Instantaneous Velocity Measurements Research Articles

Uncertainty quantification for velocity measurement with 2D2C particle image velocimetry

Abstract In this paper, a theoretical model of dimensionless instantaneous and average velocity measurement uncertainty quantification with 2D2C particle image velocimetry (PIV) is established under the framework of generally adopted international uncertainty quantification standards. The effectiveness of the model is verified using uniform flow field testing data. Combined with semi-quantitative analysis of the theoretical model, uncertainty control suggestions for PIV measurements are given. The major sources affecting the uncertainty of instantaneous velocity measurements are the reference velocity, particle instantaneous pixel displacement, and their correlation term. For average velocity measurement uncertainty quantification, the uncertainty of particle average pixel displacement is effectively controlled by taking a large number of particle images. Thus, three single-component terms — the calibration factor, particle average pixel displacement and reference velocity — and two correlation terms — the particle average pixel displacement–calibration factor and the particle average pixel displacement–reference velocity — all make an important contribution to the average velocity measurement uncertainty. To reduce the uncertainty of PIV velocity measurement, one can reduce the reference velocity measurement uncertainty, optimize the PIV algorithm and improve the calibration factor by applying a high spatial resolution imaging system in experiments. In addition, reducing the reference velocity measurement uncertainty and improving the spatial resolution are key feasible methods.

Spatially-Resolved Freestream Velocity Measurements At The NASA Langley 31-Inch Mach 10 Air Tunnel Using FLEET

Freestream velocity measurements in the NASA Langley 31-inch Mach 10 wind tunnel are reported in this paper using Femtosecond Laser Electronic Excitation Tagging (FLEET). The freestream measurements acquired during the January 2023 test campaign were the first direct measurement of freestream velocity in this hypersonic wind tunnel facility. Spatial distributions of time-averaged and instantaneous velocity measurements were obtained at all three typical wind tunnel freestream unit Reynolds number conditions of Re∞ /L = 1800000 [1/m] , 3600000 [1/m], and 6400000 [1/m], though the current paper focuses on centerline measurements for the three Re∞ /L and spatial distributions for one Re∞ /L. Measured values for time-averaged velocity and mean of the instantaneous velocity at the wind tunnel centerline agree within 5 m/s or 0.4% of the calculated velocity from the facility data acquisition system. Measurements acquired at locations away from the wind tunnel centerline reveal the spatial extent of the core flow of the hypersonic facility.

Hydraulic Effect of Vegetation Zones in Open Channels: An Experimental Study of the Distribution of Turbulence

The development of vegetation in riverbeds is an important part of river engineering, and an in-depth understanding of its hydraulic influence is greatly needed. Our research focuses primarily on common reed (Phragmites australis) in riverbeds. To date, little is known about the hydraulic impact of the Phragmites australis reed and both field and laboratory data are still very scarce. Consequently, the main goal of our study was to evaluate the effect of vegetation zones on the spatial distribution of turbulence. Based on laboratory measurements of local instantaneous velocities, the values of the turbulence intensity (degree) Tu were determined, and its spatial distribution was illustrated. Analysis of the results showed that the relatively dense clusters of plants (reeds) act as “openwork deflectors” of the current and very clearly shape its spatial distribution. This can also be observed in the case of the distribution of the turbulence parameter Tu. For example, in the case of the development of riparian vegetation in the form of quasi-triangular communities of common reed (Phragmites australis) located alternately, there is a channelization of the flow, but also spatial changes in its character that occur. This work only presents results for preliminary hydraulic tests for Phragmites reed. These experiments should also be continued for other species of flexible riparian vegetation such as wicker. In the laboratory, the hydraulic influence of only triangle-shaped vegetation zones has been studied. Therefore, there is also a need for further hydraulic studies on vegetation zones of shapes other than triangular, e.g., rectangular, as well as vegetation zones with irregular shapes The authors see the need for such research and have already planned its continuation. Research on the interactions between vegetation and the structure of water flow in the riverbed is a very important aspect of contemporary trends in river environment management. Conscious, planned, and model-tested locating (or removing) of vegetation in a stream allows for shaping hydraulic and morphological conditions, thus controlling the processes of erosion, transport, and accumulation of debris.

Experimental and numerical investigation on the hydraulic design criteria for a step-pool nature-like fishway

Hydraulic considerations specific for the design of step-pool nature-like fishways (NLFs) are limited to the body dimensions of the target species. Additional hydraulic criteria for flow depth, maximum values for each of pool depth, velocity, and turbulent kinetic energy in terms of the weir opening width and discharge can help design an optimum step-pool NLF. The present study developed design charts and rating curves based on numerical modeling using the computational fluid dynamics software FLOW-3D® HYDRO. Instantaneous velocity measurements on a 1:4 scaled physical model of a step-pool nature-like fishway designed as per the available design guidelines have been used to validate the numerical model. The hydrodynamics of the fishway with respect to the weir opening ratio b r (0.10, 0.25, 0.45, 0.65, and 1.00) and discharge Q (0.1–1.5 m3/s) was analyzed through numerical simulations on a prototype scale. The simulation results showed that the maximum flow velocity and the averaged velocity over the crest at b r = 0.10 and 0.25 are considerably lower than at b r > 0.25. The maximum turbulent kinetic energy and energy dissipation factors for the tested range of discharges were within recommended limits for b r = 0.10 and 0.25. The present study outcome in terms of the design charts and rating curves that illustrate the relationship between different variables can be used for an optimum design and ease in field implementation. In addition, the bed structure of the step-pool NLF presented in this study can be used to recreate full-scale or pilot models.

Flow measurement in open channels using imaging techniques in conjunction with a convolutional neural network

Data related to river velocity and discharge are important for water resource management. Non-intrusive image measurement techniques based on direct cross-correlation (DCC) algorithms, such as particle image velocimetry (PIV), are widely used to measure velocity and discharge in the field. However, environmental noise is highly complex and uncontrollable in the field, significantly reducing the accuracy of DCC-based methods. Convolutional neural networks (CNNs) are commonly used in image recognition because of their outstanding accuracy, which far exceeds that of conventional imaging methods. However, these accuracy levels cannot be directly extrapolated for flow movement estimation. Therefore, in this study, we developed an innovative sub-pixel correction technique that allows CNN-based methods to obtain stable measurements in the PIV framework. This is the first study that successfully applied the concept of CNN to measure velocity data using images. The Hamel-Oseen vortex-flow, uniform steady-flow, and plane laminar jet-flow models are established as benchmark vector fields. Non-uniform illumination and Gaussian noise with varying degrees of interference are added to the synthetic data to evaluate the performance of the CNN-based method in PIV. For noiseless images, the DCC-based and CNN-based methods achieve lower measurement errors than benchmark errors. For noisy images, the DCC suffers a fold error increase ranging from 2.77 to 31.13, whereas the CNN suffers only a fold error increase ranging from 1.25 to 1.68. A 30-m-long flume is then used in an uncontrolled environment to mimic real-world flow measurement. The dispersion of the instantaneous velocity measurements for the CNN is more concentrated than that for the DCC. The acoustic Doppler velocimetry yields an error of only 7.87% in discharge estimation using CNN. These results indicate that the CNN-based method is more robust than conventional methods and has the potential to be effectively applied to measurements in the field.

Spectral analysis of the transition to turbulence downstream a delta winglet pair vortex generator in an airflow channel

The purpose of this experimental study is to provide a detailed analysis of the transition to turbulence in an airflow channel perturbed by a delta winglet pair vortex generator. Measurements of instantaneous velocity are carried out by a laser Doppler anemometry technique. Experiments are conducted for Reynolds numbers (based on the hydraulic diameter) ranging from Re = 400 to Re=12 000 and at several axial position downstream of the vortex generator. The flow behavior is characterized in each regime by means of a frequency analysis. We identified the inlet conditions corresponding to laminar weakly unsteady, transitional, and fully turbulent flow regimes. Furthermore, we have constructed a correlation between the Strouhal number and the Reynolds number that characterizes the vortex instability mechanism. Finally, under turbulent flow conditions, the dissipation rate was estimated, which showed an increase followed by an exponential decrease with the distance downstream of the vortex generator.

Picking up Speed: Continuous-Time Lidar-Only Odometry Using Doppler Velocity Measurements

Frequency-Modulated Continuous-Wave (FMCW) lidar is a recently emerging technology that additionally enables per-return instantaneous relative radial velocity measurements via the Doppler effect. In this letter, we present the first continuous-time lidar-only odometry algorithm using these Doppler velocity measurements from an FMCW lidar to aid odometry in geometrically degenerate environments. We apply an existing continuous-time framework that efficiently estimates the vehicle trajectory using Gaussian process regression to compensate for motion distortion due to the scanning-while-moving nature of any mechanically actuated lidar (FMCW and non-FMCW). We evaluate our proposed algorithm on several real-world datasets, including publicly available ones and datasets we collected. Our algorithm outperforms the only existing method that also uses Doppler velocity measurements, and we study difficult conditions where including this extra information greatly improves performance. We additionally demonstrate state-of-the-art performance of lidar-only odometry with and without using Doppler velocity measurements in nominal conditions. Code for this project can be found at: <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/utiasASRL/steam_icp</uri> .

Instantaneous velocity measurement method of projectile with double ballistic zone-block apparatus

传统测试方法采用区截装置进行弹丸测速，总是假设弹丸为匀速直线运动，忽略了空气阻力等因素的影响。基于空气动力学及理论力学原理，提出一种使用两套区截测速装置进行弹丸瞬时速度测试的方法。该方法通过两个相距一定距离的测速点的速度值，计算测试过程中弹丸在测试区域飞行的速度衰减系数<i>B</i>，并通过<i>B</i>值计算得到测试区域附近弹道内任意点的瞬时速度。仿真分析表明，该方法在0.8倍音速以内的相对测量误差小于0.01%，远低于0.1%的工程误差要求。弹弓、气枪和步枪实弹实验发现，弹丸飞行速度在0.8倍音速以内或1.2倍音速以上的测试精度不低于所采用区截测速装置0.1%的精度，验证了此方法的可行性。研究为弹道综合参数测试系统的设计和优化提供了新的思路和方法。

Time-resolved multi-parameter flow diagnostics by filtered Rayleigh scattering: system design through multi-objective optimisation

The measurement of the time-resolved three-component (3C) velocity field together with scalar flow quantities such as temperature or pressure by laser-optical diagnostics is a challenging task. Current approaches usually employ combinations of different methods relying on tracer particles or molecules. This typically requires usage of at least two laser systems and detection units as well as elaborate calibration of the luminous properties of the applied tracer species with regard to the specific thermodynamic conditions anticipated for the flow case at hand. In contrast to this, the tracer-free filtered Rayleigh scattering (FRS) technique has been proven to obtain combined time-averaged velocity and scalar fields and might offer a viable alternative for unsteady flow diagnostics. By applying multiple perspective views, two detection system variants are presented, combining (1) six observation branches with one camera/molecular filter and (2) three camera views with two cameras and molecular filters of differing vapour densities. Both configurations in principle allow for the simultaneous measurement of instantaneous 3C velocity, temperature and pressure fields. Multi-objective optimisation is used to enhance the detection setups for different sets of experimental configurations. It is shown that a higher number of observation positions and the associated dynamics of the FRS signal prove to be advantageous compared to the use of less views in combination with two acquisition channels equipped with different molecular filters. It is also shown that the use of circularly polarised laser light offers no advantage over linear polarisation. By demonstrating a moderate sensitivity of the optimised observation arrangement to alignment errors, the presented FRS concept provides a practical solution for the simultaneous measurement of time-resolved 3C flow velocity and scalar fields.

Unsteady Multi-Parameter Flow Diagnostics By Filtered Rayleigh Scattering: System Design By Multi-Objective Optimisation

The measurement of the time-resolved three-component (3C) velocity field together with scalar flow quantities such as temperature or pressure by laser-optical diagnostics is a challenging task. Current approaches typically employ combinations of different methods relying on tracer particles or molecules, which requires elaborate calibration procedures of the tracer's photo-physical properties and extensive instrumentation. In contrast to this, the tracer-free filtered Rayleigh scattering (FRS) technique has been proven to obtain combined time-averaged velocity and scalar fields and might offer a viable alternative for unsteady flow diagnostics. By applying multiple perspective views, two detection system variants are presented, combining 1) six observation branches with one camera/molecular filter and 2) four camera views with two cameras and molecular filters of differing vapour densities. Both configurations in principle allow for the simultaneous measurement of instantaneous 3C velocity, temperature and pressure fields. Multi-objective optimisation is used to enhance the detection setups for different sets of experimental configurations. It is shown that a higher number of observation positions and the associated dynamics of the FRS signal prove to be advantageous compared to the use of less views in combination with two acquisition channels equipped with different molecular filters. It is also demonstrated that the use of linearly polarised laser light is preferred over circular polarisation. Future work will focus on the realisation of the multiple-view FRS concept for the combined measurement of 3C velocity and scalar fields.

Experimental Investigation of Ground Effect on the Vortical Flow Structure of a 40° Swept Delta Wing

The ground effect influences the flow structure on a delta wing during landing and take-off processes. In this regard, comprehensive instantaneous velocity measurements and flow visualizations were carried out by particle image velocimetry and dye flow visualization techniques to reveal the ground effect on leading-edge vortex characteristics of a 40° swept delta wing. The flow behaviors on the delta wing under the impact of the ground were analyzed at two angles of attack, 8° and 11°, and the space between the ground and lower surface of the wing was nondimensionalized with the wing’s chord length. It was found that the presence of the ground caused premature leading-edge vortex breakdown due to the increasing adverse pressure gradient on the wing’s suction side along the chord direction. The ground effect caused an increase in peak value and distributions of turbulent kinetic energy on the wing surface that depended on the earlier leading-edge vortex bursting and complex and disorganized flow structures. The value of time-averaged vertical velocity was lower when the delta wing descended from the free-stream flow zone into the ground effect zone because of the blocking of fluid flow in the gap between the ground and pressure surface of the wing. Thus, it can be concluded that the ground effect is very influential on the change of vortical flow characteristics of nonslender delta wings.

Uncertainty estimation for ensemble particle image velocimetry

We present a novel approach to estimate the uncertainty in ensemble particle image velocimetry (PIV) measurements. The ensemble PIV technique is widely used when the cross-correlation signal-to-noise ratio is insufficient to perform a reliable instantaneous velocity measurement. Despite the utility of ensemble PIV, uncertainty quantification for this type of measurement has not been studied. Here, we propose a method for estimating the uncertainty directly from the probability density function of displacements found by deconvolving the ensemble cross-correlation from the ensemble autocorrelation. We then find the second moment of the probability density function and apply a scaling factor to report the uncertainty in the velocity measurement. We call this method the moment of probability of displacement (MPD). We assess MPD’s performance with synthetic and experimental images. We show that predicted uncertainties agree well with the expected root mean square (RMS) of the error in the velocity measurements over a wide range of image and flow conditions. MPD shows good sensitivity to various PIV error sources with around 86% accuracy in matching the RMS of the error in the baseline data sets. So, MPD establishes itself as a reliable uncertainty quantification algorithm for ensemble PIV. We compared the results of MPD against one of the existing instantaneous PIV uncertainty approaches, moment of correlation (MC). We adapted the MC approach for ensemble PIV, however, its primary limitations remain the assumption of the Gaussian probability density function of displacements and the Gaussian particles’ intensity profile. In addition, our analysis shows that ensemble MC consistently underestimates the uncertainty, while MPD outperforms that and removes the limiting Gaussian assumption for the particle and probability density function, thus overcoming the limitations of MC.

Aeolian sediment transport over sandy gobi: Field studies in the Nanhu gobi along the Hami-Lop Nor Railway

Wind-blown sand over sandy gobi with an abundant sediment supply can cause severe sand hazards. However, compared with the study of aeolian transport over gravel gobi with a limited sediment supply, less attention has been devoted to sandy gobi, and thus, our understanding of wind-blown sand movement on sandy gobi is still poor. Here, we report the results of observations of three transport events on a sandy gobi along the Hami-Lop Nor Railway based on high-frequency saltation particle count and horizontal sediment flux measurements coupled with instantaneous wind velocity measurements. The results reveal that, unlike the notably intermittent aeolian saltation over gravel gobi, continuous transport occurred on the sandy gobi. The mean saltation layer height was 0.23 ± 0.07 m, and it was positively related to both the grain size of surface particles and the wind velocity regardless of the gobi type. The sediment transport rates could be expressed as the power function Q = ap/g[u∗ (u∗2-u∗t2)]b, and the scaling parameter (b) reached to 2.5, which is much larger than that of other gobi areas (b = 1). Our findings suggest that the wind-blown sand over sandy gobi is much more severe than that over gravel gobi, and the Nanhu sandy gobi is the major sand source for sand hazards of the Hami-Lop Nor Railway. Sand-fixation measures such as checkerboard sand barriers with enhanced checkerboard size and barrier height should be the main subject of sand control systems for the Hami-Lop Nor Railway in sandy gobi.

A Review of the Recent PIV Studies &amp;lt;br/&amp;gt;—From the Basics to the Hybridization with CFD

The purpose of this article is to review recent PIV Studies from the basic to hybrid analysis, focusing on explaining epoch-making development of PIV. The overwhelming advantage of PIV over other velocity measurement methods is that it enables instantaneous and simultaneous velocity measurement of whole flow fields. We roughly classify PIV development and/or progress into the following five categories; A) Basics of PIV and post-processing. B) Simultaneous measurement of velocity and temperature, and 3D-PIV. C) Application to multiphase turbulent flows. D) Application to fluid machinery. E) Hybridization of PIV and CFD. This paper introduces the epoch-making research results from papers published in international journals as milestones related to (A) to (E), and concludes with additional forecast of future development of PIV research.

Design of a High Uniformity Laser Sheet Optical System for Particle Image Velocimetry

Particle image velocimetry (PIV) is a non-contact, instantaneous and full-flow velocity measurement method based on cross-correlation analysis of particle image. It is widely used in fluid mechanics and aerodynamics. Laser sheet optical system is one of the key equipment of PIV, and it is an important guarantee to obtain high definition particle image. In the PIV measurement task of large low speed wind tunnel, in order to solve the problem of sheet light illumination uniformity of large size model and take into account the requirements of PIV technology on the thickness of the sheet light, a hybrid algorithm is used to design a high uniformity laser sheet optical system based on the theory of physical optics. The simulation results show that the size of the sheet light is 400 mm × 1 mm, the diffraction efficiency reaches 97.77%, and the non-uniformity is only 0.03%. It is helpful to acquire high-resolution images of particles in the full field of view. It also can be applied to a series of non-contact flow field measurement techniques such as plane laser induced fluorescence, filtered Rayleigh scattering and two-color plane laser induced fluorescence temperature measurement.

Gas and particle instantaneous velocity measurement in swirling particle-laden turbulent reacting flow

Experimental study of particle-laden turbulent reacting flow was conducted on a test facility for swirl combustor. The Three-Dimension Particle Dynamic Analyzer (PDA) was employed to measure the gas and particle instantaneous velocities. The measured results provide the distributions of time-averaged axial and tangential velocities, root mean square of axial and tangential fluctuating velocities, and correlation moments of axial-tangential fluctuating velocities for both gas and particle phases and the distribution of particle mean diameter. The Probability Density Functions (PDF) for the instantaneous particle axial and tangential velocities are also obtained at each measuring location. The gas and particle axial and tangential velocities as well as axial and tangential fluctuating velocities are large in the upstream central region of the combustor. Differences are found evidently between the gas and particle fluctuating velocity components.

Uncertainty Estimation for Ensemble Particle Image Velocimetry

We present a novel approach to estimate the uncertainty in ensemble particle image velocimetry (PIV) measurements. Ensemble PIV is widely used when the cross-correlation signal-to-noise ratio (SNR) is insufficient to perform a reliable instantaneous velocity measurement. Despite the utility of ensemble PIV, uncertainty quantification for this type of measurement has not been studied. The existing uncertainty quantification algorithms for PIV are developed and used only for instantaneous PIV measurement and do not account for the improved SNR in ensemble PIV. Existing instantaneous uncertainty quantification methods can be divided into direct and indirect categories. Indirect methods require calibration based on the effect of various image parameters (such as noise, particle size, density, velocity gradient, etc.) on the correlation SNR. Indirect methods have not been calibrated for error sources relevant in an Ensemble PIV measurement. Also, they have lower sensitivity to the error sources compared to direct approaches. Direct methods, such as the moment of correlation (MC) and Image Matching (IM), find the uncertainty based on the images and correlation planes without any calibration and are more reliable (Bhattacharya et al., 2018; Sciacchitano et al., 2013). Ensemble PIV is based on ensemble correlations; therefore, MC, which uses the generalized cross-correlation (GCC) plane as a measure of uncertainty, is the most suitable method to be modified to be applicable for the ensemble PIV. The GCC plane is the inverse Fourier transform of the phase correlation and represents the probability density function (PDF) of particles’ displacements (Bhattacharya et al., 2018; Eckstein and Vlachos, 2009). We replaced instantaneous GCC with ensemble GCC and modified MC’s normalization factor to account for the number of ensembles. The MC’s primary limitation is that it assumes a Gaussian shape for the PDF of displacements and estimate the standard deviation of the underlying PDF using a fitted Gaussian. However, the PDF deviates from Gaussian distribution due to velocity gradient or non-Gaussian random displacements. Therefore, MC’s reliability and applicability are reduced for flow fields with non-Gaussian PDFs. Also, our analysis shows that ensemble MC consistently underestimates the uncertainty. So, a generalized and reliable method for uncertainty quantification for ensemble PIV is needed.

Vorticity fields around a pier on rigid and mobile bed channels

ABSTRACT Experimental investigation with reference to vorticity fields around circular bridge pier having diameter, d = 8.8 cm, at different angles, namely, θ = 0°, 90°, and 180° with respect to center of pier diameter, on rigid and mobile beds, is compared for identical flow conditions. The instantaneous velocity measurements were carried out using 16 MHz down looking micro-Acoustic Doppler Velocimeter (ADV) at different grids along the flow depths. The sediments having mean size, d50 = 0.75 mm, and geometric standard deviation, σg = 1.29, are used in experimentation. The results reveal that, on both rigid and mobile bed, with increasing the angle, the strength of primary vortex is decreased. On the other hand, the strength of secondary vortex has been found to increase with the angle, that is, the primary vortex is found to be strong in front of the pier, whereas the secondary vortex is predominant behind the pier. Further, the strengths of primary and secondary vortices are found to be ≈30% more on rigid bed than mobile bed for same flow condition.

Near-surface particle image velocimetry measurements over a yawed slender delta wing

In this study, extensive instantaneous velocity measurements were conducted within a flow area by stereo particle image velocimetry (SPIV) to investigate the influence of the yaw angle, β, on the vortical flow structure formed on a slender delta wing. This sideslip angle, β, in the yaw plane was varied from 4° up to 20° with an interval of 4° at two critical angles of attack, α = 25° and 35°, respectively. In order to reveal the influence of the yaw angle, β over the flow structure of the delta wing, time-averaged flow statistics, and instantaneous flow data obtained by the SPIV technique in the plan-view plane close to the suction surface of the delta wing were presented. It was observed that even a low yaw angle, for instance β = 8°, becomes to be effective on the flow characteristics of the delta wing, and this effect was augmented with increasing β. The influence of β is quite high on the vortical flow structure at α= 35° compared to the angle of attack of α = 25°. The flow structure that is symmetrical with respect to the centerline of the wing in the case of no yaw has disrupted with the existence β. Furthermore, the extent of the asymmetry enlarges with increasing β. The leading-edge vortex (LEV) on the windward side broken earlier and dominated the flow on the wing surface. It is concluded that this asymmetric flow structure can deteriorate the aerodynamic performance and cause other adverse effects such as unsteady loading.

Complex-Valued Channel Attention and Application in Ego-Velocity Estimation With Automotive Radar

Attention mechanisms have been widely integrated with various neural networks to boost performance. However, when an attention mechanism was applied to a radar ego-velocity estimation network, the importance of carefully handling the amplitude and phase of complex-valued tensor was revealed. Therefore, in this study, we present a self-attention mechanism designed to handle complex-valued tensors in order to capture the rich contextual relationships implied within amplitude and phase. To exploit the advantages of complex-valued attention (CA), we evaluated its impact while performing ego-velocity estimation tasks based on radar data, whose amplitude and phase are related to the electromagnetic scattering of the target being observed. Radars are suitable sensors for such tasks as they are capable of long-range detection and instantaneous velocity measurement under variable weather and lighting conditions. In particular, we coupled our CA module with complex-valued neural networks, known to be particularly powerful for handling wave phenomena. The proposed method exhibits robust estimation performance, regardless of whether the Doppler ambiguity problem occurs and eliminates the dependence on preprocessing stages, including target detection and static target indication. Furthermore, it achieves improved stability during training via geometrical constraint regularization, and implicitly allows velocity conversion between the sensor and vehicle frames, even if the mount information of the sensor was not provided. Finally, ablation experiments conducted on extensive real-world datasets show noticeable improvement in estimation performance.