Source Number Estimators Using Transformed Gerschgorin Radii

Hsien Tsai Wu, Jar Ferr Yang, Fwu Kuen Chen

Research output: Contribution to journalArticlepeer-review

291 Citations (Scopus)


In this paper, we introduce the effective uses of Gerschgorin radii of the unitary transformed covariance matrix for source number estimation. There are two approaches, likelihood and heuristic, used for developing the detection criteria. The likelihood approach combines the Gerschgorin radii to the well-known source number detectors and improves their detection performances for Gaussian and white noise processes. It is verified that the Gerschgorin likelihood estimators (GLE) are consistent. The Gerschgorin AIC yields a consistent estimate and the Gerschgorin MDL criterion does not tend to underestimate at small or moderate data samples. The heuristic approach applying the Gerschgorin disk estimator (GDE) developed from the projection concept, overcomes the problem in cases of small data samples, an unknown noise model, and data dependency. Furthermore, the detection performances of both approaches through the suggested rotations and averaging can be further improved. Finally, the proposed and existing criteria are evaluated in various conditions by using simulated and measured experimental data.

Original languageEnglish
Pages (from-to)1325-1333
Number of pages9
JournalIEEE Transactions on Signal Processing
Issue number6
Publication statusPublished - 1995 Jun

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering


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