Non-line-of-sight Bias Research Articles

An ADMM approach for elliptic positioning in non-line-of-sight environments

Elliptic positioning (EP) has recently emerged as a prevailing subject within localization research, holding significant relevance for a variety of multistatic systems including distributed multiple-input multiple-output radar, sonar, and wireless sensor networks. Mathematically, EP refers to estimating the location of a signal-reflecting/relaying target from the bistatic range (BR) measurements acquired by employing multiple spatially separated transmitters and receivers. BRs, as a specific type of range-based sensor observations, will however be positively biased when non-line-of-sight (NLOS) signal propagation occurs. Such a phenomenon is widespread across various localization scenarios, which can seriously degrade the positioning accuracy if not properly addressed. Through the alternating direction method of multipliers, this contribution introduces a computationally efficient iterative algorithm designed for error-mitigated EP in NLOS environments. In addition to target position coordinates, we incorporate a non-negatively bounded balancing parameter into the formulation and perform joint estimation, thereby achieving NLOS bias error reduction in a simple yet impactful manner. Numerical simulations are conducted to validate the functionality of the presented EP approach in NLOS situations.

CASTELO: Convex Approximation based Solution To Elliptic Localization with Outliers

This short communication considers mitigating the negative effects of possibly unreliable path delay measurements acquired in non-line-of-sight (NLOS) environments on the positioning performance, a problem deserving further investigation within the expanding research area of elliptic localization. We present CASTELO, a Convex Approximation based Solution To Elliptic Localization with Outliers, to achieve such a goal. Our proposal corresponds to a mixed semidefinite (SD)/second-order cone (SOC) programming formulation derived from an error-mitigated nonlinear least squares (LS) location estimator, presenting itself as a remedy for the neglect of positivity of NLOS biases suffered by the majority of currently fashionable outlier-handling approaches. In terms of analytical discussions, we provide rationales supporting the incorporation of the SOC constraints, which serve to tighten the problem obtained after SD relaxation, and conduct a complexity analysis for the ultimate mixed SD/SOC programming formulation. Simulations are carried out to confirm the strong ability of CASTELO to attain reliable elliptic localization in the presence of NLOS outliers.

Fast RSSD multi-target localization in NLOS environments

Signal strength–based localization is commonly employed in wireless sensor networks due to its low complexity and simplicity. However, in non-line-of-sight (NLOS) environments with unknown transmit power, effective and efficient multi-target localization is a challenging task. In this paper, a fast multi-target localization based on a neural network (FMLNN) is proposed. The received signal strength difference (RSSD) is employed and NLOS bias is considered. Determining the maximum likelihood (ML) estimator is a complex and highly non-convex problem, so it is solved indirectly using a neural network. First, prior data composed of known target information and RSSD values are used in offline training to learn the nonlinear relationship. Then, the locations of multiple targets are estimated online using the trained network. Results are presented which show the proposed method provides fast and efficient localization of multiple targets, and has greater robustness to NLOS bias than conventional state-of-the-art methods.

A UAV-Assisted Search and Localization Strategy in Non-Line-of-Sight Scenarios

Recently, unmanned aerial vehicle (UAV)-assisted ground targets localization is widely used in search and rescue (SAR) scenes. In this article, we propose a UAV search and localization strategy, which can search and locate unknown number of victims. The proposed strategy uses the UAV as a mobile anchor to measure time of arrival (TOA) and can effectively mitigate localization errors caused by non-line-of-sight (NLOS) propagation. Generally speaking, the strategy is divided into two parts: 1) trajectory planning and 2) localization. By selecting waypoints and planning a suitable search trajectory, UAV can obtain all the measurement information in deployment area and ensure that each target has at least three anchors for localization even in the NLOS propagation environment. In the localization stage, a new estimator is proposed based on maximum-likelihood estimation (MLE), which estimates average NLOS bias together with the coordinates of target and can be well solved by the particle swarm algorithm. The simulation results show that the proposed strategy outperforms for mitigating NLOS error compared with other methods, and can effectively ensure high localization accuracy in the NLOS propagation environment.

Range Difference-Based Target Localization Under Stratification Effect and NLOS Bias in UWSNs

This letter proposes a robust target localization technique for acoustic underwater wireless sensor networks (UWSNs) that simultaneously experience the stratification effect and the non-line-of-sight (NLOS) bias. Specifically, we develop the range difference (RD)-based majorization minimization expression and its theoretical analysis, which leads to a surrogate function coupling with an iterative form. To figure out the initial estimate of the iteration, the proposed method converts the original localization problem into an RD-based generalized trust-region subproblem (RD-GTRS) after selecting a reference node. Eventually, an RD-based target localization approach (RD-TLA) is presented to iteratively estimate the final location. Simulation results show that the proposed RD-TLA method achieves better localization accuracy compared with other state-of-the-art methods in different scenarios.

A Majorization-Minimization Algorithm for Hybrid TOA-RSS Based Localization in NLOS Environment

This letter investigates the problem of accurate localization of a target node in wireless sensor networks using time of arrival (TOA) and received signal strength (RSS) measurements in an adverse non-line of sight (NLOS) environment. The proposed methodology works without any requirement of the NLOS path identification or the prior knowledge of NLOS bias distribution. A non-linear weighted least squares (NLWLS) problem is formulated through general approximations on the hybrid data model. The formulated NLWLS problem is solved using a computationally efficient majorization-minimization (MM) algorithm in which the NLWLS objective is iteratively minimized via simple update steps. The proposed MM algorithm is guaranteed to converge to a stationary point of the NLWLS objective. Simulation results and computational complexity analysis validate that the proposed MM algorithm attains fast convergence with lower latency. Moreover, the proposed hybrid localization algorithm outperforms the state-of-art methods in terms of estimation accuracy and computational complexity.

Characterizing the First-Arriving Multipath Component in 5G Millimeter Wave Networks: TOA, AOA, and Non-Line-of-Sight Bias

This paper presents a stochastic geometry-based analysis of propagation statistics for 5G millimeter wave (mm-wave) cellular. In particular, the time-of-arrival (TOA) and angle-of-arrival (AOA) distributions of the first-arriving multipath component (MPC) are derived. These statistics find their utility in many applications such as cellular-based localization, channel modeling, and link establishment for mm-wave initial access (IA). Leveraging tools from stochastic geometry, a Boolean model is used to statistically characterize the random locations, orientations, and sizes of reflectors, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , buildings. Assuming non-line-of-sight (NLOS) propagation is due to first-order ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , single-bounce) reflections, and that reflectors can either facilitate or block reflections, the distribution of the path length ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , absolute time delay) of the first-arriving MPC is derived. This result is then used to obtain the first NLOS bias distribution in the localization literature that is based on the absolute delay of the first-arriving MPC for outdoor time-of-flight (TOF) range measurements. This distribution is shown to match exceptionally well with commonly assumed gamma and exponential NLOS bias models in the literature, which were only attained previously through heuristic or indirect methods. Continuing under this analytical framework, the AOA distribution of the first-arriving MPC is derived, which gives novel insight into how environmental obstacles affect the AOA and also represents the first AOA distribution derived under the Boolean model.

Robust Source Positioning Method With Accurate and Simplified Worst-Case Approximation

Worst-case robust approximation was proven to be efficient in alleviating the non-line-of-sight (NLOS) influence for source positioning. However, the existing time-difference-of-arrival (TDOA)-based worst-case solutions still have two issues: 1) Inaccurate objective transformations are introduced in some algorithms, which reduce the accuracy; 2) A method with higher accuracy is computationally intensive. This study proposes an accurate and simplified worst-case approximation method to tackle the troubles. Precisely, we first prove that the nonconvex worst-case objective is piecewise monotone to the NLOS bias. We further use monotonicity to derive an accurate and convex expression of the worst-case objective. Then, we propose simplified transformations to redefine the worst-case approximation problem with fewer constraints. Besides, we prove the effectiveness of the simplified transformations. Simulations and experiments demonstrate that the proposed method with moderate computation exhibits better performance than the state-of-the-art worst-case approximation algorithms.

Directional Target Localization in NLOS Environments Using RSS-TOA Combined Measurements

This letter addresses the localization problem of a directional source in non-line-of-sight (NLOS) environments. To estimate both the position and the orientation of the source, we propose an iterative algorithm that skillfully adopts the received-signal-strength (RSS) and time-of-arrival (TOA) measurements. The algorithm is derived by converting the non-convex estimating problem into a generalized trust region subproblem (GTRS). The converted problem could be efficiently solved by a bisection process. Considering that the directivity of the target could greatly affect its RSS measurements in different directions, a preliminary estimate for the target’s location is conducted using only the TOA measurements, based on which we then estimate the orientation of the source and the NLOS biases. The alternating process of the algorithm can converge quickly. Finally, the excellent performance of the proposed algorithm is demonstrated through simulations.

Performance Analysis of Wireless Location and Velocity Tracking of Digital Broadcast Signals Based on Extended Kalman Filter Algorithm

In order to improve the accuracy and reliability of wireless location in NLOS environment, a wireless location algorithm based on artificial neural network (ANN) is proposed for NLOS positioning error caused by non-line-of-sight (NLOS) propagation, such as occlusion and signal reflection. The mapping relationship between TOA and TDOA measurement data and coordinates is established. The connection weights of neural network are estimated as the state variables of nonlinear dynamic system. The multilayer perceptron network is trained by the real-time neural network training algorithm based on extended Kalman (EKF). Combined with the statistical characteristics of NLOS error, the state component NLOS bias estimation is modified to realize TDOA data reconstruction. Simulation and experimental data analysis show that the algorithm can effectively weaken the influence of NLOS error. The localization method does not depend on the specific NLOS error distribution, nor does it need LOS and NLOS recognition. It can significantly improve the mobile positioning accuracy.

A Semi-Supervised Learning Approach for UWB Ranging Error Mitigation

Non-line-of-sight (NLOS) propagation conditions can severely degrade wireless localization accuracy due to the biases in range measurements. Machine learning methods such as support vector machine (SVM) can mitigate the effect of NLOS biases when sufficient labeled ranging measurements are available. This letter proposes a semi-supervised learning approach for NLOS identification and mitigation, which leverages low-cost unlabeled measurements by self-training to complement only a small portion of labeled ones. Experimental results show that the proposed semi-supervised approach can increase the NLOS identification probability from 90% to 94% and reduce the ranging error by 10% by exploiting the unlabeled measurements.

Robust NLOS Bias Mitigation for Hybrid RSS-TOA Based Source Localization Under Unknown Transmission Parameters

This letter addresses the problem of source localization in non-line of sight (NLOS) environment using received signal strength (RSS) and time of arrival (TOA) measurements when both transmission time and power are unknown. To mitigate the NLOS bias, a robust weighted least square (RWLS) problem is formulated from original non-convex maximum-likelihood (ML) estimation problem using a set of tight approximations. The RWLS problem is further tightened by a novel convex-hull constraint and is ultimately solved using second-order cone programming (SOCP). Simulation results confirm the optimal performance of the proposed robust method in various network scenarios and also validate its excellence over state-of-art methods.

GPS multipath and NLOS mitigation for relative positioning in urban environments

Multipath interference and non-line-of-sight (NLOS) reception are major error sources when using global navigation satellite system-based cooperative positioning (CP) in urban environments. In this paper, we develop a multipath and NLOS mitigation algorithm that significantly improves the relative positioning accuracy in urban environments, compared with the absolute positioning and conventional tight CP technique, respectively. In this proposed method, each receiver fuses the Global Positioning System (GPS) pseudorange and Doppler shift measurements, and the linear cooperative navigation observation model is formulated by considering the multipath and NLOS biases as additive sparse errors. We investigate a sparse estimation algorithm to solve the navigation problem and estimate the multipath and NLOS biases, with the weighting matrix designed as function of satellite carrier-to-noise density ratio and the regularization parameter selected by Bayesian information criterion. Based on a least absolute shrinkage and selection operator problem, an ℓ1 regularization is introduced to enforce sparsity in the biases estimation model, which can be solved by the reweighted-ℓ1 algorithm. The GPS measurements can be corrected by subtracting the estimated multipath and NLOS biases, and the relative positioning performance of proposed method is verified by analytical and experimental results.

RSS-Based Byzantine Fault-Tolerant Localization Algorithm Under NLOS Environment

Localization is one of the most critical tasks in wireless sensor networks, but achieving a relatively accurate location estimation is challenging when there have Byzantine fault and non-line-of-sight (NLOS) bias simultaneously. In this context, a localization method, based on received signal strength (RSS), is proposed in this letter to mitigate the impact of Byzantine fault and NLOS bias on the localization accuracy of wireless sensor networks. The proposed method relies on a Byzantine fault-tolerant localization algorithm (BFLA), which converts the localization problem into a generalized trust-region subproblem (GTRS) by applying certain approximations. In order to obtain a feasible solution to the GTRS, a block-coordinate update (BCU) function with a regularization term is used to divide the localization problem into two subproblems. An iterative method, whose start-point is obtained by an unconstrained squared-range (USR) algorithm, is then used to obtain a solution. Numerical simulations are carried out to show the effectiveness of the proposed method, compared with the state-of-the-art approaches in different scenarios.

Robust Localization of Signal Source Based on Information Fusion

A robust algorithm for locating the signal source is proposed based on information fusion from different domains to improve the passive localization accuracy under the non-line-of-sight (NLoS) environment. The localization scenario is established by utilizing the information about energy domain, time domain, and frequency domain. The Cramer-Rao lower bounds are derived, and the performance improvement is proved in different domains. By substituting NLoS bias with the statistical average, the localization equations of information fusion are established. A nonconvex localization problem is transformed into a generalized trust domain subproblem by introducing the squared range and the weighted least squares. The position and velocity of the source are obtained by using the bisection procedure. An iterative method is used to estimate the NLoS deviation and refine the position accuracy simultaneously. Simulation results demonstrate the efficiency and robustness of the proposed algorithm.

NLOS Effect Mitigation via Spatial Geometry Exploitation in Cooperative Localization

Accurate wireless positioning of mobile agents is challenging in non-line-of-sight (NLOS) propagation environments due to unknown range or angle biases. In this paper, we develop a cooperative localization algorithm for mixed line-of-sight (LOS)/NLOS environments where the NLOS effect is mitigated by exploiting the geometric relationship of the range biases. In particular, we cast the localization problem as a detection-aided optimization program, in which all the distance measurements are initially treated as NLOS links with unknown nonnegative biases, followed by iterative agent position estimation and LOS identification. Moreover, the maximum-likelihood estimator for the agent positions and NLOS biases is relaxed into a semidefinite program where the geometric relationship of the biases is introduced as constraints. We also characterize the cooperation gain for LOS identification, and derive the constrained Cramer-Rao bound to show the localization accuracy improvement by the geometric constraints. Finally, numerical results validate the superior performance of the proposed algorithm compared with other competitive methods.

Estimating Directional Data From Network Topology for Improving Tracking Performance

This work proposes a novel approach for tracking a moving target in non-line-of-sight (NLOS) environments based on range estimates extracted from received signal strength (RSS) and time of arrival (TOA) measurements. By exploiting the known architecture of reference points to act as an improper antenna array and the range estimates, angle of arrival (AOA) of the signal emitted by the target is first estimated at each reference point. We then show how to take advantage of these angle estimates to convert the problem into a more convenient, polar space, where a linearization of the measurement models is easily achieved. The derived linear model serves as the main building block on top of which prior knowledge acquired during the movement of the target is incorporated by adapting a Kalman filter (KF). The performance of the proposed approach was assessed through computer simulations, which confirmed its effectiveness in combating the negative effect of NLOS bias and superiority in comparison with its naive counterpart, which does not take prior knowledge into consideration.

Improved MDS-based Localization with Non-line-of-sight RF Links

The performance of indoor localization techniques adopted in robot localization systems that use radio positioning is usually degraded in non-line-of-sight (NLOS) environments. In this paper, we propose a technique for estimating NLOS biases and measurement noise in distances under multidimensional scaling (MDS) based positioning with fixed nodes. An ideal matrix of pairwise distance measurements exhibits a symmetry that allows to compute mobile node positions from those of fixed ones, and then recompute exactly the fixed node positions from the earlier computed mobile node positions. In a NLOS environment, this symmetry is lost; fixed node positions can not be reproduced exactly. This work exploits the error in the recomputation of fixed node positions for the correction of NLOS biases and noise in the pairwise distances. A constrained-optimization problem is formulated to estimate biases for each measured distance and final mobile node positions under the MDS scheme. A supplementary approach is presented for special cases where the number of mobile nodes is less than 3. Experimental results show that position errors can be reduced by up to 28% for a set up of 4 fixed and 3 mobile nodes. Simulations are used to further validate the results for larger deployments of nodes.

A Robust NLOS Bias Mitigation Technique for RSS-TOA-Based Target Localization

This letter proposes a novel robust mitigation technique to address the problem of target localization in adverse non-line-of-sight (NLOS) environments. The proposed scheme is based on combined received signal strength and time of arrival measurements. Influence of NLOS biases is mitigated by treating them as nuisance parameters through a robust approach. Due to a high degree of difficulty of the considered problem, it is converted into a generalized trust region sub-problem by applying certain approximations, and solved efficiently by merely a bisection procedure. Numerical results corroborate the effectiveness of the proposed approach, rendering it the most accurate one in all considered scenarios.

GNSS Positioning Enhancement Based on NLOS Multipath Biases Estimation Using Gaussian Mixture Noise

Global navigation satellite systems (GNSS) have been widely used in many applications where positioning plays an important role. However, the performances of these applications can be degraded in urban canyons, due to Non-Line-Of-Sight (NLOS) and Multipath interference affecting GNSS signals. In order to ensure high accuracy positioning, this article proposes to model the NLOS and Multipath biases by Gaussian Mixture noise using Expectation Maximization (EM) algorithm. In this context, an approach to estimate the Multipath and NLOS biases for real time positioning is presented and statistical tests for searching the probability distribution of NLOS and Multipath biases are illustrated. Furthermore, a hybrid approach based on PF (Particle Filter) and EM algorithm for estimating user position in hard environment is presented. Using real GPS (Global Positioning System) signal, the efficiency of the proposed approach is shown, and a significant improvement of the positioning accuracy over the simple PF estimation is obtained.