Point positioning and direction of arrival (DOA) localization require separate estimators, depending on the source is near or distant from the sensors. The use of modified polar representation (MPR) for the source location enables the integration of the two to a single estimator, resulting in more direct and accurate processing and, most importantly, eliminating the need of the a priori knowledge if the source is in near or far field. The previous work on MPR only provides an iterative implementation of the Maximum Likelihood Estimator (MLE), using a coarse semidefinite relaxation (SDR) solution as the initialization. This paper proposes a formulation for time difference of arrival (TDOA) localization of a single source in MPR that would lead to a closed-form solution through the minimization of a quadratic function with a quadratic constraint. Two techniques, the successive unconstrained minimization (SUM) and the generalized trust region subproblem (GTRS), are applied to solve the optimization. The resulting solutions are applicable for both 2-D and 3-D scenarios. Detailed analysis in the first order for mean-square and in the second order for estimation bias are performed for both methods. The theoretical results illustrate the closed-form solution from each of the methods provides the Cram\'er-Rao lower bound (CRLB) performance for Gaussian noise.

This paper focuses on the development and analysis of algebraic solution for source localization using angles of arrival (AOAs) in the modified polar representation (MPR), where sensor position errors are present. MPR uses the arrival angle(s) and inverse-range to represent the source location, thereby integrating the localization of the source to a single framework regardless it is in the near-field or far-field. Previous solution for AOA localization in MPR ignores sensor position errors and uses the iterative Maximum Likelihood method with a coarse semi-definite relaxation solution as the initialization, which is computationally demanding and does not ensure global convergence. We propose the constrained eigenspace technique to this localization problem that yields computationally attractive algebraic solution without having the global convergence issue. Depending on the constraints imposed, two solutions are developed. One is more computationally efficient and the other has smaller bias. The solutions are studied theoretically by mean-square analysis to characterize their statistical performance. Simulations validate the CRLB performance of the two proposed solutions under Gaussian noise.

Higher-order cyclic cumulants (CCs) have been widely adopted as the features for automatic modulation recognition (AMR). However, the requirement of high-rate sampling has greatly restricted the application of CCs. In order to relieve this sampling burden, we attempt to bring AMR into the framework of compressive sensing. By exploiting the sparsity of CCs, the proposed AMR algorithm is implemented with a significantly small number of nonuniform samples of the observed signal. Simulation results demonstrate the availability and robustness of the proposed approach.

A new joint synchronization and localization method for wireless sensor networks using two-way exchanged timestamps is proposed in this paper. The goal is to jointly localize and synchronize the source node, assuming that the locations and clock parameters of the anchor nodes are known. We first form the measurement model and derive the Cramér-Rao lower bound (CRLB). An analysis of the advantages and disadvantages of a recent scheme on joint synchronization and localization motivates us to develop a maximum likelihood estimator (MLE) that effectively resolves the issues of this existing scheme. A novel semidefinite programming method is then proposed to transform the nonconvex MLE problem into a convex optimization problem. Extensive simulation results are obtained to compare the synchronization and localization performances of proposed scheme and a few state-of-the-art existing schemes.

Localization is perhaps one of the most interesting research subjects in signal processing. Traditional localization methods rely on the prior information whether the source is located in the near-field or far-field. Since the prior knowledge is hard to obtain in practice, neither positioning nor bearing may not be able to provide reliable performance for both cases. The modified polar representation (MPR) is proposed to solve this contradictory problem in a uniform framework and eliminate the thresholding effect as the source range increases. The maximum likelihood estimator (MLE) in the state-of-art research realizes excellent performance reaching the Cramér-Rao Lower Bound (CRLB) but it’s computation-complex and timeconsuming. Besides, it has the possible divergence problem if the initial value is not close enough to the true value. This paper focuses on the localization problem using TDOA measurements in MPR. Formulating it in a new form, we develop a twostep least squares (LS) estimator for the MPR model. The weighted total LS (WTLS) is applied in the first step and the weighted LS (WLS) for the final solution, where the second step is based on the natural constraint of the unknowns. The proposed method is closed-form and able to reach CRLB in low noise power situation irrespective of the source range. The covariance is analyzed and proved to provide CRLB accuracy for Gaussian noise theoretically. Simulation supports our theoretical results and verifies the advocated performance that is comparable with MLE but simpler and computationally more efficient. It outperforms the classical closed-form solution.

Utilizing the bistatic range (BR) and bistatic range rate (BRR) obtained from time delay difference and Doppler shift difference, a moving target can be localized with the passive multistatic radar (PMR) network. This paper presents a two-stage closed-form method for target localization in PMR. Different from the conventional two-stage weighted least squares (TSWLS) methods, the proposed method employs the weighted spherical-interpolation method to obtain an initial estimate in the first stage and reduces the error in the initial estimate with the deviation refinement in the second stage. Theoretical analysis through mean-square error (MSE) shows the proposed method approaches the Cram’r-Rao lower bound (CRLB) accuracy under the assumption of mild measurement noises. Simulation results validate the analytical results. The proposed method is also shown to achieve the accuracy improvement in target velocity estimate at relatively higher noise levels.