Canonical Analysis of Several Sets of Variables

Employment of ground-based positioning systems has been consistently growing over the past decades due to the growing number of applications that require location information where the conventional satellite-based systems have limitations. Such systems have been successfully adopted in the context of wireless emergency services, tactical military operations, and various other applications offering location-based services. In current and previous generation of cellular systems, i.e., 3G, 4G, and LTE, the base stations, which have known locations, have been assumed to be stationary and fixed. However, with the possibility of having mobile relays in 5G networks, there is a demand for novel algorithms that address the challenges that did not exist in the previous generations of localization systems. This paper includes a review of various fundamental techniques, current trends, and state-of-the-art systems and algorithms employed in wireless position estimation using moving receivers. Subsequently, performance criteria comparisons are given for the aforementioned techniques and systems. Moreover, a discussion addressing potential research directions when dealing with moving receivers, e.g., receiver’s movement pattern for efficient and accurate localization, non-line-of-sight problem, sensor fusion, and cooperative localization, is briefly given.

A Look at the Recent Wireless Positioning Techniques With a Focus on Algorithms for Moving Receivers

Time difference of arrival (TDoA) based on a group of sensor nodes with known locations has been widely used to locate targets. Two-step weighted least squares (TSWLS), constrained weighted least squares (CWLS), and Newton–Raphson (NR) iteration are commonly used passive location methods, among which the initial position is needed and the complexity is high. This paper proposes a hybrid firefly algorithm (hybrid-FA) method, combining the weighted least squares (WLS) algorithm and FA, which can reduce computation as well as achieve high accuracy. The WLS algorithm is performed first, the result of which is used to restrict the search region for the FA method. Simulations showed that the hybrid-FA method required far fewer iterations than the FA method alone to achieve the same accuracy. Additionally, two experiments were conducted to compare the results of hybrid-FA with other methods. The findings indicated that the root-mean-square error (RMSE) and mean distance error of the hybrid-FA method were lower than that of the NR, TSWLS, and genetic algorithm (GA). On the whole, the hybrid-FA outperformed the NR, TSWLS, and GA for TDoA measurement.

Time Difference of Arrival (TDoA) Localization Combining Weighted Least Squares and Firefly Algorithm

This letter proposes an improved version of the popular two-stage weighted least squares (TSWLS) algorithm for source localization using time difference of arrival (TDOA) measurements in the presence of sensor position errors. The new technique remains to be closed-form and approximately efficient as TSWLS. But it exhibits lower estimation bias and better robustness to increased noise over TSWLS via using a new Stage-2 processing, where the localization error of its Stage-1 is estimated and subtracted from the Stage-1 output to generate the final source position estimate. Simulations corroborate the theoretical developments.

An Improved Algebraic Solution for TDOA Localization With Sensor Position Errors

The problem of passive source localization has been extensively studied due to its many applications in signal processing and wireless communications. Signal strength-based localization methods have the advantages of low cost and simple implementation. In this paper, blind source localization with unknown transmit power and unknown path loss exponent is considered based on the received signal strength difference (RSSD). A nonlinear RSSD-based model is formulated for systems perturbed by noise. Solutions obtained using conventional least squares methods suffer from significant performance degradation as they only consider errors in the data vector. Thus, an extended total least squares (ETLS) method is developed for blind localization which considers perturbations in the system parameters as well as the constraints imposed by the relationship between the observation matrix and data vector. The nonlinear and nonconvex RSSD-based localization problem is then transformed to an ETLS problem with fewer constraints. This is transformed to a convex semidefinite programming (SDP) problem using relaxation. The corresponding ETLS-SDP method is extended to the case with an unknown path loss exponent to jointly estimate the unknown source location and path loss exponent without resorting to transmit power estimation which is sensitive to errors. The mean squared error of the proposed ETLS method is obtained and the corresponding Cramer-Rao lower bound (CRLB) is derived as a performance benchmark. Performance results are presented that show that the RSSD-based ETLS-SDP method attains the CRLB for a sufficiently large signal-to-noise ratio (SNR).

Blind Received Signal Strength Difference Based Source Localization With System Parameter Errors

In this paper, by utilizing the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements of a signal received at a number of receivers, an efficient constrained weighted least-squares (CWLS) algorithm for estimating the position and velocity of a moving source is proposed, which exploits the known relation between the intermediate variable and the source location coordinates explicitly. On basis of Newton's method, a numerical iterative solution can be obtained allowing real-time implementation and ensuring global convergence. Simulation results show that the proposed estimator achieves remarkably better performance than the two-step weighted least squares (WLS) approach, which makes the Cramr-Rao lower bound (CRLB) at a sufficiently high noise level before the threshold effect occurs.

An Efficient Constrained Weighted Least Squares Algorithm for Moving Source Location Using TDOA and FDOA Measurements

In this study, a constrained total least-squares (CTLS) algorithm for estimating the position and velocity of a moving source with sensor location uncertainties that uses the time difference of arrival and frequency difference of arrival measurements of a signal received at a number of sensors is proposed. The CTLS method, as a natural extension of LS when noise occurs in all the data and the noise components of the coefficients are linearly dependent, is more appropriate than the LS method for the above problem. By utilising the Lagrange multipliers technique, the known relation between the intermediate variables and the source localisation coordinates has been exploited to constrain the solution. In addition, the Lagrange multipliers can be obtained efficiently and robustly, which can allow real-time implementation as well as ensure global convergence. After a perturbation analysis, the bias and covariance of the proposed CTLS algorithm are also derived, indicating that the proposed CTLS algorithm is an unbiased estimator, and it could achieve the Cramer Rao lower bound (CRLB) when the measurement noise and the sensor location errors are sufficiently small. The simulation results show that the proposed estimator achieves remarkably better performance than the TLS and two-step weighted least squares approach, which makes it possible that the CRLB is attained at a sufficiently high noise level before the threshold effect occurs.

Constrained total least-squares localisation algorithm using time difference of arrival and frequency difference of arrival measurements with sensor location uncertainties

Practical constrained least-square algorithm for moving source location using TDOA and FDOA measurements

To solve the problem of nonlinear blind source separation (BSS), a novel algorithm based on kernel multi- set canonical correlation analysis (MCCA) is presented. Combining complementary research fields of kernel feature spaces and BSS using MCCA, the proposed approach yields a highly efficient and elegant algorithm for nonlinear BSS with invertible nonlinearity. The algorithm works as follows: First, the input data is mapped to a high-dimensional feature space and perform dimension reduction to extract the effective reduced feature space, translate the nonlinear problem in the input space to a linear problem in reduced feature space. In the second step, the MCCA algorithm was used to obtain the original signals.

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Nonlinear Blind Source Separation Using Kernel Multi-set Canonical Correlation Analysis

To solve the problem of blind source separation, a robust algorithm based on generalized variance is presented by exploiting the different temporal structure of uncorrelated source signals. In contrast to higher order cumulant techniques, this algorithm is based on second order statistical characteristic of observation signals, can blindly separate super-Gaussian and sub-Gaussian signals successfully at the same time without adjusting the contrast function, and the computation burden of it is relatively light. Simulation results confirm that the algorithm is efficient and feasible.

Huagang Yu

Papers

An Efficient Constrained Weighted Least Squares Algorithm for Moving Source Location Using TDOA and FDOA Measurements

Constrained total least-squares localisation algorithm using time difference of arrival and frequency difference of arrival measurements with sensor location uncertainties

Practical constrained least-square algorithm for moving source location using TDOA and FDOA measurements

Nonlinear Blind Source Separation Using Kernel Multi-set Canonical Correlation Analysis

A robust blind source separation algorithm based on generalized variance