Gridless Evolutionary Approach for Line Spectral Estimation With Unknown Model Order

Bai YAN, Qi ZHAO, Jin ZHANG, J. Andrew ZHANG, Xin YAO

Research output: Journal PublicationsJournal Article (refereed)peer-review


Gridless methods show great superiority in line spectral estimation. These methods need to solve an atomic l 0 norm (i.e., the continuous analog of l 0 norm) minimization problem to estimate frequencies and model order. Since this problem is NP-hard to compute, relaxations of the atomic l 0 norm, such as the nuclear norm and reweighted atomic norm, have been employed for promoting sparsity. However, the relaxations give rise to a resolution limit, subsequently leading to biased model order and convergence error. To overcome the above shortcomings of relaxation, we propose a novel idea of simultaneously estimating the frequencies and model order using the atomic l 0 norm. To accomplish this idea, we build a multiobjective optimization model. The measurement error and the atomic l 0 norm are taken as the two optimization objectives. The proposed model directly exploits the model order via the atomic l 0 norm, thus breaking the resolution limit. We further design a variable-length evolutionary algorithm to solve the proposed model, which includes two innovations. One is a variable-length coding and search strategy. It flexibly codes and interactively searches diverse solutions with different model orders. These solutions act as steppingstones that helpfully exploring the variable and open-ended frequency search space and provide extensive potentials toward the optima. Another innovation is a model-order pruning mechanism, which heuristically prunes less contributive frequencies within the solutions, thus significantly enhancing convergence and diversity. Simulation results confirm the superiority of our approach in both frequency estimation and model-order selection.

Original languageEnglish
Article number9800984
Pages (from-to)935-947
Number of pages13
JournalIEEE Transactions on Cybernetics
Issue number2
Early online date20 Jun 2022
Publication statusPublished - Feb 2024
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2023 IEEE.


  • Atomic measurements
  • Computational modeling
  • Estimation
  • Frequency estimation
  • Gridless
  • line spectral estimation (LSE)
  • Minimization
  • multiobjective evolutionary algorithm
  • Optimization
  • Search problems
  • sparse representation


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