Multireference TDOA-based source localization

Abstract

Time difference of arrival (TDOA)-based methods usually achieve the most accurate source localization in passive systems. In these methods, one of the sensors is assigned as the reference and the TDOA of the others with respect to the reference is measured. The source location is estimated by processing these TDOAs. In this paper, a multireference maximum likelihood (ML)-Taylor algorithm is proposed in order to decrease the source localization error of the TDOA methods. In the proposed algorithm, TDOAs are measured assuming 2 different reference sensors, and then the ML objective function of this multireference TDOA algorithm is derived and solved using Taylor series linearization. The developed method is evaluated regarding a 2-dimensional space with some different but deterministic sensor locations. Monte Carlo simulation is used to evaluate the proposed solution. The simulation results show that the proposed method has better performance relative to the other traditional TDOA-based algorithms.

Analysis of condition number and position estimation error for multiangulation position estimation system

“…A 4-GRS square layout as shown in Figure 4 with a separation distance of 2.5 km is adopted. This layout is chosen for its simplicity and convenience due to its symmetry, which enables results in one quadrant to be applied to other quadrants [11]. Figure 5 shows the contour plots of the coefficient matrix condition number and the azimuthal coordinate PE RMSE distributions based on the variation of the AOA error SD with target range estimated in Section 4.2 (illustrated in Figure 3b).…”

“…We therefore choose the singular value decomposition (SVD) to find the solution to the LS problem in (11).…”

“…The coefficient matrix condition number k[A T A] is used to correlate with the PE error distribution of the multiangulation system through the analysis of the eigenvalues of the coefficient matrix. Since SVD is used to determine the solution shown in (11), the singular values obtained can be used to determine the condition number without additional computation. The process for generating the SVD begins with estimating the singular matrix, Σ, followed by the computation of the eigenvector V and then subsequently the unitary matrix U [31].…”

“…Since our assumption in this paper is that the target is an UAS that operates on a 2400 MHz link, the MCMC, based on its document 'Use of Frequencies for UAS', limits the transmit power for frequency of 2400 MHz to a maximum of 500 mW as shown in Table 1. Based on the UAS's altitude and the height of the GRS antenna, the maximum range R (km) that can achieve direct LOS communication, which depends on the earth's curvature as referenced in (11), is about 50 km. This can be shown using a mathematical formula as follows [37]:…”

“…While the former uses an angulation algorithm to determine the PE, the later woks with a lateration algorithm to compute the PE. Both methods are implemented as a two-stage process that involves first determining the PDSP and the use of the PDSP to perform PE [10,11]. MLAT can perform PE in 2D with a minimum of three GRS sensors and with more sensors it can perform 3D PE [12].…”