Unknown RSSD-Based Localization CRLB Analysis With Semidefinite Programming

Passive source positioning is of great interest due to the numerous applications. Energy based localization methods are popular because of their low cost and simplicity. In this paper, source localization with unknown transmit power is considered based on received signal strength difference (RSSD) measurements. An efficient three stage estimator is presented. First, a nonlinear RSSD-based model is formulated and the corresponding Fisher information for Gaussian distributed noise is derived. Next, a mean squared error (MSE) estimator is developed based on an unknown linear bias and Fisher information minimization. This results in a nonlinear optimization problem to minimize the MSE directly considering the linear bias. Finally, semidefinite relaxation is employed to transform this nonconvex problem into a convex minimization problem. This can be solved efficiently to obtain the optimal solution of the corresponding semidefinite programming (SDP) problem. Necessary and sufficient conditions for the optimality of the proposed RSSD based linear biased MSE SDP method (RLBM-SDP) are derived. Further, the corresponding bias sensitivity is formulated which yields an extension of the proposed method to a bounded RLBM-SDP (BRLBM-SDP) algorithm that includes a new constraint on the norm of the bias sensitivity. The computational complexity of the proposed methods is evaluated. Performance results are presented which confirm the efficiency of the proposed methods for sufficiently large signal to noise ratios.

The authors propose a method for reducing the effects of GDOP (geometric dilution of precision) in position-fix navigation systems. The idea is to incorporate ridge regression into the aircraft navigation signal processor. MSE (mean square error) performance of an ordinary LMS (least mean square) signal processor was compared with one using ridge regression. Computer simulations confirmed the theory that variance inflation caused by GDOP can be measurably reduced by the ridge regression algorithm. The technique is applicable not only to DME/DME (distance measuring equipment) and GPS but applies also to any position-fix navigation aid, e.g. Loran-C, Omega, and JTIDS relative navigation. >

As an emerging technique with a promising application prospect, the device-free localization (DFL) technique has drawn considerable attention due to its ability of realizing wireless localization without the need of equipping the target with any device. The DFL technique detects the shadowed links and realizes localization with the received signal strength (RSS) measurements of these links. However, one major disadvantage of the DFL technique is that the RSS signal is too sensitive, and a slight variation of the environment will cause the variation of RSS measurements, which incurs the misjudgment of shadowed links and degradation of localization performance. To solve this problem, a robust DFL scheme based on differential RSS is proposed. The scheme utilizes the novel differential RSS to judge whether a link is shadowed, which not only eliminates the need of acquiring reference RSS measurements but also overcomes the negative effect incurred by the environment. Meanwhile, an outlier detection scheme is presented to filter out the outlier links that are far away from the target. We present the observation model of the shadowed links and incorporate it into the particle filter framework to realize location estimation robustly. Experimental results demonstrate the outstanding performance of the proposed scheme.

This paper is concerned with optimal trajectory control for two unmanned aerial vehicles (UAVs) in a multisource localization environment. The received signal strength (RSS) at the UAVs in specified time intervals permits passive differential RSS (DRSS)-based localization of multiple radio frequency (RF) sources with unknown transmit powers. A steering algorithm is proposed to update the UAV waypoints in order to minimize the summation of the uncertainty of the source locations. The UAV paths are optimized by maximizing the determinant of the Fisher Information Matrix (FIM). The FIM is approximated at successive waypoints using the estimated locations of the sources. In addition to maximizing the localization accuracy, the objectives of the proposed trajectory control are to minimize the number of UAVs, the mission time and the path length. As the DRSS is a non-linear measurement, an extended Kalman filter (EKF), which is a non-linear filtering technique, is considered in this paper. The efficiency of the approach is depicted through simulations.

The ability to determine the location of a sensor node in a wireless sensor network is essential in many applications. We propose a received signal strength (RSS) based cooperative localization technique. The target nodes, whose locations are unknown during the deployment phase, communicate with the anchor nodes (whose locations are known) and the neighboring target nodes to localize themselves. In the proposed technique the target nodes behave as pseudo anchor nodes after they have localized themselves. It is observed that in such cooperative techniques the localization error propagates from one iteration to the next. We mitigate this error propagation by eliminating the network edge nodes from updating their location information after the first iteration. We propose two distributed edge node detection techniques: quadrant method (Quad) and geometric dilution of precision (GDOP) based method. Extensive simulations have been carried out, on uniform anchor and non-uniform network topologies, to analyze the performance of the proposed edge detection techniques and the iterative localization algorithm. The proposed localization algorithm is compared with state of the art localization techniques using simulations as well as experiments, and is shown to achieve improved localization accuracy. The Cramer-Rao lower bound (CRLB) is also derived and used as a performance benchmark.

The orientation- and device-dependent received signal strength (RSS) diversity has become a challenge for improving performance of localization using low-cost Internet of Things (IoT) devices. The existing orientation-compensation methods are based on the principle of database matching; thus, they are susceptible to performance degradation if the testing node orientation does not exist in the training data. To alleviate this issue, the orientation-compensation model (OCM) is proposed to compensate for the orientation-dependent RSS diversity. In contrast to the existing orientation-compensation methods that involve only the device orientation, the proposed method presents the device and anchor (i.e., base station) deflection angles and uses these angles as variables for the OCM. The introduction of these angles can significantly reduce the requirement for device orientations in the training data. Furthermore, based on the characteristics of the OCM and differential RSS (DRSS), this paper proposes an OCM/DRSS integrated data-processing strategy. This strategy is demonstrated to be effective in enhancing localization in IoT applications that have multiple devices with three-dimensional orientation diversity.

This paper presents a cost-effective localization method by using received signal strength (RSS) from single wireless access point (AP) that has only three directional antennas. To reduce the requirement for the costly database training process, a three-step parametric model-based approach is proposed. This approach estimates the AP-device angle, distance, and the device location analytically by making use of wireless path-loss models, antenna radiation patterns, and differential RSS. Meanwhile, the differential antenna gain is introduced to eliminate the need for known AP-device distances when estimating the AP-device angle. Furthermore, to circumvent the difficulty in detecting outliers in a single-AP system, this paper further integrates single-AP solutions with dead-reckoning (DR) to obtain more robust solutions. Three types of measurement models (i.e., the device location updates, AP-device angle updates, and AP-device distance updates) are built from the single-AP localization system. Static and dynamic field tests with the new Bluetooth 5 signals indicated the possibility for using RSS from three directional antennas on single AP to obtain a low-cost localization solution and the effectiveness of integrating with DR on mitigating the impact of outliers.

Realizing accurate detection of an unknown radio transmitter (URT) has become a challenging problem due to its unknown parameter information. A method based on received signal strength difference (RSSD) fingerprint positioning technique and using factor graph (FG) for 2-D scenario has been developed. However, the URT positioning under 3-D scenario is more difficult with the large number of unknown parameters and has greater practical significance. In addition, the previous RSSD-based FG model is not accurate enough to express the relationship between the RSSD and corresponding location coordinates since the RSSD variances of reference points are different in practice. This paper proposes a more accurate 3-D FG model to reduce the influence of difference of RSSD measurement variances on positioning accuracy effectively by utilizing weighted least square (WLS). With the proposed RSSD-based 3-D WLSFG model and sum-product rule, positioning process of the proposed 3-D RSSD-WLSFG algorithm is derived. To verify the feasibility of the proposed method, we also explores the effects of different signal receiver numbers and grid distances on positioning accuracy. The simulation experiment results show that the proposed algorithm can obtain the best positioning performance compared with the conventional K nearest neighbor (KNN) algorithm and RSSD-FG algorithm under different grid distances and signal receiver numbers.

Received Signal Strength (RSS) localization is widely used due to its simplicity and availability in most mobile devices. The RSS channel model is defined by the propagation losses and the shadow fading. These parameters might vary over time because of changes in the environment. In this paper, the problem of tracking a mobile node by RSS measurements is addressed, while simultaneously estimating a two-slope RSS model. The methodology considers a Kalman filter with Interacting Multiple Model architecture, coupled to an on-line estimation of the observation's variance. The performance of the method is shown through numerical simulations in realistic scenarios.

In this paper, considering a mobile wireless sensor network, we study the problem of exploiting sensor mobility information in the process of sensor localization under two range measurement models, namely the time-of-arrival (TOA) model and the received signal strength (RSS) model. To do so, for each model, we first derive the maximum likelihood (ML) location estimator for the case of error-free velocity measurements. As the corresponding optimization problems are non-convex, we resort to semi-definite relaxation (SDR) techniques to find approximate solutions to each problem using semi-definite programming (SDP). We then extend our results to the cases where the velocity measurements are subject to measurement errors. Our simulation results show that exploiting the mobility information in the localization process can significantly improve the performance of the sensor localization. Moreover, mobility-aided localization has the potential to address some of typical positioning problems, such as sensitivity to the ranging measurement errors and the requirement on the number of the anchors needed to uniquely localize the sensor nodes.

Deploying multiple unmanned aerial vehicles (UAVs) to locate a signal-emitting source covers a wide range of military and civilian applications like rescue and target tracking. It is well known that the UAVs-source (sensors-target) geometry, namely geometric configuration, significantly affects the final localization accuracy. This paper focuses on the geometric configuration optimization for received signal strength difference (RSSD)-based passive source localization by drone swarm. Different from prior works, this paper considers a general measuring condition where the spread angle of drone swarm centered on the source is constrained. Subject to this constraint, a geometric configuration optimization problem with the aim of maximizing the determinant of Fisher information matrix (FIM) is formulated. After transforming this problem using matrix theory, an alternating direction method of multipliers (ADMM)-based optimization framework is proposed. To solve the subproblems in this framework, two global optimal solutions based on the Von Neumann matrix trace inequality theorem and majorize-minimize (MM) algorithm are proposed respectively. Finally, the effectiveness as well as the practicality of the proposed ADMM-based optimization algorithm are demonstrated by extensive simulations.

Motivated by recent work on atomic norms in inverse problems, we propose a new approach to line spectral estimation that provides theoretical guarantees for the mean-squared-error (MSE) performance in the presence of noise and without knowledge of the model order. We propose an abstract theory of denoising with atomic norms and specialize this theory to provide a convex optimization problem for estimating the frequencies and phases of a mixture of complex exponentials. We show that the associated convex optimization problem can be solved in polynomial time via semidefinite programming (SDP). We also show that the SDP can be approximated by an l1-regularized least-squares problem that achieves nearly the same error rate as the SDP but can scale to much larger problems. We compare both SDP and l1-based approaches with classical line spectral analysis methods and demonstrate that the SDP outperforms the l1 optimization which outperforms MUSIC, Cadzow's, and Matrix Pencil approaches in terms of MSE over a wide range of signal-to-noise ratios.

In the wireless sensor network (WSN) based rigid body target localization systems, the error caused by the non-line-of-sight (NLoS) transmission of wireless signal can seriously deteriorate the localization accuracy. To improve the estimation performance of rigid body posture, including the parameters of the position and the direction, a rigid body localization (RBL) technology is proposed based on the semi-definite programming (SDP) with NLoS error elimination. By taking the unknown NLoS errors as the balancing parameters in the received signal strength (RSS) model, the results of the maximum likelihood estimation (MLE) is obtained according to a nonlinear least squares (NLS) problem, which is solved by using the semi-definite relaxation (SDR) method. The obtained balancing parameters are then re-substituted into the model to refine the parameters in the semi-definite programming problem to mitigate the effect of the NLoS error on the localization performance. Finally, the singular value decomposition (SVD) is used to solve the parameters of rigid body posture. The effectiveness of the algorithm is verified by computer simulation.

Sybil attack refers to the situation when a malicious node falsely claims to have numerous identities and is known to be one of the security threats to the Internet of Things (IoT). Due to recent increase usage of unmanned aerial vehicles (UAVs) in various applications, Sybil attack has been identified as a threat to the flying ad hoc network (FANET) paradigm and its integration with the IoT to form the Internet of Flying Things (IoFT). In this paper, we propose an intelligent Sybil attack detection approach for FANETs-based IoFT using physical layer characteristics of the radio signals emitted from the UAVs as detected by two ground nodes. A supervised machine learning approach is employed and experimented with several different classifiers available in the Weka workbench platform. The experiment was carried out based on two features of the radio signals, namely, the received signal strength difference (RSSD) and the time difference of arrival (TDoA). Simulation results revealed that the proposed scheme can achieve a high correct classification accuracy of above 91% on average, even for smart malicious nodes with power control capability operating at power levels not directly trained. In addition to its high performance, the proposed scheme is also less susceptible to various attacks commonly carried out on the upper layers, such as data spoofing, due to the use of only intrinsically generated physical layer data. Furthermore, no additional communications overheads of the UAV nodes are required for the functionality of this scheme.

Geolocation is an important topic nowadays. Among other applications, geolocation can be used by frequency regulators to monitor the time, frequency and space domain. In this case of a passive geolocation system, Time Difference of Arrival (TDOA) is often used. In this paper we analyze a geolocation system based on a combination of TDOA and Received Signal Strength Differences (RSSD). The benefit of combining the two measurement types is shown using the Cramer Rao Lower Bound (CRLB). The suitability of the Unscented Kalman Filter (UKF) as an algorithm for the hybrid geolocation system is investigated. Simulation results show that by using the UKF, the instability of RSSD geolocation, that is often caused by bad geometry, is compensated. The UKF nearly approaches the CRLB and greatly outperforms the previously proposed least squares hybrid solution. Using the UKF, the information about the signal power can be definitely used to enhance the position estimation accuracy.