctuations and steep slopes was developed to accurately represent the terrain features of mountainous regions. Driving cycle and road condition data specific to hydrogen fuel cell buses in these areas were collected and processed as for the training sets of EMSs. Subsequently, an EMS based on the Proximal Policy Optimization (PPO) algorithm was devised to address the unique characteristics of these mountainous regions. Simulation results indicate a 26.16 % improvement in fuel economy and a 44.98 % enhancement in convergence efficiency compared to traditional methods that do not consider road slopes. Further validation through new bus route trials and standard driving cycle tests confirms the strategy's robustness and adaptability.

Comprehensive Analysis of Magnetic Flux Density and RF-EMF Exposure in Electric Buses: A Case Study from Samsun, Turkey.

This study investigates magnetic flux density (B) and radiofrequency electromagnetic field (RF-EMF) measurements on electric buses operating in Samsun, Turkey, focusing on two bus routes (called E1 and E4) during the morning and evening hours. Measurements were taken under diverse operational conditions, including acceleration, cruising, and braking, at locations of peak passenger density. Along the E1 route, the magnetic field intensity varied significantly based on the bus position, road slope, and passenger load, with notable increases during braking. In contrast, the E4 route showed a lower magnetic field intensity and RF-EMF values due to its straighter trajectory and reduced operational stops. The highest RF-EMF measurement recorded was 6.01 V/m, which is below the maximum levels established by the ICNIRP guidelines. In 11 out of the 12 different band-selective RF-EMF measurements, the highest contribution came from the downlink band of the base stations, while in only one measurement, the highest contribution originated from the uplink bands of the base stations. All data were subject to the Anderson-Darling test, confirming the generalized extreme value distribution as the best fit for both B and RF-EMF measurements. Additionally, the study assessed B levels inside and outside the bus during charging, revealing heightened readings near the pantograph. These findings significantly contribute to our understanding of electromagnetic field exposure in electric bus environments, highlighting potential health implications and informing the development of targeted mitigation strategies.

Small Endemic Birds and Hot Climate: Avian and Environmental Predictors of Avifauna Road Mortality in Santa Cruz Galapagos

In the Galapagos Islands, the main road in Santa Cruz is one of the elements involved in bird road mortality along with vehicles and the impacted species. This study reports the number of roadkilled birds found on the road from the Itabaca Channel to Puerto Ayora, and the main factors, whether avian or environmental, involved in bird roadkill mortality. We collected individual carcasses in 2004, 2005, 2006, and 2018 with a prevalence of 278, 252, 265, and 294, respectively, across 21 species. The endemic Yellow Warbler Setophaga petechia aureola was the most affected bird. We used a PRIDIT model to rank the top avian and environmental predictors of road mortality. We found that for the sampled years, bird body size (i.e., 8–35 g) and the endemism status (i.e., endemic/native) were the main predictors of roadkill mortality, along with seasonality (i.e., hot season). Weaker predictors related to the bird (i.e., age and sex) and the environment (ecosystem, road slope, vegetation, or precipitation) are also reported as determinants of roadkill mortality. This study on avian mortality aims to inform conservation strategies to reduce the rate of wildlife avian roadkill on Santa Cruz Island and other islands with similar problems.

Vehicle dynamics analysis and adaptive control scheme design under coupled slope for trajectory tracking of four-wheel independent drive autonomous vehicles

Trajectory tracking is the core function of autonomous vehicle motion control. On variable road slopes, vehicles will encounter extra forces due to gravity, distinct from driving on flat roads. These forces will cause significant deviations in trajectory tracking and even instability, especially for four-wheel independent drive autonomous vehicles (4WIDAVs) with closely coupled longitudinal-lateral dynamics. To address above issues, first, a modified dynamics model considering coupled slopes is built, and the slope effect on vehicle motion and stability is analysed. Secondly, treating coupled slopes as augmented states, a square root cubature Kalman filter (SRCKF) is designed for real-time slope estimation. Then, a slope-adaptive model separate predictive trajectory tracking control strategy is proposed, decoupling the slope-adaptive tracking system into longitudinal and lateral subsystems. Predictive control is performed separately to ensure real-time performance, and prediction information is exchanged between subsystems to preserve dynamics coupled characteristics, enhancing tracking accuracy. Finally, the effectiveness of the proposed scheme is validated by simulations and real-vehicle experiment under the varying slope condition. Results show that the proposed scheme improves tracking accuracy by 17.59% and reduces computation time by 55.02% compared to existing scheme in simulations, and in experiment, the tracking error is reduced by 17.89%.

A hierarchical estimation of road grade based on tire force observation

Road grade is important for autonomous vehicles, but it is difficult to measure directly. To address this issue, a hierarchical estimation of road grade is suggested based on the observation of tire forces. First, a 7-degree-of-freedom (DOF) dynamics model, including vehicle longitudinal, lateral, and yaw motions together with wheel rotations, is developed while considering the road grade. Subsequently, a dual-layer road grade estimation strategy is proposed based on an unscented Kalman filter (UKF). The lower-layer UKF estimates the longitudinal and lateral tire forces for road grade observation, and the upper-layer UKF is employed to estimate the road grade by considering the vehicle’s lateral acceleration and yaw rate. Finally, CarSim and MATLAB joint simulations and road tests are performed under different conditions to validate the correctness and effectiveness of the proposed estimation method. The results show that the proposed tire force observation-based estimator exhibits a lower mean absolute error and root mean square error on sloping roads and combined curved and sloping roads, and presents a better overall estimation performance on road grade compared with the widely used kinematics and dynamics model-based estimators.