New Semidefinite Programming Joint Localization and Synchronization Using Sequential One-Way TOAs and Doppler Shifts
Bibliographic record
Abstract
In a time division broadcast localization and synchronization (TDBLAS) system, moving user nodes (UNs) with the clock offset and the clock drift usually use the sequential one-way time-of-arrival (TOA) and Doppler shift measurements from the anchor nodes (ANs) to resolve the joint localization and synchronization (JLAS) problem in the presence of the AN position error. The objective function of the maximum likelihood (ML) method to solve the above JLAS problem in a TDBLAS system is high-dimensional nonlinear and nonconvex. Thus, the existing iterative method for solving the above ML estimation problem usually encounters issues like local minima or non-convergence when an accurate initial guess is missing. In this paper, we propose a new semidefinite programming (SDP) method to address this issue, which can guarantee the global optimal solution without requiring initialization. We introduce the optimization variable and formulate a nonconvex constrained weighted least square (CWLS) minimization problem. Subsequently, we propose a novel semidefinite relaxation (SDR) approach to relax the complex and nonconvex CWLS problem into a convex and tractable SDP problem. Through theoretical estimation error analysis, we demonstrate that the CWLS solution can achieve the Cramér-Rao lower bound (CRLB) under small Gaussian noise. Simulation results in a 2D scenario show that the proposed SDP method reaches the CRLB under small Gaussian noise. Compared to the conventional iterative method, the proposed SDP method exhibits greater robustness, achieving the global optima without requiring initialization under small Gaussian noise.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".