A Robust Semidefinite Source Localization TDOA/FDOA Method with Sensor Position Uncertainties

This paper investigates the problem of received signal strength (RSS) based target localization with sensor position uncertainties and unknown model parameters. Transmit power and path-loss exponent (PLE) are two key parameters of the path-loss model that is critical for RSS schemes to work well. In practice, however, these parameters change dynamically and are difficult to estimate in real time. Four combinations of the two parameters are considered: both parameters are known; only one of the two is known; and both are unknown. We develop new semidefinite programming (SDP) methods to relax the nonconvex maximum likelihood estimator (MLE) problem for each case, and these methods are further optimized when sensor position uncertainties are taken into consideration. We present a comprehensive set of simulation results to compare the performance of the proposed scheme with existing methods.

Efficient semidefinite solutions for TDOA-based source localization under unknown PS

This paper considers the problem of moving source localization by introducing an additional Doppler frequency shift (DFS) measurement into the previous location system using time differences of arrival (TDOAs) and frequency differences of arrival (FDOAs). Because of the separation of associated data channels and the difference in the estimation techniques, the DFS is independent of TDOA and FDOA measurements. The Cramer-Rao lower bound (CRLB) analysis shows that introducing DFS can improve source localization accuracy comparing with that of the TDOA and FDOA localization system, especially for the velocity location accuracy. An improved two-step weighted least-squares (I-TSWLS) source localization method utilizing DFS as well as TDOA and FDOA is developed. The solution is shown analytically to achieve the CRLB over small noise region, and have a better performance than that of the TSWLS method, especially when the sensor station error noises become large. Simulation results demonstrate the good performance of the proposed method.

In this paper, we introduce a rank-one Semi-Definite Programming (SDP) solution method for mobile source localization in sensor networks. The position and velocity of mobile source are jointly estimated using Time Delay (TD) measurements. To obtain the position and velocity of mobile source, a Relaxed Semi-Definite Programming (RSDP) algorithm is firstly designed by dropping the rank-one constraint. However, dropping the rank-one constraint leads to produce a suboptimal solution. To improve the performance, we further put forward the Penalty Function Semi-Definite Programming (PF-SDP) method to obtain the rank-one solution of the estimation problem by introducing the penalty terms. By adaptively choosing the penalty coefficient, an Adaptive Penalty Function Semi-Definite Programming (APF-SDP) algorithm is also proposed to avoid the excessive penalty. We also conduct experiments in both a simulated environment and a real system to demonstrate the effectiveness of the proposed methods. The results have demonstrated that the proposed APF-SDP outperforms the PF-SDP in terms of the position and velocity estimation whether the noise level is large or not.

We consider the source and network localization problems, seeking to strengthen the relationship between the Weighted-Least-Square (WLS) and the Maximum-Likelihood (ML) solutions of these problems. To this end, we design an optimization algorithm for source and network localization under the principle that: a) the WLS and the ML objectives should be the same; and b) the solution of the ML-WLS objective does not depend on any information besides the set of given distance measurements (observations). The proposed Range-Global Distance Continuation (R-GDC) algorithm solves the localization problems via iterative minimizations of smoothed variations of the WLS objective, each obtained by convolution with a Gaussian kernel of progressively smaller variances. Since the last (not smoothed) WLS objective derives directly from the ML formulation of the localization problem, and the R-GDC requires no initial estimate to minimize it, final result is maximum-likelihood approach to source and network localization problems. The performance of the R-GDC method is compared to that of state-of-the-art techniques such as semidefinite programming (SDP), nonlinear Newton least squares (NLS), and the Stress-of-a-MAjorizing-Complex-Objective-Function (SMACOF) algorithms, as well as to the Cramér-Rao Lower Bound (CRLB). The comparison reveals that the solutions obtained with the R-GDC algorithm is insensitive to initial estimates and provides a localization error that closely approaches that of the corresponding fundamental bounds. The R-GDC is also found to achieve a complexity order comparable to that of the SMACOF, which is known for its efficiency.

In order to improve the deficiency generated from uneven distribution of anchors in the distributed semidefinite programming (SDP) method, improved distributed method is proposed for solving Euclidean metric localization problems that arise from large-scale wireless sensor networks (WSN). By introducing the change of factorization, nonlinear programming (NLP) model is presented on each subarea, and feasible direction algorithm is introduced for solving NLP problems, which can be executed in parallel. Numerical results on large-scale sensor network problems with more than 10000 nodes demonstrate that, the proposed method performs better than the distributed SDP method.

This paper considers the problem of tracking a moving target using the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements obtained at two unmanned aerial vehicles (UAVs) with varying baseline. Accumulation time is necessary because the emitter position cannot be estimated at each emission when there are only two UAVs as sensors. And the target position and velocity estimation accuracy often suffer from low convergence in conventional formation flight mode no matter what nonlinear filtering algorithm is used. Based on the analysis of the influence of different flight modes on the positioning performance, a moving target tracking system from two UAVs with varying baseline is proposed. The performance of unscented Kalman filter (UKF) under proposed system is analysed and compared with the Cramer-Rao lower bound (CRLB). Simulation results show that the proposed system can speed up the convergence.

Acoustic source localization based on time difference of arrival (TDOA) measurements from spatially separated sensors is an important problem in wireless sensor networks (WSNs). While extensive research works have been performed on algorithm development, limited attention has been paid in how to form the sensor pairs. In the literature, most of the works adopt a centralized sensor pairing strategy, where only one common sensor node is chosen as the reference. However, due to the multi-hop nature of WSNs, it is well known that this kind of centralized signal processing method is power consuming since raw measurement data is involved in the transmissions. To reduce the requirements for both network bandwidth and power consumptions, we propose an in-network sensor pairing method to collect the TDOA measurements while guaranteeing the quality of source localization. The solution involves finding a minimal sized dominating set (MSDS) for a graph of the muti-hop network. It has been proved that in-network sensor pairing can result in the same Cramer-Rao-Bound (CRB) as the centralized one but at a far more less communication cost. Furthermore, the structure of the proposed in-network sensor pairing coincides with the decentralized source localization, which is an important application of our method.

This paper presents a comprehensive study of methods for detecting and localizing electronic warfare (EW) sources under complex conditions, which include the influence of intensive intentional jamming, multipath signal propagation, time-varying emission parameters, and dynamic movement of the sources. The relevance of the research is driven by the growing role of EW means in modern armed conflicts and the need to ensure timely detection and neutralization of such threats. The classification of EW sources based on spectral, energy, and spatial characteristics is considered, along with an analysis of their impact on communication, radar, and navigation systems. Traditional methods for determining the coordinates of sources—such as amplitude, phase, TDOA (Time Difference of Arrival), and FDOA (Frequency Difference of Arrival)—are examined in detail, as well as modern approaches that rely on adaptive antenna arrays, spectral analysis, and artificial intelligence algorithms for signal identification. Special attention is given to algorithms for improving localization accuracy in noisy and dynamic environments, including adaptive filtering methods, multiposition signal processing (data fusion), optimization of sensor network configurations, and trajectory prediction of moving objects. Results of computer simulations are presented, with error assessments for various application scenarios and different interference levels. The proposed approaches can be applied in advanced electronic intelligence systems and automated EW countermeasure complexes to enhance the efficiency of real-time detection, identification, and localization of emission sources. Keywords: electronic warfare, source localization, TDOA, FDOA, adaptive antennas, artificial intelligence, multisensor processing, intensive jamming, simulation.

The position and velocity estimation of underwater moving targets is an important part of the application of underwater sensor networks. The commonly used fusion of time difference of arrival (TDOA) and angle of arrival (AOA) can only roughly estimate the target position, but also has some limitations for nonlinear problems. So in order to overcome the nonlinear problem and improve the accuracy of underwater target location.Based on TDOA and AOA, this paper adopts a three-step location method which combines frequency difference of arrival (FDOA).At the same time, the whale algorithm is used to optimize the measurement error based on the weighted least square method (Tswls). Finally, the experimental results show that compared with TDOA location method and tdoa/aoa hybrid location algorithm, this method is superior to the above methods in the accuracy and bias of position and velocity estimation.

We consider the problem of single source localization using time-difference-of-arrival (TDOA) measurements. By analyzing the maximum-likelihood (ML) formulation of the problem, we show that under certain mild assumptions on the measurement noise, the estimation errors of both the closed-form least-squares estimate proposed in [1] and the ML estimate, as measured by their distances to the true source location, are of the same order. We then use this to establish the curious result that the objective function of the ML estimation problem is actually locally strongly convex at an optimal solution. This implies that some lightweight solution methods, such as the gradient descent (GD) and Levenberg-Marquardt (LM) methods, will converge to an optimal solution to the ML estimation problem when properly initialized, and the convergence rates can be determined by standard arguments. To the best of our knowledge, these results are new and contribute to the growing literature on the effectiveness of lightweight solution methods for structured non-convex optimization problems. Lastly, we demonstrate via simulations that the GD and LM methods can indeed produce more accurate estimates of the source location than some existing methods, including the widely used semidefinite relaxation-based methods.

Direct solution for fixed source location using well-posed TDOA and FDOA measurements

The problem of distributed parameter estimation from binary quantized observations is studied when the unquantized observations are corrupted by combined multiplicative and additive Gaussian noise. These results are applicable to sensor networks where the sensors observe a parameter in combined additive and nonadditive noise and to a case where dispersed receivers are employed with analog communication over fading channels where the receivers employ binary quantization before noise-free digital communications to a fusion center. We first discuss the case in which all the quantizers use an identical threshold. The parameter identifiability condition is given, and, surprisingly, it is shown that unless the common threshold is chosen properly and the parameter lies in an open interval, the parameter will not generally be identifiable, in contrast to the additive noise case. The best achievable mean square error (MSE) performance is characterized by deriving the corresponding Cramer-Rao Lower Bound (CRLB). A closed-form expression describing the corresponding maximum likelihood (ML) estimator is presented. The stability of the performance of the ML estimators is improved when a nonidentical threshold strategy is utilized to estimate the unknown parameter. The thresholds are designed by maximizing the minimum asymptotic relative efficiency (ARE) between quantized and unquantized ML estimators. Although the ML estimation problem is nonconvex, it is shown that one can relax the optimization to make it convex. The solution to the relaxed problem is used as an initial solution in a gradient algorithm to solve the original problem. Next, the case where both the variances of the additive noise and multiplicative noise are unknown is studied. The corresponding CRLB is obtained, and the ML estimation problem is transformed to a convex optimization, which can be solved efficiently. Finally, numerical simulations are performed to substantiate the theoretical analysis.

To weaken the effect of receiver location error on localization accuracy and make the localization model closer to the practical scenario, this paper considers the receiver location errors, usually neglected in prior studies into the measurement model, and proposes an algebraic method for locating a moving source using time difference of arrival (TDOA), frequency difference of arrival (FDOA), and differential Doppler rate measurements. The proposed method is based on the pseudo-linear set of equations and two-step weighted least square estimator. Only noise values of receiver locations and three types of positioning measurements are available for processing. In addition, a new Cramér-Rao lower bound (CRLB) combining TDOA, FDOA, and differential Doppler rate in the presence of receiver location errors is also derived in this paper. Theoretical analysis and simulation results both indicate that the proposed method can attain CRLB at a moderate noise level, avoid the rank deficiency problem efficiently, and achieve a significant improvement over the existing methods.

Efficient closed-form solution for target localization using TDOA measurements in the presence of sensor position errors