Time Difference Of Arrival Research Articles

Accuracy and Precision of Earthquake Location Programs: Insights from a Synthetic Controlled Experiment

Abstract Earthquake location programs employ diverse approaches to address the challenges posed by incomplete knowledge and simplified representation of complex Earth structures. Assessing their reliability in location and uncertainty characterization remains challenging as benchmark datasets with known event locations are rare, and usually confined to particular sources, such as quarry blasts. This study evaluates eight earthquake location methods (GrowClust, HypoDD, Hypoinverse, HypoSVI, NonLinLoc, NonLinLoc_SSST, VELEST, and XCORLOC) through a controlled synthetic computational experiment on 1000 clustered earthquakes based on the setting of the 2019 Ridgecrest, California, earthquake sequence. We construct a travel-time dataset using the fast-marching method and a 3D velocity model extracted from the Community Velocity Model, supplemented with a von Karman perturbation to represent small-scale heterogeneity, and including elevation effects. Picking errors, phase availability, and outliers are introduced to mimic difficulties encountered in seismic network monitoring. We compare the location results from eight programs applied to the same travel-time dataset and 1D velocity structure against the ground-truth locations. For this aftershock sequence, our results reveal the superior accuracy and precision of differential time-based location methods compared to single-event location methods. The results validate the significance of compensating for deviations from assumed 1D velocity structure either by path or site correction modeling or by cancellation of unmodeled structure using differential arrival times. We also evaluate the uncertainty quantification of each program and find that most of the programs underestimate the errors.

Deep Learning-Aided Acoustic Source Localization in Thin-Walled Waveguides

The timely detection of fault locations represents a critical task in Structural Health Monitoring (SHM) of thinwalled elements. In particular, the localization of acoustic emission sources is particularly important for the identification of damages caused by stress and can be achieved by estimating the Difference in Time of Arrival (DToA) between the waves captured by a sparse sensor array. In this work, a novel method for DToA extraction suitable for isotropic structures is proposed. Our approach is based on the combination of Convolutional Neural Networks (CNNs) and a dispersion compensation operator, the Warped Frequency Transform (WFT). CNNs are deployed to enhance the localization process against the detrimental losses caused by non-ideal conditions, such as the presence of reflections and multiple propagation modes. The results show that such method yields localization errors of a few centimetres, with an average below 2 cm, when only relying on hundreds of real data for training.

WSN Localization in Smart Cities Using Hybrid (TDOA & RSSI) Localization Techniques with Extended Kalman Filter

In the context of smart cities, localization technologies are essential for tracking objects in both indoor and outdoor environments. The characteristics of urban settings such as building density, signal interference, and multipath propagation significantly impact the accuracy of localization algorithms. This paper reviews existing localization techniques, categorizing them into range-based and range-free methods, and discusses key algorithms including trilateration, multilateration, and triangulation. We propose a hybrid localization framework that combines Time Difference of Arrival (TDOA) and Received Signal Strength Indicator (RSSI) techniques, enhanced by an Extended Kalman Filter (EKF) for improved accuracy and robustness. Additionally, we present a design architecture for a transmitter and receiver system utilizing Long Range (LoRa) technology, facilitating the development of low-cost, low-power tracking devices that operate independently of Global Positioning System (GPS). Our approach aims to enhance the efficacy of localization in smart city applications, ultimately contributing to improved urban management and safety.

Distributed Passive Positioning and Sorting Method for Multi-Network Frequency-Hopping Time Division Multiple Access Signals.

When there are time division multiple access (TDMA) signals with large bandwidth, waveform aliasing, and fast frequency-hopping in space, current methods have difficulty achieving the accurate localization of radiation sources and signal-sorting from multiple network stations. To solve the above problems, a distributed passive positioning and network stations sorting method for broadband frequency-hopping signals based on two-level parameter estimation and joint clustering is proposed in this paper. Firstly, a two-stage filtering structure is designed to achieve control filtering for each frequency point. After narrowing down the parameter estimation range through adaptive threshold detection, the time difference of arrival (TDOA) and the velocity difference of arrival (VDOA) can be obtained via coherent accumulating based on the cross ambiguity function (CAF). Then, a multi-station positioning method based on the TDOA/VDOA is used to estimate the position of the target. Finally, the distributed joint eigenvectors of the multi-stations are constructed, and the signals belonging to different network stations are effectively classified using the improved K-means method. Numerical simulations indicate that the proposed method has a better positioning and sorting effect in low signal-to-noise (SNR) and low snapshot conditions compared with current methods.

Single Station Seismic Event Location With a Neural‐Guided Mixture Model: Model‐Based Weighting for Improved Accuracy

AbstractIn many regions of the world with complex seismic activity, the availability of seismic stations is limited. This motivated us to develop a probabilistic method for single‐station earthquake location. Single station location methods may provide an efficient and cost‐effective way to monitor small‐magnitude seismic events over large areas of the world. This method relies on the outputs of two neural networks, which predict the initial spatial location of specific areas (convolutional) used in the prior probability and seismic phase recognition (combination of convolutional and Long Short Term Memory) used in the likelihood function. These estimates and a 3D travel time likelihood function are used in a Bayesian framework. In this model, the initial spatial location is expressed as a Multivariate Gaussian Mixture Model, and the likelihood function refines the localization using the arrival time difference between S and P waves in a 3D space. The likelihood function uses a Fast Marching Eikonal method with a 3D velocity structure. We tested this method on the Ridgecrest 2019 seismic sequence (Mw = 7.1) and on West Texas and found promising results for locating with a single station. Our approach demonstrates that using a Bayesian model with strong priors obtained through deep learning algorithms is effective. Our model can predict epicenter and depth with mean errors of 7.55 km in longitude, 13.54 km in latitude and 0.630 km in depth at the two different locations studied. This method demonstrates the effectiveness of combining deep learning for initial estimations with probabilistic 3D location refinement.

A Seismic Precursor 15 min Before the Giant Eruption of Hunga Tonga‐Hunga Ha'apai Volcano on 15 January 2022

AbstractThe 15 January 2022, eruption at Hunga Tonga‐Hunga Ha'apai (HTHH) volcano started shortly after 4:00UTC. There had been noted unconfirmed precursory events. We analyzed seismometer data recorded in Fiji and Futuna, the closest stations operated during the eruption and located over 750 km away. We extracted Rayleigh waves and estimated their powers and source directions, assuming retrograde particle motions. We found a Rayleigh wave from the HTHH's direction about 15 min before the eruption onset. The arrival time difference of the Rayleigh wave between the two stations was consistent with that of the M5.8 earthquake during the eruption located beneath the HTHH. Referring to other seismic signals and satellite images, we concluded that the Rayleigh wave was the most significant eruption precursor with no apparent surface activity. Including our findings and results of previous studies, we propose a scenario of the beginning of the caldera‐forming eruption.

Numerical investigation of bandgap characteristics in integrated metallic metafilters for nonlinear guided wave applications

Guided waves propagating in nonlinear media, featuring second harmonic generation, represent a promising avenue for early-stage damage detection due to their high sensitivity and long-range propagation capabilities. However, nonlinear ultrasonic measurements are hindered by nonlinearities induced by the experimental system, necessitating careful calibrations that have restricted their application to laboratory settings. While several phononic crystal and metamaterial designs have been devised to enhance nonlinear-based ultrasonic testing, most are tailored for suppressing second harmonics within a frequency range of 100–300 kHz, primarily utilizing low-frequency excitation. In this paper, we propose a metallic ring-shaped metafilter designed to explore high-order bandgaps. To fully understand the bandgap characteristics, we begin by analyzing mode shapes, providing insights into the underlying wave mechanics. The efficacy of the designed filter is subsequently assessed through 3D time step elastodynamic simulations. In addition, this study underscores the significance of parameters such as the number of rings employed in the filter, signal duration, and bandgap width in optimizing its performance. Furthermore, the observed mode conversion phenomena from S0 to A0 guided wave modes underscore the filter’s capacity to influence guided wave propagation. The defect localization technique, based on the time difference of arrival of second-order wave modes, accurately predicts the defect location with an error margin of less than 0.2%. The present investigation showcases advancements in the sensitivity of nonlinear-based guided wave testing for characterizing microstructural changes, promising substantial potential for detecting incipient damage in practical structural health monitoring applications.

A theoretical analysis of the logging-while-drilling dipole acoustic reflection measurement

Post-drilling wireline acoustic single-well imaging technology can now detect geological structures tens of meters away from boreholes. Further development of this single-well imaging technology in the logging-while-drilling (LWD) environment will have significant values in real-time applications such as geosteering and reservoir navigation. Based on the wireline imaging application, we propose a new method for the LWD application. In wireline imaging, the four-component (4C) dipole acoustic data are azimuthally rotated to scan the reflectors around the borehole. In LWD, azimuthal scanning is achieved by drilling rotation such that the 4C dipole system in the wireline is replaced by a one-dipole-source and two-receiver LWD system, where the two receivers are mounted on opposite sides of the drill collar. For the LWD application, we first developed the theory for LWD dipole shear-wave reflection imaging and validated the theory using 3D finite-difference waveform modeling. Using the analytical solution, we analyzed the far-field radiation directivity of an acoustic LWD dipole source and the effect of drilling rotation on the shear-wave reflection imaging using the LWD acoustic system. The LWD analysis results show that, for fast formations, the SH-wave is the dominant component for imaging, whereas for slow formations, the P-wave becomes important and can be used for imaging. Our results also indicate that the reflection data acquired by the system are affected by the speed of drilling rotation. The take-off azimuth at the wave radiation may be different from the incident azimuth at the wave reception. Knowing the rotation speed, this azimuth difference can be corrected. A further advantage of using the oppositely mounted receivers is that the reflected wave arrives earlier (later) at the front (back)-side receiver; thus, the arrival time difference between the receivers can be used to eliminate the 180°-azimuth ambiguity of dipole acoustic imaging. For reflection imaging, using the proposed LWD system configuration, we tested its azimuth sensitivity and validated its 180°-ambiguity solution using synthetic LWD and field wireline dipole data. The results of this work, therefore, provide a theoretical foundation for the development of the LWD acoustic reflection imaging system.

A triangular acoustic emission source location method considering its anisotropic propagation behavior on the surface of finger-joint-laminated board

ABSTRACT To understand the anisotropic propagation characteristics of acoustic emission (AE) signals in finger-joint-laminated boards, an improved planar localization method for AE sources is proposed. Initially, the AE source was generated by the pencil-lead break (PLB) at a fixed position on the surface of the glued wood specimen, and two AE sensors were arranged in different directions at a fixed distance of 60 mm, and the AE propagation velocity was calculated according to the time difference of arrival (TDOA). For clarity, the grain parallel direction was defined as 0 degrees, with velocities measured every 10 degrees through a counterclockwise rotation. Using these measurements, two angular anisotropic wave velocity models were developed. Subsequently, three AE sensors arranged linearly on the specimen surface pinpointed the AE source’s location. This source location problem was formulated as a multi-parameter optimization model, constrained by the geometric relationships between the AE source and the sensors. A particle swarm optimization (PSO) algorithm was utilized to estimate the AE source’s angles relative to each sensor. The findings indicate that the located AE sources deviated by 6.0–19.0 mm from the predetermined PLB positions, with inaccuracies largely attributed to the anisotropic AE wave velocity models’ precision.

Numerical modelling of bridge deck reinforcement corrosion based on analysis of GPR data

AbstractThis study explores the impact of corrosion on Ground Penetrating Radar (GPR) responses through practical experiments and numerical modelling, focusing on rebar diameter reduction, corrosion product layer thickness, crack formation and corrosion product filling in vertical and transverse crack. Practical experiments involved GPR testing of reinforced concrete slab. By analyzing B-scans we identify areas with moderate and severe corrosion. Numerical modelling using the Finite Difference Time Domain (FDTD) Method to model GPR signal propagation in a concrete bridge deck with corrosion is applied. Key finding includes a significant 26.70% increase in reflected wave amplitude when corrosion product filling in vertical crack increased by 400%, highlighting its extensive effect on signal GPR propagation. Reduced rebar diameter led to a 9.79% amplitude decrease and a 0.06 ns arrival time delay. Increased corrosion product layer thickness primarily affected arrival time with a 0.06 ns extension but significantly amplified GPR signal amplitude. These findings offer insights for improving GPR based corrosion detection and assessment methods, leading to more robust systems for concrete bridge deck inspection and maintenance. This paper contributes to understanding how corrosion affects the signal that is detected by GPR. This information can be used to improve the way that we manage and assess corrosion in concrete bridge deck.

Retraction notice: Enhanced gray wolf optimization for estimation of time difference of arrival in WSNs

Retraction notice: Enhanced gray wolf optimization for estimation of time difference of arrival in WSNs

Quasi-real-time earthquake relocation and monitoring in the northeastern Noto Peninsula

The seismicity rate markedly increased in the northeastern Noto Peninsula of Ishikawa Prefecture around the end of 2020, with an Mw6.2 event on 5 May, 2023, followed by many aftershocks. Previous earthquake relocation studies have detected upward migration of microearthquakes via multiple faults and clusters, suggesting the involvement of crustal fluids in this sequence. Since some active faults exist near the source region, there was concern that this sequence could lead to a larger earthquake; it became a reality with the Mw7.5 earthquake on 1 January 2024. This study aims to develop an algorithm to precisely relocate microearthquake hypocenters in quasi-real time for better monitoring. A fine view of seismicity requires relative relocation methods such as the double-difference (DD) method with numerous arrival time difference data precisely measured by the waveform correlation analysis. However, the standard DD method has the disadvantage of huge computational costs when data increase, making it unsuitable for real-time monitoring in such situations. We developed a quasi-real-time algorithm that relocates only new earthquakes using the DD method each time a new time window of data is added. The major improvement is that our method incorporates a traditional simple relative relocation and preserves constraints between different time windows; the relative locations of new events are constrained from reference events that were already relocated in the previous time windows. We tested a daily relocation algorithm on 11,546 events from 19 June, 2022, to 31 May, 2023, in the Noto Peninsula earthquake sequence. We found that our modification substantially reduced artificial hypocenter offsets between different time windows and succeeded in resolving the fine fault structures from the cloud-like distribution of initial hypocenters. If we do not impose constraints between different windows, the relocated hypocenters are scattered and do not show fine planar structures. Our algorithm greatly reduces the computational cost, allowing for quasi-real-time earthquake relocation and monitoring. We hope this algorithm will help monitor the spatio-temporal distribution of future earthquake sequences.Graphical

Enhanced Method for Localization of Partial Discharges in Oil-Filled Transformers Using Acoustic Emission Signals

The accurate measurement of partial discharges (PD) in power transformers is a critical component in identifying faults and planning effective maintenance strategies. Acoustic emission (AE) sensing technology is suitable for detecting partial discharges in transformers because it is less affected by external electromagnetic interference and detects PD non-invasively. This paper delves into examining the relationship between the detection intensity, the specific type of PD source, and the distance to the discharge source, using AE sensors. It was observed that AE wave intensities from corona discharges tend to be relatively strong, indicating a higher detection probability. Creepage discharges usually exhibit the next level of intensity, followed by the PD occurring in bubbles. It is considered that the intensity of the AE waves varies significantly depending on both the speed at which the discharge propagates and the medium and volume of the discharge space. Furthermore, this study has conducted experimental comparisons among three distinct methods for calculating the Time Difference of Arrival (TDOA) in localization calculations. These methods are the energy criterion, Generalized Cross-Correlation (GCC), and GCC with Phase Transformation (PHAT). The experimental results suggest that the energy criterion method is particularly effective when sensors are distributed placement around the entire tank. In contrast, the GCC-PHAT method shows greater suitability in scenarios where sensors are centralized placement in certain sections of the tank. It was clearly observed that the GCC-PHAT method, which suppresses the impact of noise and reflections, consistently achieves higher estimation accuracy in comparison to the standard GCC method. Notably, this method has shown the ability to maintain its accuracy levels even in cases of low discharge intensities. The implications of these findings are significant, as they could improve the precision and effectiveness of maintenance diagnostics in power transformers.

Sediment Corrections for Distributed Acoustic Sensing

AbstractOn continental margins, sediments cause significant and spatially variable delays in seismic phase arrival times. The strong impedance contrast of the sediment‐bedrock interface causes P‐wave splitting that is clearly seen on distributed acoustic sensing recordings of earthquakes, resulting in additional phase arrivals that must be picked separately. We introduce sediment corrections to correctly account for those additional phases in the hypocenter localization procedure. Conceptually, the sediment correction method differs from the commonly‐used station corrections; instead of introducing a mathematically optimal constant time delay for each station and each phase, the corrections are derived from a physical, first‐order modeling of the wave propagation in the sediments. To calibrate the sediment corrections, a two‐step procedure is adopted: (a) the delay between the P‐phase and the converted Ps‐phase is taken as a proxy of the sediment thickness; (b) the P‐ and S‐wave speeds are determined through inversion. We show that sediment corrections are able to account for most of the observed bias while considerably reducing the number of free parameters compared to classical station correction. Moreover, the observed local delays are almost fully explained by the presence of the sedimentary layer, rather than by the 3D velocity variations of the bedrock. We retrieve and values that are compatible with values commonly found for sediments. Given the simplicity and physical foundation of the proposed method, we recommend the use of sediment corrections over station corrections whenever significant P‐wave splitting can be observed.

Coherent Radio Emission from “Main-sequence Radio Pulse Emitters”: A New Stellar Diagnostic to Probe 3D Magnetospheric Structures

Main-sequence radio pulse emitters (MRPs) are magnetic early-type stars that produce coherent radio emission observed in the form of periodic radio pulses. The emission mechanism behind this is the electron-cyclotron maser emission (ECME). Among all kinds of magnetospheric emission, ECME is unique due to its high directivity and intrinsically narrow bandwidth. The emission is also highly circularly polarized and the sign of polarization is opposite for the two magnetic hemispheres. This combination of properties makes ECME highly sensitive to the three-dimensional structures in the stellar magnetospheres. This is especially significant for late-B and A-type magnetic stars that do not emit other types of magnetospheric emission such as Hα, the key probe used to trace magnetospheric densities. In this paper, we use an ultra-wideband observation (0.4–2 GHz) of a late B-type MRP HD 133880 to demonstrate how we can extract information on plasma distribution from ECME. We achieve this by examining the differences in pulse arrival times (“lags”) as a function of frequencies and qualitatively comparing those with lags obtained by simulating ECME ray paths in hot stars’ magnetospheres. This reveals that the stellar magnetosphere has a disk-like overdensity inclined to the magnetic equator with a centrally concentrated density that primarily affects the intermediate frequencies (400–800 MHz). This result, which is consistent with the recent density model proposed for hotter centrifugally supported magnetospheres, lends support to the idea of a unifying model for magnetospheric operations in early-type stars, and also provides further motivation to fully characterize the ECME phenomenon in large-scale stellar magnetospheres.

Robust Indoor Positioning with Smartphone by Utilizing Encoded Chirp Acoustic Signal.

Recently, indoor positioning has been one of the hot topics in the field of navigation and positioning. Among different solutions on indoor positioning, positioning with acoustic signals has its promise due to its relatively high accuracy in the line of sight scenarios, low cost, and ease of being implemented in smartphones. In this work, a novel acoustic positioning method, called RATBILS, is proposed, in which encoded chirp acoustic signals are modulated and transmitted by different acoustic base stations. The smartphones receive the signals and perform the following three steps: (1) preprocessing; (2) time of arrival (TOA) estimation; and (3) time difference of arrival (TDOA) calculation and location estimation. In the preprocessing stage, we use band pass filters to filter out low-frequency noise from the environment. At the same time, we perform a signal decoding function in order to lock onto the positioning source. In the TOA estimation stage, we conduct both coarse and fine detection to enhance the accuracy and robustness of TOA estimation. The primary goal of coarse detection is to establish a noise range for fine detection. The main objective of fine detection is to emphasize the intensity of the first arrival diameter and resistance with multipath and non-line-of-sight (NLOS) caused by human body obstruction. In the TDOA calculation and location estimation stage, we estimate the TDOA based on the TOA estimation and then use the TDOA results for position estimation. In order to evaluate the performance of the proposed RATBILS system, two indoor field tests are carried out. The test results show that the RATBILS system achieves a positioning error of 0.23 m at 92% in region 1 of scene 1 and is superior to the traditional threshold method. The RATBILS system achieves a positioning error of 0.56 m at 92% in region 2 of scene 1 and is superior to the traditional threshold method. In scene 2, the maximum average positioning error was 1.26 m, which is better than the 3.33 m and 3.87 m of the two traditional threshold methods.

Testing the Origins of Neutrino Mass with Supernova-Neutrino Time Delay.

The origin of neutrino masses remains unknown. Both the vacuum mass and the dark mass generated by the neutrino interaction with dark matter (DM) particles or fields can fit the current oscillation data. The dark mass squared is proportional to the DM number density and, therefore, varies on the galactic scale with much larger values around the Galactic Center. This affects the group velocity and the arrival time delay of core-collapse supernovae (SN) neutrinos. This time delay, especially for the ν_{e} neutronization peak with a sharp time structure, can be used to distinguish the vacuum and dark neutrino masses. For illustration, we explore the potential of the Deep Underground Neutrino Experiment (DUNE), which is sensitive to ν_{e}. Our simulations show that DUNE can distinguish the two neutrino mass origins at more than 5σ C.L., depending on the observed local value of neutrino mass, the neutrino mass ordering, the DM density profile, and the SN location.

Application of optical fiber distributed acoustic sensing system in ultrasonic detection

Abstract The optical fiber distributed acoustic sensing system can continuously detect acoustic signals along the optical fiber, with the characteristics of wide response frequency band, large capacity, anti-electromagnetic interference and so on. An ultra-sensitive distributed optical fiber acoustic sensing system (uDAS) was produced with a high response frequency up to 100 kHz and thousands of sensing points. The arrayed ultrasonic detection can be realized by the distributed characteristics of the system. For verifying its ultrasonic detection ability, it is applied to ultrasonic nondestructive testing of structural defects. 20 optical fiber ultrasonic detection units were constructed. Each one is a fiber ring with a diameter of about 1.5 cm and a length of 2 meters. Two cubic cement structures with a side length of 30 cm were manufactured for experiment, one of which had an artificial internal defect. The optical fiber array was attached to the surface of the cement structure, and the ultrasonic signal with a frequency of 40 kHz was excited at a single point on the opposite side. The ultrasonic propagation speed changes on account of the defects such as holes and loose texture in the propagation path. The defects in the structure are identified and located by analyzing the difference of arrival time of waves. It is expected that such sensing system could found important applications in structure defect detection.

Timing offset calibration for TOF PET using stationary line source scans at multiple positions

Background. Accurate timing offset calibration is crucial for time-of-flight (TOF) positron emission tomography (PET) to mitigate image artifacts and improve quantitative accuracy. However, existing methods are often time-consuming, complex, or costly.Objective. This paper presents a method for TOF PET timing offset calibration that eliminates the need for costly equipment, phantoms, short-half-life sources, and precise source positioning.Approach. We estimate channel timing offsets using stationary scans of a68Ge line source, typically used for routine quality control, at a minimum of three non-coplanar positions, with each position scanned for two minutes. The line source positions are accurately determined by applying a simple algorithm to their reconstructed images, allowing precise calculation of arrival time differences. Channel timing offsets are estimated by solving a least squares problem. This method is assessed through analyses of phantoms and patient images using a RAYSOLUTION DigitMI 930 scanner.Main results. The estimated timing offsets ranged from -500 ps to 500 ps across all channels. Calibration with a minimum of three scanned positions was sufficient to correct these offsets, achieving less than a 1% discrepancy across various metrics of the image quality (IQ) phantom compared to 12 positions. This calibration significantly reduced edge artifacts in TOF reconstruction of both phantoms and patients. Furthermore, the IQ phantom displayed a 14% increase in average contrast recovery, a 61% reduction in average background variability across all spheres, and a 90% reduction in average residual error. Consistent with the phantom results, patient data revealed enhancements in maximum standardized uptake values (SUVmax) from 14% to 55% for lesions measuring 6 mm to 14 mm. The calibration also improved lesion-to-background contrast and eliminated artifacts caused by the spillover effect of the kidneys and bladder.Significance. The proposed method is fast, user-friendly, and cost-effective, effectively improving lesion detection and diagnostic accuracy.

A TDOA sequence estimation method of underwater sound source based on hidden Markov model

To address the time difference of arrival (TDOA) estimation problem in the passive positioning system with wideband underwater motion sound sources and distributed hydrophones, a hidden Markov model-based (HMM) TDOA sequence estimation method is proposed in this paper. The method estimates the TDOA with multi-frame output of cross-correlated signals received on hydrophones. The transfer equation of the TDOA is established as a first-order hidden Markov process by analyzing the motion characteristics of the moving sound source and delays obtained from different hydrophones. Dynamic assignment of the HMM parameters is proposed to address the inconsistent change rate of the TDOA. We then achieve an HMM expression of the TDOA sequence by fitting the transfer equation and dynamic assignment of parameters into the HMM. Then, the Viterbi algorithm (VA) is applied to distinguish the optimal sequence of the TDOA among ambiguous estimations. To deal with the problem of data loss or unreliable issues caused by interferences, a data prediction algorithm which could produce possible time delays is added to VA to avoid the impact of outliers on the estimation results. By utilizing multi-frame processing, the proposed method reduces the signal-to-noise ratio (SNR) requirement of single frames since it does not require accurate estimations of TDOA for each frame. Moreover, the method adapts to a lower SNR, which has significant advantages in terms of whole sequence estimation compared with common methods. The results from the simulations and lake experiments validated the proposed TDOA sequence estimation method.