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Super-Resolution Time Delay Estimation in Multipath Environments

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Abstract

The super-resolution time delay estimation in multipath environment is very important for many applications. Conventional super-resolution approaches can only deal with signals with wideband and flat spectra. In this paper, we propose a novel super-resolution time delay estimation method that can treat signals with narrowband spectra. In our method, the time delay estimation is first transformed into the frequency domain, in which the problem is converted into the parameter estimation of sinusoidal signals with lowpass envelopes. Then a MUSIC-type algorithm taking account of the envelope variation is applied to achieve the super-resolution estimation. Time delay estimation in active and passive systems are considered. Simulation results confirm that the proposed estimators provide better performance than the classical correlation approach and the conventional MUSIC algorithm for separating closely spaced signals with narrowband spectra.

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... Let us first analyse the performance attainable with three APs versus their mutual displacement. In detail, we considered displacements D in the range [20,50] meters, while the distance L between the ARPs of the AP and vehicle antennas at the crossover took values in the range [1,10] The standard deviation of the odometer measurement varied in the range [0.1, 10] times the RTT standard devion at r0=10 metres. ...
... As illustrated by Figure 7.a, where the results related to L=5m are reported, increasing the displacement D increases the performance degradation up to a factor 2.5 for D in the range [20,50]. On the other hand the larger D, the lesser the number of APs needed to covered a given track segment. ...
... Future activities will include the evaluation of the collaborative scheme proposed in [17], in order to reduce overhead and mitigate the clock drift, as well as the study of solutions for multipath mitigation, like in [19] and in [20]. ...
Conference Paper
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Vehicle’s positioning with high accuracy, integrity and continuity is a mandatory requirement for Automated trains, Connected cars and Driverless metros. Even if GNSS positioning is being introduced for train and car automation in conjunction with other sensors its availability is not guaranteed everywhere as inside tunnels and in cutting edge areas. The objective of our paper is to investigate the Fine Timing Measurement (FTM) function recently introduced in the IEEE 802.11 standard for the determination of the distance between pairs of stations for locating vehicles in GNSS denied areas. This solution can be extended also to the metros where this kind of networks is used for the communication between the trains and control center. We combine the use of the RTT of signals exchanged by a vehicle equipped with a Wi-Fi unit and a Wi-Fi beacon supporting the Fine Timing Measurement protocol with the physical or the virtual track constraint to overcome the limitation of positioning based on Round- Trip Time (RTT) which implies that measures with respect to different beacons are sequentially acquired. A reference architecture applicable to train, cars and metros is presented and the localization performance are simulated with the Monte Carlo tool. This approach can be used to complement the GNSS positioning in areas where the signals are not available or affected by interferences and in the case of metros to reuse the Wi-Fi network for assessing the train positioning. This work has been developed under the grant of the “ERSAT GGC” project of the H2020-GALILEO-GSA-2017-1 Program (project number 776039).
... A robust Capon beamformer based on time delay or time reversal is applied for ultrasound imaging in [2]. Moreover, the authors in [3] focus on TDE in both active and passive systems and take the envelope variation into account. In the field of civil engineering, time delays are important parameters for the quantitative interpretation of Ground-Penetrating Radar (GPR) data [4,5]. ...
... In this case, high resolution methods like MUSIC [9][10][11][12] and ESPRIT [13][14][15] are more suitable for TDE. Unlike the situations in [2,3], where the signals are supposed to be totally uncorrelated, in practice, the backscattered echoes are highly correlated (even coherent). Under this condition, the cross-correlation between the backscattered echoes may be too high to degrade the performance of the high resolution methods, such as the MUSIC algorithm, due to the rank loss of the data covariance matrix [16]. ...
... According to (3) and assuming the noise to be independent of the echoes, the covariance matrix Y of r can be written as: ...
Article
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In civil engineering, Time Delay Estimation (TDE) is one of the most important tasks for the media structure and quality evaluation. In this paper, the MUSIC algorithm is applied to estimate the time delay. In practice, the backscattered echoes are highly correlated (even coherent). In order to apply the MUSIC algorithm, an adaptation of signal subspace smoothing is proposed to decorrelate the correlation between echoes. Unlike the conventional sub-band averaging techniques, we propose to directly use the signal subspace, which can take full advantage of the signal subspace and reduce the influence of noise. Moreover, the proposed method is adapted to deal with any radar pulse shape. The proposed method is tested on both numerical and experimental data. Both results show the effectiveness of the proposed method.
... It is a key technology in modern signal processing such as system identification and target location tracking [2]. After decades of development, many methods have been developed, such as the Generalized Cross Correlation (GCC) function estimation method [3][4][5][6][7], Least Mean (Least MeanSquare, LMS) adaptive filtering method [8], subspace parameter estimation method [9,10], Higher-Order-Statistics (HOS) method [11]. ...
... Based on the above analysis, no matter whether the ideal multipath signal Y is known or unknown, the minimum virtual matrix is a dual matrix, that is, only one virtual array element is needed. Thus, the virtual matrix signal can be constructed by equations (9) or (10), (11). ...
... ① Perform FFT transformation on the received signal x 0 (n) on the real array element to obtain X 0 ; ② Perform FFT transformation on the transmitted signal s(n) to obtain S. ③ Constructing a virtual array element receiving signal X 1 according to X 0 , formula (9) or (10) ...
Article
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Aiming at improving time delay estimation (TDE) in the case of single sensor, a novel method of constructing virtual sensor array is presented, and furthermore the MUSIC delay estimation algorithm based on the virtual array is proposed. The approach and complete procedure of the algorithm are given. The relationship between the number of virtual array elements and the constructed signal is studied, and the method of determining the minimum number of elements under the condition of estimation time delay accurately is given. The simulation experiments of the presented algorithm have been carried out from three angles of view. The least virtual array elements and the minimum subspace dimensions needed in this algorithm is verified. We obtained the performance of time delay estimated by the algorithm under sparse path and dense path conditions respectively. This paper also illustrated the high precision and high-resolution characteristics of the proposed method.
... In Feng et al. [8], proposed a new super-resolution TDE approach that could be used to handle narrowband signals using MUSIC-type algorithms. The TDE obtained by crosscorrelation in the time domain first transformed into a frequency domain where the TDE translated into a parameter estimate of sinusoidal signals with low-pass envelopes. ...
... Step 2. Zero-pad | | C c (τ) | | 2 and compute IDFT of zeropadded | | C c (τ) | | 2 which is viewed as the power spectrum of the analytical signal as in (8). Since | | C c (τ) | | 2 is always nonzero and the time of arrivals 1 , 2 , … P are different from each other, we have rank Φ B = P under the assumption that 1 , 2 , … P are mutually uncorrelated and we assume the number of signal components is known. ...
... When the conventional MUSIC algorithm can be directly applied to these cases in which a performance penalty is introduced, the performance degradation increases dramatically with more envelope variations. In [8], MUSIC-type methods have been proposed to account for the envelope variation. In the Proposed algorithm, the unknown transmitted signal in the Active system sampled first to form a discrete pattern data set. ...
Article
This paper introduces techniques to restore super-resolution time delay estimation (TDE) of signals in multi-path environments using the Matrix Pencil Method (MPM). To verify the proposed algorithm, estimation errors are evaluated and compared with traditional Multiple Signal Classification (MUSIC) and cross-correlation approaches. TDE uses cross-correlation to produce measurements. Cross-correlation is based on a single model that considers the ideal environment. At the same time, the measurement precision starts to deteriorate as two or more signals are progressively entered at times shorter than the time interval, requiring super-resolution for accurate time delay measurement. The results of the proposed super-resolution MPM algorithm provide better performance over conventional methods by accurately identifying and quantifying all components to their resolution limits and solving closely spaced frequencies.
... There exist a few methods to estimate the CIR length [19], [20], [21], [22], [23], [24], [25], [26], [27], [28]. The CIR length can be estimated by using the time-domain correlation between the received signal and the pilot sequence [19], [20]. ...
... These methods, however, have a drawback that the CIR length is frequently underestimated, especially when the multipaths are sparsely spaced. The high-resolution methods such as multiple signal classification (MUSIC) [27] or compressed sensing [28] were proposed for CIR estimation, which are, however, too complicated to be used for adaptive channel estimation. ...
... Whereas the CIR length is underestimated more frequently as the threshold is raised higher, which is due to the increased miss probability for the last path. The miss probabilities of the last path for SUI-5 model are observed as 3.0 × 10 −3 , 9.1 × 10 −3 , and 1.45 × 10 −2 , for T = 5, 15, and 25 respectively, which are very close to the theoretical values calculated by (27). Fig. 5 compares the average values of the CIR length estimates obtained by SHT and SOT with T = 15 and 25 selected for SHT. ...
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This paper addresses an adaptive implementation of frequency-domain channel estimators for orthogonal frequency-division multiplexing (OFDM) systems to reduce computational complexity. The linear minimum mean-square-error (LMMSE) estimator provides optimal performance at the cost of high computational load. There are numerous approaches to achieve low-complexity channel estimation, but many of them suffer from irreducible error floor due to channel energy leakage. In this paper we present an adaptive channel estimation based on channel impulse response (CIR) length estimation. We introduce a simple and efficient method for estimating the CIR length and then apply the method to the singular value decomposition (SVD)-based low-rank approximation. Simulation results demonstrate that the proposed method for CIR length estimation is highly efficient and that the adaptive implementation of the SVD-based estimator can reduce the complexity significantly when the channel delay spread is small and also achieves a considerable performance improvement in a time-varying channel.
... Channel estimation is fundamental to wireless communications, but many works use this information for equalization [13]- [16], where the precise knowledge of multipath parameters is not crucial. Methods for high-resolution delay estimation exploit the sparse nature of MPCs, and can be classified into those based on (i) subspace estimation [17]- [19], (ii) compressive sensing (CS) [20], [21], and (iii) finiterate-of-innovation (FRI) sampling [22]- [24]. ...
... Therefore, if we can choose the design parameter P such that both LP ≥ K and Q ≥ K and if all factors in (19) are full rank, then H has rank K, the number of MPCs present in the channel. This means that from the column span of H we can estimate matrix A up to a K × K non-singular matrix T. In other words, we can write A = UT −1 , where the columns of U form a K-dimensional basis of the column space of H. ...
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In wireless networks, an essential step for precise range-based localization is the high-resolution estimation of multipath channel delays. The resolution of traditional delay estimation algorithms is inversely proportional to the bandwidth of the training signals used for channel probing. Considering that typical training signals have limited bandwidth, delay estimation using these algorithms often leads to poor localization performance. To mitigate these constraints, we exploit the multiband and carrier frequency switching capabilities of wireless transceivers and propose to acquire channel state information (CSI) in multiple bands spread over a large frequency aperture. The data model of the acquired measurements has a multiple shift-invariance structure, and we use this property to develop a high-resolution delay estimation algorithm. We derive the Cramér-Rao Bound (CRB) for the data model and perform numerical simulations of the algorithm using system parameters of the emerging IEEE 802.11be standard. Simulations show that the algorithm is asymptotically efficient and converges to the CRB. To validate modeling assumptions, we test the algorithm using channel measurements acquired in real indoor scenarios. From these results, it is seen that delays (ranges) estimated from multiband CSI with a total bandwidth of 320 MHz show an average RMSE of less than 0.3 ns (10 cm) in 90% of the cases.
... where U N is the × ( − ) L L K noise matrix whose columns are the − L K noise eigenvectors. Referring to[36], P(t) is equal to the minimum generalized eigenvalue λ min of ...
... where U N is the × ( − ) L L K noise matrix whose columns are the − L K noise eigenvectors. Referring to [36], P(t) is equal to the minimum generalized eigenvalue λ min of ...
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In civil engineering, roadway structure evaluation is an important application whichcan be carried out by ground penetrating radar. In this paper, firstly a signal modeltakes into account the inuence of interfaces roughness (surface and interlayer) isproposed. In order to estimate the time delay and interface roughness, we propose amethod composed of 2 steps: 1) a modified MUSIC algorithm is proposed for timedelay estimation; 2) the interface roughness can be estimated by using MaximumLikelihood method (MLE) with the estimated time delays. The proposed algorithmsare tested on data obtained by a method of moment (MoM). Numerical examplesare provided to demonstrate the performance of the proposed algorithm.Keywords: Ground Penetrating Radar (GPR), Time-Delay Estimation (TDE),Roughness, modified MUSIC, Method of Moment (MoM), Maximum Likelihoodmethod (MLE).
... Various techniques for decomposition of multipath signals have been proposed recently [1][2][3][4][5][6][7]. These methods are such as short-time Fourier transform, Wigner-Ville distribution, discrete wavelet transform, discrete cosine transform, chirp transform, and fractional Fourier transform. ...
... The source signal (4) is sampled with the sampling frequency ten times the signal frequency . The received multipath signal is simulated by convolving ( ) with the delayed discrete impulses: where 1 = 200, 2 = 300, 3 = 400 (all in sample unit), 1 = 1, 2 = 0.6, and 3 = 0.5. The first component is normalized already with the same scale as the source signal. ...
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Decomposition of composite multi-path signals is a complex problem. The windowing approach in the time domain cannot be used for overlapping signals. While the filtering approach in the frequency domain cannot separate the overlapping signal spectrum. One of the key solutions to this problem is to estimate the time-delay for each signal component. This study discusses techniques for separating multi-path signal components through time-delay estimation by analysing residual signal and its correlation with original signal. The residual signal is the error between the reference and the received signal. Overlapping multi-path signal components are detected in two different approaches. First, when the residual signal is random, the whiteness analysis is applied to detect the signal component. Second, when the whiteness test failed, which means the residual signal has a correlation with the reference signal, the correlation test can then be applied. The simulation results show that this proposed method successfully detected the signal components.
... In expression (25), for a given τ 1n , the estimate x^1 n of x 1n could be obtained by the least-square estimation: x^1 n τ 1n = a n H t′ z 1 = y 1n t′ (26) which corresponds to a matched filtering process (scaled by a constant). ...
... We use quadrature phase shift keying waveforms without a special optimisation. The signal subspace-based methods require that the transmitted waveforms should have a flat power spectrum to transform a single snapshot model to a multiple snapshots model to evaluate the signal subspace, either by smoothing samples or constructing a Toeplitz matrix [26]. This requirement cannot be always satisfied hence the results from the subspace-based algorithms are not presented. ...
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In a distributed coherent aperture radar, the time delay differences and the phase differences among received echoes from each pair of transmitter–receiver should be estimated and then can be compensated to realise coherent processing. Most of the existing algorithms improve the outputs of the matched filtered signals of each transmitter–receiver pair separately. In this study, a structure of equal time delay differences existing in the signal model can be exploited to jointly perform coherence parameter estimation. With this idea, a structure‐based joint estimation algorithm is presented to enhance the performance of the coherence parameter estimation. Simulation results verify that this algorithm can have better estimation performance compared with some existing algorithms in the case of low signal‐to‐noise ratios. Especially, its performance advantage is more significant in the multiple nearfield target scenarios.
... Assuming that the receiver recognizes the signal at the first sample of the preamble, the smallest possible resolution of the distance estimate is 15 m for 20 MHz bandwidth, 7.5 m for 40 MHz, and 3.74 m for 80 MHz. To allow finer resolution, the receiver uses super-resolution, maximum-likelihood or machine learning methods to allow sub-sample resolution [24][25][26]. However, such implementation details are usually not documented by the hardware manufacture, and therefore, assumed as black box. ...
... In contrast to the other two methods, a new position estimate is always obtained, even when there are no new measurements available. The position is estimated with the weighted average over all particles as in (25). The primitive transition model is used without map information. ...
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With the addition of the Fine Timing Measurement (FTM) protocol in IEEE 802.11-2016, a promising sensor for smartphone-based indoor positioning systems was introduced. FTM enables a Wi-Fi device to estimate the distance to a second device based on the propagation time of the signal. Recently, FTM has gotten more attention from the scientific community as more compatible devices become available. Due to the claimed robustness and accuracy, FTM is a promising addition to the often used Received Signal Strength Indication (RSSI). In this work, we evaluate FTM on the 2.4 GHz band with 20 MHz channel bandwidth in the context of realistic indoor positioning scenarios. For this purpose, we deploy a least-squares estimation method, a probabilistic positioning approach and a simplistic particle filter implementation. Each method is evaluated using FTM and RSSI separately to show the difference of the techniques. Our results show that, although FTM achieves smaller positioning errors compared to RSSI, its error behavior is similar to RSSI. Furthermore, we demonstrate that an empirically optimized correction value for FTM is required to account for the environment. This correction value can reduce the positioning error significantly.
... Obtaining an accurate time-delay estimate in a dense-multipath environment is challenging and requires an accurate detection of the first signal path, which is associated with the line of sight (LoS) between the two stations and estimation of its arrival time. This is implemented using either super-resolution methods [3], [4], or maximum-likelihood methods [5], applied to the estimated channel response. The channel response is estimated using training sequences of orthogonal-frequency-divisionmultiplex (OFDM) symbols with known subcarrier modulation included in the exchanged messages [2]. ...
... The accuracy of the maximum-likelihood algorithms rely on the availability of an accurate propagation channel modeling. Super-resolution algorithms, such as MUSIC (MUltiple SIgnal Classification), do not require prior knowledge of the propagation channel model, but require the knowledge of the number of channel components (paths) in advance [3], [4]. ...
Conference Paper
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Data set available below. We present a supervised, deep-learning, neural network approach for range estimation based on IEEE 802.11 wireless local area network (WLAN) round-trip timing (RTT) measurements. The range estimation accuracy is compared against a standard, time-of-arrival (TOA), maximum likelihood estimation (MLE) based range estimation. The deep learning approach is based on a “Siamese”, artificial neural network (ANN), which was trained using both indoor channel simulation, as well as actual channel measurements collected in a real, indoor office environment. Both the MLE and ANN range estimators were tested using real-channel measurements and estimation accuracy was analyzed using “ground-truth” information collected using a LiDAR system . It is shown that the ANN-based approach outperforms the accuracy achieved by the classical MLE approach. The dataset used for this paper can be found at: https://www.researchgate.net/publication/329894394_A_Machine_Learning_Approach_for_Wi-Fi_RTT_Ranging_Datasetzip
... The problem of TDE can be regarded as a special case of the harmonic retrieval problems that are well studied in the literature. Therefore, the high-resolution algorithms that were originally proposed for spectral estimation or direction-of-arrival (DOA) estimation can be applied to the TDE of closely spaced signals [2][3][4][5][6][7][8][9][10][11]. Various algorithms, such as multiple signal classification [2][3][4], estimation of signal parameters via rotational invariance techniques (ESPRIT) [5,6], maximum-likelihood (ML) method [7,8], and minimum entropy [9] were applied to achieve highresolution TDE. ...
... Therefore, the high-resolution algorithms that were originally proposed for spectral estimation or direction-of-arrival (DOA) estimation can be applied to the TDE of closely spaced signals [2][3][4][5][6][7][8][9][10][11]. Various algorithms, such as multiple signal classification [2][3][4], estimation of signal parameters via rotational invariance techniques (ESPRIT) [5,6], maximum-likelihood (ML) method [7,8], and minimum entropy [9] were applied to achieve highresolution TDE. Among them, the ML method provides the best performance but its main drawback is that it is computationally intensive due to the complicated multi-dimensional optimisation of a non-linear least squares (NLSs) criterion. ...
Article
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This study addresses the high‐resolution time delay estimation (TDE) via sparse parameter estimation methods. Two representative algorithms, Sparse Asymptotic Minimum Variance (SAMV) and SParse Iterative Covariance‐based Estimation are devised in both the time and frequency domains for application to the TDE of spread‐spectrum signals and their performances are analysed in various multipath environments. The authors also proposes the combined approach of SAMV and weighted RELAX, referred to as SAMV‐WRELAX, to reduce the computational load. Numerical examples demonstrate that the frequency‐domain approaches with a proper type of snapshots not only outperform the corresponding time‐domain approaches but also mitigate the problem of the noise correlation encountered in time‐domain processing. They also show that the computational load of SAMV‐WRELAX with a grid size of 0.1Tc decreases up to a few tenths of that of SAMV with a fine grid, e.g. a size of 0.01Tc, without any performance degradations.
... Voice echoes in line, not just the pure speech signal, it is always mixed with noise. Many of the methods developed so far, the noise by using the Gaussian model to describe more, but a lot of practical study shows that the actual telecommunication lines in the system with pulse noise often [8, 9], the classic algorithm based on Gaussian noise model is not robust, algorithm performance degradation, and can't even use [10][11][12][13][14][15]. In this paper, according to the characteristics of the noise in practical communication system, using Gaussian distribution than the more in conformity with the actual noise, stable and Robust α distribution to describe the noise, Echo in minimum average p Norm (further Mean p Norm, LMP) criterion, design a kind of impulse noise Robust Adaptive Line Echo Canceller (Robust Adaptive Line Echo Canceller, RALEC). ...
Article
In the actual communication system, the line echo is a frequent problem, so the line echo canceller is necessary. Traditionally, the cancellers are designed according to line noises based on the Gaussian noise model. However, the noises do not obey the Gaussian distribution; therefore the performances of algorithms decrease, even cannot be used. In order to solve this problem, this paper proposes a line echo canceller based on alpha stable distribution model. The Method in this line echo canceller has Robust and Adaptive. Alpha stable distribution modeling impulse noise, and under the rule of minimum average p norm, adaptive time delay estimator offsets the echo. This method can not only effectively offset the line echo with the Gaussian noise, but also to have the effect of good to echo with impulse noise. Theoretical analysis and computer simulation experiments show that it is very kind of the line echo canceller. It is robust to impulse noises and adaptive to echo cancellation.
... where J inv = J −1 . Applying L = 1 and h = 1, the CRLB of the estimated ToA over the AWGN channel can be represented by formerly discussed equation in [3] and [7] as follow (see Appendix D for details): ...
Article
This paper introduces a novel method to improve the Time of Arrival (ToA) estimation resolution for a fixed available bandwidth in the presence of unknown multipath frequency selective (MPFS) channels. Here, the maximum rising level detector (MRLD) technique is proposed which utilizes oversampling and multiple correlation paths to evaluate with high resolution the path corresponding to the maximum rising level of matched filters output. However, employing such technique demands for transmission of waveform that creates a very high rising level at autocorrelation center. This paper proposes an efficient technique to design proper waveforms (very high rising level at autocorrelation center) via minimization of weighted integrated sidelobe level (WISL), exploiting the trust-region algorithm. The performance of the proposed technique is evaluated via simulations of the ToA mean square error (MSE), and compared to the state-of-the-art approaches considering the same bandwidth, and Cramer-Rao lower bound (CRLB) as benchmark. Simulations confirm that the ToA resolution is improved as the number of correlation paths increases and verify the feasibility of the proposed technique compared to the available approaches for the MPFS channels.
... The hardware-imposed latency (e.g. the receive/transmit filters' group-delay and other hardware latencies), is measured and pre-calibrated by the chipset in order to reach the required timing resolution. Obtaining an accurate time delay estimate in a dense-multipath environment is typically implemented using some super-resolution method , which are applied to the estimated channel response, [9], [10]. FTM is a point-to-point (P2P), single-user protocol, which includes an exchange of multiple message frames between an initiating WLAN station (STA) and a responding STA. ...
Article
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Collaborative time of arrival (CToA) is the next generation, indoor geolocation protocol, which is designed for enabling scalability of the existing IEEE802.11/Wi-Fi-based, geolocation systems. The protocol leverages on the IEEE802.11 fine timing measurements (FTM) capabilities, enabled in state-ofthe-art Wi-Fi chipsets, and supports two concurrent operation modes; the CToA “client-mode” enables “GPS-like” operation indoors, and allows an unlimited number of clients to privately estimate their position and navigate indoors, without exposing their presence to the network. The CToA “network-mode” is designed for large-scale asset-tracking applications, and enables a centric positioning server to pinpoint objects equipped with wireless, Wi-Fi-based, low-power electronic tags (e-Tags). The CToA protocol is a broadcast-based protocol that operates over an un-managed network, built out of cheap, unsynchronized units called “CToA broadcasting stations” (bSTA). The bSTAs, which are stationed at known locations, periodically broadcast a unique beacon transmission and publish its time of departure (ToD). Neighbor bSTA units and clients that receive the beacon broadcast, measure and log its time of arrival (ToA). Every bSTA publishes its most recent timing measurement log as part of its next beacon broadcast. CToA clients combine their own ToA measurements with those published by the bSTAs, in order to estimate and track their location. CToA e-Tag clients act similar to bSTAs, and simply wake-up sporadically to broadcast a CToA beacon. The ToA of that broadcast is measured and logged by the receiving bSTAs similarly to beacons broadcast by other bSTAs. The timing measurement report is then delivered to a centric positioning server that can estimate and track the location of numerous CToA-based e-Tags, simultaneously. The paper outlines the principles of the CToA protocol and the mathematical background of the position estimation algorithms. In addition, performance examples as well as theoretical analysis of the expected positioning accuracy are provided.
... The key technique of location finding based on TOA method is to estimate the propagation delay of the radio signal arriving from the direct line-of-sight (DLOS) propagation path accurately. The existing TOA methods mainly include cross-correlation method [1], multiple signal classification (MUSIC) algorithm [2], delay estimation algorithm based on Markov Monte Carlo [3], propagator algorithm [4], and matrix pencil algorithm [5]. If the array antenna can be used to obtain the signal DOA for joint estimation [6,7], then it will effectively reduce the number of nodes and system overhead of the localization system. ...
Article
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The estimation speed of positioning parameters determines the effectiveness of the positioning system. The time of arrival (TOA) and direction of arrival (DOA) parameters can be estimated by the space-time two-dimensional multiple signal classification (2D-MUSIC) algorithm for array antenna. However, this algorithm needs much time to complete the two-dimensional pseudo spectral peak search, which makes it difficult to apply in practice. Aiming at solving this problem, a fast estimation method of space-time two-dimensional positioning parameters based on Hadamard product is proposed in orthogonal frequency division multiplexing (OFDM) system, and the Cramer-Rao bound (CRB) is also presented. Firstly, according to the channel frequency domain response vector of each array, the channel frequency domain estimation vector is constructed using the Hadamard product form containing location information. Then, the autocorrelation matrix of the channel response vector for the extended array element in frequency domain and the noise subspace are calculated successively. Finally, by combining the closed-form solution and parameter pairing, the fast joint estimation for time delay and arrival direction is accomplished. The theoretical analysis and simulation results show that the proposed algorithm can significantly reduce the computational complexity and guarantee that the estimation accuracy is not only better than estimating signal parameters via rotational invariance techniques (ESPRIT) algorithm and 2D matrix pencil (MP) algorithm but also close to 2D-MUSIC algorithm. Moreover, the proposed algorithm also has certain adaptability to multipath environment and effectively improves the ability of fast acquisition of location parameters.
... In the ''information-fusion'' step, the position of the target source is estimated by solving a set of nonlinear equations. 16 Over the past decades, WSN as a significant technology has attracted considerable research interest. 17,18 Due to small size, low cost, wireless network, and deployment in large numbers, WSN can provide unprecedented opportunities for information collection, monitoring, and device control. ...
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Passive localization of the wireless signal source attracts a considerable level of research interest for its wide applications in modern wireless communication systems. To accurately locate the signal source passively in the downtown area, sensors are carried on the unmanned aerial vehicles flying in the air, where the wireless sensor network can be established with an optimal geometry configuration conveniently. In this case, the influence of multipath fading can be avoided and the time difference of arrival measurement can be estimated precisely in Rician channel. By employing the operating center as a calibration source to refine the positions of the unmanned aerial vehicles, we present a simplified formulation of the time difference of arrival localization method according to the min-max criterion. To accurately estimate the position of the source, the nonlinear equations are relaxed using semidefinite programming to obtain an initial solution, which is utilized as the starting point of the iterative algorithm to refine the solution. In the simulation section, the validity and the robustness of the proposed methods are verified through the performance comparison with the Cramer–Rao lower bound.
... Obtaining an accurate time-delay estimate in a dense-multipath environment is challenging and requires an accurate detection of the first signal path, which is associated with the line of sight (LoS) between the two stations and estimation of its arrival time. This is implemented using either superresolution methods [7], [8], or maximumlikelihood methods [9], applied to the estimated channel response. The channel response is estimated using training sequences of orthogonal frequency-division multiplexing (OFDM) symbols with known subcarrier modulation included in the exchanged messages [3]. ...
Article
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This paper presents a protocol that enables an unlimited number of Wi-Fi users to position themselves within a meter-level accuracy and navigate indoors using time-delay-based Wi-Fi measurements. The proposed protocol, called collaborative time of arrival, is broadcast-based and relies on cooperation between the network sensors that support IEEE 802.11 fine-timing measurements (FTMs) capabilities, which are enabled in state-of-the-art Wi-Fi chipsets. The clients can estimate and track their position by passively listening to timing measurements that are exchanged between the FTM-sensors. The passive nature of the clients' operation enables them to maintain their privacy by not exposing their presence to the network. This paper outlines the principles of the protocol and the mathematical background of the position estimation algorithms. Both theoretical analysis of the expected positioning accuracy, as well as real-life system performance examples, are provided. The protocol's performance analysis is based on a publicly available database of real network measurements. **************************************************************************************** **************************************************************************************** Full text is freely available at https://ieeexplore.ieee.org/document/8579543 ****************************************************************************************
... Theorem 2. P md of the proposed E2E PLA scheme in a dualhop wireless network with an untrusted relay can be given in (38). ...
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End-to-end (E2E) physical layer authentication for multi-hop wireless networks is still not well-explored by now. As one step forward in this direction, this paper focuses on the E2E physical layer authentication in a dual-hop wireless network with an untrusted relay and proposes a corresponding physical layer authentication scheme. The scheme fully utilizes the location-specific features of both channel amplitude and delay interval of cascaded channels, and adopts the artificial jamming technique, so that it is not only resistant to the impersonate attack from an unauthorized transmitter but also resilient to the replay attack from the untrusted relay. Theoretical analysis is further conducted to derive the expressions for the probabilities of false alarm and missed detection, which are two fundamental metrics of authentication performance. Finally, numerical and simulation results are provided to illustrate both the efficiency of these theoretical results and the E2E authentication performance of dual-hop wireless networks under the proposed scheme.
... In [17], a TDE method based on ML is proposed for application in multipath environments. In order to overcome the influence of multipath enviroments, a kind of super-resolution TDE method is proposed on the basis of subspace decomposition [18,19] inspired by multiple signal classification (MUSIC) [20,21]. In [22], a field programmable gate array (FPGA) implementation is introduced based on TDOA, which is suitable for multipath environments. ...
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Without the estimation of the intermediate parameters, the direct position determination (DPD) method can achieve higher localization accuracy than conventional two-step methods. However, multipath environments are still a key problem, and complex high-dimensional matrix operations are required in most DPD methods. In this paper, a time-difference-of-arrival-based (TDOA-based) DPD method is proposed based on the subspace orthogonality in the cross-spectra between the different sensors. Firstly, the cross-spectrum between the segmented received signal and reference signal is calculated and eigenvalue decomposition is performed to obtain the subspaces. Then, the cost functions are constructed by using the orthogonality of subspace. Finally, the location of the radiation source is obtained by searching the superposition of these cost functions in the target area. Compared with other DPD methods, our proposed DPD method leads to better localization accuracy with less complexity. The superiority of this method is verified by both simulated and real measured data when compared to other TDOA and DPD algorithms.
... The transmitted signal is: x(0), x(T s ), · · · , x(kT s ), · · · , k = 1, 2, 3, · · · N, where N is the number of consecutive samples, the sampling interval is T s , and the measurement time is N × T s . Under the underwater acoustic multipath channel, the received signal can be assumed to be a linear superposition of multipath signals [19]. The discrete time model of the received signal is: ...
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This paper proposes underwater acoustic time delay estimation based on the envelope differences of correlation functions (EDCF), which mitigates the delay estimation errors introduced by the amplitude fluctuations of the correlation function envelopes in the traditional correlation methods (CM). The performance of the proposed delay estimation method under different time values was analyzed, and the optimal difference time values are given. To overcome the influences of digital signal sampling intervals on time delay estimation, a digital time delay estimation approach with low complexity and high accuracy is proposed. The performance of the proposed time delay estimation was analyzed in underwater multipath channels. Finally, the accuracy of the delay estimation using this proposed method was demonstrated by experiments.
... In the first step, the physical parameters of the transmitted signals are measured. In the second step, the system determines the transmitter's position based on the results that were obtained in the first step.Both of these steps have attracted considerable research interest over the past few decades [2][3][4][5] . ...
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... Time delay resolution is associated with the frequency band of the transmitted signal. Generally, a wideband signal provides a high resolution in time delays, such that time delay estimates may be accurately achieved with super-resolution methods [31,32]. In the time delay estimation procedure, two similar estimated values may appear sometimes, particularly in cases with low SNRs. ...
Preprint
Direct blast is a strong interference in bistatic sonar and difficult to suppress due to multipath propagation for blasts and signals. A generalized likelihood ratio test (GLRT) based detection scheme in the frequency domain of the received signals is proposed in this study, and the unknown parameters are estimated using Maximum Likelihood Estimates and Weighted Fourier Transform and Relaxation in a multipath environment. The distributions of the test statistic of detectors for known and unknown noise power are given in theory, and the detection probability is determined. The performance of the detector decreases by 4 dB when the noise power is evaluated with maximum likelihood estimates. Simulations show the effectiveness of the detector under a forward scattering detection configuration with a low signal-to-direct blast ratio. The sensitivity of many factors is discussed, and robustness is achieved.
... Several super-resolution methods are used, such as MUSIC, ESPRIT, and pencil matrix [19][20][21][22][23][24][25][26]. These are based on specific assumptions about the transfer function of the communication channel. ...
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... where p, q ∈ 0, · · · , K 2 − 1 . Based on the eigendecomposition ofRz, the signal and noise subspaces can be separated [2], [4], [8]. Under the assumption of high signal-to-noise ratio (SNR) and uncorrelated noise, the signal subspace is spanned by the eigenvectors corresponding to the L largest eigenvalues, whereas the noise subspace is spanned by the remaining K 2 −L eigenvectors corresponding to the least eigenvalues, which are, under the high SNR assumption, much smaller than the eigenvalues corresponding to the signal subspace. ...
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We present an analysis of a "spatial smoothing" preprocessing scheme, recently suggested by Evans et al., to circumvent problems encountered in direction-of-arrival estimation of fully correlated signals. Simulation results that illustrate the performance of this scheme in conjunction with the eigenstructure technique are described.
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A computationally efficient algorithm for parameter estimation of superimposed signals based on the two-step iterative EM (estimate-and-maximize, with an E step and an M step) algorithm is developed. The idea is to decompose the observed data into their signal components and then to estimate the parameters of each signal component separately. The algorithm iterates back and forth, using the current parameter estimates to decompose the observed data better and thus increase the likelihood of the next parameter estimates. The application of the algorithm to the multipath time delay and multiple-source location estimation problems is considered
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This paper suggests a method to improve the resolution of estimation of time delay for narrow band by using the autoregressive method. The principle and performance analysis of this method is presented. Finally some preliminary results of computer simulation are given.
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The Cramer-Rao bound (CRB) for the time delays of closely spaced echoes is derived. It is shown that the variance of the i th echo delay estimate depends on the relative delays of all other echoes, but not on their amplitudes. This results from the restriction that the estimator must be unbiased. A single replica correlation algorithm is suggested for the case of two echoes with highly unequal amplitudes, and its performance is evaluated. For echo spacings below some threshold, the estimate for the dominant echo is slightly biased, but its mean square error is significantly lower than the CRB. The estimation of the weak echo is discussed
Conference Paper
The capabilities of the multiple signal classification (MUSIC) algorithm have been enhanced by development of two techniques to allow the algorithm to operate on a single snapshot, such as phased array radar, and at a much lower computational cost than previously possible. This paper derives the extensions applicable to a uniform linear array, and implements the algorithms on simulated data. The results are discussed and evaluated against previous variants of MUSIC
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The problem of estimating the frequency of the sinusoidal signals with low pass envelopes in the presence additive white Gaussian noise is addressed. A super-resolution frequency estimator based on the eigenanalysis and quadratic programming is proposed. The frequency estimation is achieved from the single experiment data without a priori knowledge of the lowpass envelop, which is omnipresent in many applications. The performance studies, which include the theory analysis, the numerical simulations of the mean square errors (MSEs) of the frequency estimates compared with the Cramer-Rao bound (CRB), the comparisons between the proposed method and the other representative methods, are presented.
Conference Paper
In this paper, the frequency estimation of the sinusoidal signals with unknown lowpass envelope is addressed. Due to mismodeling, the performance of the conventional subspace-based method degrades significantly in these cases. By developing the method applied to the parametric localization of distributed sources, an eigenanalysis-based method is proposed for the frequency estimate. The comparisons of the proposed method and the nonlinear least-squares (NLS) approach with each other as well as the Cramer-Rao bound (CRB), are presented. The simulations illustrate the good performance in the precision and super-resolution.
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This paper addresses a new approach to time-delay estimation based upon the autocorrelation estimator (AE). The primary aim of this paper is to estimate time-delays in a multipath environment in absence of prior knowledge of the channel. The maximum likelihood estimator (MLE) and AE are two computational tools that are used to determine the parameters of a multipath channel. MLE requires some priori knowledge of the source signal and the channel; AE can be a blind estimator but it is more suitable for a simple propagation model (one extra path). Under the multipath assumption we prove that if the observation sequence is zero padded the performance of MLE exceeds that of AE, however, at the price of higher computational efforts. The general autocorrelator estimator (GAE), based on autocorrelation of the received signal, is introduced. The GAE is formulated as a blind estimator, and the pertinent Cramer-Rao lower bounds (CRLB) are derived. We also develop an algorithm to estimate the parameters of a multipath environment based on the new generalization. The performance of this algorithm is examined for different signal-noise scenarios. Our results show that the time-delays are estimated accurately based on the proposed algorithm.
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The problem of estimating multiple time delays in presence of colored noise is considered. This problem is first converted to a high-resolution frequency estimation problem. Then, the sample lagged covariance matrices of the resulting signal are computed and studied in terms of their eigenstructure. These matrices are shown to be as effective in extracting bases for the signal and noise subspaces as the standard autocorrelation matrix, which is normally used in MUSIC and the pencil-based methods. Frequency estimators are then derived using these subspaces. The effectiveness of the method is demonstrated on two examples: a standard frequency estimation problem in presence of colored noise and a real-world problem that involves separation of multiple specular components from the acoustic backscattered from an underwater target
Article
In a parametric multipath propagation model, a source is received by an antenna array via a number of rays, each described by an arrival angle, a delay, and a fading parameter. Unlike the fading, the angles and delays are stationary over long time intervals. This fact is exploited in a new subspace-based high-resolution method for simultaneous estimation of the angle/delay parameters from multiple estimates of the channel impulse response. A computationally expensive optimization search can be avoided by using an ESPRIT-like algorithm. Finally, we investigate certain resolution issues that take the fact that the source is bandlimited into account
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In this correspondence, the MUSIC and ESPRIT frequency estimates of sinusoidal signals with lowpass envelopes are analyzed. To achieve computational simplicity, the frequency estimation is conducted as if the signal had a constant amplitude. The aim of the correspondence is to analyze the degradation of performance induced by the aforementioned mismodeling. Unified expressions for the bias and variances of the MUSIC and ESPRIT frequency estimators are derived under the hypothesis of small bandwidth of the signal envelope. Numerical simulations illustrate the agreement between theoretical and empirical results and study the influence of the envelope bandwidth on the frequency estimation performance
Article
Two different high-resolution time-delay estimation (HRTDE) methods, a temporal method and a frequency method, specially adapted to large bandwidth duration (BT) product time-resolvent signals, are described. The performance gain of these methods is shown to be about four times better in comparison with the classical time-delay resolution methods. The frequency HRTDE method is applied to real data obtained from an ocean acoustic experiment. Although classic methods cannot distinguish close signal components, the method presented yields estimates of the delay differences and the attenuation associated with each propagation path
Sonar and radar systems not only detect targets but also localize them. The process of localization involves bearing and range estimation. These objectives of bearing and range estimation can be accomplished actively or passively, depending on the situation. In active sonar or radar systems, a pulsed signal is transmitted to the target and the echo is received at the receiver. The range of the target is determined from the time delay obtianed from the echo. In passive sonar systems, the target is detected from acoustic signals emitted by the target, and it is localized using time delays obtained from received signals at spacially separated points. Several authors have calculated the variance of the time delay estimate in the neighborhood of true time delays and have presented their results in terms of coherence function and signal and noise autospectra. These derivations are analyzed, and it is shown that they are the same for the case of low snr.
A maximum likelihood (ML) estimator is developed for determining time delay between signals received at two spatially separated sensors in the presence of uncorrelated noise. This ML estimator can be realized as a pair of receiver prefilters followed by a cross correlator. The time argument at which the correlator achieves a maximum is the delay estimate. The ML estimator is compared with several other proposed processors of similar form. Under certain conditions the ML estimator is shown to be identical to one proposed by Hannan and Thomson [10] and MacDonald and Schultheiss [21]. Qualitatively, the role of the prefilters is to accentuate the signal passed to the correlator at frequencies for which the signal-to-noise (S/N) ratio is highest and, simultaneously, to suppress the noise power. The same type of prefiltering is provided by the generalized Eckart filter, which maximizes the S/N ratio of the correlator output. For low S/N ratio, the ML estimator is shown to be equivalent to Eckart prefiltering.
The performance of the MUSIC and ML methods is studied, and their statistical efficiency is analyzed. The Cramer-Rao bound (CRB) for the estimation problems is derived, and some useful properties of the CRB covariance matrix are established. The relationship between the MUSIC and ML estimators is investigated as well. A numerical study is reported of the statistical efficiency of the MUSIC estimator for the problem of finding the directions of two plane waves using a uniform linear array. An exact description of the results is included
The resolution limits to multipath time delay estimation for broadband random signals are examined. First, appropriate Cramer-Rao lower bounds (CRLBs) are derived to establish baseline performance for unbiased estimation. The bounds are then compared to computer simulation results. For the two-path case, a maximum-likelihood estimator is implemented, while for the three-path case, the modified forward-backward linear prediction algorithm developed for high-resolution frequency estimation is used. It is shown that both of these techniques can achieve performance close to the appropriate CRLB; in particular, reliable multipath estimation can be achieved even when the multipath time delays are much closer than could be resolved by conventional autocorrelation processing. A criterion is developed for predicting when the bound is no longer reachable. It is shown that even relatively poor a priori knowledge of the attenuation can significantly help the estimate of time delay for small delays
Article
Processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions. The general problem considers sensors with arbitrary locations and arbitrary directional characteristics (gain/phase/polarization) in a noise/interference environment of arbitrary covariance matrix. This report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution. A description is given of the multiple signal classification (MUSIC) algorithm, which provides asymptotically unbiased estimates of 1) number of incident wavefronts present; 2) directions of arrival (DOA) (or emitter locations); 3) strengths and cross correlations among the incident waveforms; 4) noise/interference strength. Examples and comparisons with methods based on maximum likelihood (ML) and maximum entropy (ME), as well as conventional beamforming are included. An example of its use as a multiple frequency estimator operating on time series is included.
Article
Time resolution of multipath delay profiles measured by using the autocorrelation of a pseudonoise (PN) code sequence is generally limited by the chip interval of the PN code sequence. A superresolution PN correlation method (SPM) is proposed which improves the time resolution of delay profiles measured by the conventional PN correlation method. The SPM is based on a decomposition of the eigenvector space of the correlation matrix of the delay profile data vector and gives the number of paths and their delay times with higher resolution. It is verified by computer simulations and experiments using coaxial delay lines that the SPM can resolve two paths with a delay difference of a few tenths of the chip interval. The applicability of the SPM to the analysis of an indoor multipath environment in which many delayed waves arrive with short delay differences is demonstrated by an indoor radio propagation experiment at 2.3 GHz
A new time-delay estimation in multipath IEEE Communications Society 11251125 0-7803-8344-3/04/$20.00 © 2004 IEEE0-7803-8344-3/04/$20
  • P P Moghaddam
  • H Amindavar
  • R L Kirlin
P. P. Moghaddam, H. Amindavar, and R. L. Kirlin, “A new time-delay estimation in multipath,” IEEE Trans. SP, vol. 51, no. 5, pp. 1129-1142, 2003. WCNC 2004 / IEEE Communications SocietyWCNC 2004 / IEEE Communications Society 11251125 0-7803-8344-3/04/$20.00 © 2004 IEEE0-7803-8344-3/04/$20.00 © 2004 IEEE
The Parameter Estimation for Wireless Location in Cellular Communication System
  • F X Ge
F. X. Ge, The Parameter Estimation for Wireless Location in Cellular Communication System, Ph.D dissertation, Tsinghua University, 2003.
Extending MUSIC to single snapshot and on line direction finding applications
  • Q S Ren
  • A J Willis
Q. S. Ren and A. J. Willis, "Extending MUSIC to single snapshot and on line direction finding applications," IEE Conference Publication, Radar 97, pp. 783-787.