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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]. ...

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: ...

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) ...

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. ...

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. ...

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. ...

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 ...

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. ...

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. ...

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. ...

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]. ...

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. ...

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). ...

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): ...

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. ...

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. ...

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. ...

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]. ...

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.
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Full text is freely available at
https://ieeexplore.ieee.org/document/8579543
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... Theorem 2. P md of the proposed E2E PLA scheme in a dualhop wireless network with an untrusted relay can be given in (38). ...

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. ...

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: ...

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] . ...

We focus on the Direct position determination (DPD) of a moving narrowband source based on Doppler frequency shifts of signals with known waveforms. Two common motion models are considered: the Constant velocity (CV) model and the Constant acceleration (CA) model. The DPD cost function is obtained after some algebraic manipulations using the Maximum likelihood (ML) criterion. To develop a computationally efficient optimization algorithm, we present a preliminary mathematical result that plays a fundamental role in development of the proposed algorithm. Subsequently, a Newton iterative algorithm is tailored to the two motion models to determine the moving transmitter's trajectory. When compared with multidimensional grid searching, the proposed algorithm is more computationally attractive without compromising its estimation accuracy. Simulation results confirm the superiority of the proposed algorithm.

... 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. ...

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. ...

Determination of indoor position based on fine time measurement (FTM) of the round trip time (RTT) of a signal between an initiator (smartphone) and a responder (Wi-Fi access point) enables a number of applications. However, the accuracy currently attainable—standard deviations of 1–2 m in distance measurement under favorable circumstances—limits the range of possible applications. An emergency worker, for example, may not be able to unequivocally determine on which floor someone in need of help is in a multi-story building. The error in position depends on several factors, including the bandwidth of the RF signal, delay of the signal due to the high relative permittivity of construction materials, and the geometry-dependent “noise gain” of position determination. Errors in distance measurements have unusal properties that are exposed here. Improvements in accuracy depend on understanding all of these error sources. This paper introduces “frequency diversity,” a method for doubling the accuracy of indoor position determination using weighted averages of measurements with uncorrelated errors obtained in different channels. The properties of this method are verified experimentally with a range of responders. Finally, different ways of using the distance measurements to determine indoor position are discussed and the Bayesian grid update method shown to be more useful than others, given the non-Gaussian nature of the measurement errors.

... 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. ...

Utilizing the sparsity of the clutter time delay, a novel clutter cancellation method based on sparse representation is proposed to improve the cancellation performance when fractional time delay exists in the clutter of the surveillance signals. The proposed method performs the cancellation by transforming the clutter cancellation problem to the sparse signal reconstruction problem, in which the spectrum division technique is introduced to establish the signal model of the clutter time delay measurement. Taking advantage of the sparse representation theory, high estimation accuracy and resolution of the time delay are achieved in the proposed method. The simulation results prove that compared with the traditional methods, the proposed method improves the clutter cancellation and weak target detection performance when there exists clutter with fractional time delay at low signal-to-noise ratio.

Time delay estimation is of great significance in multipath propagation to recover overlapped signals and identify the channel characteristics. However, achieving a high accuracy in this purpose may pose many problems in ultra-wideband (UWB) applications. In UWB systems, capturing a signal with high sampling rates cannot readily be done; hence classical methods for time delay estimation substantially lose their precision. To overcome this challenge, the authors incorporate a robust estimation approach and supplementary sampling process in a unified algorithm to retrieve time delays from signals with low sampling rates. Toward that pursuit, a model based least squares estimator is proposed as the main approach to calculate time delays and a modified method based on multiple signal classification (MUSIC) is also presented for comparison aim. Then, the authors have developed the algorithm by embedding two additional pre-processing steps of under sampling and interpolation to achieve a higher sampling rate and a better resolution. To show the high accuracy of work, root mean square error is computed in different values of time delay. Simulation and experiment results show the considerably higher precision of the proposed algorithm in comparison with presented MUSIC type method and also previously proposed methods in literature.

The purpose of this article is to identify differences in the perception of the US foreign and security policy by the first and the second Bush presidency. Due to the fact that both presidencies of George W. Bush were strongly influenced by neoconservative view on the US role in the World, the first chapter is dedicated to the impact of neoconservativism on foreign and security policy of President George W. Bush. Finally, it introduces reader to basic principles of President's Bush foreign and security policy implemented after September 11 terrorist attacks. The second chapter is the core chapter. It compares two major documents of Bush Administrations, which materialized his foreign and security policies. These are National Security Strategy 2002 and National Security Strategy 2006.

The estimation of the time differences of arrival (TDOAs) is significant in passive source localisation systems. The TDOA estimation accuracy may directly affect the source location performance. For co-frequency interference environments, the authors address the problem of the passive blind estimation of time-delays for uncorrelated interference source signals based on wireless sensor networks. The received mixtures at the sensors are modelled as unknown linear combinations of the differently delayed versions of the communication signal and the interference signal. Blind source separation and secondary interference signal extracting are both introduced in the proposed method. The interference signals in the mixed receiving signals of all the sensors are extracted effectively and the effect of the mixed communication signals can be significantly reduced. Simulations show that the proposed method has a more accurate performance compared to other TDOA estimation methods, and is therefore valid and practical in the TDOA localisation systems.

The time delay estimation of the TDOA is signification in passive source localization systems, and the estimation accuracy may directly affect the source location performance. We address the problem of passive blind estimation of time-delay for uncorrelated co-frequency interference source signal based on wireless sensor network (WSN). The received mixtures are modeled as unknown linear combinations of differently delayed versions of communication signal and interference signal. Two methods of Blind Source Separation (BSS) and Secondary Interference Signal Extracting (SISE) are introduced in the proposed method. The interference signals in the mixed receiving signals of all sensors are extracted effectively and the affection of the mixed communication signals can be significantly reduced. Simulations results demonstrate that the proposed method has a more accurate performance compared to some other time delay estimation methods.

This paper introduces a novel and effective ranging approach in nonhomogeneous (NH) media consisting of frequency dispersive submedia via time-of-arrival (ToA). Here, the NH environment consists of sublayers with a specific thickness that is estimated throughout the ranging process. First, a novel technique for ToA estimation in the presence of frequency dispersive submedia via orthogonal frequency division multiple access subcarriers is proposed. In the proposed technique, preallocated orthogonal subcarriers are utilized to construct a ranging waveform that enables high-performance ToA estimation in dispersive NH media in the frequency domain. The proposed ToA technique is exploited for multiple ToA measurements at different carrier frequencies, which leads to a system of linear equations that can be solved to compute the thickness of the available submedia and calculate the range. Simulation results for underwater-airborne media and underground channel confirm that the proposed technique offers high-resolution ranging at different signal to noise ratio regimes in the NH media.

The passive synthetic aperture antenna array (PSAAA) technology is inspired by the idea of synthetic aperture sonar and synthetic aperture radar, which is a new method used to the passive radar source localization using only one small aircraft. Virtual time difference of arrival (VTDOA) estimation is critical for the PSAAA technology, it is defined as the time difference of the radar pulse transmission from the radar source position to different virtual receivers, where the virtual receivers are the flight track position of the small aircraft at different flight time. In this paper, we present three different algorithms of curve fitting to approximate the main-beam pattern of the radar antenna, then the VTDOA can be estimated using the corresponding time of the peak of the curve. The simulation results show that the second-order polynomial of the least squares (LS) curve fitting algorithm is the optimal method to approximate the main beam pattern of the radar antenna at the receiver, which also is the optimal method to be used in the VTDOA estimation.

The evolution of ElectroMagnetic (EM) models and modern EM solvers permit resolving a variety of real-life EM propagation and radiation problems, in which antenna design and optimization account a large proportion. However, understanding of EM propagation processes on antenna structures and design achievements can be limited when only total antenna responses are considered and there is lacking of near-field analysis. This chapter provides a better insight into the EM propagation processes on traveling-wave antennas. A near-field propagation analysis method is proposed based on simulated near-field data with corresponding meshed structure data. This overcomes the insufficiencies and obstacles for observation of the conventional analysis methods. The EM-solver-run optimization and accurate sampling for field and structure data are the first important steps for the analysis. For general propagation problems such as paths recognition and characterization of the propagation , the EM signal models, impulse response analysis and super-resolution algorithms for Time of Arrival (ToA) estimation are studied and proposed. A particular space/time/frequency analysis is implemented for traveling-wave Vivaldi antennas, in which the phenomenon of EM energy transfer out of the conducting elements into the free space and higher-order scattering processes are revealed. The refined adjustment and optimization for the antennas are also proposed.

In the ice-covered underwater environment of the Arctic area, impulsive noise is one of the most challenging problems for target echo time-delay estimation (TDE) and severely degrades the performance of some so-called traditional TDE algorithms. In this work, we propose a TDE approach called “ℓp-norm-based correlation,” which is explored for use in active sonar systems in an impulsive environment. The ℓp-norm-based optimization is presented here to improve the robustness, and we introduce the Toeplitz matrix to formulate the received signal. The different columns of the desired matrix represent the various time-delay replicas of the transmitted signal, and the global minimizer can be found by rewriting the optimization problem. Thus, all global minimizers are efficiently solved simultaneously. The proposed TDE technique can enhance time-delay resolution and provide reliable estimation results compared with conventional matched filtering and other competing approaches. Furthermore, we show that the performance of the resulting method can be verified by the results of numerical simulation and by comparison with the experimental data collected from the 11th Chinese National Arctic Research Expedition.

Massive connectivity in the near future puts forward an urgent demand for the accurate time delay estimation (TDE). However, the accuracy of the traditional TDE methods is severely degraded by the multi-path interference (MPI) and multi-device interference (MDI). In this paper, we propose a path integration based delay estimation (PRIDE) method. For the first time, the unique delay structure of each device is utilized, and the MPI is converted to an assistance. Considering the practical case where multi-path delays are non-integer times of the sampling period, PRIDE is carried out in two steps to estimate the integer and fractional parts of the delay sequentially. Theoretical analysis and simulations show that the TDE accuracy in the multidevice multi-path environment can be greatly improved by the proposed PRIDE method with comparatively low computational complexity.

Refined optimisation of complex curve-linear shaped
radiators, such as travelling wave Vivaldi antennas, can be
achieved by considering simulated near-fields to interpret in
detail the structural influences of a design. The relationships
between space- and time- distributions of electromagnetic (EM)
energy clusters and the geometric features are revealed with
appropriate use of impulse response analysis combined with
the MUSIC algorithm. This article reports a deeper approach
when applied to the adjustment of the geometric features of
a travelling wave antenna based on analysis of near-fields
propagation features.

Determination of indoor location based on fine time measurement (FTM) of the round trip time (RTT) of a signal between an initiator (smartphone) and a responder (Wi-Fi access point) enables a number of applications. However, the accuracy currently attainable — standard deviations of 1–2 meter in distance measurement under favorable circumstances — limits the range of possible application. A first responder, for example, may not be able to unequivocally determine on which floor someone in need of help is in a multi-story building. The error in location depends on several factors, including the bandwidth of the RF signal, delay of the signal due to the high relative permittivity of construction materials, and the geometry-dependent “noise gain” of location determination. Errors in distance measurements have unusual properties that are exposed here for the first time. Improvements in accuracy depend on understanding all of these error sources. This paper introduces “frequency diversity,” a method for doubling the accuracy of indoor location determination using weighted averages of measurements with uncorrelated errors obtained in different channels. The properties of this method are verified experimentally with a range of responders. Finally, different ways of using the distance measurements to determine indoor location are discussed and the Bayesian grid update method shown to be more useful than others, given the non- Gaussian nature of the measurement errors.

This thesis presents an original solution for extracting, from OFDM communication signals, the information related to the time difference of arrival (TDOA) between two closed transmitters and one receiver. This solution, which shows to be super-resolution, makes it possible to extract TDOA below the Rayleigh limit set by the useful bandwidth.Inthis work, we perform, using a Multiple Inputs Simple Output, channel characterization and modeling for TDOA estimation. By handling these channel frequency responses in different ways, xe minimize different cost functions expresses as the difference between measured channel response and a predefined direct model. For validation, the simulation based on different topologies exhibit results is compared to the Cramer Rao Lower Band. The effects of the multipath are taken into account and some proposed solutions are discussed ans simulated. Moreover, the experimental part of this work validates the direct and inverse models in different channel configurations.

In this paper, frequency estimation of sinusoidal signals in multiplicative and additive noise is addressed. Based on the parametric localization of distributed sources and theminimax theorem, an eigenanalysis-based frequency estimator is proposed. Furthermore, we present processing and analysis for pseudofrequency estimates in the proposed method. Especially, a priori knowledge ofmultiplicative noise is not required as compared with the distributed signal parameter estimator (DSPE). Monte Carlo experiments are carried out to evaluate performance. Simulation results confirm that the proposed method provides better performance than the nonlinear least squares (NLS) approach and the conventional MUSIC algorithm for separating closely spaced sinusoidal signals in multiplicative and additive noise.

The problem of estimating the DOA of spatially distributed signals
is examined. A mathematical model is first established by making some
reasonable assumptions. The correlation matrix of a distributed signal
is then derived. The important properties of the correlation matrix are
studied, revealing that even if the matrix is of full rank (being equal
to the number of sensors), which renders conventional high resolution
array processing methods inapplicable, the dimensionality of the signal
subspace can be approximated to a number usually much smaller than the
number of sensors. From the observation, the quasi-signal and noise
subspaces are identified, and, utilising the orthogonality of the signal
and noise subspaces, an algorithm (DISPARE) has been developed. Analytic
studies and numerical evaluations are carried out to examine the
performance of the algorithm under various environments and show that it
is indeed effective

The quintessential goal of sensor array signal processing is the
estimation of parameters by fusing temporal and spatial information,
captured via sampling a wavefield with a set of judiciously placed
antenna sensors. The wavefield is assumed to be generated by a finite
number of emitters, and contains information about signal parameters
characterizing the emitters. A review of the area of array processing is
given. The focus is on parameter estimation methods, and many relevant
problems are only briefly mentioned. We emphasize the relatively more
recent subspace-based methods in relation to beamforming. The article
consists of background material and of the basic problem formulation.
Then we introduce spectral-based algorithmic solutions to the signal
parameter estimation problem. We contrast these suboptimal solutions to
parametric methods. Techniques derived from maximum likelihood
principles as well as geometric arguments are covered. Later, a number
of more specialized research topics are briefly reviewed. Then, we look
at a number of real-world problems for which sensor array processing
methods have been applied. We also include an example with real
experimental data involving closely spaced emitters and highly
correlated signals, as well as a manufacturing application example

In sonar and many other applications, time-delay estimation is an
important problem. When bandpass probe signals are used, the correlation
function between the received and the known transmitted signals
oscillates near the carrier frequency of the transmitted signal. In this
case, many existing time-delay estimation algorithms perform poorly due
to converging to local optimum points. In this paper, two efficient
algorithms, Hybrid-WRELAX and EXIP-WRELAX, are proposed to deal with the
above problem. They are relaxation-based global minimizers of a highly
oscillatory nonlinear least-squares cost function. Both algorithms are
shown to achieve the Cramer-Rao bound and require only a sequence of
weighted Fourier transforms

We present a new method for estimating the number and arrival times for overlapping signals with a priori known shape from noisy observations received by a sensor. The method is based on a recently developed eigenstructure technique for multitarget direction finding with passive antenna arrays and exploits the structure of the received signal covariance matrix. This problem is important in various applications such as radar and sonar data processing, geophysical/seismic exploration, and biomedical engineering. In many of these applications, a known signal is launched into a scattering medium and the returning response-in the form of delayed overlapping echos in noise-has to be processed to yield information on the nature and location of scatterers. The method presented also solves more general problems of signal detection and resolution.

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.

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

The authors are interested in estimating the Doppler shift occurred in weather radar returns, which yields precipitation velocity information. Conventional techniques including the pulse pair processor rely heavily on the assumption that the additive noise is white and hence their performance degrades when the noise color is unknown. Because the data length for a given range gate is usually small, the authors employ the high resolution MUSIC algorithm to estimate the Doppler shift. The challenge lies not only in proving that MUSIC is applicable to weather radar signals which are affected by multiplicative noise, but also in showing that MUSIC is robust when the additive noise is colored. The resulting algorithm can also be used to infer wind speed from a small number of lidar observations where the velocity is approximately constant. Assuming linear shear over a longer range, they employ the ambiguity function to estimate the acceleration and instantaneous wind velocity. Real weather radar and lidar data as well as simulated examples are provided to illustrate the performance of the algorithms.

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.

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

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

DOI: 10.1057/palgrave/2601338

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.

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.

First Page of the Article

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.

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

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

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

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

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.

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.