Time Difference Of Arrival Estimation Research Articles

Accurate TDOA estimation using matching cumulative estimator for LFM signal with small samples

This paper introduces two matching cumulative estimators designed for achieving gridless time difference of arrival (TDOA) estimation for linear frequency modulated (LFM) signals with limited samples. A designed matching basis function, customized to the source signal waveform, is employed to calculate with the received data. Time delay matching is then utilized to formulate a monotonic objective function related to the estimated TDOA, enabling gridless estimation. To enhance robustness, especially in scenarios characterized by small samples and low signal to noise ratios (SNRs), a nonlinear cumulative transformation, comprised of a series of strongly convex operations, is incorporated to mitigate the impact of noise on the peak calculation of the objective function. Simulation results validate the efficacy of the two proposed TDOA estimators, particularly under challenging conditions involving small samples and low SNRs.

Time-difference reassigned transform with application to time difference of arrival for impulsive signal

Time difference of arrival (TDOA) is essential in localization, communication, and navigation. Under ambient noise interference, the impulsive signal is transmitted over a long distance and reaches the sensor with a low signal-to-noise ratio (SNR). Aiming to achieve a precise time delay estimation in scenarios with low SNR, this paper extends the time-reassigned extracting transform (TRET) theory to TDOA and proposes a time difference rearrangement extracting transform (TDRT) algorithm. The implementation process of the proposed algorithm comprises three steps. Initially, a rough two-dimensional time delay estimation is obtained by calculating the partial derivative of the short-time cross-power spectrum with respect to the frequency variable. Secondly, a rearrangement operation separates the signal's time-frequency (TF) points from the noise. Thirdly, a refined TDOA estimation is obtained by inverse Fourier transforming TF points extracted from the time-delay energy ridge. Simulation results show that the TDRT algorithm is effective in time delay estimation. Furthermore, experimental results prove that the performance of the TDRT algorithm outperforms comparable algorithms in low SNR environments.

A method for localization TDOA estimation based on signal‐level fusion and analysis

AbstractPassive localization using time difference of arrival (TDOA) is one of the common methods for radiated source target localization, and its localization performance depends on the accuracy of TDOA estimation. In many localization scenarios, the signals of target are intricate and often contain multiple ones, so how to effectively extract the time difference parameters from them becomes a difficult problem. This letter proposes a signal‐level fusion method for TDOA estimation to address this problem. At the receiver terminal, multiple signals are fused to obtain their cross‐ambiguity function, so as to estimate the TDOA value for target localization. The effect of fused signals on the accuracy of TDOA estimation is analyzed and the concept of frequency depression is proposed. Simulation experiments verify that the estimation method with signal‐level fusion gets a higher accuracy of the TDOA value and a smaller position error in target localization.

Improving the Robustness of Time Difference of Arrival Estimation Based on the Energy Center of Gravity Rearrangement.

An accurate estimation of the time difference of arrival (TDOA) is crucial in localization, communication, and navigation. However, a low signal-to-noise ratio (SNR) can decrease the reliability of the TDOA estimation result. Therefore, this study aims to improve the performance of the TDOA estimation of dual-channel sensors for single-sound sources in low-SNR environments. This study introduces the theory of time rearrangement synchrosqueezing transform (TRST) into the time difference of arrival estimation. While the background noise TF points show random time delays, the signal time-frequency (TF) points originating from uniform directions that exhibit identical lags are considered in this study. In addition, the time difference rearrangement synchrosqueezing transform (TDST) algorithm is developed to separate the signal from the background noise by exploiting its distinct time delay characteristics. The implementation process of the proposed algorithm includes four main steps. First, a rough estimation of the time delay is performed by calculating the partial derivative of the short-time cross-power spectrum. Second, a rearrangement operation is conducted to separate the TF points of the signal and noise. Third, the TF points on both sides of the time-delay energy ridge are extracted. Finally, a refined TDOA estimation is realized by applying the inverse Fourier transformation on the extracted TF points. Furthermore, a second-order-based time difference reassigned synchrosqueezing transform algorithm is proposed to improve the robustness of the TDOA estimation by enhancing the TF energy aggregation. The proposed algorithms are verified by simulations and experiments. The results show that the proposed algorithms are more robust and accurate than the existing algorithms.

Design and Performance Analysis of Sound Source Localization using Time Difference of Arrival Estimation

Sound source localization (SSL) is a process of processing sound signals received from sound sensors and locating the sound origin. In many applications, precise localization of these sound sources is crucial. The accuracy of the localization of the sound source depends on several factors, and one of the factors is the number of sound sensors. This work aims to develop a microcontroller-based sound sensor localization system using the Time Difference of Arrival (TDOA) method, as well as to analyze SSL by comparing the time difference received by two and three sound sensors with respect to the distance of sound, and to compare the angle accuracy of the sound localization through TDOA with the real sound location. A few experimental tests were conducted using a constant sound of 90db and a frequency range of sound of 50Hz to 10kHz. The mean error (inaccuracy) of the experimental test of the angle acquired within 5cm of the source is 34.66°, while the angle obtained within 10cm of the source is 34.29°. The difference in angle inaccuracy between two and three sensors has a reduction of 27.64%. By adding more sound sensors, angle accuracy can be increased through the TDOA method.

Multiple Signal TDOA/FDOA Joint Estimation with Coherent Integration

Passive localization relies significantly on the estimation of the Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) to accurately determine the location of a target. The precision of TDOA and FDOA estimation is affected by signal parameters of time and frequency distribution. In case of multiple signals arising at different frequency bands and intercepted simultaneously by spatially separate sensors covering a wide frequency band, the traditional method is first to separate the signals from the mixed wideband signal through digital down conversion (DDC), which brings multiple narrowband signals, and then the estimation of TDOA and FDOA of each narrowband signal can be performed using cross ambiguity function (CAF). The paper introduces a novel approach for estimating TDOA and FDOA of multiple signals simultaneously, which employs a coherent integration method. First, the cross ambiguity function for each signal is realized with the narrowband signal as the same as the traditional method. Next, the phase relation of each CAF is analyzed, then the joint CAF can be obtained with phase compensation, from which multiple signal TDOA and FDOA estimations will be implemented simultaneously. Numerical simulations are performed to compare the two methods, and the results demonstrate the superiority of the proposed algorithm.

Bayesian detection and tracking of odontocetes in 3-D from their echolocation clicks.

Localization and tracking of marine animals can reveal key insights into their behaviors underwater that would otherwise remain unexplored. A promising nonintrusive approach to obtaining location information of marine animals is to process their bioacoustic signals, which are passively recorded using multiple hydrophones. In this paper, a data processing chain that automatically detects and tracks multiple odontocetes (toothed whales) in three dimensions (3-D) from their echolocation clicks recorded with volumetric hydrophone arrays is proposed. First, the time-difference-of-arrival (TDOA) measurements are extracted with a generalized cross-correlation that whitens the received acoustic signals based on the instrument noise statistics. Subsequently, odontocetes are tracked in the TDOA domain using a graph-based multi-target tracking (MTT) method to reject false TDOA measurements and close gaps of missed detections. The resulting TDOA estimates are then used by another graph-based MTT stage that estimates odontocete tracks in 3-D. The tracking capability of the proposed data processing chain is demonstrated on real acoustic data provided by two volumetric hydrophone arrays that recorded echolocation clicks from Cuvier's beaked whales (Ziphius cavirostris). Simulation results show that the presented MTT method using 3-D can outperform an existing approach that relies on manual annotation.

Polynomial Fitting and Interpolation Method in TDOA Estimation of Sensors Network

Time difference of arrival (TDOA) estimation is the key part of TDOA positioning technology in sensors network, whose result will directly affect the positioning accuracy of the signal source. Aiming at the problem that the accuracy of TDOA estimation is greatly limited by the system sampling frequency, this article proposes an improved TDOA estimation method combining polynomial fitting and interpolation. Based on the classical generalized cross correlation (GCC) method, the peak location of the correlation function is adjusted slightly by polynomial fitting. Furthermore, linear interpolation is used to process the original signal to improve the time resolution between the samples, so as to improve the system sampling frequency indirectly and promote the estimation accuracy to the subsampling level. At the end of the article, the proposed method is validated by simulation and some measured data from a certain place in Lanzhou. The results show that the polynomial fitting method can precisely determine the peak location of the GCC correlation function, especially after interpolating 2–4 points in the original signal, the overall TDOA estimation accuracy can be improved by 0.2%–3.6%, which may provide good reference information for practical engineering application of TDOA positioning technology.

UHF Sensors Based Localization of Partial Discharge Sources in Air-Insulated Electrical Substation Using TDOA and Relative RSS Information

Time-difference of arrival (TDOA) based localization of partial discharge (PD) sources using Ultra High Frequency (UHF) technique often provides uncertain accuracy because of unavoidable errors in TDOA estimation between PD pulses. This paper presents a novel localization approach utilizing TDOA and relative received signal strength (RRSS) information together for improving the localization accuracy of PD sources within air-insulated substations (AIS). A complete PD localization system governed by this approach has been developed using multiple UHF PD sensors. The effectiveness of the proposed PD source localization approach has been validated through laboratory and field-based experiments in real-life AIS.

Time Difference of Arrival Estimation of Stationary Targets Utilizing Deep Neural Network

Time difference of arrival (TDOA) is widely used in the field of passive location because of its flexible base station deployment and simple principle. However, when solving the solution of stationary targets position, the traditional method, such as the two-stage weighted least squares (TSWLS) algorithm, is easily affected by noise, and cannot achieve good localization results in practical situations. To solve this problem, we propose a deep neural network (DNN) for TDOA estimation of stationary targets. First, a large number of simulation samples are generated according to the TDOA model. Each sample contains the time difference from each secondary base station to the main base station, the error of time difference, and the real three-dimensional (3-D) coordinates of the targets. Next, a suitable DNN architecture is designed to solve the solution of the stationary target position. The simulation results prove that the method proposed herein outperforms TSWLS for multiple base stations based on the TDOA model.

Coordinated Positioning Method for Shortwave Anti-Multipath Based on Bayesian Estimation.

Coordinated positioning based on direction of arrival (DOA)–time difference of arrival (TDOA) is a research area of great interest in beyond-visual-range target positioning with shortwave. The DOA estimation accuracy greatly affects the accuracy of coordinated positioning. With existing positioning methods, the elevation angle’s estimation accuracy in multipath propagation decreases sharply. Accordingly, the positioning accuracy also decreases. In this paper, the elevation angle is modeled as a random variable, with its probability distribution reflecting the characteristics of multipath propagation. A new coordinated positioning method based on DOA–TDOA and Bayesian estimation with shortwave anti-multipath is proposed. First, a convolutional neural network is used to learn the three-dimensional spatial spectrogram to make an intelligent decision on the number of single and multiple paths, and to obtain a probability distribution of the elevation angle under multiple paths. Second, the elevation angle’s estimated value is modified using the elevation angle’s probability distribution. The modified elevation angle’s estimated value is substituted into a DOA pseudo-linear observation equation, and the target position’s estimated value is obtained using the matrix QR decomposition iteration algorithm. Finally, a TDOA pseudo-linear observation equation is established using the target estimate obtained in the DOA stage, and the coordinated positioning result is obtained using the matrix QR decomposition iteration algorithm again. Simulation results demonstrated that the proposed method had a stronger anti-multipath capability than traditional methods, and it improved the coordinated positioning accuracy of the DOA and TDOA. Measured data were used to validate the proposed method.

Fast TDOA and FDOA Estimation for Coherent Pulse Signals

Time difference of arrival (TDOA) and frequency difference of arrival (FDOA) have been widely used for localizing temporally continuous signals passively. Temporal sparsity of pulse signals makes their TDOA and FDOA estimation processes much different, and computational complexity is a major concern in this area. This paper addresses the problem of fast TDOA and FDOA estimation of pulse signals and focuses mainly on narrowband coherent pulses. By decoupling the effects of TDOA and FDOA in the cost function of localization approximately, we propose a fast coarse TDOA and FDOA estimation method. The estimates are then refined with the cross-ambiguity function (CAF) algorithm within a small TDOA and FDOA neighborhood. In the simulations, the proposed method is demonstrated to have satisfying TDOA and FDOA estimation precisions, and it exceeds existing counterparts largely in computational efficiency.

A Coherent Integrated TDOA Estimation Method for Target and Reference Signals

The performance of a time difference of arrival (TDOA) localization system is severely affected by time synchronization errors, and making use of reference signals is a common solution for the problem. The traditional method has two steps, first to measure the TDOAs of the target signal and reference signal separately, and next, to compensate the estimated target TDOA with the difference of the estimated reference TDOA and the true reference TDOA. Since the performance of the TDOA estimation is mainly decided by the frequency information, a coherent integration TDOA estimation method for the target signal and reference signal is proposed in this paper, based on cross correlation phase difference compensation, with use of the signals’ frequencies. First, as per the traditional method, the separated cross correlation functions of the target signal and reference signal were obtained by cross correlation, and the target TDOA and reference TDOA of the separate method were estimated. Next, the cross correlation phase was analyzed for each signal. Then the coherent integration cross correlation was obtained with phase compensation, from which the estimation of the target TDOA and reference TDOA could simultaneously be achieved. We performed simulation comparisons with the two methods, and showed that the proposed algorithm provided better performance.

A Multi-Pulse Cross Ambiguity Function for the Wideband TDOA and FDOA to Locate an Emitter Passively

The time difference of arrival (TDOA) and frequency difference of arrival (FDOA) between two receivers are widely used to locate an emitter. Algorithms based on cross ambiguity functions can simultaneously estimate the TDOA and FDOA accurately. However, the algorithms, including the joint processing of received data, require transferring a large volume of data to a central computing unit. It can be a heavy load for the data link, especially for a wideband signal obtained at a high sampling rate. Thus, we proposed a multi-pulse cross ambiguity function (MPCAF) to compress the data before transmitting and then estimate the TDOA and FDOA with the compressed data. The MPCAF consists of two components. First, the raw data are compressed with a proposed two-dimensional compression function. Two methods to construct a reference pulse used in the two-dimensional compression function are considered: a raw data-based method constructs the pulse directly from the received signal, and a signal parameter-based method constructs it through the parameters of the received signal. Second, a wideband cross-correlation function is studied to refine the TDOA and FDOA estimates with the compressed data. The simulation and Cramer–Rao lower bound (CRLB) analyses show that the proposed method dramatically reduces the data transmission load but estimate the TDOA and FDOA well. The hardware-in-the-loop simulation confirms the method’s effectiveness.

Bi-Long Short-Term Memory Networks for Radio Frequency Based Arrival Time Detection of Partial Discharge Signals

Partial discharge (PD) monitoring of electrical substations could provide early warning of insulation failures. Among the various technologies, Radio Frequency (RF) based PD monitoring system could be a promising solution. The RF-based monitoring system detects PD sources in the substation and can also localise the PD sources. The time difference of arrival (TDOA) based PD localisation system primarily require arrival time (AT) of the impulsive RF signal. Though many localisation algorithms have been proposed in the recent past to overcome the TDOA estimation errors, less attention has been given to the accurate estimation of RF PD signal arrival time. This paper presents the AT's automatic labelling in the RF PD signal using Bi-Long Short-Term Memory (Bi-LSTM) network applied on the continuous wavelet transformed (CWT) signal. Further, it also shows PD signal augmentation to overcome the problem of limited representative training data set. The behavior of the radiated RF signals is influenced by many factors and has almost stochastic characteristics. The proposed system has been validated with laboratory-based experimental signals and the data set obtained from different electrical substations. The results show that the improved performance is obtained from the combination of a multilayer Bi-LSTM model and an augmented training set.

Performance Analysis of TDOA and FDOA Estimation for Pulse Signals

Time difference of arrival (TDOA) and frequency difference of arrival (FDOA) are effective measurements for localizing emitters’ radiating pulse signals, such as radar. Temporal sparsity of pulse signals makes their TDOA and FDOA estimation precisions much different from that of continuous communication and acoustic signals. The way how the precisions are affected by various parameters, e.g., temporal duration of signals, may also deviate significantly in scenarios of pulse signals from that of continuous ones. In this paper, theoretical analyses are carried out to reveal the Cramer–Rao lower bounds (CRLBs) of TDOA and FDOA estimation precisions of pulse signals and also to obtain insights on how the CRLBs are affected by various parameters, including pulse number, signal-to-noise ratio (SNR), pulse width, and pulse repetition interval (PRI). Simulation results verify the correctness of the derived CRLBs and their variations with different parameters.

Indoor Localization with a Single Access Point Based on TDoA and AoA

Indoor localization in 5G and the Internet of Things has been paid increasing attentions. Recent advances have demonstrated reasonable localization accuracy that can be provided by using a single access point (AP). Yet, existing single AP localization solutions require frequency hopping or suffer from degraded accuracy performance due to complicated indoor propagation environment. This paper proposes a new single AP indoor localization method based on time difference of arrival (TDoA) and angle of arrival (AoA). We divide multiple antennas into two groups, one group with close distance for AoA estimation and the other group with the farther distance for TDoA estimation. Then, a joint estimation of AoA and ToA is carried by a spatial smoothing-based multiple signal classification (MUSIC) algorithm. Finally, we propose a weighted least squares method based on TDoA and AoA estimations to achieve indoor localization. Simulation results verify the effectiveness of the proposed single AP localization method.

Asymptotic Performance of TDOA Estimation Using Satellites

We present novel lower bounds on the localization error using a network of satellites randomly deployed on a sphere around Earth. Our new analysis approach characterizes the localization performance by its asymptotic behavior as the number of satellites gets large while assuming a dense network. Using the law of large numbers, we derive closed-form expressions for the asymptotic Cramér Rao bound (CRB) from which we draw valuable insights. The resulting expressions depend solely on the network statistics and are not a function of a particular network configuration. We consider two types of estimators. The first uses the exact statistical model, and hence employs both timing and amplitude information. The second estimator ignores the amplitudes and hence uses only time difference of arrival (TDOA) information. The asymptotic CRB indicates that for practical system setup, a TDOA estimator approaches the performance of the ideal estimator. For both estimators, the localization accuracy improves as satellites get closer to Earth. The latter finding is essential in light of the proliferation of low-Earth-orbit (LEO) satellites and motivates a further study of localization-performance in such networks. Besides, we show that the vertical localization accuracy is lower than the horizontal accuracy and is also more sensitive to the receiver field-of-view.

Localizing Sources Using a Network of Synchronized Compact Arrays

The problem of passive acoustic estimating the position of a source using a network of synchronized underwater compact arrays is considered. Maximum-likelihood estimators using angle of arrival (AOA), time difference of arrival (TDOA), as well as a combination of AOA/TDOA estimates are developed. The localization accuracy provided by the AOA-based, TDOA-based, and hybrid estimators is evaluated using Cramér–Rao bounds, statistical simulations, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> test. Test results demonstrated that the efficiency of AOA-based and TDOA-based estimators strongly depends on variances of the AOA and TDOA estimates. Relative efficiency of the hybrid estimator is higher than any of the AOA-based and TDOA-based algorithms.

Fundamental study on sound source localization inside a structure using a deep neural network and computer-aided engineering

This study proposes a sound source localization (SSL) method applicable to sources inside structures such as mechanical equipment or buildings. Presently, an SSL system employing a microphone array based on the time difference of arrival estimation can be used to localize a sound source in the same acoustic space as the microphone. However, conventional SSL methods cannot be adopted when the sound source is located inside a structure. Achieving SSL is more difficult in the case of an indirect sound than in that of a direct sound, because the correlation between the observed signals becomes stronger owing to the effect of coupling between the acoustics and structure. To solve this problem, an SSL method employing a deep neural network and computer-aided engineering, which is applicable to the structure’s interiors, is proposed. The proposed method’s effectiveness and feasibility are examined via numerical and actual experimentation. The proposed method can estimate the position of the sound source inside the structure based on the spectrum measured by an accelerometer on the surface of the structure. The results of the numerical experiment indicate a test accuracy of 93.20%, whereas the actual experiment yielded an accuracy of 61.53%. The learning and validation curves show that the accuracy of the actual experiment is lower owing to the occurrence of overlearning, which results from the small amount of data applied. To overcome this issue, data augmentation was used; consequently, the accuracy was improved to 99.82%.