Terahertz (THz) frequency band has been widely studied and is recognized as a promising candidate for centimeter-level localization. However, the limited coverage of THz networks may result in localization failures, while a heterogeneous deployment of millimeter-wave (mmWave) and THz radio units (RUs) offers a viable solution to mitigate this issue. This paper presents a theoretical framework for evaluating the performance limits of localization systems in mmWave and THz heterogeneous networks. In this architecture, the mmWave RUs serve as macro base stations (BSs), while the THz RUs function as micro BSs distributed around each mmWave RU. By leveraging the standard tools of stochastic geometry to model the spatial distributions of the RUs and ambient obstacles, the localizability of a target is computed to evaluate the probability of achieving sufficient signal-to-interference-plus-noise ratio for localization in both line-of-sight (LoS) and non-line-of-sight (NLoS) conditions. Furthermore, the Cram é r-Rao lower bounds in both LoS and NLoS scenarios are analytically derived to characterize the overall positioning performance. Numerical results demonstrate that the hybrid deployment strategy significantly improves both the network coverage and localization accuracy compared to mmWave-only and THz-only networks.

Subspace location estimators are a class of range-based source localization (SL) methods built upon the multidimensional similarity (MDS) theory. Since they are computationally lightweight while maintaining a reasonably good level of positioning accuracy, these techniques can be well-suited for the context of Internet of Things (IoT), where precise localization is necessary but the on-device computational resources turn out to be relatively limited. MDS analysis (MDSA), in signal processing terms, is the statistical process of disentangling the signal subspace components from their disturbance counterparts for an observed MDS matrix that measures the similarity among multiple source-sensor coordinate differences. A prominent drawback of traditional MDSA schemes devised under the assumption of Gaussian noise is their vulnerability to outliers in the available range-type data, which are frequently encountered in IoT SL applications due to adverse environmental factors like non line-of-sight signal propagation and interference. In this contribution, we use symmetric$\alpha $-stable$(S \alpha S)$distributions to systematically characterize the MDS matrix observation errors, thus accounting for the existence of outliers. To resist against$S \alpha S$disturbances, we cast MDSA as an$\ell _{p}$-norm-based robust low-rank approximation problem. We then develop a practical optimization solution by means of the alternating direction method of multipliers, for which we further conduct a theoretical analysis of convergence. Simulations and real-world experiments confirm the feasibility of our robust subspace positioning approach.

This contribution considers the problem of robust target localization using the possibly unreliable hybrid received signal strength and time-of-arrival measurements, in the Internet of Things (IoT) context. Traditional positioning approaches relying on either extra a priori error information for robustification or the computationally intensive convex programming techniques for optimization do not fit well into the IoT applications with limited computing resources. Such concerns, however, will jeopardize the straightforward applicability of many ready-made solutions to the IoT positioning services if left untreated. In this article, the problem is resolved in a different manner. We adopt here a Geman–McClure like loss function, which is much less sensitive to the biased sensor observations, in order to statistically robustify the$\ell _{2}$-sapce-based location estimator. A computationally attractive iterative message passing algorithm is then developed to conduct efficient optimization. Simulation results demonstrate the performance superiority of the proposed scheme over its competitors in various localization environments.

This letter considers the denoising of possibly unreliable bistatic range (BR) measurements for elliptic target positioning in multistatic systems. Built upon the BRs over all transmitter–target–receiver paths, the concept of BR matrix is introduced here to handle the problem in an algebraic manner. Specifically, the rank of the ideal BR matrix is proven to be at most 2, which constitutes the foundation of a low-rank matrix approximation (LRMA) formulation presented to enhance the quality of raw datasets. An alternating direction method of multipliers (ADMM) is subsequently devised to perform efficient optimization. Simulations validate the proposed LRMA scheme for denoising.

The inadvertent incorporation of deviating samples into the measured indirect and direct path delays is generally unavoidable in the practical implementation of passive elliptic localization. These outlying observations, however, can do great harm to the positioning performance if left untreated. Here, a robust statistics based method is put forward as the solution to such a problem. The non-outlier-resistant ℓ2cost function in the traditional least squares formulation is replaced by a certain differentiable error measure that possesses resistance to the presence of abnormally large fitting errors. A globally optimized hybrid quasi-Newton and particle swarm optimization algorithm is then developed for an efficient realization of the robust estimator. The strong capability of the presented approach to deal with outliers and its applicability to typical adverse localization environments are demonstrated via simulations.

Passive multistatic localization (PML) refers to locating a signal-reflecting/relaying target using the bistatic range and direct range measurements acquired by employing multiple spatially-separated transmitters and receivers, where the transmitter positions are unknown. In real-world applications, one of the major technical challenges faced in PML is the non-lineof-sight (NLOS) propagation of signals, and recent studies have turned to the concept of robust statistics to tackle such an issue. Continuing to delve into this research direction, here we address the discrepancy arising from the fact that the conventional robust statistical PML schemes inherently assume zero-centered error samples, which may not hold true when the positive NLOS biases are present. In contrast to the existing PML solutions, our proposal is based on the maximum correntropy criterion with variable center (MCC-VC), thereby taking into consideration the potential non-zero-centrality of error samples in the estimator derivation. Subsequently, we develop an alternating minimization algorithm to handle the nonconvex MCC-VC optimization problem in a way that can strike a fine balance between accuracy and computational efficiency. The superiority of our PML approach over its competitors is demonstrated via computer simulations

Elliptic target positioning from the bistatic ranges (BRs), as an emerging localization scheme, has recently gained considerable traction for its diverse applications in multistatic systems such as radar, sonar, and wireless sensor networks. This contribution extends the work of previous research on the low-rank property of the BR matrix (Xiong, “Denoising of bistatic ranges for elliptic positioning,” IEEE Geosci. Remote Sens. Lett., vol. 20, pp. 1–3, 2023, Art. no. 3500503) to the brand new use case of robust elliptic positioning in the presence of missing data. Due to the structures of the outlier-inducing errors when embodied in the BR matrix, many of the off-the-shelf low-rank matrix completion (LRMC) solutions cannot be applied. We address this challenge by formulating the problem of outlier-resistant BR matrix recovery as constrained minimization of an ℓ2,1-norm based loss function, and devising an algorithm based on alternating direction method of multipliers to efficiently solve the resultant LRMC. Simulations are conducted to demonstrate the efficacy of the developed robust elliptic positioning technique in various localization scenarios.

Elliptic positioning (EP) has been a topic of lively interest to localization practitioners owing to widespread adoption of the bistatic configuration in many location-enabling technologies nowadays. This letter addresses the problem of non-Gaussian error mitigation in EP, by formulating it as joint estimation of target position coordinates and a balancing parameter (BP) for the bias errors. An alternating minimization algorithm is put forward to break the original formulation down into a conventional weighted nonlinear least squares (WNLS) location estimator and a closed-form BP-update step. With its objective being properly decomposed, the WNLS subproblem is converted into the difference-of-convex programming framework, to which an efficient iterative solution based on the concave-convex procedure is applicable. Simulation results demonstrate that the proposed error-reduced EP approach can outperform a number of existing methods in terms of localization accuracy.

In this article, a direction of arrival (DOA) based estimation method is proposed for the localization of acoustic gas leakage sources indoors, with the use of a microphone array. Since the narrowband signal assumption for the uniform circular array (UCA)-MUSIC and ESPRIT methods are not applicable to the case of gas leakage sources, different approaches including the incoherent, coherent, and frequency-domain frequency-invariant beamformer ones are leveraged and optimized for the signal shape considered. The proposed method is evaluated with real-world experimental results obtained with a gas pistol resembling a leakage. The evaluation using experimental data demonstrates that coherent subspace (CSS)-MUSIC is ahead of other methods in the error metrics.

This paper proposes two efficient and easy-to-use error mitigation solutions to the problem of three-dimensional (3-D) angle-of-arrival (AOA) source localization in the mixed line-of-sight (LOS) and non-line-of-sight (NLOS) indoor environments. A weighted linear least squares estimator is derived first for the LOS AOA components in terms of the direction vectors of arrival, albeit in a sub-optimal manner. Next, data selection exploiting the sum of squared residuals is carried out to discard the error-prone NLOS connections. In so doing, the first approach is constituted and more accurate closed-form location estimates can be obtained. The second method applies a simulated annealing stochastic framework to realize the robust ℓ1-minimization criterion, which therefore falls into the methodology of statistical robustification. Computer simulations and ultrasonic onsite experiments are conducted to evaluate the performance of the two proposed methods, demonstrating their outstanding positioning results in the respective scenarios.

We revisit herein the problem of time-difference-of-arrival (TDOA) based localization under the mixed line-of-sight/non-line-of-sight propagation conditions. Adopting the strategy of statistically robustifying the non-outlier-resistantl2loss, we formulate it as the minimization of a possibly non-differentiable generalized robust cost function, which is rooted in the analog locally competitive algorithm (LCA) for sparse approximation. We then present a Lagrange programming neural network to address the optimization formulation, with the non-differentiability issues being handled by grafting thereon the LCA concept of internal state dynamics. Compared with the existing algorithms, our approach is computationally less expensive, less reliant on the use of a priori error information, and observed to be capable of producing higher localization accuracy.

This letter focuses on time-of-arrival based localization using multidimensional similarity (MDS) analysis under non-line-of-sight (NLOS) propagation. To handle row-column structured outliers in the MDS matrix introduced by NLOS errors, we present a novel robust matrix approximation scheme with the use ofℓ2,1-norm and apply the alternating direction method of multipliers to solve the resultant nonlinear constrained optimization problem. The proposed method does not require any prior knowledge of NLOS information and can benefit from a comparatively low complexity. Simulation results show that our algorithm is superior to several existing approaches in mild and moderate NLOS environments.