Velocity Estimation Error Research Articles

Comparison of the estimation performance of coherent and non-coherent ambiguity functions for an ultrawideband multi-input–multi-output noise radar

The authors start by analysing the mean square error (MSE) of target velocity and location estimation in ultrawideband (UWB) multi-input–multi-output (MIMO) noise radar. In the authors' system architecture, transmit antennas are illuminated by UWB-independent noise waveforms to meet the requirement of MIMO spatial diversity. The ambiguity function (AF) formulation is applied to implement the estimations. Since the maximum value of the AF is attained when the time-delay and Doppler stretch of replica signals are exactly matched with the ones corresponding to the reflections, this estimation is also a peak localisation problem. When noise is added, the peak may be located in a different place causing error. In this study, the authors formulate probability density functions (pdfs) to approximate the distributions of coherent and non-coherent ambiguity functions (CAFs and NCAFs) that are then applied to analyse MSE of their estimates. The pdfs are also applied to analyse the detection performance based on different AF approaches. Based on the analyses, the authors demonstrate that the NCAF-based estimation is a better approach in spatial diversity MIMO radars.

3D IMAGING METHOD FOR STEPPED FREQUENCY GROUND PENETRATING RADAR BASED ON COMPRESSIVE SENSING

Long data collecting time is one of the bottlenecks of the stepped-frequency continuous-wave ground penetrating radar (SFCW- GPR). We discuss the applicability of the Compressive Sensing (CS) method to three dimensional buried point-like targets imaging for SFCW-GPR. It is shown that the image of the sparse targets can be reconstructed by solving a constrained convex optimization problem based on l1-norm minimization with only a small number of data from randomly selected frequencies and antenna scan positions, which will reduce the data collecting time. Target localization ability, performance in noise, the efiect of frequency bandwidth, and the efiect of the wave travel velocity in the soil are demonstrated by simulated data. Numerical results show that the presented CS method can reconstruct the point-like targets in the right position even with 10% additive Gaussian white noise and some wave travel velocity estimation error.

Effects of measurement resolution on the analysis of temperature time series for stream‐aquifer flux estimation

From its inception in the mid‐1960s, the use of temperature time series (thermographs) to estimate vertical fluxes has found increasing use in the hydrologic community. Beginning in 2000, researchers have examined the impacts of measurement and parameter uncertainty on the estimates of vertical fluxes. To date, the effects of temperature measurement discretization (resolution), a characteristic of all digital temperature loggers, on the determination of vertical fluxes has not been considered. In this technical note we expand the analysis of recently published work to include the effects of temperature measurement resolution on estimates of vertical fluxes using temperature amplitude and phase shift information. We show that errors in thermal front velocity estimation introduced by discretizing thermographs differ when amplitude or phase shift data are used to estimate vertical fluxes. We also show that under similar circumstances sensor resolution limits the range over which vertical velocities are accurately reproduced more than uncertainty in temperature measurements, uncertainty in sensor separation distance, and uncertainty in the thermal diffusivity combined. These effects represent the baseline error present and thus the best‐case scenario when discrete temperature measurements are used to infer vertical fluxes. The errors associated with measurement resolution can be minimized by using the highest‐resolution sensors available. But thoughtful experimental design could allow users to select the most cost‐effective temperature sensors to fit their measurement needs.

Moving Target Indication via Three-Antenna SAR with Simplified Fractional Fourier Transform

Ground moving target indiction (GMTI) is of great important for surveillance and reconnaissance, but it is not an easy job. One technique is the along-track interferometry (ATI) synthetic aperture radar (SAR), which was initially proposed for estimating the radial velocity of ground moving targets. However, the measured differential phase may be contaminated by overlapping stationary clutter, leading to errors in velocity and position estimates. As effective clutter suppression can be achieved by multiple aperture or phase center antennas, this article presents a simplified fractional Fourier transform (SFrFT) for three-antenna-based SAR GMTI applications. This approach cancels clutter with three-antenna-based methods and forms two-channel signals through which moving targets are detected and imaged. Next, the Doppler parameters of the moving targets are estimated with the SFrFT-based estimation algorithm. In this way, both target location and target velocity are acquired. Next, the moving targets are focused with one uniform imaging algorithm. The feasibility is validated by theory analysis and simulation results.

Shear Wave Velocity Estimation by Virtual Sensing Array Spectrum Analysis

Tissue displacement by continuous shear wave propagation successfully gives local wavelength, which depends on the local velocity of the shear wave. Our goal for velocity distribution estimation in future clinical applications is to achieve less than 10% error and less than 5 mm spatial resolution. However, this has been difficult to achieve owing to the presence of multiple shear waves generated by complicated propagation such as reflection, scattering, and diffraction. In this paper, we propose a velocity estimation method based on wave number spectrum analysis from the limited small area of the displacement distributions. To increase the spatial resolution, we derive a deconvolution-based displacement estimation method for high-frequency excitation. The effectiveness of this method is demonstrated through numerical simulations and experiments with agar phantom. Even if a large reflected wave from a boundary exists, it is found that this method achieved the velocity estimation error of 10% and spatial resolution of 4.5 mm at a wavelength of 2.2 mm.

Real-Time Upper Limb Motion Estimation From Surface Electromyography and Joint Angular Velocities Using an Artificial Neural Network for Human–Machine Cooperation

A current challenge with human-machine cooperation systems is to estimate human motions to facilitate natural cooperation and safety of the human. It is a logical approach to estimate the motions from their sources (skeletal muscles); thus, we employed surface electromyography (SEMG) to estimate body motions. In this paper, we investigated a cooperative manipulation control by an upper limb motion estimation method using SEMG and joint angular velocities. The SEMG signals from five upper limb muscles and angular velocities of the limb joints were used to approximate the flexion-extension of the limb in the 2-D sagittal plane. The experimental results showed that the proposed estimation method provides acceptable performance of the motion estimation [normalized root mean square error (NRMSE) <0.15, correlation coefficient (CC) >0.9] under the noncontact condition. From the analysis of the results, we found the necessity of the angular velocity input and estimation error feedback due to physical contact. Our results suggest that the estimation method can be useful for a natural human-machine cooperation control.

A Method for Mathematical Modeling Spatial Harmonics in a SynRM for Sensorless Control

In this paper, we propose a new method for modeling the inductance spatial harmonic components in a SynRM for position-sensorless control. The conventional methods for sensorless control based on a mathematical model consider only the fundamental components of the inductances. As a result, several problems arise, including limited controller bandwidth. The proposed method is based on the fact that the back electromotive force (EMF) estimated by the observer includes harmonic voltages induced by the inductance spatial harmonics. We process and analyze the estimated EMF in every operational region so that only the component with the desired order from among the harmonic voltages is investigated for mathematical modeling. Sensorless control with the proposed model involves simple feedforward compensation to the observer's input voltage; as a result, the error in velocity and position estimation is reduced considerably, and high bandwidth can be achieved for the speed controller.

Formation and Attitude Control for the CanX-4 and CanX-5 Formation Flying Mission

AbstractFormation and attitude control strategies for the CanX-4 and CanX-5 nanosatellite formation flying mission are discussed. An innovative strategy for managing reaction wheel momentum build-up using planned formation control thrusts is presented, and an attitude control method to maximize GPS signal acquisition is reviewed. Fine formation keeping mode, formation reconfiguration mode, and station keeping mode controllers are reviewed. High fidelity simulations with representative control and estimation errors show that the proposed attitude and formation control strategies are effective and meet performance requirements in all cases. It was found that errors in the relative velocity estimates have the largest effect on formation control errors.

Target Velocity Estimation and Antenna Placement for MIMO Radar With Widely Separated Antennas

This paper studies the velocity estimation performance for multiple-input multiple-output (MIMO) radar with widely spaced antennas. We derive the Cramer-Rao bound (CRB) for velocity estimation and study the optimized system/configuration design based on CRB. General results are presented for an extended target with reflectivity varying with look angle. Then detailed analysis is provided for a simplified case, assuming an isotropic scatterer. For given transmitted signals, optimal antenna placement is analyzed in the sense of minimizing the CRB of the velocity estimation error. We show that when all antennas are located at approximately the same distance from the target, symmetrical placement is optimal and the relative position of transmitters and receivers can be arbitrary under the orthogonal received signal assumption. In this case, it is also shown that for MIMO radar with optimal placement, velocity estimation accuracy can be improved by increasing either the signal time duration or the product of the number of transmit and receive antennas.

A Dual-Phantom System for Validation of Velocity Measurements in Stenosis Models Under Steady Flow

A dual-phantom system is developed for validation of velocity measurements in stenosis models. Pairs of phantoms with identical geometry and flow conditions are manufactured, one for ultrasound and one for particle image velocimetry (PIV). The PIV model is made from silicone rubber, and a new PIV fluid is made that matches the refractive index of 1.41 of silicone. Dynamic scaling was performed to correct for the increased viscosity of the PIV fluid compared with that of the ultrasound blood mimic. The degree of stenosis in the models pairs agreed to less than 1%. The velocities in the laminar flow region up to the peak velocity location agreed to within 15%, and the difference could be explained by errors in ultrasound velocity estimation. At low flow rates and in mild stenoses, good agreement was observed in the distal flow fields, excepting the maximum velocities. At high flow rates, there was considerable difference in velocities in the poststenosis flow field (maximum centreline differences of 30%), which would seem to represent real differences in hydrodynamic behavior between the two models. Sources of error included: variation of viscosity because of temperature (random error, which could account for differences of up to 7%); ultrasound velocity estimation errors (systematic errors); and geometry effects in each model, particularly because of imperfect connectors and corners (systematic errors, potentially affecting the inlet length and flow stability). The current system is best placed to investigate measurement errors in the laminar flow region rather than the poststenosis turbulent flow region. (E-mail: P.Hoskins@ed.ac.uk)

A statistical analysis of systematic errors in temperature and ram velocity estimates from satellite-borne retarding potential analyzers

The use of biased grids as energy filters for charged particles is common in satellite-borne instruments such as a planar retarding potential analyzer (RPA). Planar RPAs are currently flown on missions such as the Communications/Navigation Outage Forecast System and the Defense Meteorological Satellites Program to obtain estimates of geophysical parameters including ion velocity and temperature. It has been shown previously that the use of biased grids in such instruments creates a nonuniform potential in the grid plane, which leads to inherent errors in the inferred parameters. A simulation of ion interactions with various configurations of biased grids has been developed using a commercial finite-element analysis software package. Using a statistical approach, the simulation calculates collected flux from Maxwellian ion distributions with three-dimensional drift relative to the instrument. Perturbations in the performance of flight instrumentation relative to expectations from the idealized RPA flux equation are discussed. Both single grid and dual-grid systems are modeled to investigate design considerations. Relative errors in the inferred parameters for each geometry are characterized as functions of ion temperature and drift velocity.

Error in estimates of tissue material properties from shear wave dispersion ultrasound vibrometry

Shear wave velocity measurements are used in elasticity imaging to find the shear elasticity and viscosity of tissue. A technique called shear wave dispersion ultrasound vibrometry (SDUV) has been introduced to use the dispersive nature of shear wave velocity to locally estimate the material properties of tissue. Shear waves are created using a multifrequency ultrasound radiation force, and the propagating shear waves are measured a few millimeters away from the excitation point. The shear wave velocity is measured using a repetitive pulse-echo method and Kalman filtering to find the phase of the harmonic shear wave at 2 different locations. A viscoelastic Voigt model and the shear wave velocity measurements at different frequencies are used to find the shear elasticity (mu(1)) and viscosity (mu(2)) of the tissue. The purpose of this paper is to report the accuracy of the SDUV method over a range of different values of mu(1) and mu(2). A motion detection model of a vibrating scattering medium was used to analyze measurement errors of vibration phase in a scattering medium. To assess the accuracy of the SDUV method, we modeled the effects of phase errors on estimates of shear wave velocity and material properties while varying parameters such as shear stiffness and viscosity, shear wave amplitude, the distance between shear wave measurements (delta r), signal-to-noise ratio (SNR) of the ultrasound pulse-echo method, and the frequency range of the measurements. We performed an experiment in a section of porcine muscle to evaluate variation of the aforementioned parameters on the estimated shear wave velocity and material property measurements and to validate the error prediction model. The model showed that errors in the shear wave velocity and material property estimates were minimized by maximizing shear wave amplitude, pulse-echo SNR, delta r, and the bandwidth used for shear wave measurements. The experimental model showed optimum performance could be obtained for delta r = 3 - 6 mm, SNR =35 dB, with a frequency range of 100 to 600 Hz, and with a shear wave amplitude on the order of a few microns down to 0.5 microm. The model provides a basis to explore different parameters related to implementation of the SDUV method. The experiment confirmed conclusions made by the model, and the results can be used for optimization of SDUV.

Velocity Estimation: Assessing the Performance of Non-Model-Based Techniques

The performance of modern motion control systems is strongly related to the resolution of the position sensor and to the digital filtering algorithm used to estimate the velocity. This brief discusses a systematic approach to analyze and assess the performance of non-model-based estimators. A new methodology for the analytical characterization of the velocity estimation error, both in the time and in the frequency domains, is proposed. A case study illustrates how this methodology can be exploited in the analysis of existing velocity measurement systems and/or in the design of a new one.

On the Quality of Real-Time Altimeter Gridded Fields: Comparison with In Situ Data

Abstract The timeliness of satellite altimeter measurements has a significant effect on their value for operational oceanography. In this paper, an Observing System Experiment (OSE) approach is used to assess the quality of real-time altimeter products, a key issue for robust monitoring and forecasting of the ocean state. In addition, the effect of two improved geophysical corrections and the number of missions that are combined in the altimeter products are also analyzed. The improved tidal and atmospheric corrections have a significant effect in coastal areas (0–100 km from the shore), and a comparison with tide gauge observations shows a slightly better agreement with the gridded delayed-time sea level anomalies (SLAs) with two altimeters [Jason-1 and European Remote Sensing Satellite-2 (ERS-2)/Envisat] using the new geophysical corrections (mean square differences in percent of tide gauge variance of 35.3%) than those with four missions [Jason-1, ERS/Envisat, Ocean Topography Experiment (TOPEX)/Poseidoninterlaced, and Geosat Follow-On] but using the old corrections (36.7%). In the deep ocean, however, the correction improvements have little influence. The performance of fast delivery products versus delayed-time data is compared using independent in situ data (tide gauge and drifter data). It clearly highlights the degradation of real-time SLA maps versus the delayed-time SLA maps: four altimeters are needed in real time to get the similar quality performance as two altimeters in delayed time (sea level error misfit around 36%, and zonal and meridional velocity estimation errors of 27% and 33%, respectively). This study proves that the continuous improvement of geophysical corrections is very important, and that it is essential to stay above a minimum threshold of four available altimetric missions to capture the main space and time oceanic scales in fast delivery products.

Determination and sensitivity analysis of the seismic velocity of a shallow layer from refraction traveltimes measures

In this paper, we are interested in determining the seismic velocity of a shallow under-ground layer from refraction traveltimes measures. We present a study case taken from an experimental seismic survey. The study case is a wide-angle seismic inversion using experimental traveltimes measures and based on ray tracing technique and genetic algorithms. The hypothesis on the velocity distribution, coming from the seismic experiment, makes the computation of some seismic rays expensive in time. We propose to reduce the computations time by introducing a formulation of the inverse problem that avoids such costly rays, hence the inversion becomes feasible. Also we present a sensitivity analysis based on a singular value decomposition of the jacobian of the traveltimes with respect to velocity. We give the relationship between the traveltimes measure errors and the velocity estimation error. We discuss the advantages of this method over the classical one based on the resolution matrix.

Speed-Sensorless Estimation for Induction Motors Using Extended Kalman Filters

In this paper, extended-Kalman-filter-based estimation algorithms that could be used in combination with the speed-sensorless field-oriented control and direct-torque control of induction motors (IMs) are developed and implemented experimentally. The algorithms are designed aiming minimum estimation error in both transient and steady state over a wide velocity range, including very low and persistent zero-speed operation. A major challenge at very low and zero speed is the lost coupling effect from the rotor to the stator, which makes the information on rotor variables unobservable on the stator side. As a solution to this problem, in this paper, the load torque and the rotor angular velocity are simultaneously estimated, with the velocity taken into consideration via the equation of motion and not as a constant parameter, which is commonly the case in most past studies. The estimation of load torque, on the other hand, is performed as a constant parameter to account for Coulomb and viscous friction at steady state to improve the estimation performance at very low and zero speed. The estimation algorithms developed based on the rotor and stator fluxes are experimentally tested under challenging variations and reversals of the velocity and load torque (step-type and varying linearly with velocity) over a wide velocity range and at zero speed. In all the scenarios, the current estimation error has remained within a very narrow error band, also yielding acceptable velocity estimation errors, which motivate the use of the developed estimation method in sensorless control of IMs over a wide velocity range and persistent zero-speed operation

Effect of antennas on velocity estimates obtained from crosshole GPR data

To obtain tomographic images with the highest possible resolution from crosshole ground-penetrating radar (GPR) data, raypaths covering a wide range of angles between the boreholes are required. In practice, however, the inclusion of high-angle ray data in crosshole GPR inversions often leads to tomograms so dominated by inversion artifacts that they contain little reliable subsurface information. Here, we investigate the problems that arise from the standard assumption that all first-arriving energy travels directly between the centers of the antennas. Through numerical modeling, we show that this assumption is often incorrect at high transmitter-receiver angles and can lead to significant errors in tomographic velocity estimates when the antenna length is a significant fraction of the borehole spacing.

Experimental measurements of the phase and group velocities of body waves in a transversely isotropic medium

In this study, we perform an experimental result for measurements of the body wave phase and group velocities in transversely isotropic media (TIM) by through-transmission technique. After comparing the experimental and theoretical first arrival times of the waves, a difference between the phase velocity and group velocity is observed. When the ratio between propagation distance ( d) of the wave and the diameter ( D) of transducer is 2.4 for measuring phase velocity and the point probes configuration for measuring group velocity, the accuracy in velocity estimation can reach the limit of system's resolution. However if d/ D is 7.8, the wave will propagate with an intermediate velocity between the phase and group velocities. The rapid change of the wave velocity and waveform for qSV-wave propagation with the group velocity has been observed at the propagation direction near the cusps. Therefore, in order to reduce the error in group velocity estimation of qSV-waves, the optimum directions are suggested at 20 and 60°.

Effects of beam steering in pulsed-wave ultrasound velocity estimation

Experimental and computer simulation methods have been used to investigate the significance of beam steering as a potential source of error in pulsed-wave flow velocity estimation. By simulating a typical linear-array transducer system as used for spectral flow estimation, it is shown that beam steering can cause an angle offset resulting in a change in the effective beam-flow angle. This offset primarily depends on the F-number and the nominal steering angle. For example, at an F-number of 3 and a beam-flow angle of 70°, the velocity error changed from −5% to + 5% when the steering angle changed from −20° to + 20°. Much higher errors can occur at higher beam-flow angles, with smaller F-numbers and greater steering. Our experimental study used a clinical ultrasound system, a tissue-mimicking phantom and a pulsatile waveform to determine peak flow velocity errors for various steering and beam-flow angles. These errors were found to be consistent with our simulation results. (E-mail: cobbold@ecf.utoronto.ca)

Validity of Dynamics Model for Estimation of VO2 and VCO2 During 12-Minute Run

0808 To better define the dose-response relationship between exercise training and performance, it is necessary to accurately quantify exercise intensity such as oxygen uptake (VO2) during exercise. Conventionally, the monitoring of heart rate (HR) is used to estimate VO2 during exercise. However, since kinetics of VO2 and HR to workload is different, dynamic estimation (DE) of VO2 during exercise is important. PURPOSE: To construct a DE model with use of expired gas data obtained during an incremental run test and to estimate kinetics of VO2 and carbon dioxide output (VCO2) during twelve-minute run test by the system dynamics method. METHODS: Five healthy males took part in this study. All subjects performed an incremental run test by a treadmill in laboratory for the purpose of developing individualized velocity-VO2, −VCO2 equations. Then, the subjects undertook sub maximal 12-minute run test at free intensities in the field. In this modeling, it was assumed that 1) the kinetics of VO2 is function of workload, 2) VCO2 is the sum of metabolic VCO2 that stems from increased VO2 and VCO2 that is generated for buffering blood lactate. Fitness of the DE model was examined by determination coefficient (R2) of estimated and measured VO2 and VCO2. Robustness of simulation to the change in workload was examined by a correlation coefficient (r) between estimation error and change of velocity (acceleration). The data of the incremental run test were used for modeling, and data of 12-minute run test for criteria of validity. RESULTS: The distance covered in 12- minute run test was 2750+/−153 m, mean velocity and coefficient variance of velocity was 230+/−15 m/min, 7.0+/−3.0 %. In all subjects, the goodness of fit index of the estimated VO2 and VCO2 to measured data for the incremental run test was high (R2 >0.97, P < .05), so that the DE model was verified. For estimation of 12-minute run test, estimated VO2 and VCO2 were significantly fitted to the measurements (R2>0.97, P<.05). In a correlational analysis between estimation error and acceleration, there were found not significant correlations (r <0.18, P>.05), thereby indicating robustness of the DE model. CONCLUSIONS: The estimation of dynamics of VO2 and VCO2 using the system dynamics was valid and robust to change of velocity.change of velocity.