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This paper presents a simple and fast closed-form solution approach for two-dimensional (2D) target localization using range difference (RD) measurements. The formulation of the localization problem is derived using a pentagram array. The target position is determined using passive radar measurements (RDs) between the target and the (N+1=10) receivers’ locations. The method facilitates the problem of target position and can be used as a counter-parallel method for spherical interpolation (SI) and spherical intersection (SX) methods in time difference of arrival (TDOA) and radar systems. The performance of the method is examined in 2D target localization using numerical analysis under the distribution of receivers in the pentagram array. The simulations are conducted using four different far-distance targets and comparatively large-area distributed receivers. The RD measurements were distorted by two different values of Gaussian errors based on ionosphedriec time delays of 20 and 50 nsec owing to the different receivers’ positions. The findings highly verified the validity of the method for addressing the problem of target localization. Additionally, a theoretical accuracy study of the method is given, which solely relies on the RD measurements.

Antenna arrays are used for signal processing in sonar and radar direction of arrival (DOA) estimation. The well-known array geometries used in DOA estimation are uniform linear array (ULA), uniform circular array (UCA), and rectangular grid array (RGA). In these geometries, the neighboring elements are separated by a fixed distance λ/2 (λ is the wavelength), which does not perform well for d greater than λ/2. Uniform rectangular arrays introduce grating lobes, which cause poor DOA estimation performance, especially for wideband sources. Random sampling arrays are sometimes practically not realizable. Periodic geometries require numerous sensors. Based on the minimization of the number of sensors, this paper developed a novel pentagram array to address the problem of DOA estimation of wideband sources. The array has a fixed number of elements with variable element spacing and is abbreviated as (FNEVES), which offers a new idea for array design. In this study, the geometric structure is designed and mathematically analyzed. Also, a DOA signal model is designed based on a spherical radar coordinate system to derive its steering manifold matrix. The DOA estimation performance comparison with ULA and UCA geometries under the multiple signal classification (MUSIC) algorithm using different wideband scenarios is presented. For further investigation, more simulations are realized using the minimum variance distortionless (MVDR) technique (CAPON) and the subtracting signal subspace (SSS) algorithm. Simulation results demonstrate the effectiveness of the proposed geometry compared to its counterparts. In addition, the SSS, through the simulations, provided better results than the MUSIC and CAPON methods.