This paper focuses on reducing the effect of systematic uncertainties on the near-field or far-field source direction-finding accuracy by introducing a calibration emitter, which suffers the same uncertainties as the actual source. We propose a modified polar representation (MPR)-based closed-form algebraic algorithm, i.e., the improved successive unconstrained minimization (SUM), to eliminate the common errors of time difference of arrival (TDOA) measurements, thereby refining the source direction-finding accuracy. The simulations show that the proposed algorithm can approach the Cramer–Rao Lower Bound´ (CRLB); and demonstrate the positive effect of the calibration emitter on the direction-finding performance under the condition of varying measurement error, source range, and sensor position error.

This paper focuses on improving the sensor selection performance in the time difference of arrival (TDOA)-based localization scenario with the presence of source estimation error. In existing schemes, a coarse source position is first estimated and regarded as the actual counterpart for selecting optimal sensors. However, if the estimated position deviates from the actual position, the localization accuracy determined by the selected sensor subset will severely degrade. To solve the issue, we devise a distance-related weighted average Cramér Rao lower bound (WA-CRLB) to include the spatial information of the actual position by scattering sampling points around the estimated source position according to its distribution. Then, we formulate a Boolean vector-based sensor selection optimization problem to minimize WA-CRLB and propose a modified iterative swapping greedy (MISG) algorithm. Simulation results show that the proposed MISG algorithm achieves higher localization robustness with the increase of TDOA measurement error strength, and has lower computational complexity compared with the previous semi-definite relaxation (SDR)-based algorithms.

This letter addresses the time-of-arrival based localization problem when the source and sensors are not synchronized, whereby an unknown transmission time is introduced. A non-convex weighted least squares (WLS) minimization problem is first formulated to jointly estimate the source position and the unknown transmission time by transforming the measurement model, and then semidefinite relaxation is applied to relax the WLS problem as a convex semidefinite program (SDP). The relaxed SDP problem is always tight and thus the optimal solution of the WLS problem can always be obtained. The proposed method is then extended to the moving source localization scenario, where the source velocity is assumed to be a constant for a sufficiently small observation period. Simulation results show that the proposed method is able to reach the Cramer-Rao lower bound accuracy when the noise is not very large.

Accurate location estimation of Internet-of-Things (IoT) devices within an Area of Interest (AoI) is a challenging issue, especially in a global navigation satellite system (GNSS)-constrained environment. In this article, we present a space-air integrated localization network (SAILN) architecture to exploit the advantages of the unmanned-aerial-vehicle (UAV)-based localization through joint position and power optimization (JPPO) strategies. In SAILN, UAVs can utilize their flexible movement to obtain the line-of-sight (LOS) path with a high probability, thereby providing the potential IoT devices in the AoI with supplementary localization information. The JPPO of UAVs aims to improve the regional localization accuracy for the entire AoI, considering the no-fly-zone (NFZ) and the total energy constraint. We propose the average localization accuracy increment (ALAI) of the sampling points in the AoI as the metric to measure the performance of SAILN compared with that of only satellites, which is regarded as the objective to formulate the JPPO problems for UAV operations in both static and dynamic SAILN. The intractable problems can be resolved by the pure genetic algorithm (PGA) that has a low computational cost and unique features suiting the JPPO of UAVs. Then, by taking advantage of the ALAI convexity to the UAVs' power, we propose a power reallocation-based two-step algorithm (PRTSA) to further explore an improved JPPO solution. Simulation results validate that the proposed PRTSA can obtain a higher localization accuracy for the entire AoI than the PGA and the other straightforward baselines.

Unmanned aerial vehicles (UAV) deployment is of pivotal importance in the promising space-air integrated localization network (SAILN), which is a typical partially controllable network and supports 3- dimensional (3D) localization. To improve the localization accuracy for specific area or user, several UAVs need to be deployed. This paper proposes an iterative UAV deployment strategy for SAILN, which can minimize the localization error by determining accurate 3D coordinate information (elevation and azimuth angles, distance) for all the supplementary UAVs. Specifically, based on the analysis of accuracy increment when a new UAV is added into SAILN, the genetic algorithm (GA) is leveraged to find its optimal geometric position in a constrained area that can maximize the accuracy increment. Then, UAVs are iteratively added until the desired number, i.e., the quantity budget of deployed UAVs, is achieved. Simulation results demonstrate that the proposed UAV deployment strategy provides considerably better localization accuracy compared with uniform angular arrays (UAA) and random deployment (RD).

This paper investigates the sensor selection problem for time difference of arrival (TDOA) localization in wireless sensor networks. Specifically, a multi-objective optimization problem is formulated in which a Boolean vector is involved to find the best tradeoff between the localization accuracy and the energy consumption. The ε- constraints method is introduced to convert the original multi- objective optimization problem to a tractable single-objective problem. To solve the converted sensor selection problem, we propose the polyblock outer approximation (POA) algorithm based on discrete monotonic optimization (DMO) in order to find the global optimal solution, which however can not be obtained by the traditional semidefinite relaxation (SDR) approach. Further, for the sake of practical implementation, we propose another two suboptimal algorithms, namely, POA-based accelerated cutting (POA-AC) algorithm and POA-based monotonic cutting (POA-MC) algorithm. Simulation results validate that the localization accuracy for sensors selected by the POA-AC algorithm and POA-MC algorithm is greater than the semidefinite relaxation (SDR) solution and achieves the same results as that by the exhaustive search method.

Rigid body localization (RBL) extends the traditional point positioning by determining not only the position but also the orientation of the body. This paper considers RBL using the range measurements between the sensors on the body and the outside anchors that have position uncertainties, where a calibration emitter at an inaccurate location is employed to mitigate the anchor position errors. This is a highly nonlinear constrained optimization problem as the rotation matrix defining the orientation must belong to the special orthogonal group. We first propose the use of rotation angles to parameterize the orientation, which enables the reduction of the problem to an unconstrained optimization. It is then sufficient to consider the unconstrained Cramér-Rao Lower Bound (CRLB) for analyzing the effects of anchor position errors and noisy calibration position on the localization performance, and such an analysis is prohibitive when using the constrained CRLB. We next propose and analyze three Maximum Likelihood estimators obtained from the unconstrained formulation that have different levels of approximation and complexity. We also enhance the divide and conquer and the semi-definite programming solution from the literature such that they can work with the presence of a calibration emitter and account for anchor position errors.

We focus on the 3-dimensional (3D) source localization passively by using TDOA and AOA in the presence of sensor errors. Determining the position from the TDOA and AOA measurements is not an easy task because the relationship between them is nonlinear. We present a new WLS solution that the TDOA equation is simpler than relevant literature (Yin and Wan, A Simple and Accurate TDOA-AOA Localization Method Using Two Stations). However, the bias of the WLS solution is larger. Hence, we propose a bias reduced method by imposing a quadratic constraint so that the expectation of cost function can attain the minimum value at the true position. The simulation illustrates the method is effective and the performance of this method can achieve the Cramer-Rao Lower Bound (CRLB) when the noises are Gaussian and in small region.

A definition of least cyclostationary order (LCO) is proposed based on the inner cyclic period of single carrier and orthogonal frequency division multiplexing (OFDM) signals. The LCOs of single carrier and OFDM signals are derived. Since the LCO has a relationship with the carrier frequency offset (CFO), a blind CFO estimation scheme for single carrier and OFDM signals can be proposed. The novel scheme is entirely blind without any priori information and is proved to be the same as cumulants estimation when the LCO is known. However, the new scheme is superior to the estimation based on cumulant when the LCO is unknown. The mean‐square error of M ‐phase shift keying signals approaches the Cramér–Rao bound in additive white Gaussian noise (AWGN) channel. Simulation results are given to verify the effectiveness of the proposed blind estimation scheme in Rician fading channel and in AWGN channel.

The estimation of the time differences of arrival (TDOAs) is significant in passive source localisation systems. The TDOA estimation accuracy may directly affect the source location performance. For co‐frequency interference environments, the authors address the problem of the passive blind estimation of time‐delays for uncorrelated interference source signals based on wireless sensor networks. The received mixtures at the sensors are modelled as unknown linear combinations of the differently delayed versions of the communication signal and the interference signal. Blind source separation and secondary interference signal extracting are both introduced in the proposed method. The interference signals in the mixed receiving signals of all the sensors are extracted effectively and the effect of the mixed communication signals can be significantly reduced. Simulations show that the proposed method has a more accurate performance compared to other TDOA estimation methods, and is therefore valid and practical in the TDOA localisation systems.

In this study, the authors investigate the impact of the frequency‐hopping (FH) sequence on the packet transmission performance of the asynchronous frequency‐hopping multiple‐access (FHMA) network. According to the model of the asynchronous FHMA network given in this study, the authors analyse the impact of the two important FH sequence factors – uniformity and frequency slot number – on the correct transmission probability and the packet transmission frequency efficiency. According to the non‐collision probability analysed in this study, the uniformity of the FH sequence is an important issue to determine the correct packet transmission probability. Moreover, based on the definition of the packet transmission frequency efficiency given in this study, the optimal frequency slot number employed to obtain the maximum frequency efficiency is obtained. By employing three typical FH sequences, the simulation results are also included, which validates the theoretical analysis about the packet transmission performance of the asynchronous FHMA network.

Traditional symbol rate estimators based on wavelet transform (WT) suffer from difficulties in choosing wavelet scale. Additionally, the most estimators are only adapted to limited signal types. Furthermore, those estimators are susceptible to noise, which is impractical to implement. In this paper, to overcome shortages of those traditional estimators, a self- adapting symbol rate estimator is proposed. The proposed estimator has advantages in reliably working under low Eb-to-N0. More importantly, it can be widely used to estimate various types of signal. The numerical simulations show that the proposed estimator has superiority in performance compared with the improved estimators based on wavelet transform.

The accuracy of sources locations and velocities estimate is very sensitive to the accurate knowledge of sensor locations and velocities. In the presence of sensor position and velocity errors, this study considers the problem of simultaneously locating multiple disjoint sources and refining erroneous sensor positions and velocities using time differences of arrival and frequency differences of arrival. The previous work by Sun and Ho to solve this problem provided an efficient estimator for multiple disjoint sources, but it cannot provide optimum accuracy for the sensor positions and sensor velocities. In many practical applications, it is necessary and helpful to refine sensor locations and velocities while localising multiple sources. The proposed method improves the previous method so that both the source and the sensor position and velocity estimates can achieve the Cramér–Rao lower bound accuracy very well over small noise region. The theoretical derivation is corroborated by simulations.

In practice, sensing results often affect the data transmission in cognitive radio systems. Therefore, a hybrid interweave/underlay cognitive radio system is presented by jointly considering spectrum sensing and data transmission. In particular, multiple relays are deployed for both the spectrum sensing and data transmission. The secondary user (SU) source and the relays cooperatively sense the spectrum with energy detection and decision fusion. According to the cooperative spectrum sensing results, the SU adaptively switches between interweave and underlay spectrum access mode. Moreover, to improve the spectral efficiency, an adaptive modulation technique is integrated into SU's transmission. In this context, undertaking the interference from the primary user (PU), the upper bound for average spectral efficiency of the SU with continuous-rate adaptive modulation is derived over Rayleigh fading channels. Further, we study the performance of SU, where adaptive L-ary quadrature amplitude modulation (L-QAM) with fixed switching threshold is adopted. Simulation results verify our analysis and show that both hybrid interweave/underlay scheme and adaptive modulation can improve the SU's performance significantly.

Passive source localization has been the focus of considerable research efforts due to its usefulness in various applications. This paper performs a fundamental investigation of whether the gain ratios of arrival (GROAs) can be utilized in conjunction with the time differences of arrival (TDOAs) to improve the multiple sources localization accuracy with erroneous sensor positions. It's an urgent need to find a closed-form solution with good localization accuracy for this challenging problem. This paper takes the advantage that the TDOAs and GROAs from different sources have the same sensor position displacements and proposes an estimator that jointly estimates the unknown sources and sensor positions. In order to establish an closed-form solution for multiple sources location estimates using GROAs and TDOAs, we use the idea of hypothesized source locations in the algorithm development to enable the formulation of pseudo-linear equations. The proposed algebraic solution does not require initialization and does not have divergence problem. Our conclusion is that the improvement from GROAs is obvious for multiple sources localization compared with methods only using TDOAs. Numerical simulations are included to support and corroborate the theoretical developments.

Passive source localization has been the focus of considerable research efforts due to its usefulness in various applications. This paper performs a fundamental investigation of whether the gain ratios of arrival (GROAs) can be utilized in conjunction with the range differences of arrival (RDOAs) to improve the multiple sources localization accuracy in the presence of sensor location uncertainties. In this paper, we derive the Cramer-Rao lower bound (CRLB) of multiple source location estimate using both RDOAs and GROAs when sensor positions have errors. Simulations show that the localization accuracy improvements contributed by GROA measurements are significant for two far-field sources, two near-field sources and two enclosed sources as the SNR, jamming signal bandwidth factor C/ωoor sensor position error power σs2increases. The CRLB will provide reasonable reference for localization algorithm research in the future.

High complexity of frequency-hopping (FH)/spread- spectrum(SS) sequence is of great importance to high-security multiple-access communication systems, for it makes FH/SS sequence difficult to be analyzed. In this paper, a new complexity metric to evaluate the unpredictability of FH/SS sequence based on the Fuzzy Entropy(FuzzyEn) is presented. Simulation and analytical results show that, the proposed FuzzyEn works can effectively discern the changing complexities of the FH/SS sequences, and are compared with complexity metric based on the Approximate Entropy(ApEn). The FuzzyEn scheme has obvious advantages in the robustness to resolution parameter, the dependence to observation length and the sensitivity to vector dimension.