Jianfeng Li

The unmanned aerial vehicle (UAV) position tracking via non-cooperative anchors is an effective alternative method when global navigation satellite systems (GNSS) are interrupted. We propose a three-dimension (3-D) UAV self-tracking method based on the minor subspace (MS) update and the majorization-minimization (MM) result iteration. An enhanced approximate inverse-power (EAIP) algorithm, which is integrated with the new residual term, the novel orthonormal matrix and the eigenvalue update, is proposed to improve the MS update precision and achieve noise suppression. Simulation has shown that EAIP performs less MS error than orthogonal data projection method (ODPM), fast data projection method (FDPM), yet another subspace tracker (YAST) and approximate inverse-power (AIP). Then, continuous MM iteration tracking is applied to eliminate the initial value setting issue, extract position information from MS and reduce the complexity by avoiding grid search. Finally, the Kalman filter (KF) for tracking result intervals is proposed to suppress the positioning interference and the moving averaging (MA) is employed to control the acceleration parameter of the UAV dynamics, thereby avoiding construction of the state transition equation. Moreover, the Cramer-Rao lower bound (CRLB) of each dimension in the 3-D self-tracking is derived, establishing a theoretical benchmark for performance analysis. The proposed method has lower complexity and better tracking performance compared to ‘AIP+MUSIC+KF’ and ‘AIP+SSF+KF’, which have been verified by both complexity analysis and simulation experiments.

Time Difference of Arrival (TDOA)-based localization is widely used for its stability and high accuracy. However, in multi-source scenarios, TDOA measurements from multiple sources become entangled, making it difficult to separate and correctly associate them for accurate localization. To address this challenge, this paper proposes a cascaded DOA-TDOA-based multi-source weighted localization algorithm that leverages the strengths of Direction of Arrival (DOA)-based methods for separating multi-source signals and the high precision of TDOA-based methods for single-source localization. The proposed method first estimates the DOAs of multiple sources and performs DOA matching based on geometric consistency to obtain initial coarse position estimates. Subsequently, it applies wideband spatial filtering to wideband signals using the Minimum Variance Distortionless Response (MVDR) to separate multi-source signals, enhance the signal-to-noise ratio (SNR), and thereby guide the selection of the reference station and the performance of TDOA estimation. Then, TDOA estimation is performed, while the weights are assigned based on the difference in GDOP (D-GDOP), computed from the initial coarse estimate, and a weighted least-squares (WLS) method is applied to obtain the refined estimate. Finally, the D-GDOP of the refined estimate can be computed and used to reassign weights, yielding more accurate position estimate. Simulation results validate the effectiveness of the proposed method, showing superior estimation accuracy and robustness relative to existing approaches.

The sensor-target geometry has a significant impact on localization performance. Existing sensor placement strategies for three-dimensional (3-D) angle-of-arrival (AOA) localization have not accounted for general convex deployment constraints. This paper extends and improves a recently proposed block majorization-minimization (block-MM) method for 3-D AOA sensor placement, making it capable of handling general convex deployment constraints for AOA sensors. Specifically, we formulate the problem based on the A-optimality criterion, and each sensor's position is subject to the constraint of lying within a pre-defined deployment constraint set. We derive a quadratic surrogate function for the formulated problem. The method guarantees a successive reduction in the objective function value until convergence. Simulation results demonstrate that the proposed method can effectively find an appropriate sensor-target geometry that enhances performance.

Recently, multiple unmanned aerial vehicle (UAV) systems have been widely applied, particularly in the localization field. Though localization methods based on time difference of arrival (TDOA) offer high accuracy, they demand precise clock synchronization, which can be difficult to ensure in practical scenarios. Moreover, a more complex electromagnetic environment leads to more frequent multipath propagation. To address these challenges, two direct position determination (DPD) cost functions are proposed for dual UAVs with synchronization error in multipath environments. First, the signal model considering synchronization error is established. Subsequently, the received data are segmented and transformed into the cross-power spectral domain to reduce the complexity and signal coherence. For the first cost function, the subspace orthogonality within the effective cross-power spectra across different UAV movements is fused. The second cost function fuses the orthogonality across multiple frequencies divided from the cross-power spectra. Furthermore, Kalman filtering (KF) is employed to improve localization accuracy in the presence of UAV position errors. Ultimately, the Cramér-Rao bound (CRB) is derived for the proposed cross-power spectral model. Compared with other DPD methods, the proposed methods achieve lower computational complexity and higher positioning accuracy, which are demonstrated by complexity analysis and simulation results.

Direct position determination (DPD) outperforms traditional two-step methods in accuracy. However, its practical application is hindered by two primary challenges: (1) the necessity to transmit raw data to the fusion center, which imposes significant demands on bandwidth and hardware resources, and (2) the absence of a closed-form solution for DPD, necessitating exhaustive search techniques and resulting in high computational complexity. To overcome these challenges, we introduce a subspace reconstruction-based DPD approach designed for an unmanned aerial vehicle (UAV) with a mounted array. This method requires a data transmission amount equivalent to that of two-step localization, specifically angle-of-arrival (AOA) localization while achieving performance comparable to the existing DPD method based on subspace data fusion (SDF). Furthermore, we introduce a numerically convergent solution based on majorization-minimization (MM) that guarantees convergence to a stationary point, thereby significantly reducing computational complexity and grid quantization errors (GQE) by eliminating the exhaustive search process. We validate the proposed method through computer simulations and real-world measurements conducted with a rotary-wing UAV, demonstrating its effectiveness and advantages.

A substantial body of work has focused on two-dimensional (2-D) self-localization of linear arrays using wireless sensor networks (WSN). However, tackling the higher-dimensional three-dimensional (3-D) case remains an open research question. This paper explores the use of one-dimensional (1-D) angle-of-arrival (AOA) measurements, also referred to as space angles (SA), to achieve 3-D self-localization of a linear array in the presence of anchor position errors. Unlike traditional 3-D source localization using SAs, 3-D self-localization requires simultaneous estimation of the array’s position and orientation (direction vector). First, we acquire a coarse solution to the weighted least-squares (WLS) problem via semidefinite relaxation (SDR), and then we enhance it through perturbation analysis. We then address the maximum likelihood (ML) estimation problem using block majorization-minimization (block-MM), which guarantees convergence to the Karush-Kuhn-Tucker (KKT) point. In addition, we propose an improved and tighter quadratic upper bound for a Rayleigh-quotient-like function introduced in our previous work. Simulations confirm that the proposed algorithm reaches the Cramér-Rao lower bound (CRLB) performance in low-noise regimes, with the block-MM-based ML method exhibiting minimal bias.

The Direct Position Determination (DPD) algorithm usually demonstrates superior effectiveness in target localization scenarios compared to conventional two-step methods. However, as the target-radar distance increases, the conventional DPD algorithm faces challenges maintaining height measurement accuracy. To address this issue, this paper proposes a weighted fusion direct position determination algorithm for a three-dimensional target in a distributed one-dimensional radar system. The algorithm first employs spatial smoothing techniques to construct the covariance matrix. To address the limitations of the Multiple Signal Classification (MUSIC) algorithm, we propose a weighted subspace processing technique that enhances the fidelity of the noise subspace estimation. This approach achieves a closer approximation to the true noise subspace through adaptive weighting while effectively incorporating signal subspace characteristics, thereby substantially improving the algorithm's noise robustness. Furthermore, we innovatively integrate Vertical Dilution of Precision (VDOP) into the cost function design to achieve optimized weighted fusion. To tackle the high computational complexity of three-dimensional search, we propose an efficient solution, which substantially reduces computational burden while maintaining localization accuracy. The simulation results demonstrate that the proposed algorithm improves localization accuracy, particularly in height estimation.