Gradient estimation for particle flow induced by log-homotopy for nonlinear filters

Frederick Daum; Jim Huang; A. J. Noushin; Misha Krichman

doi:10.1117/12.817391

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28 April 2009 Gradient estimation for particle flow induced by log-homotopy for nonlinear filters

Frederick Daum, Jim Huang, A. J. Noushin, Misha Krichman

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Proceedings Volume 7336, Signal Processing, Sensor Fusion, and Target Recognition XVIII; 733602 (2009) https://doi.org/10.1117/12.817391
Event: SPIE Defense, Security, and Sensing, 2009, Orlando, Florida, United States

Abstract

We study 17 distinct methods to approximate the gradient of the log-homotopy for nonlinear filters. This is a challenging problem because the data are given as function values at random points in high dimensional space. This general problem is important in optimization, financial engineering, quantum chemistry, chemistry, physics and engineering. The best general method that we have developed so far uses a simple idea borrowed from geology combined with a fast approximate k-NN algorithm. Extensive numerical experiments for five classes of problems shows that we get excellent performance.

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Frederick Daum, Jim Huang, A. J. Noushin, and Misha Krichman "Gradient estimation for particle flow induced by log-homotopy for nonlinear filters", Proc. SPIE 7336, Signal Processing, Sensor Fusion, and Target Recognition XVIII, 733602 (28 April 2009); https://doi.org/10.1117/12.817391

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