### Abstract

This paper considers a multi-step selection procedure to estimate the upper limit of the number of signals. The unknown number of signals present in a radar data can be formulated as the difference between the total number of components in the observed multivariate data vector and the multiplicity of the smallest eigenvalue. We propose a selection procedure to estimate the lower limit for the multiplicity of the common smallest eigenvalue, which is significantly smaller than the other eigenvalues. As a consequence, an estimate for the upper limit of the number of signals can be obtained. With a guaranteed probability requirement, the proposed procedure selects a subset that contains the smallest eigenvalues. The size of the subset is random from sample to sample. The number of signals present is estimated as the difference of the number of components and the cardinality of the selected subset. Therefore, our estimate gives an upper bound for the number of signals present. Numerical examples are presented to illustrate our proposed procedure.

Original language | English (US) |
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Pages (from-to) | 2265-2277 |

Number of pages | 13 |

Journal | Signal Processing |

Volume | 83 |

Issue number | 10 |

DOIs | |

State | Published - Oct 1 2003 |

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### Keywords

- Eigenvalue
- Ranking and selection
- Upper limit

### ASJC Scopus subject areas

- Control and Systems Engineering
- Software
- Signal Processing
- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering

### Cite this

*Signal Processing*,

*83*(10), 2265-2277. https://doi.org/10.1016/S0165-1684(03)00166-X