Direct Position Determination Method Research Articles

Self-Position Awareness Based on Cascade Direct Localization Over Multiple Source Data

The global positioning system (GPS), which provides ubiquitous location-awareness with a constellation of satellites, has become an instrumental function of multiple mass-market applications. Satellite signals, however, may not be capable of penetrating obstacles in harsh environments (e.g., urban canyons, tree canopies, and flyovers). Hence, GPS may not provide adequate localization accuracy for applications like autonomous vehicles. Resorting to data fusion of heterogeneous signals emanating from multiple anchors, we advocate a self-localization method that provides accurate estimates of the vehicle position. To be more specific, several heterogenous emitters whose positions are known are used as anchors to determine the vehicle's position based on the weighted direct position determination (DPD) method that eliminates nonhomogeneity among different emitters. However, the weighted DPD method requires an exhaustive search of the parameter search space and is thus time-consuming. To reduce the computational burden, we propose a weighted cascade compensation estimator (WCCE) that is tailored for real-time tracking and self-localization. The proposed WCCE outperforms traditional DPD methods in terms of computational complexity while achieving nearly comparable localization accuracy. The effectiveness of the proposed method is corroborated by extensive simulated examples.

A Direct Position Determination Method Using Distributed UAVs With Synchronization Error

A Direct Position Determination Method Using Distributed UAVs With Synchronization Error

A Low-Complexity Direct Position Determination Method Based on the Diffusion Strategy in Wireless Sensor Array Networks

A Low-Complexity Direct Position Determination Method Based on the Diffusion Strategy in Wireless Sensor Array Networks

Sparse Direct Position Determination Based on TDOA Information in Correlation-Domain

The sparse direct position determination (DPD) method requires reconstructing the emitter position with prior knowledge. However, in non-cooperative localization scenarios, it is difficult to reconstruct the transmitted signal with the unknown signal form and propagation model. In this paper, a sparse DPD method based on time-difference-of-arrival (TDOA) information in correlation-domain is proposed. Different from the traditional sparse DPD method, the received signal is converted into correlation-domain, and the proposed dictionary matrix is generated by the quantized delay difference, which solves the pseudo-positioning problem. Compared to the conventional multi-signal classification (MUSIC) method, multi-frequency fusion (MFF) method, and two-step positioning algorithm, the proposed algorithm achieves higher positioning accuracy. The feasibility of the algorithm has been verified by both simulation and real-world measured tests.

Multi-TDOA Estimation and Source Direct Position Determination Based on Parallel Factor Analysis

In this paper, source localization exploiting time difference of arrival (TDOA) information is discussed, and a parallel factor (PARAFAC) analysis based method for multi-TDOA estimation and direct position determination (DPD) is proposed. Firstly, signals from the radiation source are received by multiple antennas through synchronous sensing. Then, the data from multiple antennas is fused by extracting the time delay matrix to construct a PARAFAC model. Thereafter, the time delay matrix is obtained by fast iterative decomposition using the trilinear alternating least square (TALS) algorithm. In the case of no multipath or weak multipath, where the typical scenario is the antennas being deployed on the airborne platform, the multi-TDOA estimation can be obtained simultaneously according to the time delay matrix to improve the processing speed. In the case of multipath, such as the antennas being located on the ground, the DPD cost function directly related to the source position can be established based on the time delay matrix, and the source position estimation can be achieved through grid search. Compared with other DPD methods, the proposed DPD method has better positioning performance and lower complexity. The effectiveness and superiority of the proposed methods are verified by both simulations and actual scenario tests.

Direct Position Determination Using Compressive Sensing Measurements Without Reconstruction

This paper proposes a direct position determination (DPD) method for stationary emitters with compressed signal measurements. Employing Hadamard matrix properties, the method estimates the source location directly in the compressing measurement domain, without the step of signal reconstruction and time-differences-of-arrival (TDOA) parameter extraction. In case of free space propagation, an augmented DPD method is proposed to further utilize the position related received signal strength (RSS) information. In addition, the Cramér-Rao lower bounds (CRLBs) for emitter position of both DPD methods are derived for performance evaluation.

A Direct Position Determination Method under Unknown Multi-Perturbation with Moving Distributed Arrays

Distributed array manifold perturbation, which includes synchronization errors, amplitude-phase errors, and path attenuation, has seriously degraded the accuracy of existing direct position determination (DPD) methods. In this paper, a DPD method under unknown multi-perturbation with moving distributed coprime arrays is advocated for. Firstly, by means of array position interchange, the integrated signals received from distributed arrays can be fused, which contributes to multi-position fusion. Subsequently, by resorting to the orthogonality between the noise subspace and steering vector received via distributed arrays, a quadratic optimization problem is constructed. Finally, we realize multi-parameter decoupling and achieve localization regardless of unknown perturbations. The superiority of the advocated method is substantiated from simulation examples.

A Mixed-Integer Solution for TDOA Based Direct Positioning of Digital Modulation Signal

This paper proposes a direct position determination (DPD) method for a digital modulation signal based on time difference of arrival (TDOA) measurements. Unlike the two-step positioning process, the measurements are used to directly estimate the source position. Fully utilizing information in a transmitted waveform can improve the accuracy of source localization in a single-step method. Based on maximum likelihood (ML) estimates, when the digital modulation scheme is known to the location system, an alternating iterative DPD method is developed to locate the emitter. The objective function of the proposed algorithm takes into account the source position and transmitted symbol sequence, which makes it a mixed-integer optimization problem. In particular, ML sequence estimation is adopted and the complex envelope is restored using a genetic algorithm. Then, based on Newton’s method, an alternating iterative algorithm is proposed to update the position and symbol sequence results. Compared with the existing DPD method, the proposed algorithm gives more accurate location results for unknown waveforms. In addition, the proposed algorithm can reach the Cramér-Rao bound (CRB) for known signal waveforms, as verified using comprehensive simulations.

A Direct Position Determination Method Based on Subspace Orthogonality in Cross-Spectra under Multipath Environments.

Without the estimation of the intermediate parameters, the direct position determination (DPD) method can achieve higher localization accuracy than conventional two-step methods. However, multipath environments are still a key problem, and complex high-dimensional matrix operations are required in most DPD methods. In this paper, a time-difference-of-arrival-based (TDOA-based) DPD method is proposed based on the subspace orthogonality in the cross-spectra between the different sensors. Firstly, the cross-spectrum between the segmented received signal and reference signal is calculated and eigenvalue decomposition is performed to obtain the subspaces. Then, the cost functions are constructed by using the orthogonality of subspace. Finally, the location of the radiation source is obtained by searching the superposition of these cost functions in the target area. Compared with other DPD methods, our proposed DPD method leads to better localization accuracy with less complexity. The superiority of this method is verified by both simulated and real measured data when compared to other TDOA and DPD algorithms.

Localizing GNSS Spoofing Attacks Using Direct Position Determination

Global Navigation Satellite System (GNSS) receivers are vulnerable to all types of interferences due to the inherently low power of GNSS signals. Whereas GNSS jammers aim at denial-of-service attacks, GNSS spoofers bring even more risks, since they can fabricate a fake position and/or time without recognizing it. This paper presents a direct position determination method to improve the localization accuracy of GNSS spoofing attacks, which is called despreading direct position determination (DS-DPD). The localization algorithm utilizes a prior knowledge of the satellites’ code sequences, which in turn provides significant gains in localization accuracy. Firstly, the received signal model is established, which takes the time delay, Doppler shift, direction-of-arrival (DOA), and modulation codes into account. Then, the maximum likelihood (ML) criterion is utilized to construct the objective function of DS-DPD. Finally, the location parameters of the spoofers can be obtained through a two-dimensional spectral search of the objective function. Numerical simulations verify the localization performance improvement of the proposed DS-DPD algorithm. Especially when the interference-to-noise ratio (INR) approaches −30dB, the localization accuracy could be improved by more than ten times due to its full utilization of the delay, Doppler shift, DOA, and code sequences information.

Direct Position Determination for Noncooperative Source with Fast Moving Receivers

The problem of position estimation for a noncooperative source has always been widely discussed in the field of wireless communication. Direct position determination (DPD) for a noncooperative source with fast moving receivers is discussed in this paper. The sinc function is used to reconstruct the signals, which is an important step in DPD for wideband signals. A DPD method based on the baseband signal is proposed which is more practical in communication signal with high carrier frequency. And based on the proposed DPD method, a DPD method for multiple noncooperative stationary sources by single-channel receivers is presented. In order to evaluate the performance of the proposed DPD method, the Cramér-Rao lower bound (CRLB) for DPD based on baseband signal is derived. Several numerical investigations are carried out to evaluate the performance of the proposed method.

Weighted Direct Position Determination via the Dimension Reduction Method for Noncircular Signals

This work studies the direct position determination (DPD) of noncircular (NC) signals with multiple arrays. Existing DPD algorithms of NC sources ignore the impact of path propagation loss on the performance of the algorithms. In practice, the signal-to-noise ratios (SNRs) of different observation stations are often different and unstable when the NC signal of the same radiation target strikes different observation locations. Besides, NC features of the target signals are applied not only to extend the virtual array manifold but also to bring high-dimensional search. For the sake of addressing the above problems, this study develops a DPD method of NC sources for multiple arrays combing weighted subspace data fusion (SDF) and dimension reduction (RD) search. First, NC features of the target signals are applied to extend the virtual array manifold. Second, we assign a weight to balance the error and obtain higher location accuracy with better robustness. Then, the RD method is used to eliminate the high computational complexity caused by the NC phase search dimension. Finally, the weighted fusion cost function is constructed by using the eigenvalues of the received signal covariance matrixes. It is verified by simulation that the proposed algorithm can effectively improve the location performance, get better robustness, and distinguish more targets compared with two-step location technology and SDF technology. In addition, without losing the estimation performance, the proposed algorithm can significantly reduce the complexity caused by the NC phase search dimension.

A Single-Step Method for Over-the-Horizon Geolocation Using Importance Sampling

This paper investigates the geolocation for an over-the-horizon (OTH) transmitter observed by widely separated arrays. We propose a maximum likelihood (ML) based direct position determination (DPD) method to directly locate the transmitter in a single step by exploiting the position information embedded in azimuth angles. The Monte Carlo importance sampling (IS) technique is employed to find an approximate global solution to this DPD problem, where the importance function analogous to Gaussian distribution is derived. This enables the transmitter to be precisely located with low complexity in a noniterative manner. Additionally, we derive the Cramér–Rao bound (CRB) expression for the investigated problem. The simulation results corroborate the superior localization performance of the proposed method with respect to the conventional two-step approaches and the iterative DPD method.

A Frequency Domain Direct Localization Method Based on Distributed Antenna Sensing

Traditional two-step passive localization methods need to extract the parameters like the direction of arrival (DOA), time of arrival (TOA), and time difference of arrival (TDOA) from the original data to determine the source position, which causes the poor positioning accuracy due to error accumulation. In this paper, a direct position determination (DPD) method is proposed to improve the positioning accuracy and robustness, which is based on a correlation algorithm. Firstly, the cost function directly related to the location of the source can be established by synthesizing the data received by multiantenna in the frequency domain. Then, the position of the source is estimated by the correlation DPD method to search the monitoring area. Compared to the improved TDOA algorithm and Least Squares DPD algorithm, the proposed method shows better localization accuracy of different SNRs. Finally, based on real measured data, it can be seen that the results of the proposed algorithm are better than the improved TDOA algorithm.

Simultaneous Localization of Multiple Unknown Emitters Based on UAV Monitoring Big Data

The increasing of illegal radiations, which are either artificial or unintentional, has seriously influenced the reliable communication and operation of industrial facilities. In this article, we discuss the simultaneous localization of multiple emitters based on big data monitored by a moving unmanned aerial vehicle. Conventional direct position determination (DPD) method suffers from the non-homogeneity of the observation error and is sensitive to the environment, so we develop the weight DPD methods. First, we consider to strengthen the spectrums obtained at slots with higher signal-to-noise ratio, which is blindly calculated. Thereafter, an improved weight is designed to further enhance the localization accuracy, and it can obtain the asymptotically optimal performance under the general Gaussian noise model, which is proved theoretically. Numerical simulations demonstrate that the proposed weight DPD methods outperform the conventional two-step methods and subspace data fusion DPD method in terms of localization accuracy and resolution.

Direct Tracking of Co-Channel Moving Sources With Different Cyclic Frequencies

Mobile source tracking is an important topic in the field of radio monitoring. A direct position determination method based on particle filtering is proposed in this letter for tracking multiple co-channel mobile transmitters. The co-channel signals, which have different symbol rates, overlap in both the time and frequency domains but can be distinguished in the cyclic frequency domain. We determine the positions of mobile targets directly from different cyclic cross-spectrum slices without time difference of arrival (TDOA) measurements. The particle filtering technique is employed to improve the accuracy in estimating motion states. Simulation results are given to demonstrate that the proposed algorithm outperforms other mobile tracking algorithms in the presence of co-channel interference.

Direct Position Determination of Moving Sources Based on Delay and Doppler

In this paper, we address the problem of direct position determination (DPD) for moving sources. Different from traditional two-step localization methods where the intermediate time difference of arrival (TDOA) and frequency difference of arrival (FDOA) parameters are estimated and used for the subsequent moving source localization, in this paper the locations and velocities of moving sources are estimated directly from the received signals. To address the difficulty of estimating the high-dimensional unknown parameters simultaneously, a new multiple particle filter based DPD method is proposed, where the position and velocity are updated alternately using separate local particle filters. The proposed method requires smaller particle numbers compared to the classic particle filters, and its convergence is proved both theoretically and numerically. Moreover, the Cramer Rao lower bound for the considered moving source DPD is developed. Simulation results corroborate the effectiveness of the proposed method in terms of computational efficiency and estimation accuracy.

Self-Calibration direct position determination using a single moving array with sensor gain and phase errors

The problem of direct position determination (DPD) using a single moving array in the presence of deterministic sensor gain and phase errors is considered. To eliminate the localization bias caused by these errors, an eigenstructure based self-calibrating DPD method is first introduced, in which the sensor gain and phase errors and the emitter positions are jointly estimated by an iterative process. Considering the performance deterioration of eigenstructure methods when the signal to noise ratio or the number of samples is not sufficiently large, a maximum likelihood (ML) based two-step self-calibration approach for DPD is subsequently proposed. The sensor gain errors are provided using the diagonal of the covariance matrix of the array output by a closed form solution at the first step. Then, the phase errors and the emitter positions are jointly estimated by an iterative scheme based on ML, in which the phase errors are also determined by a closed form solution in each iteration. Besides, detailed analyses and discussions about the differences between the introduced eigenstructure based and the proposed ML based self-calibration DPD methods are also provided. At last, numerical simulations are involved to examine their performance.

Direct Position Determination in Asynchronous Sensor Networks

Source positioning using time difference of arrival (TDOA) has received much research interest in the field of vehicular technology during the past decades. In practice, sensor networks may be disturbed by clock biases, and extra active anchor sources with known positions could be exploited to calibrate these clock biases. Although there exist numerous two-step localization methods on this issue, they are inherently suboptimal. In this paper, we address the TDOA-based source direct position determination (DPD) problem in asynchronous sensor networks. First, the clock biases are demonstrated via theoretical analyses to cast significant influences on localization accuracy negatively. Then, a DPD method is proposed, exploiting anchor sources to jointly calibrate clock biases and determine the unknown source position, which integrates an expectation-maximization (EM) algorithm and a Gauss–Newton algorithm for coarse and refined parameter estimation, respectively. In this way, the computational load of the considered DPD problem is reduced considerably compared with exhaustive search-based DPD method. Moreover, the Cramer–Rao lower bound is derived for the considered DPD problem, and how anchor sources affect the localization performance is further analyzed. Simulation results demonstrate the necessity of clock bias calibration and the satisfactory performance of the proposed method.

Direct Position Determination for Wideband Sources Using Fast Approximation

In this correspondence paper, we address the direct position determination (DPD) problem for wideband stationary sources using time-delayed and Doppler-stretched signals collected by multiple moving receivers. The source signals are assumed to be zero-mean, stationary, and Gaussian distributed, which is reasonable in most passive sonar and acoustics scenarios. A scaled formulation is used for wideband signals to elaborate the Doppler effect, as significant biases will be introduced if such signals are approximated with narrowband models directly. In this paper, wideband signals are decomposed into a small number of low-dimensional components with high accuracy, and a computationally efficient DPD method is proposed by jointly utilizing the time delay and scaling information of received signals. In order to evaluate the performance of the proposed DPD method, the Cramer Rao lower bound for source localization in the considered scenario is derived. Numerical results validate the approximation of wideband signals and demonstrate the performance of the proposed method.