### Abstract

We consider a problem in which exactly one of n+1 distinct signals {S_{0}, ..., S_{n}}, say S_{0}, may be present in a noisy environment and the presence or absence of S_{0} needs to be determined. The performance is given by the false alarm probabilities P_{f(i)}, i = 1, ..., n, where P_{f(i)} is the probability that S_{i} is declared as S_{0}, and the detection probability P_{d} which is the probability that S_{0} is correctly recognized. It is required that P_{d} be maximized while P_{f(i)}≤c_{i}, i = 1, ..., n, where c_{1}, ..., c_{n} are prescribed non-negative constants. The solution is an extended Neyman-Pearson test in which p_{0}(x) is tested against (w_{1}p_{1}(x)+...+w_{n}p_{n}(x)) where p_{i}(x) is the probability density function of observation X when S_{i} occurs. We propose two methods to obtain w_{1}, ..., w_{n} for any given c_{1}, ..., c_{n}. For certain simple cases, analytical or graphical solution is used. For the general case, we propose a search algorithm on w_{1}, ..., w_{n} which provides a sequence of extended Neyman-Pearson tests that converge to the optimal solution. Numerical examples are given to illustrate these methods.

Original language | English (US) |
---|---|

Pages (from-to) | 378-389 |

Number of pages | 12 |

Journal | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 3720 |

DOIs | |

State | Published - Jan 1 1999 |

Event | Proceedings of the 1999 Signal Processing, Sensor Fusion, and Target Recognition VIII - Orlando, FL, USA Duration: Apr 5 1999 → Apr 7 1999 |

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering

## Fingerprint Dive into the research topics of 'On the design of extended Neyman-Pearson hypothesis tests'. Together they form a unique fingerprint.

## Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*,

*3720*, 378-389. https://doi.org/10.1117/12.357178