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Algebraic Solution for Linear Array-Based 3D Localization Without Deployment Limitations
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DOI：10.1109/LSP.2025.3551200.png)
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Abstract
En 中文
Localizing a three-dimensional (3D) source using linear arrays (LAs) is a promising new localization technology. Existing solutions are either designed for specific LA deployments, are computationally intensive, or rely on iterative methods that do not guarantee convergence. This paper presents a novel algebraic solution algorithm for 3D source localization using space angle (SA) measurements from LAs. We propose a new formulation of the SA measurement equation, which leads to a constrained weighted least squares (CWLS) problem. Solving it by Lagrangian multipliers, the optimal estimation is obtained with an error correction. The solution does not require specific arrangement and placement of LAs and effectively balances accuracy with computational efficiency. We analyze the performance and complexity of the proposed solution, demonstrating its ability to achieve the Cram & eacute;r-Rao Lower Bound (CRLB) in the small error region under Gaussian noise with a low computational load. Simulations validate the analysis and confirm the superiority of the proposed solution compared to existing ones.
Keywords:
Location awareness
Three-dimensional displays
Maximum likelihood estimation
Mathematical models
Iterative methods
Covariance matrices
Computational modeling
Accuracy
Vectors
Polynomials
3D localization
algebraic solution
space angle
linear arrays
constrained weighted least squares
Journal
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1.1W
Citations:
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