A Primer on Evolutionary Optimization Frameworks for Near-Field Multi-Source Localization
Authors: Seyed Jalaleddin Mousavirad, Parisa Ramezani, Mattias O'Nils, Emil Björnson
Organizations: Department of Computer and Electrical Engineering, Mid Sweden University, Sundsvall, Sweden · the school of electrical and data engineering, University of Technology Sydney, Sydney, Australia · the Department of Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden
This paper introduces evolutionary optimization as a grid-free training-free continuous-domain search mechanism for near-field multi-source localization, addressing the major limitations of grid-based subspace methods such as MUSIC and data-driven deep learning approaches. To this end, we develop two complementary evolutionary localization frameworks that operate directly on the continuous spherical-wave signal model and support arbitrary array geometries without requiring labeled data, discretized angle-range grids, or architectural constraints. The first framework, termed NEar-field MultimOdal DE (NEMO-DE) associates each individual in the evolutionary population to a single source and optimizes a residual least-squares objective in a sequential manner, updating the data residual and enforcing spatial separation to estimate multiple source locations. To overcome the limitation of NEMO-DE under large power imbalances among the sources, we propose the second framework, named NEar-field Eigen-subspace Fitting DE (NEEF-DE), which jointly encodes all source locations and minimizes a subspace-fitting criterion that aligns a model-based array response subspace with the received signal subspace. The proposed formulations are not intrinsically tied to a specific optimizer; however, this work adopts differential evolution (DE) as a representative evolutionary search strategy because of its simple implementation, small number of control parameters, and strong empirical performance in continuous nonconvex optimization problems. Numerical results show that the proposed frameworks provide competitive accuracy compared with MUSIC-type baselines while avoiding pre-defined grid construction and labeled training data. This work establishes evolutionary computation as a powerful and flexible paradigm for model-based near-field localization, paving the way for future innovations in this domain.
Figures & tables
Fig. 1 : System model for near-field multi-source localization.
Aspect
NEMO-DE (Sequential Multimodal DE)
NEEF-DE (Joint Subspace Fitting DE)
Representation
Single-source representation \bm{\theta}=[\phi,r]^{\mbox{\tiny\mathrm{T}}} ; each DE run estimates one source location.
Expanded joint representation \mathbf{x}=[\bm{\theta}_{1}^{\mbox{\tiny\mathrm{T}}},\dots,\bm{\theta}_{K}^{\mbox{\tiny\mathrm{T}}}]^{\mbox{\tiny\mathrm{T}}} ; all source locations are estimated simultaneously.
Search Strategy
Sequential multimodal evolutionary search; K DE runs.
Single joint evolutionary search in a 2K -dimensional space; one DE run.
Objective Function
Residual reconstruction error in the data domain; depends on residual signal after each detection.
Subspace mismatch; uses the signal subspace and is evaluated once per candidate solution.
Multimodality Handling
Explicit multimodality via repeated searches, penalization, and residual updates.
Implicit multimodality arising from joint parameterization and the objective function landscape.
Residual Update
Yes; contribution of each detected source is subtracted after each run.
No residual update required; all sources modeled jointly.
Penalization
Explicit distance-based penalization to avoid redundant detections.
Not required; joint search inherently avoids repeated solutions.
TABLE I : Comparison Between NEMO-DE and NEEF-DE Localization Frameworks
Parameter
Value
Np
50
Gmax
300
F
0.5
Cr
0.8
δmin
0.08
α
1000
TABLE II : DE parameter values.
Fig. 2 : RMSE vs. SNR for NEMO-DE, 2D MUSIC, and modified MUSIC. The BS antennas are spaced by λ/4 .
Fig. 3 : RMSE vs. number of sources for NEMO-DE, 2D MUSIC, and modified MUSIC. The BS antennas are spaced by λ/4 .
Fig. 4 : RMSE vs. SNR for NEMO-DE and 2D MUSIC. The BS antennas are spaced by λ/2 .
Fig. 5 : RMSE vs. number of sources for NEMO-DE and 2D MUSIC. The BS antennas are spaced by λ/2 .
Fig. 6 : Exact locations and estimated ones by NEMO-DE and MUSIC for three sources over 10 random realizations.
Fig. 7 : RMSE of NEEF-DE, NEMO-DE, 2D MUSIC, and modified MUSIC under unequal received SNRs across sources.
Fig. 8 : Exact locations and estimated ones by NEEF-DE and MUSIC for three sources over 10 random realizations.
Method
Runtime [s]
RMSE [m]
NEMO-DE
4.101
0.0293
NEEF-DE
70.64
0.0788
3D MUSIC
355.3
0.0687
TABLE III : Runtime and RMSE for DE-based schemes and MUSIC.
Near-field localization is a promising technique for high-resolution multi-user positioning in future wireless systems, but its performance is often degraded by scattering-induced coherent propagation. Existing near-field localization methods, which require separate parameter estimation and path/source association, suffer from high computation overhead and accumulated errors, and usually do not provide any guarantee on reliability. In this paper, we propose MUSIC-Net, an end-to-end near-field positioning deep learning (DL) framework informed by two-stage MUltiple SIgnal Classification (MUSIC) in mixed line-of-sight (LoS) and non-LoS (NLoS) multi-path scenarios, which embeds the two-stage MUSIC objects into training to isolate the LoS-related signal subspace and to identify a surrogate distance. The proposed framework directly recovers multi-user positions without the need for involved NLoS parameter estimation or path/source association. Furthermore, we introduce split conformal prediction (SCP) to move beyond point-estimation-based positioning towards statistically guaranteed (confidence) set estimation for all users. Numerical results show that the proposed MUSIC-Net achieves lower mean positioning error (MPER) than existing benchmarks and yields tighter SCP-calibrated prediction regions, demonstrating both accurate LoS localization and efficient uncertainty quantification (UQ) in coherent multi-path environments.
Jiaying Li, Haifeng Wen, Changsheng You +2
The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China · Southern University of Science and Technology, Shenzhen, China · The University of Hong Kong, HK SAR, China +1
Reliable sound source localization is fundamental to robot audition, enabling autonomous robots to perceive spatial cues and operate effectively in dynamic environments. Classical methods such as Multiple Signal Classification (MUSIC) offer strong theoretical foundations but degrade under low signal-to-noise ratios. While deep learning-based approaches achieve promising performance, they often struggle with limited generalization across conditions. To address these challenges, we propose NeuralMUSIC, a hybrid neural-subspace framework for robotic sound source localization. Specifically, a neural network first estimates the spatial covariance matrix from multichannel microphone observations. The predicted covariance is then integrated into a classical MUSIC pipeline with eigenvalue decomposition (EVD) and pseudo-spectrum computation, followed by a Frequency Attention Fusion (FAF) module to produce the final DOA estimates. To improve data efficiency, we further introduce a Self-supervised Spatial Correlation Learning (SSCL) strategy that leverages unlabeled acoustic data to capture spatial structure. Extensive experiments across different robotic tasks demonstrate that NeuralMUSIC achieves competitive localization accuracy while exhibiting improved robustness and cross-domain generalization.
Yizhuo Yang, Junqiao Fan, Shenghai Yuan +1
School of Electrical and Electronic Engineering, Nanyang Technological University. Address: 50 Nanyang Avenue, Singapore 639798 · NTU–VinUni Joint Research Laboratory for Embodied AI and Robotics, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 and VinUniversity, Hanoi, Vietnam
Joint source localization and geoacoustic inversion requires optimizing an objective built from an expensive normal mode propagation model. Bayesian optimization (BO) with a Gaussian process (GP) surrogate can obtain accurate parameter estimates within a limited number of forward model evaluations, but its performance depends on the choice of kernel family. With few observations in a seven-dimensional search space, no single kernel can be expected to perform consistently well across individual inversions. To reduce this dependence, we use a weighted ensemble of GPs with different kernel families, allowing the surrogate to adapt to the observed objective without committing to one kernel in advance. The ensemble is combined with an optimum-conditioned acquisition function that determines where the expensive objective should be evaluated next. Experiments on simulated and measured SWellEx-96 data show that the resulting method achieves the lowest mean final objective among the considered BO strategies and reduces parameter estimation error on most coordinates. Ablation results further show that the ensemble provides robustness to kernel choice, while the acquisition function accounts for most of the optimization gain.
Heng Zhang, Haotian Xiang, Florian Meyer +1
School of Electrical and Computer Engineering, University of Georgia, Athens, GA, USA · Scripps Institution of Oceanography, University of California, San Diego, CA, USA