Effects of Anodal tDCS Applied Over the Cerebellum Combined with Physical Therapy on Center of Gravity Sway in a Patient with Cerebellar Ataxia: A Single-Case Study.

Damage to the cerebellum results in dysfunctional standing postural control. Patients with cerebellar ataxia have a larger sway in the center of gravity (COG) while standing. Transcranial direct current stimulation (tDCS) has been applied in the rehabilitation of patients with central nervous system disorders; however, its effect on COG sway in patients with cerebellar ataxia remains unknown. We aimed to confirm the effects of anodal cerebellar tDCS (ctDCS) combined with physical therapy on COG sway in a patient with cerebellar ataxia using a retrospective ABA single-case study design. This study involved a patient with left cerebellar hemorrhage. Walking and postural balance rehabilitation were conducted in phase A. Anodal ctDCS was combined with the walking and postural balance rehabilitation in phase B. We measured COG sway in the open- and closed-eyes standing conditions daily throughout all the phases. In the open-eyes standing condition, there was no significant change in COG sway in phase B. Conversely, in the closed-eyes standing condition, the circumferential area, total sway path length, and anteroposterior sway path length decreased in phase B. No change was observed in the mediolateral sway path length. The combination of anodal ctDCS and physical therapy may decrease COG sway in patients with cerebellar ataxia in the closed-eyes standing condition, and its effect may be greater in the anteroposterior direction.

Selected Errors in Spatial Measurements of Surface Asperities.

This work presents issues related to selected errors accompanying spatial measurements of surface roughness using contact profilometry. The influence of internal heat sources, such as engines or control electronics, on the thermal expansion of the drive responsible for the measurement probe's movement in the X-axis direction was investigated. In terms of starting measurements on a thermally unstable device, the synchronization error of individual profile paths was 16.1 µm. Based on thermographic studies, the time required for full thermal stabilization of this drive was determined to be 6-12 h from when the device was turned on. It was demonstrated that thermal stabilization of the profilometer significantly reduced positioning errors of the measurement probe on the X-axis. Thermal stabilization time should be determined individually for a specific device variant. This research also determined how changes in the center of gravity caused by the measurement probe's movement affected the overall rigidity of the profilometer structure and the leveling of the tested surface. Laser interferometry was used for this purpose. The determined vulnerability of the profilometer structure was 0.8 µm for a measurement section of 25 mm. Understanding the described relationships will reduce errors associated with conducting measurements and preparing equipment for tests. Additionally, it will enable the correct evaluation of surface geometry.

Implications of Stabilometric Assessment in Determining Functional Deficits in Patients with Severe Knee Osteoarthritis: Observational Study.

Background: Osteoarthritis is one of the most frequent joint disorders in the world. The specialists in the field strongly support the role of physical exercise as a key component in the holistic management of arthrosis. The aim of the current study was to identify and assess the functional deficit of these patients and to identify means to alleviate it through pre-surgery physiotherapy programs. Methods: The study was conducted on two samples of patients: a witness sample, encompassing 126 subjects without pathologies at the level of their lower limbs, and a study sample, formed of 116 subjects diagnosed with severe gonarthrosis with total knee arthroplasty indication. The assessment protocol was accomplished with the GPS 400 stabilometric platform. Results: The barycenter differences within the support polygon, recorded for the two samples within sagittal deviation, emphasize that the barycenter shifting mainly towards the healthy lower limb will demand, from the individual, more intense rebalancing postural reactions that will place the center-of-gravity projection in the sagittal plane, closer to the central area of the support polygon. Conclusions: In the case of gonarthrosis and other joint disorders, the use of functional testing to assess body weight distribution and center-of-gravity imbalances represents a promising direction in the research on and management of these disorders, providing essential information for functional diagnosing and thus enabling the elaboration and monitoring of individualized functional rehabilitation plans.

The center of a face catches the eye in face perception.

Using the "Don't look" (DL) paradigm, wherein participants are asked not to look at a specific feature (i.e., eye, nose, and mouth), we previously documented that Easterners struggled to completely avoid fixating on the eyes and nose. Their underlying mechanisms for attractiveness may differ because the fixations on the eyes were triggered only reflexively, whereas fixations on the nose were consistently elicited. In this study, we predominantly focused on the nose, where the center-of-gravity (CoG) effect, which refers to a person's tendency to look near an object's CoG, could be confounded. Full-frontal and mid-profile faces were used because the latter's CoG did not correspond to the nose location. Although we hypothesized that these two effects are independent, the results indicated that, in addition to the successful tracing of previous studies, the CoG effect explains the nose-attracting effect. This study not only reveals this explanation but also raises a question regarding the CoG effect on Eastern participants.

Baduanjin is Better Balance Training Compared to Walking: A Cross-Sectional Study Based on Center of Gravity Trajectories.

BACKGROUND:  It has already been demonstrated by previous studies that Baduanjin training can improve the body's balance. However, its biomechanical mechanism remains unknown. Center of gravity (COG) trajectory analysis is an essential biomechanical test to explore the balance ability of the human body. Previous studies have not used the COG trajectory analysis technique to research Baduanjin training. The study utilizes COG trajectory analysis to analyze the trajectory of COG during Baduanjin training and compare it with that of walking, which is a common exercise for improving balance and aerobic ability, to determine if Baduanjin exercises affect the COG more than walking. MATERIALS AND METHODS:  Eight healthy female college students performed the walking and the eight forms of Baduanjin, a total of nine motions. The lower body kinematics were captured by the Vicon Motion Capture and Analysis System, while the kinetic data were acquired by the Kistler 3D Force Platform. The data were imported into Visual 3D to process the trajectory of the COG displacement amplitude, velocity, and acceleration of each motion. The COG horizontal envelope areas were calculated by Origin 9.0 Software (Origin Lab, Northampton, Massachusetts, USA) . RESULTS: Specific motions of Baduanjin provided significantly higher COG displacement amplitude, velocities, and acceleration training than walking. The F2 and F5 motions could provide a larger COG horizontal envelope area than walking. On the x-axis, F2 provided a greater COG displacement amplitude than walking, F1, F2, and F5 provided greater velocities, while all the motions provided greater accelerations. On the y-axis, all the motions except F2 provided greater COG displacement velocities and accelerations than walking. On the z-axis, F1-7 provided a greater COG displacement amplitude than walking, all the motions provided greater velocities, while all the motions except F2 provided greater accelerations. CONCLUSION: Baduanjin training provides a more intense COG perturbation than walking, which may be a more challenging balance training than walking.

Do Postural and Walking Stabilities Change over a Decade by Aging? A Longitudinal Study.

BACKGROUND: Previous studies have demonstrated that the center of gravity (COG) is more unstable in the elderly than in young people. However, it is unclear whether aging itself destabilizes the COG. This study aimed to investigate changes in COG sway and gait kinematics over time by a longitudinal study of middle-aged and elderly adults. METHODS: This study included 198 healthy middle-aged and elderly people who underwent stabilometry at ten-year intervals. The participants' mean age at baseline was 62.9 ± 6.5 years, and 77 (39%) of them were male. The results of stabilometry (mean velocity, sway area, postural sway center in the medial-lateral direction [X center], and postural sway center in the anterior-posterior direction [Y center]), and results of exercise tests (the height-adjusted maximum stride length [HMSL] and the 10 m walk test [10MWT]) were analyzed. The destabilized group with 11 participants, whose mean velocity exceeded 3 cm/s after 10 years, was compared with the stable group with 187 participants, whose mean velocity did not exceed 3 cm/s. RESULTS: Mean velocity increased significantly over ten years (open-eye, from 1.53 ± 0.42 cm to 1.86 ± 0.67 cm, p < 0.001); however, the sway area did not change significantly. X center showed no significant change, whereas Y center showed a significant negative shift (open-eye, from -1.03 ± 1.28 cm to -1.60 ± 1.56 cm, p < 0.001). Although the results of 10MWT and initial HMSL did not differ significantly, the HMSL in the destabilized group at ten years was 0.64, which was significantly smaller than the 0.72 of others (p = 0.019). CONCLUSIONS: The ten-year changes in COG sway in middle-aged and elderly adults were characterized by a significant increase in mean velocity but no significant difference in sway area. Because the destabilized group had significantly smaller HMSL at ten years, instability at the onset of movement is likely to be affected by COG instability.

Postural control and trunk stability on sway parameters in adults with and without chronic low back pain.

BACKGROUND: Postural sway changes often reflect functional impairments in adults with chronic low back pain (LBP). However, there is a gap in understanding how these individuals adapt their postural strategies to maintain stability. PURPOSE: This study investigated postural sway distance and velocity, utilizing the center of pressure (COP) and center of gravity (COG), between adults with and without LBP during repeated unilateral standing trials. METHODS: Twenty-six subjects with LBP and 39 control subjects participated in the study. Postural sway ranges, COP/COG sways, and sway velocities (computed by dividing path length by time in anteroposterior (AP) and mediolateral (ML) directions over 10 s) were analyzed across three unilateral standing trials. RESULTS: A significant group interaction in sway range difference was observed following repeated trials (F = 5.90, p = 0.02). For COG sway range, significant group interactions were demonstrated in both directions (F = 4.28, p = 0.04) and repeated trials (F = 5.79, p = 0.02). The LBP group demonstrated reduced ML sway velocities in the first (5.21 ± 2.43 for the control group, 4.16 ± 2.33 for the LBP group; t = 1.72, p = 0.04) and second (4.87 ± 2.62 for the control group, 3.79 ± 2.22 for the LBP group; t = 1.73, p = 0.04) trials. CONCLUSION: The LBP group demonstrated decreased ML sway velocities to enhance trunk stability in the initial two trials. The COG results emphasized the potential use of trunk strategies in augmenting postural stability and optimizing neuromuscular control during unilateral standing.

Calculation and Verification Method of Three-Dimensional Center of Gravity Based on Human Joint Points / 医用生物力学

Objective To explore the accuracy of the multiplication coefficient method and the moment synthesis method for determining the spatial position of the center of gravity(CoG)of the human body based on machine vision.Methods The mechanical measurement platform was built,and the three-dimensional(3D)human body CoG measurement method under static and dynamic conditions were designed to calculate the space coordinates of the CoG.Through experiments,the calculation accuracy of the multiplication coefficient and moment synthesis method were studied and analyzed.Results In the static experiments,the calculation results of the torque synthesis method were more accurate than those of the multiplication coefficient method for each dimension.The errors in the 3D CoG of the human body in the X,Y,and Z directions calculated using the torque synthesis method were 3.9%,4.1%,and 8.5%,respectively.In the dynamic experiment,the average and relative errors of the torque synthesis method in the X or Y direction were lower than those of the multiplication-coefficient method.When the action decomposition method was used to analyze the height direction of the CoG along the Z axis,the final rendering effect of the torque synthesis method improved.Conclusions The accuracy of the 3D CoG calculated by the moment synthesis method was relatively high,and was closer to the measurement data of the mechanical measurement platform.The 3D CoG calculated using the moment synthesis method can replace the mechanical measurement platform and can be used in subsequent studies.

[Continuing work after 64 years of age and postural balance.]

The objective of this study was to assess the components of postural balance among working and non-working men and women aged 65-69. A total of 120 people within the age range of 65-69 were screened. The first group included 30 female and 30 male patients who continued working beyond retirement. The second group comprised 30 women and 30 men who had ceased working by the time of the examination. For comprehensive assessment of postural balance components the computer complex of dynamic postrography «Smart Equitest Balance Manager¼ was used. Sensory Organization Test (SOT) and Motor Control Test (MCT) were conducted. An analysis of SOT and MCT results showed that compared to non-workers aged 65-69, working men and women of the same age range demonstrated more effective maintenance of static and static-dynamic balance, increased postural control performance, including neuromuscular control of balance, as well as optimal balancing and centre of gravity control while maintaining static and static-dynamic balance. The reduced participation of somatosensory, visual and vestibular information in postural control and visual-motor coordination will negatively impact the ability of people over 64 to continue working.

Centroid position estimating method for observational analysis.

[Purpose] This study aimed to develop a clinical observation method to evaluate the position of the mass center. From the human visual capability, we considered it would be practical to divide the body into two parts: the upper and the lower body mass. If we could identify their optimal position, we could observe the middle point in between as the center of mass. [Participants and Methods] Twenty healthy males performed forward bending, backward bending, squatting, and walking. The three-dimensional coordinates were analyzed using a conventional model. In addition, five "virtual" markers were assigned as upper and lower mass, respectively. The midpoints of each five virtual marker combinations defined the mass centers, providing 25 coordinates. We calculated the difference in the coordinates between mass centers from virtual markers and mass centers using a conventional model. The combination with the slightest error was evaluated to determine the 95% confidence interval of the observed points and whether the value was clinically beneficial. [Results] The optimal combination of the upper and lower mass was Th8 and in the middle of both hip and knee centers. [Conclusion] The overall magnitude of error was about 30 mm and enough to evaluate the center of mass with macroscopy.

Spatial and temporal variations of vegetation cover and its influencing factors in Shandong Province based on GEE.

Economic development has rapidly progressed since the implementation of reform and opening up policies, posing significant challenges to sustainable development, especially to vegetation, which plays a crucial role in maintaining ecosystem service functions and promoting green low-carbon transformations. In this study, we estimated the fractional vegetation cover (FVC) in Shandong Province from 2000 to 2020 using the Google Earth Engine (GEE) platform. The spatial and temporal changes in FVC were analyzed using gravity center migration analysis, trend analysis, and geographic detector, and the vegetation changes of different land use types were analyzed to reveal the internal driving mechanism of FVC changes. Our results indicate that vegetation cover in Shandong Province was in good condition during the period 2000 to 2020. The high vegetation cover classes dominated, and overall changes were relatively small, with the center of gravity of vegetation cover generally shifting towards the southwest. Land use type, soil type, population density, and GDP factors had the most significant impact on vegetation cover change in Shandong Province. The interaction of these factors enhanced the effect on vegetation cover change, with land use type and soil type having the highest degree of influence. The observational results of this study can provide data support for the policy makers to formulate new ecological restoration strategies, and the findings would help facilitate the sustainability management of regional ecosystem and natural resource planning.

Research on the Prediction Method of Braking Rotation Angle for Remote-Controlled Excavator.

To calculate, analyze, and predict the rotation angle during the deceleration and braking process of large remote-controlled excavators, this article established a spatial coordinate system based on a simplified model of a hydraulic excavator's upper structure. Using the D-H parameter method, a mathematical model of the working device's center of gravity and its rotational inertia was established. Based on the characteristics of the excavator's hydraulic system and the relationship between brake torque variations, a prediction model was developed to forecast the stopping position (brake rotary angle) of the excavator's bucket after braking. Subsequently, the predicted results were validated using simulation and compared with existing experimental data to assess the accuracy of the model. The findings demonstrate that the predictive model exhibited high precision with minimal error. The utilization of this model enabled effective forecasting of the excavator's braking position changes, providing a theoretical foundation for the intelligent remote control of excavators.

A novel method of assessing balance and postural sway in patients with hypermobile Ehlers-Danlos syndrome.

Patients with hypermobile Ehlers-Danlos syndrome (hEDS) frequently suffer from poor balance and proprioception and are at an increased risk for falls. Here we present a means of assessing a variety of balance and postural conditions in a fast and non-invasive manner. The equipment required is commercially available and requires limited personnel. Patients can be repeatedly tested to determine balance and postural differences as a result of disease progression and aging, or a reversal following balance/exercise interventions.

Remission of cervicogenic dysphagia associated with biomechanical dysfunction following chiropractic therapy.

Cervicogenic dysphagia is a complex condition that can arise from biomechanical dysfunction in the cervical spine. Conventional treatment outcomes are not always guaranteed. Chiropractic treatment is considered an alternative treatment for dysphagia, yet there is a lack of evidence supporting its effectiveness. We present the case of a 48-year-old male who had difficulty swallowing for eight months. He had a feeling of food stuck in his throat when eating hard food but without any pain when swallowing, and eventually, he could not swallow any dry food. He was diagnosed with dysphagia associated with an anxiety disorder and was treated with medication, but there was no improvement in his condition. A full-spine radiograph revealed biomechanical dysfunction, including reduced cervical lordosis and levoscoliosis of the upper thoracic spine. After nine months of conventional physiotherapy, the patient completely recovered from his symptoms, with significantly improved biomechanical parameters. This study highlights the potential mechanism of cervicogenic dysphagia and the effect of chiropractic treatment in managing it. Applying chiropractic treatment, including spinal manipulative therapy, instrument-assisted soft tissue manipulation, and mechanical traction, might bring a positive outcome for dysphagia patients with careful consideration.

Effects of various hyperopia intervention levels on male college students' gait kinematics.

Background: Hyperopia is a common blurred vision phenomenon that affects postural control in gait; however, current research has focused on the alteration and correction of hyperopia's physiological characteristics, ignoring the effect of hyperopia on gait kinematic characteristics. The effect of hyperopia on the basic form of movement walking is a worthy concern. Objective: To investigate the gait kinematic characteristics of male college students with varying degrees of visual acuity (normal vision, hyperopia 150°, and hyperopia 450°), as well as to provide a theoretical foundation for the effect of visual acuity on gait and fall risk reduction. Methods: Twenty-two male college students with normal visual acuity were chosen. Their vision was tested using a standard visual acuity logarithm table at normal and with 150° and 450° concave lenses. Gait kinematic data were collected under normal vision and hyperopic conditions using the PN3 Pro advanced inertial motion capture system and Axis Studio application program. Results and conclusion: 1. The change of center of gravity in Pre-double support was smaller than normal vision; Late-single support and Late-swing was larger than normal vision; 2. The percentage of the double-leg support decreased; the percentage of the single-leg support and the Late-swing increased; 3. For the joints' range of motion, Trunk flexion and extension range of motion in Pre-single support, Late-double support and Pre-swing smaller than normal visual acuity, and Late-swing larger than normal; hip internal abduction and adduction and internal and external rotation are larger than normal vision in Late-single support; knee and ankle in abduction and adduction direction are larger than normal vision in the swing stage; hip flexion and extension, internal external rotation are larger than normal vision in the swing stage. Hyperopic interventions have an impact on the kinematic characteristics of gait in male college students, mainly in terms of altered balance, increased instability, increased difficulty in maintaining trunk stability, and increased risk of injury.

Effect of slope change on kinematics of amateur golfers' full swing.

BACKGROUND: Golf courses are designed with uneven terrain. These factors are especially important when facing (slope), players need to straighten the posture of each part of the body in order to complete the swing on an inclined surface such as flat ground. Amateur players may be more likely to change the movement patterns of their shots due to uneven terrain. Therefore, it may be necessary to clarify the shot characteristics of amateur players and provide reference materials for technical improvement. OBJECTIVE: The purpose of this study was to examine the effect of slope on amateur golfers' swing kinematics by analyzing the variation of time variables, body center of gravity (COG), and shot parameters of amateur golfers' swing at different ground slopes. METHODS: Six male amateur golfers participated in the experiment. The 7-iron was used for 5 swings each at three slopes: flat ground (FG, 0∘), ball below foot (BBF, +10∘), and foot below ball (FBB, -10∘). The OptiTrack-Motion capture system was used to collect kinematic data, and the three-dimensional motion data will be transmitted to Visual3D software for subsequent data analysis such as golf swing division and body COG changes. Shot parameters (carry, swing speed, ball speed, and smash factor) were recorded for each swing using the Caddie SC300 radar monitoring device. RESULTS: The results showed that there was no difference in the overall swing time and the time required for each interval at different slopes (p> 0.05) there is no significant difference in the change of the COG of the body in the forward and backward directions (p> 0.05). The three slopes of swing speed, ball speed, carry and smash factor were not significantly different (p> 0.05). CONCLUSION: The rhythm of the amateur golfer's swing was not affected by the slope, but the slope restricts the movement of the body's COG, which may affect the weight movement, and ultimately cause the performance parameters to not reach the level of the FG.

2011 to 2021 rehabilitation professionals distribution from system of China Disabled Persons' Federation using geographical gravity model / 中国康复理论与实践

ObjectiveTo investigate the distribution and trend of rehabilitation personnel of China Disabled Persons' Federation (CDPF) system and the people with disabilities (PWDs) using geographical gravity model. MethodsBased on ArcGIS and statistical data, the distribution of geographical center of gravity of the rehabilitation personnel of the CDPF system from 2011 to 2021 was analyzed. According to the economic development, the areas were divided into three regions, and the eastern region included eleven provincial units, the central region includes eight provincial units, and the western region included twelve provincial units. ResultsCompared with 2011, rehabilitation staffs per thousand PWDs increased at 107.5% in 2021, 81.1%, 114.2% and 174.1% for the eastern, central, and western regions, respectively; professional staffs increased at 190.5%, 148.8%, 284.6% and 280.6% for the eastern, central, and western regions, respectively; managerial staff increased at 80.0%, 46.8%, 554.3% and 128.1% for the eastern, central, and western regions, respectively. Compared with 2011, the geographical center of gravity of the rehabilitation personnel moved about 330.9 km in 2021, while the geographical center of gravity of the PWDs moved about 169.64 km. ConclusionThe rehabilitation personnel in the CDPF system is the most in the eastern region and least in the western region. The tracks of the geographical center of gravity of the three kind of rehabilitation personnel in the CDPF system are relatively consistent. The rehabilitation personnel in the eastern region are more concentrated than those in the western region, and the density of the PWDs is more westward than that of the rehabilitation personnel, and coordination is not a perfect match yet. It is necessary to strengthen the rehabilitation personnel allocation in the western region, to balance distribution of human resources for rehabilitation of PWDs among regions.

Kinematic characteristics of gait with different myopia: a cross-sectional study.

Background: Myopia, a condition affecting approximately one-quarter of the world' s population, has been projected to double in prevalence by the year 2050. It can have an impact on postural control during walking and can increase the risk of falls and injuries. Objective: (1) To examine the abnormal performance of postural control during walking in male college students who used convex lenses for myopia intervention from a kinematic perspective; (2) to establish theoretical foundation for preventing falls and injuries in the myopic population. Methods: A total of 22 male college students participated in this study. The center of gravity (COG), the percentage of gait cycle (PGC) and the joint angle(JT) were collected as indications of postural control during walking. A quantitative analysis was conducted using a One-Way Repeated Measures ANOVA to examine the variations among the three groups. Results: During myopic interventions, (1) the range of vertical COG changes is significant to be greater compared with normal vision (P < 0.05). (2) there was an significant increase in the PGC in single-legged support, accompanied by a decrease in the PGC in double-legged support, compared with normal vision (P < 0.05). (3) The myopic intervention leads to increased variability in JT of the hip and the knee during the single-leg support and swing, as compared to individuals with normal vision (P < 0.05). Severe myopic interventions result in more changes in JT of ankle. Conclusion: Myopia has been found to have a negative impact on postural control during walking, leading to changes in balance, increased instability, and an elevated risk of injury.

Wheelchair Axle Position Effect on the Propulsion Performance of Persons With C7 Tetraplegia: A Repeated-Measures Study.

Objectives: To assess the changes in speed, stroke frequency, acceleration, and shoulder range of motion (ROM) associated with different wheelchair axle positions in people with chronic C7 tetraplegia. Methods: This repeated-measures study was conducted at the Chronic Spinal Cord Injury Unit, FLENI Escobar, Argentina. The speed, stroke frequency, acceleration, and shoulder ROM during wheelchair propulsion were measured in nine participants with C7 spinal cord injury (SCI) in four different axle positions (forward and up, forward and down, backward and down, backward and up). Two strokes performed at maximum speed were analyzed on a smooth level vinyl floor in a motion analysis laboratory. Data were analyzed for significant statistical differences using the Friedman test and the Wilcoxon signed rank test. Results: Our study showed significant differences in the speed with axle position 1 (1.57 m/s) versus 2 (1.55 m/s) and position 2 (1.55 m/s) versus 4 (1.52 m/s). The shoulder ROM showed a significant difference in the sagittal plane in position 2 (59.34 degrees) versus 3 (61.64 degrees), whereas the stroke frequency and the acceleration parameters showed no statistically significant differences with the different rear axle positions. Conclusions: Our study showed that modifying the rear axle position can improve the propulsion speed and produce changes in the shoulder ROM in the wheelchair propulsion of individuals with C7 SCI.

Joint Estimation of Mass and Center of Gravity Position for Distributed Drive Electric Vehicles Using Dual Robust Embedded Cubature Kalman Filter.

The accurate estimation of the mass and center of gravity (CG) position is key to vehicle dynamics modeling. The perturbation of key parameters in vehicle dynamics models can result in a reduction of accurate vehicle control and may even cause serious traffic accidents. A dual robust embedded cubature Kalman filter (RECKF) algorithm, which takes into account unknown measurement noise, is proposed for the joint estimation of mass and CG position. First, the mass parameters are identified based on directly obtained longitudinal forces in the distributed drive electric vehicle tires using the whole vehicle longitudinal dynamics model and the RECKF. Then, the CG is estimated with the RECKF using the mass estimation results and the vertical vehicle model. Finally, different virtual tests show that, compared with the cubature Kalman algorithm, the RECKF reduces the root mean square error of mass and CG by at least 7.4%, and 2.9%, respectively.