Compared with conventional two-step localization algorithms which are implemented by initially estimating localization parameters and then calculating the target position, the performance of direct position determination (DPD) algorithm is superior in terms of high estimation accuracy and strong resolution capability. DPD algorithms can make full use of the characteristics of signals to improve positioning performance. Using this localization mechanism as basis, this study develops a novel DPD algorithm that profits from the characteristics of orthogonal frequency division multiplexing (OFDM) signals based on the time and angle of arrival. First, the DPD optimization model is constructed based on maximum likelihood criterion and the characteristic of multiple carrier modulation technique of OFDM signals. Then, an extended subspace data fusion-based DPD algorithm is developed by constructing and decomposing the extended covariance matrices. The algorithm fuses the extended subspace data to estimate the target position without calculating the intermediate variables, which is less complex and more efficient. These properties can avoid the limitations of two-step algorithms. The last but important result is a derivation of the closed-form expression of Cramer-Rao lower bound (CRLB) on the position estimation variance for OFDM sources. Simulation results show that, the algorithm proposed in this paper outperforms existing DPD algorithms and conventional two-step localization algorithms. Especially under the condition of low signal-to-noise ratio, its localization accuracy is close to the CRLB.

Direct position determination (DPD) is currently a hot topic in wireless localization research as it is more accurate than traditional two-step positioning. However, current DPD algorithms are all based on uniform arrays, which have an insufficient degree of freedom and limited estimation accuracy. To improve the DPD accuracy, this paper introduces a coprime array to the position model of multiple non-circular sources with a moving array. To maximize the advantages of this coprime array, we reconstruct the covariance matrix by vectorization, apply a spatial smoothing technique, and converge the subspace data from each measuring position to establish the cost function. Finally, we obtain the position coordinates of the multiple non-circular sources. The complexity of the proposed method is computed and compared with that of other methods, and the Cramer–Rao lower bound of DPD for multiple sources with a moving coprime array, is derived. Theoretical analysis and simulation results show that the proposed algorithm is not only applicable to circular sources, but can also improve the positioning accuracy of non-circular sources. Compared with existing two-step positioning algorithms and DPD algorithms based on uniform linear arrays, the proposed technique offers a significant improvement in positioning accuracy with a slight increase in complexity.

The existing coprime array is mainly applicable to circular sources, while the virtual array degree of freedom (DOF) for noncircular sources is enhanced limitedly. In order to perfect the array DOF and the direction of arrival (DOA) estimation accuracy, a high degree of freedom sparse array design method for noncircular sources is put forward. Firstly, the method takes the advantages of the characteristic of the noncircular sources to expand the array manifold and then explores and solves the location distribution of the physical array sensors on the basis of the virtual array model with the help of the searching approach. The array configuration can obtain the longest continuous virtual array. The comparisons between the proposed array configuration and the common array configurations are advanced. The simulation experiments show that the sparse array presented in this paper can effectively increase the continuous virtual array aperture of noncircular sources, improve the array DOF and DOA estimation accuracy, and achieve the purpose of better estimation of multiple DOAs in underdetermined conditions.

In this paper, a novel algorithm is proposed for the two-dimensional (2D) central direction-of-arrival (DOA) estimation of coherently distributed (CD) sources. Specifically, we focus on a centro-symmetric crossed array consisting of two uniform linear arrays (ULAs). Unlike the conventional low-complexity methods using the one-order Taylor series approximation to obtain the approximate rotational invariance relation, we first prove the symmetric property of angular signal distributed weight vectors of the CD source for an arbitrary centrosymmetric array, and then use this property to establish two generalized rotational invariance relations inside the array manifolds in the two ULAs. Making use of such relations, the central elevation and azimuth DOAs are obtained by employing a polynomial-root-based search-free approach, respectively. Finally, simple parameter matching is accomplished by searching for the minimums of the cost function of the estimated 2D angular parameters. When compared with the existing low-complexity methods, the proposed algorithm can greatly improve estimation accuracy without significant increment in computation complexity. Moreover, it performs independently of the deterministic angular distributed function. Simulation results are presented to illustrate the performance of the proposed algorithm.

Recently, the design of sparse linear array for direction of arrival (DOA) estimation of non-circular (NC) signals has attracted great attention because the difference and sum co-array offered by non-circularity increases the aperture of virtual linear array. In this paper, we present a coprime array with shifted and flipped subarray for the DOA of non-circular signals. By shifting one subarray, the proposed array structure achieves a higher number of consecutive lags than the prototype coprime array with the same number of sensors. Then, through flipping the shifted subarray with the zero point as the symmetry point, the number of sensor pairs with small separation is significantly reduced, making the resulting structure much sparser. For the proposed array structure, we derive the closed-form expression for the number of consecutive lags, the optimal distribution of two subarrays with a given number of sensors and the weight function. Numerical simulations are conducted to verify the superiority of the proposed array over the existing sparse arrays.

In estimating the two-dimensional (2D) direction-of-arrival (DOA) using a coprime planar array, the main issues are the high complexity of spectral peak search and the limited degree of freedom imposed by the number of sensors. In this paper, we present an algorithm based on the matrix completion theory in coprime planar array that reduces the computational complexity and obtains a high degree of freedom. The algorithm first analyzes the covariance matrix of received signals to estimate the covariance matrix of a virtual uniform rectangular array, which has the same aperture as the coprime planar array. Matrix completion theory is then applied to estimate the missing elements of the virtual array covariance matrix. Finally, a closed-form DOA solution is obtained using the unitary estimation signal parameters via rotational invariance techniques (Unitary-ESPRIT). Simulation results show that the proposed algorithm has a high degree of freedom, enabling the estimation of more signal DOAs than the number of sensors. The proposed algorithm has reduced computational complexity because the spectral peak search is replaced by Unitary-ESPRIT, but attains similarly high levels accuracy to those of the 2D multiple signal classification algorithm.