Time Of Flight Estimation Research Articles

Image Reconstruction in Ultrasonic Speed-of-Sound Computed Tomography Using Time of Flight Estimated by a 2D Convolutional Neural Networks

In ultrasonic nondestructive testing (NDT), accurately estimating the time of flight (TOF) of ultrasonic waves is crucial. Traditionally, TOF estimation involves the signal processing of a single measured waveform. In recent years, deep learning has also been applied to estimate the TOF; however, these methods typically process only single waveforms. In contrast, this study acquired fan-beam ultrasonic waveform profile data from 64 paths using an ultrasonic-speed computed tomography (CT) simulation of a circular column and developed a TOF estimation model using two-dimensional convolutional neural networks (CNNs) based on these data. We compared the accuracy of the TOF estimation between the proposed method and two traditional signal processing methods. Additionally, we reconstructed ultrasonic-speed CT images using the estimated TOF and evaluated the generated CT images. The results showed that the proposed method could estimate the longitudinal TOF more accurately than traditional methods, and the evaluation scores for the reconstructed images were high.

Deep learning for ultrasound surface echo detection

Ultrasound array imaging techniques are often applied using a coupling medium to transmit waves from the transducer to the scanned component. In this type of tests, the echoes generated by the wave reflection at the component surface contain information that can be used to estimate the surface shape and its position relative to the probe, which are needed to compute the imaging focal laws. The most interesting feature to extract from surfaces echoes is the Time of Flight (TOF) for each reception channel. TOF measurement in acoustic signals is a problem that frequently arises not only in Non Destructive Testing (NDT), but also in medical imaging, geophysics and other fields. The surface echo in a signal is usually identified as the first high amplitude peak, and is traditionally detected with standard methods as threshold crossing, peak search or matched filters. All these methods are easily affected by Signal to Noise Ratio, which might be high in some channels, for example if the ray arrives at the corresponding element at a low sensibility angle. Moreover, spurious echoes from bubbles, the emission signal tail or echoes from other parts of the component can be incorrectly labelled as surface echoes. This kind of outliers are difficult to filter by conventional means and, thus, there is a need for more robust surface estimation methods. In this work, we study the application of a deep 3D Convolutional Neural Network (CNN) to detect surface echoes in Full Matrix Capture (FMC) ultrasound data. The CNN is trained using signals acquired with a matrix array and a reference component, using a robotic arm set-up to measure the probe position and orientation relative to the component. Thus, with knowledge of the set-up geometry, a model is used to compute the theoretical surface echo TOFs, which are used to label the data for training. The model was tested with a validation set, presenting good agreement with the ground truth. The results were compared with the threshold crossing method observing a significant reduction of outliers in the TOF estimation.

Estimation of ultrasonic flight time based on SHADE algorithm and extended kalman filtering

Abstract Traditional methods of using ultrasound to measure oxygen concentration have the issue of inaccuracy and susceptibility to noise interference when measuring the time of flight (TOF) of ultrasonic echo signals. A proposed algorithm for ultrasonic parameter estimation, utilizing an asymmetric Gaussian model, aims to enhance the precision and reliability of TOF estimation, aiming to reduce the influence of noise interference. The algorithm combines an improved Self-Adaptive Differential Evolution (SHADE) algorithm based on successful historical records with an Extended Kalman Filter (EKF). The improved SHADE algorithm controls the degree of mutation strategy greediness during the mutation operation based on the number of iterations, thereby enhancing the algorithm’s iteration speed. Then, the obtained solution is used as the initial value for the EKF to estimate the model parameters, thus addressing the issue of EKF’s dependency on accurate initial values to obtain precise outputs. Through simulation and experimental measurements of ultrasonic oxygen concentration, several commonly used parameter estimation algorithms are compared with the proposed SHADE-EKF algorithm. Results demonstrate that the SHADE-EKF algorithm exhibits superior performance in estimating the TOF of ultrasonic waves.

Transformer-CNN hybrid network for improving PET time of flight prediction

Objective. In positron emission tomography (PET) reconstruction, the integration of time-of-flight (TOF) information, known as TOF-PET, has been a major research focus. Compared to traditional reconstruction methods, the introduction of TOF enhances the signal-to-noise ratio of images. Precision in TOF is measured by full width at half maximum (FWHM) and the offset from ground truth, referred to as coincidence time resolution (CTR) and bias. Approach. This study proposes a network combining transformer and convolutional neural network (CNN) to utilize TOF information from detector waveforms, using event waveform pairs as inputs. This approach integrates the global self-attention mechanism of Transformer, which focuses on temporal relationships, with the local receptive field of CNN. The combination of global and local information allows the network to assign greater weight to the rising edges of waveforms, thereby extracting valuable temporal information for precise TOF predictions. Experiments were conducted using lutetium yttrium oxyorthosilicate (LYSO) scintillators and silicon photomultiplier (SiPM) detectors. The network was trained and tested using the waveform datasets after cropping. Main results. Compared to the constant fraction discriminator (CFD), CNN, CNN with attention, long short-term memory (LSTM) and Transformer, our network achieved an average CTR of 189 ps, reducing it by 82 ps (more than 30%), 13 ps (6.4%), 12 ps (6.0%), 16 ps (7.8%) and 9 ps (4.6%), respectively. Additionally, a reduction of 10.3, 8.7, 6.7 and 4 ps in average bias was achieved compared to CNN, CNN with attention, LSTM and Transformer. Significance. This work demonstrates the potential of applying the Transformer for PET TOF estimation using real experimental data. Through the integration of both CNN and Transformer with local and global attention, it achieves optimal performance, thereby presenting a novel direction for future research in this field.

Distance Measurement of Contra-Rotating Rotor Blades with Ultrasonic Transducers.

Coaxial rotor helicopters have great potential in civilian and commercial uses, with many advantages, but challenges remain in the accurate measurement of rotor blades' distance to prevent blade collision. In this paper, a blade tip distance measurement method based on ultrasonic measurement window and phase triggering is proposed, and the triggering time of the transmitter is studied. Due to the complexity of the measured signal, bandpass filtering and a time-of-flight (TOF) estimation based on the power density of the received signal are utilised. The method is tested on an experimental test platform with a pair of 200 kHz ultrasonic transducers. The experimental results show that the maximum ranging error is less than 1.0% for the blade tip distance in a range of 100-1000 mm. Compared with the amplitude threshold method, the proposed TOF estimation method works well on the received signal with a low SNR and improves the ranging accuracy by about 5 mm when the blade tip distance is larger than 500 mm. This study provides a good reference for the accurate measurement of rotor blade tip distance, and gives a solution for ranging high-speed rotating objects.

A novel time-of-flight auto-diagnosis model for ultrasonic signal using a sliding window technique based on empirical mode decomposition

Ultrasonic signal analysis is an essential technique used in various fields, including non-destructive testing (NDT), structural health monitoring, and medical diagnosis. Accurate auto-diagnosis of Time-of-Flight (ToF) for ultrasonic signal is crucial in defects locating, ultrasound imaging, etc. However, requisite signal extraction for ToF estimation was interfered with noise in time and frequency domain, and there is a tendency to be interrupted by spikes in ultrasound signal envelope for wave crest auto-location. In this study, a novel auto-diagnosis model for ultrasonic signals is proposed based on the empirical mode decomposition (EMD) technique and sliding window approach. The model utilizes EMD method to extract intrinsic mode functions (IMFs) and obtain time-frequency representations of the signal. Then the ultrasound signal envelope is extracted by Hilbert transform. The sliding window technique is employed to monitor the time-varying characteristics of the ultrasonic signal and capture the changes in ToF. Spline interpolation algorithm was embedded in the sliding window technique for reducing ToF error and computer burden. The proposed model can automatically estimate ToF for the ultrasonic signal without professional assistance. The performance of the proposed model is evaluated using steel plates with a thickness of 10mm and pipelines with a wall thickness of 7mm. The results demonstrate high accuracy in detecting signal abnormalities, with maximum errors of 0.25% and 1.25% for steel plates and pipelines under constant pressure, respectively. The proposed approach holds promising potential for fully automated applications in various fields in the future, such as structural health monitoring and medical diagnosis.

A novel time-of-flight estimation method of acoustic signals for temperature and velocity measurement of gas medium

Acoustic thermometry and velocimetry are widely recognized as promising methods for in situ measurement of gas temperature and velocity due to their non-invasive, low-cost, and high-resolution advantages. Accurate estimation of acoustic time-of-flight (TOF) is the key to improving the accuracy of acoustic thermometers and velocimeters. In this paper, a new TOF estimation method is developed based on the digital lock-in filtering (DLF) technique. The signal source is an audible sound with linearly modulated frequencies, and the relationship between the time and frequency domains of the signal is established using digital lock-in and low-pass filtering techniques. The linearity of the time–frequency series and the accuracy of the TOF are improved by using a least-squares-based linear fitting method. Experimental studies of gas temperature and velocity measurements with acoustic methods in static, dynamic, and different signal-to-noise ratio (SNR) environments have been carried out. The DLF method performs well in terms of accuracy and robustness to extract the modulated signals of known carriers in a strong noise environment. Furthermore, the very nature of the method predisposes the time-domain data of the acoustic source signal not to be repeatedly processed at each TOF calculation, which saves system resources for processing the source signal.

A Time-of-Flight Estimation Method for Acoustic Ranging and Thermometry Based on Digital Lock-In Filtering.

Accurate ranging and real-time temperature monitoring are essential for metrology and safety in electrical conduit applications. This paper proposes an acoustic time-of-flight (TOF) estimation method based on the digital lock-in filtering (DLF) technique for conduit ranging and thermometry. The method establishes the relationship between the frequency and the time domain by applying a linear frequency modulated Chirp signal as the sound source and using the DLF technique to extract the first harmonic of the characteristic frequencies of the transmitted and received signals. Acoustic TOF estimation in the conduit is then achieved by calculating the mathematical expectation of the time difference between each characteristic frequency in the time-frequency relationship of the two signals. The experimental results with enhanced noise interference on different conduit lengths and various temperature conditions, proved that the proposed DLF method can establish a robust linear time-frequency relationship according to the characteristics of the Chirp signal, and the measurement accuracy of TOF has also been confirmed. Compared to the conventional method, the DLF method provides the lowest absolute error and standard deviation for both distance and temperature measurements with an enhanced robustness.

Service Antenna Array-Based Parameter Estimation for Decimeter Level Indoor Localization

Since the antenna interval of service antenna array for communication is greater than half a wavelength and does not satisfy the spatial sampling theorem, it is a great challenge to leverage service antenna array for channel state information-based signal parameters estimation, such as time-of-flight (TOF) and angle-of-arrival (AOA) estimation. To overcome this challenge, this letter proposes a diagonal spatial mapping-based multiple signal classification (MUSIC) and matching pursuit (MP) fusion (DSM-MMF) algorithm. First, a new virtual linear array is constructed by mapping the service antenna array on the diagonal of the plane array. Second, a fusion AOA and TOF estimation for the signal mapped on the virtual linear array is realized by utilizing the MUSIC and MP fusion algorithm. Third, through the unique geometric relationship between the virtual linear array and the service antenna array, the AOA and TOF can be obtained. Finally, experimental results show that the DSM-MMF’s median localization error is about four decimeters.

Frequency Sweep Keying CDMA for Reducing Ultrasonic Crosstalk

Various sensors are embedded in automobiles to implement intelligent safety technologies such as autonomous driving and front–rear collision avoidance technology. In particular, ultrasonic sensors have been used in the past because they have an accuracy of centimeters to sub-centimeters in air despite their low cost and low hardware complexity. Recently, the crosstalk problem between ultrasonic sensors has been raised because the number of ultrasonic sensors in the unit space has increased as the number of vehicles increases. Various studies have been conducted to solve the crosstalk, but a demodulation error occurs when signals overlap. Therefore, in this paper, we propose a method that is robust to ultrasonic signal overlap, is robust even at shorter code length, and has reduced time of flight (TOF) error compared to the existing method by applying frequency sweep keying modulation based on code division multiple access (CDMA). As a result of the experiment, the code was detected accurately regardless of the overlap ratio of the two signals, and it was robust even in situations where the power of the two signals was different. In addition, it shows an accurate TOF estimation even if the ID code length is shorter than the existing on–off-keying, frequency shift keying, and phase shift keying methods.

Unbiased TOF estimation using leading-edge discriminator and convolutional neural network trained by single-source-position waveforms

Objective. Convolutional neural networks (CNNs) are a strong tool for improving the coincidence time resolution (CTR) of time-of-flight (TOF) positron emission tomography detectors. However, several signal waveforms from multiple source positions are required for CNN training. Furthermore, there is concern that TOF estimation is biased near the edge of the training space, despite the reduced estimation variance (i.e. timing uncertainty). Approach. We propose a simple method for unbiased TOF estimation by combining a conventional leading-edge discriminator (LED) and a CNN that can be trained with waveforms collected from one source position. The proposed method estimates and corrects the time difference error calculated by the LED rather than the absolute time difference. This model can eliminate the TOF estimation bias, as the combination with the LED converts the distribution of the label data from discrete values at each position into a continuous symmetric distribution. Main results. Evaluation results using signal waveforms collected from scintillation detectors show that the proposed method can correctly estimate all source positions without bias from a single source position. Moreover, the proposed method improves the CTR of the conventional LED. Significance. We believe that the improved CTR will not only increase the signal-to-noise ratio but will also contribute significantly to a part of the direct positron emission imaging.

Method for time-of-flight estimation of low frequency acoustic signals in reverberant and noisy environment with sparse impulse response

For acoustic procedures which rely on the speed of sound to derive process parameters, the determination of the acoustic time of flight (TOF) is essential. In this work, a method for the determination of the TOF is presented. It is intended for reverberant and noisy environments and can be applied in the gas holdup determination in bubbly liquids via acoustic transmission tomography for example. The method includes the selection and design of the transmitted signal to optimize the disambiguate of the autocorrelation, the narrowing of the time window based on the fractional Fourier transform to accelerate the TOF estimation. Furthermore, it includes the consideration of the system-induced signal distortion through prior quasi-anechoic measurements and the sparse reconstruction of the spatial impulse response for TOF estimation using non-negative sparse deconvolution algorithms. The method is tested analytically on numerically generated signals and various sparse deconvolution algorithms are investigated with respect to their applicability and limitations.

Location Estimates From Channel State Information via Binary Programming

Recent years have witnessed a marked increase in the efficacy and speed to solution of binary program solvers. Leveraging these developments, we propose converting the sparse modelling problem to a binary program, and we derive the conditions under which such a conversion yields the optimal signal support. Furthermore, we derive an upper bound on this condition, which we can minimize by designing a structured tight frame as the dictionary. We apply these theoretical insights to binary optimization of angle of arrival and time of flight estimation (BOAT) using channel state information (CSI), with the goal of localizing a transmitter in an indoor multipath-rich environment. Finally, we show how a covariance array processing approach, together with the novel binary programming paradigm, results in a system that outperforms two state-of-the-art solutions. Our claims are substantiated using both simulated data and experimental data collected using “off-the-shelf” WiFi IEEE 802.11ac routers.

Object Localization and Tracking System Using Multiple Ultrasonic Sensors with Newton–Raphson Optimization and Kalman Filtering Techniques

In this paper, an object localization and tracking system is implemented with an ultrasonic sensing technique and improved algorithms. The system is composed of one ultrasonic transmitter and five receivers, which uses the principle of ultrasonic ranging measurement to locate the target object. This system has several stages of locating and tracking the target object. First, a simple voice activity detection (VAD) algorithm is used to detect the ultrasonic echo signal of each receiving channel, and then a demodulation method with a low-pass filter is used to extract the signal envelope. The time-of-flight (TOF) estimation algorithm is then applied to the signal envelope for range measurement. Due to the variations of position, direction, material, size, and other factors of the detected object and the signal attenuation during the ultrasonic propagation process, the shape of the echo waveform is easily distorted, and TOF estimation is often inaccurate and unstable. In order to improve the accuracy and stability of TOF estimation, a new method of TOF estimation by fitting the general (GN) model and the double exponential (DE) model on the suitable envelope region using Newton–Raphson (NR) optimization with Levenberg–Marquardt (LM) modification (NRLM) is proposed. The final stage is the object localization and tracking. An extended Kalman filter (EKF) is designed, which inherently considers the interference and outlier problems of range measurement, and effectively reduces the interference to target localization under critical measurement conditions. The performance of the proposed system is evaluated by the experimental evaluation of conditions, such as stationary pen localization, stationary finger localization, and moving finger tracking. The experimental results verify the performance of the system and show that the system has a considerable degree of accuracy and stability for object localization and tracking.

Recycling Sampling Timing Offset of Wi-Fi for Estimating Multiple ToFs of Superimposed Signal

Many Wi-Fi based device free localization (DFL) methods have been proposed for indoor location based services. Unfortunately, the received signal is superimposed with Line-of-Sight signal and reflections so that multi target DFL is only possible by estimating the time of flight (ToF) of each signal. To estimate multiple ToFs, we utilize the sampling timing offset (STO) that inherently occurs by asynchronous sampling timing between TX-RX. By utilizing STO, we can generate signals mimicking oversampled signals. We put the signal to our correlation based ToF estimation algorithm. We achieved 0.75-4.65 ns median error when 2–5 signals are superimposed.

Two-Way Ranging Algorithms for Clock Error Compensation

Two-Way Ranging (TWR) is a widely used method for distance estimation in asynchronous wireless networks, but the deviation between the clocks can lead to errors in distance estimation. The ultra-wideband (UWB) technology provides the best accuracy in distance estimation, but total emission time is drastically limited by harmonized standards. Localization accuracy, latency and network scalability are key performance metrics in wireless location characterization. This article advances a new sequencing of the localization process, called Double-Beacon Two-Way Ranging (DB-TWR) algorithm, and presents the related time-of-flight (ToF) estimation formula, which is able to compensate for clock error and to reduce the localization period. The Fine Time Measurement (FTM) protocol, specified by the Wireless LAN (WLAN) standard, uses the TWR method and as a result the clock deviation leads to systematic errors in ToF estimation. The paper proposes two additional timestamps captures and a new ToF computation formula which compensates for clock deviation. The article provides a theoretical analysis and extensive simulations of errors propagation in the ranging process, both as a mean and as an uncertainty, and proves that the designed algorithms cancel the clock offsets entirely.

Channel state information-based multi-dimensional parameter estimation for massive RF data in smart environments

Smart environment sensing and other applications play a more and more important role along with the rapid growth of device-free sensing-based services, and extracting parameters contained in channel state information (CSI) accurately is the basis of these applications. However, antenna arrays in wireless devices are all planar arrays whose antenna spacing does not meet the spatial sampling theorem while the existing parameter estimation methods are almost based on the array satisfying the spatial sampling theorem. In this paper, we propose a parameter estimation algorithm to estimate the signal parameters of angle of arrival (AoA), time of flight (ToF), and Doppler frequency shift (DFS) based on the service antenna array, which does not satisfy the spatial sampling theorem. Firstly, the service antenna array is mapped to a virtual linear array and the array manifold of the virtual linear array is calculated. Secondly, the virtual linear array is applied to estimate the multi-dimensional parameters of the signal. Finally, by calculating the geometric relationship between the service antenna and the virtual linear array, the parameters of the signal incident on the service antenna can be obtained. Therefore, the service antenna can not only use the communication channel for information communication, but also sense the surrounding environment and provide related remote sensing and other wireless sensing application services. Simulation results show that the proposed parameter estimation algorithm can accurately estimate the signal parameters when the array antenna spacing does not meet the spatial sampling theorem. Compared with TWPalo, the proposed algorithm can estimate AoA within 3∘, while the error of ToF and DFS parameter estimation is within 1 ns and 1 m/s.

Single‐object localization using multiple ultrasonic sensors and constrained weighted least‐squares method

AbstractIn this paper, an active single‐object localization system with U‐shaped ultrasonic module array is presented. The proposed algorithm in this system has two stages. The first stage is time‐of‐flight (TOF) estimation of reflected ultrasonic signals. We analyze several distortion cases of reflection signals and provide solutions to improve the performance of TOF estimation. The second stage is TOF‐based object localization. A good localization algorithm can suppress the problems caused by inaccurate TOF estimation and improve the accuracy of target positioning. We propose two object‐localization algorithms to estimate the object location. One is the unconstrained least‐squares method, and the other is the constrained weighted least‐squares method based on the eigenvalues‐analyzing technique. The simulation results suggest that the performance of the proposed constrained weighted method is better than that of the unconstrained method. In addition, the median smoother and the outlier exclusion scheme are implemented in the overall system to make the object location estimation more stable. The performance of the proposed system is confirmed by the experiment results, which show that the single‐object localization has a considerable degree of accuracy and stability.

RfLoc: A Reflector-Assisted Indoor Localization System Using a Single-Antenna AP

Could we use a single access point (AP) or even an AP equipped with only a single antenna to provide high-accuracy localization service comparable to that of advanced systems using multiple APs or antenna arrays in indoor environments? To answer this question, we present RfLoc, a novel indoor localization system that enables submeter localization accuracy using a single-antenna AP in this article. To this end, RfLoc introduces a custom-designed active reflector with a simple circuit, which can create reflection paths to assist localization. Since our system does not require time synchronization between the target and AP, the absolute time-of-flight (ToF) is unavailable for localization. Instead, we use the relative ToF among the paths that are close to the ground truth to localize the target. The insight behind RfLoc is to use the designed reflector to create paths in a controllable manner, including the control of their strength and propagation delay. The created paths thus are remarkable in multipath-rich environments and can always be used for localization. Then, we employ a sparse recovery-based method, the orthogonal matching pursuit (OMP), to accurately estimate these path ToFs. With ToF estimates, the proposed two-step target localization algorithm is used to solve the target location, including coarse localization based on the semidefinite programming (SDP) and refined localization based on the least squares (LS). We prototype RfLoc using a software-defined radio platform with orthogonal frequency division multiplexing (OFDM) signal, which incorporates a standard WiFi baseband operating. Extensive experimental results show that it can achieve a median localization accuracy of 0.74 m with 100-MHz signal bandwidth. With the advantage of high localization accuracy and easy deployment, RfLoc could enable many Internet-of-Things (IoT) applications.

Toward 100 ps Coincidence Time Resolution Using Multiple Timestamps in Depth-Encoding PET Modules: A Monte Carlo Simulation Study

Coincidence time resolution (CTR) in modern time-of-flight (TOF) PET scanners is limited by properties of the detector system, namely scintillator size and material, as well as single-photon time resolution (SPTR) and photon detection efficiency of the readout pixels. Recent studies have demonstrated the effectiveness of incorporating depth of interaction (DOI) information into TOF readout to improve CTR. Having multiple timestamps per event has also been shown to improve CTR through leading edge slope estimation. We propose using convolutional neural networks (CNNs) to improve CTR in PET modules with excellent DOI resolution and access to multiple timestamps per event. Monte Carlo simulations were used to generate PET-like data on 4-to-1 coupled single-ended readout depth-encoding modules with 1.5 ×1.5 ×20 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> LYSO crystals and prismatoid light guide arrays. We trained our CNN to perform TOF estimation between the two simulated modules with and without DOI information, as well as with single and multiple timestamps. The results show using DOI and multiple timestamps provides more than 50% improvement in CTR over standard single timestamp acquisition when sufficient SPTR (<; 100 ps) is available. Our CNN demonstrates the importance of having multiple timestamps and excellent DOI resolution for improving CTR in practical depth-encoding PET modules.