Two-step Localization Method Research Articles

Direct position determination algorithm based on wideband array signal model in external illuminator system

Abstract Target location and tracking are among the most critical applications for external illuminator systems. Most traditional array signal direct position determination (DPD) techniques are based on narrowband signals. With the advancement of communication technology, various wideband signals are extensively utilized in communication systems, leading to the failure of some traditional DPD techniques. To address this issue, this article proposes a new DPD algorithm for wideband array signals. First, we suppress the direct wave (DW) interference in the received signal. Then, a cost function for the target coordinate is constructed based on the Maximum Likelihood (ML) criterion, and a phase matching matrix is created for the problem of unknown signal transmission time. Finally, the position estimation is obtained from the peak of the cost function. Simulation results demonstrate that the proposed algorithm outperforms traditional two-step localization methods based on the time difference of arrival of signals, particularly in cases where DW interference is present in the received signal.

Novel High-Precision and High-Robustness Localization Algorithm for Underwater-Environment-Monitoring Wireless Sensor Networks

In marine ecological environment monitoring, the acquisition of node location information is crucial, and the absence of location information can render the collected data meaningless. Compared to the rest of the distance-based localization methods, the received signal strength (RSS)-based localization technique has gained significant interest due to its low cost and the absence of time synchronization. However, the acoustic signal propagates in the complex and changeable aqueous medium, and, in addition to the time-varying path loss factor (PLF), there is often a certain absorption loss, which seriously deteriorates the localization accuracy of the RSS-based technique. To address the above challenges, we propose a novel high-precision and high-robustness localization (NHHL) algorithm that introduces an estimation parameter to conjointly estimate the marine node location and the ambient PLF. Firstly, the original non-convex localization problem is converted into an alternating nonnegative constrained least squares (ANCLS) framework with the unknown PLF and absorption loss, and a two-step localization method based on the primitive dual interior point method and block co-ordinate update method is presented to find the optimal solution. In the first step, the penalty function is utilized to reformulate the localization problem and find an approximate solution. Nevertheless, due to inherent errors, it is unable to approximate the constraint boundary and the global optimum solution. Subsequently, in the second step, the original localization problem is further transformed into a generalized trust region sub-problem (GTRS) framework, and the approximate solution of the interior point method is utilized as the initial estimation, and then iteratively solved by block co-ordinate update to obtain the precise location and PLF conjointly. Furthermore, the closed-form expression of the Cramér–Rao lower bound (CRLB) for the case of the unknown path loss factor and absorption loss is derived to evaluate the our NHHL algorithm. Finally, the simulation results demonstrate the superiority of the presented NHHL algorithm compared with the selected benchmark methods in various marine simulation scenarios.

A two-step method to locate multiple local nonlinearities

Nonlinear localization is an important component of structural nonlinear identification. Its accuracy is of great significance for damage localization, health monitoring, and performance prediction of structural systems. In this paper, a two-step localization method is proposed for the nonlinear localization of multi-degree-of-freedom (MDOF) systems with multiple local nonlinearities. The approach achieves accurate nonlinear localization in two steps. In the first step, subset nonlinearity detection is performed to initially narrow down the nonlinear localization range. This effectively reduces the dimensionality of the candidate nonlinear basis functions in the second step. In the second step, candidate nonlinear basis functions are used to further confirm the doubtful connections. The accuracy and effectiveness of the method are verified by two numerical examples of a one-dimensional chain-type structure and a two-dimensional structure. In addition, an experimental study is conducted on a floor structure with two local nonlinearities to verify the effectiveness of the proposed method. Results show that the proposed method has good accuracy in a noisy environment and it requires only the input and output data of the system under a wide-band excitation.

A Feature-Level Fusion-Based Target Localization Method with the Hough Transform for Spatial Feature Extraction

Traditional two-step localization methods and direct localization methods have practical problems when they are used for underwater acoustic source localization. In this paper, a localization method based on the feature-level information fusion is proposed, in which the Hough Transform is exploited to detect the line characteristics of the spatial features of the target. A secondary accumulation procedure is proposed to extract and fuse the good features instead of fusing all features. The possibility to produce a ghost target is greatly reduced. Hence, the robustness of the proposed method in low SNR scenarios is improved. Experimental results validate the efficiency of exploiting the Hough Transform to eliminate interfering spatial features without sacrificing the localization accuracy.

Time series analysis and sparse sensor network-based impact monitoring for aircraft complex structures

An impact monitoring method based on time series analysis and a sparse sensor network is proposed to identify the location of the impact event that occurs on aircraft complex structures and estimate the impact energy. Generally, a high-density sensor network is required for high localization accuracy of the impact event, but with the trade-off of high deployment costs. A sparse piezoelectric sensor network together with a coarse and fine two-step localization method is designed to balance accuracy and cost. The stress wave signals caused by impact are measured by the sensor network and regarded as time series. The impact localization problem is converted into a classification problem of time series, and the strategy of combining coarse localization (impact zone identification) and fine localization (impact localization within a zone) is used to achieve accurate identification of the impact locations. The zone where the impact event is located is first identified by the coarse localization algorithm based on K-nearest neighbor and dynamic time warping (DTW) and one-dimensional convolutional neural networks, respectively. Furthermore, the high accuracy identification of the impact location within the zone is achieved by the fine localization algorithm based on DTW and centroid localization. In terms of the impact energy estimation, the zone correction compensation algorithm is given to sufficiently reduce the estimation error of the impact energy. The low-velocity impact tests are performed on the composite stiffened panel and the aluminum alloy aircraft fuselage structure to verify the effectiveness of the proposed methods.

Performance Boosting for Two-Step Localization Methods in Distributed MIMO Radar via a Robust Post-Processing Scheme

In radar target localization using time delay (TD) measurements, reliable TD extraction is an important prerequisite for conventional two-step localization methods. In the distributed multiple-input multiple-output (MIMO) radar, the low-quality TD measurements (i.e., outliers) always occur due to the target scattering fluctuations in various transmitter-receiver paths, which results in serious performance degradation to the generic two-step localization methods. To this end, we propose a simple yet effective performance boosting scheme in this letter. It constructs a robust estimator based on the Huber loss function and solves this problem iteratively by using the majorization-minimization (MM) technique. This proposal is a general post-processing module, and thus it can be combined with any existing two-step algorithms to achieve performance improvement in the presence of outliers. The simulations verify the effectiveness of the proposed scheme by comparing with the derived theoretical lower bound. In addition, the parameter robustness and the computational burden are also evaluated.

Compressed Sensing-Based Genetic Markov Localization for Mobile Transmitters

With the strengths of quickness, low cost, and adaptability, unmanned aerial vehicle (UAV) communication is widely utilized in the next-generation wireless network. However, some risks and hidden dangers such as UAV “black flight” disturbances, attacks, and spying incidents lead to the necessity of the real-time supervision of UAVs. A compressed sensing-based genetic Markov localization method is proposed in this paper for two-dimensional trajectory tracking of the mobile transmitter in a finite domain, which consists of three modules: the multi-station sampling module, the reconstruction module, and the localization module. In the multi-station sampling module, multiple stations are deployed to receive the signal transmitted by the UAV using compressed sensing, and the motion model of the mobile transmitter is the constant turn rate and acceleration (CTRA) model. In the reconstruction module, we propose a direct reconstruction method to extract the joint cross-spatial spectrum. In the genetic Markov localization module, we propose a two-step localization method to genetically correct the inaccurate points in the preliminary results and generate the tracking result. Extensive simulations are conducted to verify the effectiveness of the proposed method. The results show that the proposed method is superior to the particle filter method and the Markov Monte Carlo method at all sampling moments. Specifically, when SNR = 15dB, the root-mean-square error (RMSE) of the proposed method is 39% and 60% lower than that of the other two methods, respectively. Moreover, under the premise that the RMSE of the localization result is less than 30 m, the reconstruction module can reduce the running time of the proposed method by 33.3%.

Long Baseline Acoustic Localization Based on Track-Before-Detect in Complex Underwater Environments

This paper considers the long baseline (LBL) acoustic localization problem. For this problem, traditional two-step localization methods first estimate the time of arrivals (TOAs) of the target signal and then solve the target’s position based on the estimated TOAs. Since TOA estimation is performed at each buoy independently, they are suboptimal without considering the physical basis that the TOAs estimated from different buoys all correspond to the same target position. To overcome this drawback, we propose a novel localization approach based on track-before-detect (TBD) and particle filtering (PF) theory, which directly determines the target’s position. Since this method breaks from the traditional two-step paradigm, several extra challenges arising from the two-step paradigm itself can be avoided. Specifically, we make two main contributions. First, a unique method is given for designing the likelihood function of the PF framework, which defines the likelihood function as the product of the matched filter outputs of multiple buoys conditioned on the particle states. As this design scheme is without any assumptions on the emission signal type, it can be applied to any signal type. Second, multiple models are employed to sample the particles to reduce the performance loss caused by target maneuvers. Additionally, an auxiliary variable is used to improve the sampling efficiency of the multiple models. The efficacy of the proposed method is demonstrated both in simulations and on real datasets. Experimental results show that the proposed algorithm outperforms the traditional LBL localization methods under harsh conditions.

A two-step localization method using wavelet packet energy characteristics for low-velocity impacts on composite plate structures

Composite plate structures are prone to damages caused by low-velocity impacts. To locate these impacts, many impact localization methods using fiber Bragg grating (FBG) sensors have been developed. However, it is difficult to achieve the high localization accuracy when impact response signals are acquired by a FBG sensing system with a low sampling frequency in previous studies. In this paper, a two-step localization method using wavelet packet energy characteristics is proposed to address this problem. The proposed impact localization method consists of the collection of impact samples, feature extraction, and two-step localization. To collect impact samples, a FBG sensing system with a sampling frequency of 5 kHz and four FBG sensors is utilized to acquire the response signals induced by the low-velocity impacts on a carbon fiber reinforced plastic (CFRP) plate. Then, a new impact feature, which is sensitive to the low-velocity impacts and can eliminate the influence of the impact height, is defined according to the wavelet packet energy characteristics. Finally, a two-step localization method is designed to achieve the accurate localization for the impacts, in which the first step is the impact area identification based on a feature database and the second step is the impact localization based on the stochastic fractal search (SFS) algorithm. The results of four sets of experiments prove the effectiveness and satisfactory performance of the proposed impact localization method for the low-velocity impact localization on the CFRP plate.

Method for Direct Localization of Multiple Impulse Acoustic Sources in Outdoor Environment

A method for the direct outdoor localization of multiple impulse acoustic sources by a distributed microphone array is proposed. This localization problem is of great interest for gunshot, firecracker and explosion detection localization in a civil environment, as well as for gun, mortar, small arms, artillery, sniper detection localization in military battlefield monitoring systems. Such a kind of localization is a complicated technical problem in many aspects. In such a scenario, the permutation of impulse arrivals on distributed microphones occurs, so the application of classical two-step localization methods, such as time-of-arrival (TOA), time-difference-of-arrival (TDOA), angle-of-arrival (AOA), fingerprint methods, etc., is faced with the so-called association problem, which is difficult to solve. The association problem does not exist in the proposed method for direct (one-step) localization, so the proposed method is more suitable for localization in a given acoustic scenario than the mentioned two-step localization methods. Furthermore, in the proposed method, direct localization is performed impulse by impulse. The observation interval used for the localization could not be arbitrarily chosen; it is limited by the duration of impulses. In the mathematical model formulated in the paper, atmospheric factors in acoustic signal propagation (temperature, pressure, etc.) are included. The results of simulations show that by using the proposed method, centimeter localization accuracy can be achieved.

A Fast Direct Position Determination Algorithm for LFM Signal Based on Spectrum Detection

For the purpose of simultaneously estimating and locating the linear frequency modulation (LFM) emitter with unknown parameters, an innovative approach, i.e., Fast Direct Position Determination (FDPD), is introduced. The proposed algorithm is based on maximum likelihood estimation (MLE) and spectrum detection. To improve the accuracy and overcome the dramatic complexity of plain maximum likelihood formulation, we further derive the objective function equation of Direct Position Determination (DPD) algorithm and present an enhanced strategy to solve the highly nonlinear optimization problem. By combining the two-step localization method, one-step localization method, and short-time Fourier transform (STFT), our approach realizes jointly estimation of the transmitted signal parameters and emitter localization. Simulation results show that the proposed method is superior compared to the existing DPD, and two-step localization algorithms in terms of localization error and computational complexity, especially for low signal-to-noise ratio (SNR).

Direct Position Determination of Moving Sources Based on Delay and Doppler

In this paper, we address the problem of direct position determination (DPD) for moving sources. Different from traditional two-step localization methods where the intermediate time difference of arrival (TDOA) and frequency difference of arrival (FDOA) parameters are estimated and used for the subsequent moving source localization, in this paper the locations and velocities of moving sources are estimated directly from the received signals. To address the difficulty of estimating the high-dimensional unknown parameters simultaneously, a new multiple particle filter based DPD method is proposed, where the position and velocity are updated alternately using separate local particle filters. The proposed method requires smaller particle numbers compared to the classic particle filters, and its convergence is proved both theoretically and numerically. Moreover, the Cramer Rao lower bound for the considered moving source DPD is developed. Simulation results corroborate the effectiveness of the proposed method in terms of computational efficiency and estimation accuracy.

Robust Direct position determination against sensor gain and phase errors with the use of calibration sources

The direct position determination (DPD) method can provide high localization performance than conventional two-step localization methods. However, the existing DPD methods only consider the scenario of parameters of the receiving arrays, and the localization performance decreases dramatically when the array model is inaccurate in practice. This paper studies the problem for positioning a stationary emitter in the presence of sensor gain and phase errors (SGPEs) aided by calibration sources. To remove these negative effects caused by SGPEs, calibration sources with known positions are introduced. The extended relationship between parameters of calibration sources and errors is used to establish a structural objective function based on the maximum likelihood estimate. The calibration parameters are jointly optimized with target-related parameters and an alternating iterative algorithm is then developed to decouple the multidimensional search into several low-dimensional optimizations. We also derive the Cramer–Rao bound (CRB) to evaluate the performance of the proposed method. Simulation results demonstrate that the proposed method outperforms the existing DPD methods and two-step methods, which incorporates the error information, and the accuracy attains the associated CRB.

Direct Position Determination in Asynchronous Sensor Networks

Source positioning using time difference of arrival (TDOA) has received much research interest in the field of vehicular technology during the past decades. In practice, sensor networks may be disturbed by clock biases, and extra active anchor sources with known positions could be exploited to calibrate these clock biases. Although there exist numerous two-step localization methods on this issue, they are inherently suboptimal. In this paper, we address the TDOA-based source direct position determination (DPD) problem in asynchronous sensor networks. First, the clock biases are demonstrated via theoretical analyses to cast significant influences on localization accuracy negatively. Then, a DPD method is proposed, exploiting anchor sources to jointly calibrate clock biases and determine the unknown source position, which integrates an expectation-maximization (EM) algorithm and a Gauss–Newton algorithm for coarse and refined parameter estimation, respectively. In this way, the computational load of the considered DPD problem is reduced considerably compared with exhaustive search-based DPD method. Moreover, the Cramer–Rao lower bound is derived for the considered DPD problem, and how anchor sources affect the localization performance is further analyzed. Simulation results demonstrate the necessity of clock bias calibration and the satisfactory performance of the proposed method.

Direct Position Determination of Multiple Constant Modulus Sources Based on Direction of Arrival and Doppler Frequency Shift

Direct position determination (DPD) methods are known to outperform classical two-step localization methods under the condition of low signal-to-noise ratios and/or small number of snapshots. Additionally, they can directly exploit the prior knowledge of signal waveforms to achieve higher estimation accuracy. In this paper, we concentrate on the DPD method for locating multiple constant modulus (CM) sources based on a single moving receiving station. Both direction of arrival and Doppler frequency shift are used for source localization. First, a received array signal model with a small time delay that can incorporate the Doppler frequency information is formed. Subsequently, the corresponding maximum likelihood estimation criterion is established. An effective alternating minimization algorithm is developed to solve the optimization problem. Subsequently, we also derive the Cramer–Rao bound expressions for parameter estimation. It is proved that the CM property of the signals is useful in reducing the lower bound for location estimation. Simulation results demonstrate that the proposed method is asymptotically efficient. Moreover, it is also shown that the estimation accuracy of direct localization can be greatly increased if the CM characteristics of the radiated signals are adequately exploited.

Single-step localization using multiple moving arrays in the presence of observer location errors

Abstract Direct position determination (DPD) is a promising technique that offers superior performance compared with conventional two-step localization methods. Existing DPD methods presume that the observer locations are known exactly, whereas in practical environments, a small error in the observer locations will lead to an erroneous localization. This study considers the localization of a stationary transmitter by separated moving arrays from passive measurements taken at different points along the trajectory. The precise locations and velocities of the observers are not available, but their errors are assumed to be Gaussian distributed. Using this probability distribution, we propose maximum likelihood-based DPD approaches in the presence of observer location errors for both unknown and known signals. The proposed DPDs rely on alternating iteration schemes, which reduce the multidimensional nonlinear optimization problem to optimizations of dimensions that are much smaller than the number of unknowns. As opposed to the conventional two-step methods that extract measurement parameters and then estimate the positions from them, the proposed DPDs achieve the localization in a single step by exploiting the information of angles, time delays, and Doppler frequency shifts, but without computing them. Additionally, we derive the Cramer–Rao bound (CRB) formula for this DPD problem in the presence of observer location errors. The simulation results prove that the performance of our methods attains the associated CRB. Moreover, they are more robust than the conventional two-step approaches with respect to observer location errors. We demonstrate our methods for the scenario of multiple moving arrays, but these methods can easily be extended to DPD problems accounting for observer location errors in different scenarios.

Robust direct position determination methods in the presence of array model errors

Direct position determination (DPD) methods are known to have many advantages over the traditional two-step localization method, especially for low signal-to-noise ratios (SNR) and/or short data records. However, similar to conventional direction-of-arrival (DOA) estimation methods, the performance of DPD estimators can be dramatically degraded by inaccuracies in the array model. In this paper, we present robust DPD methods that can mitigate the effects of these uncertainties in the array manifold. The proposed technique is related to the classical auto-calibration procedure under the assumption that prior knowledge of the array response errors is available. Localization is considered for the cases of both unknown and a priori known transmitted signals. The corresponding maximum a posteriori (MAP) estimators for these two cases are formulated, and two alternating minimization algorithms are derived to determine the source location directly from the observed signals. The Cramér-Rao bounds (CRBs) for position estimation are derived for both unknown and known signal waveforms. Simulation results demonstrate that the proposed algorithms are asymptotically efficient and very robust to array model errors.

Reflector-aided direct locations of multiple signals in the presence of small reflector position biases

Direct position determination (DPD) is a single-step method that localizes transmitters from sensor outputs without computing intermediate parameters. It outperforms conventional two-step localization methods, especially under low signal-to-noise ratio conditions. This article proposes a reflector-aided DPD algorithm for multiple signals of known waveforms received by an array observer. In previous studies, reflector-aided localization has always required very precise locations of reflectors. Therefore, the localization performance depends sensitively on accurately knowing each reflector position. This study considers the presence of small biases in reflector locations. To make the problem tractable, we simplify the signal model through an approximation using the first-order Taylor expansion and then directly localize multiple sources in a decoupled manner. Unlike most DPDs that presume noise is spatially uncorrelated, our study imposes no restriction on the correlation structure of noise, allowing this algorithm to be used in more general scenarios. In addition, we derive the Cramér–Rao bound expression and perform an analysis of the direct locations of multiple signals when the reflector positions are assumed accurate but in fact have small biases. Simulation results corroborate the theoretical results and a good localization performance of the proposed algorithm in the presence of small reflector position biases.

Direct Position Determination of Non-Circular Sources Based on a Doppler-Extended Aperture With a Moving Coprime Array

Direct position determination (DPD) is a new promising technique in wireless location. Compared with conventional two-step localization methods, DPD achieves a higher accuracy by directly estimating the source location without computing the intermediate parameters. However, all the existing angle-based DPD algorithms for non-circular sources use uniform linear arrays, which lead to low degrees of freedom and poor estimation precision, and do not make use of the Doppler characteristics of the moving station. To improve the DPD performance, this paper proposes a novel DPD algorithm for non-circular sources based on a Doppler-extended aperture with a moving coprime array. First, the coprime array is introduced to angle-based DPD, and an extended array model is established by exploiting the Doppler characteristics of the moving array. The characteristics of non-circular sources are used to further improve the positioning accuracy. Finally, merging the subspace data for each measuring position, the target positions can be obtained. The Cramer-Rao lower bound of the DPD algorithm is presented for non-circular sources in a coprime array combined with Doppler-extended aperture. Performance analysis and the simulation experiments show that compared with the conventional two-step localization method and DPD based on a uniform array, including subspace data fusion and weighted subspace fitting algorithms, the proposed algorithm effectively improves the location accuracy at the expense of a slight complexity increase and can determine the location of multiple targets in underdetermined conditions.

Performance Analysis of the Direct Position Determination Method in the Presence of Array Model Errors.

The direct position determination approach was recently presented as a promising technique for the localization of a transmitting source with accuracy higher than that of the conventional two-step localization method. In this paper, the theoretical performance of a direct position determination estimator proposed by Weiss is examined for situations in which the array model errors are present. Our study starts from a matrix eigen-perturbation result, which expresses the perturbation of eigenvalues as a function of the disturbance added to the Hermitian matrix. The first-order asymptotic expression of the positioning errors is presented, from which an analytical expression for the mean square error of the direct localization is available. Additionally, explicit formulas for computing the probabilities of a successful localization are deduced. Finally, Cramér–Rao bound expressions for the position estimation are derived for two cases: (1) array model errors are absent and (2) array model errors are present. The obtained Cramér-Rao bounds provide insights into the effects of the array model errors on the localization accuracy. Simulation results support and corroborate the theoretical developments made in this paper.