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17 May 2012Friendly rebuttal to Chen and Mehra:
incompressible particle flow for nonlinear filters
We respond to the very thorough analysis of
singularities in the incompressible flow for one dimensional
nonlinear filters by Chen and Mehra. We emphasize that
the singularities occur at a few points in d-dimensional state
space, and thus the chance of hitting a singularity is very
small for dimensions higher than one. Furthermore, in the
unlikely event of hitting a singularity, there is ample room to
flow around it in spaces of dimension higher than one.
Moreover, the deep mathematical theory of incompressible
particle flow that was developed recently by Shnirelman can
be used to provide insight into why our particle flow
algorithms work so well.
Fred Daum andJim Huang
"Friendly rebuttal to Chen and Mehra:
incompressible particle flow for nonlinear filters", Proc. SPIE 8392, Signal Processing, Sensor Fusion, and Target Recognition XXI, 839210 (17 May 2012); https://doi.org/10.1117/12.915510
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Fred Daum, Jim Huang, "Friendly rebuttal to Chen and Mehra: incompressible particle flow for nonlinear filters," Proc. SPIE 8392, Signal Processing, Sensor Fusion, and Target Recognition XXI, 839210 (17 May 2012); https://doi.org/10.1117/12.915510