Subspace design of low-rank estimators for higher-order statistics

Ivan Bradaric, Athina P. Petropulu, Konstantinos I. Diamantaras

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Higher-order statistics (HOS) are well known for their robustness to additive Gaussian noise and ability to preserve phase. HOS estimates, on the other hand, have been criticized for high complexity and the need for long data in order to maintain small variance. Since rank reduction offers a general principle for reduction of estimator variance and complexity, we consider the problem of designing low-rank estimators for HOS. We propose three methods for choosing the transformation matrix that reduces the mean-square error (MSE) associated with the low-rank HOS estimates. We also demonstrate the advantages of using low-rank third-order moment estimates for blind system estimation. Results indicate that the full rank MSE corresponding to some data length N can be attained by a low-rank estimator corresponding to a length significantly smaller than N.

Original languageEnglish (US)
Pages (from-to)161-187
Number of pages27
JournalJournal of the Franklin Institute
Issue number2
StatePublished - Mar 2002
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Applied Mathematics


  • Higher-order statistics
  • Low-rank estimates
  • System identification
  • Variance reduction


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