## Abstract

The sensor S_{i}, i = 1,2,..., N, of a multiple sensor system outputs Y^{(i)}∈ ℛ, according to an unknown probability distribution P_{Y}(i)_{|x}, in response to input X ∈ ℛ. The problem is to design a fusion rule f:ℛ^{N} → ℛ, based on a training sample, such that the expected square error I(f) = E[(X-f(Y))^{2}] is minimized over a family of functions ℱ. In general, f* ∈ ℱ that minimizes I(.) cannot be computed since the underlying distributions are unknown. We consider sufficient conditions and algorithms to compute an estimator f̂ such that I(f̂) - I(f*) < ε with probability 1 - δ, for any ε > 0 and 0 < δ < 1. We present a general method for obtaining f̂ based on the scale-sensitive dimension of ℱ. We then review three recent computational methods based on the feedforward sigmoidal networks, the Nadaraya-Watson estimator, and the finite-dimensional vector spaces.

Original language | English |
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Pages (from-to) | 285-299 |

Number of pages | 15 |

Journal | Journal of the Franklin Institute |

Volume | 336 |

Issue number | 2 |

DOIs | |

State | Published - 1999 |

### Funding

This research is sponsored by the Seed Money Project of the Oak Ridge National Laboratory, and by the Engineering Research Program of the Office of Basic Energy Sciences of the US Department of Energy, under Contract No. DE-AC05-96OR22464 with Lockheed Martin Energy Research Corp.

## Keywords

- Empirical estimation
- Feedforward networks
- Fusion rule estimation
- Nadaraya-Watson estimator
- Sensor fusion
- Vector space methods