Discussion and application of the homotopy filter

Development of the novel homotopy, or particle-flow, nonlinear filters1-10 has recently been quite rapid. There is actually a whole family of such methods, so we will refer to these collectively in this paper as "DH" filters, after their developers, the third and fourth authors of this manuscript. Unlike a particle filter, a DH filter does not resample; instead, the particles are moved in a smooth way, from a space that reflects prior (predicted) knowledge to one that is updated according to the measurements. Working versions of several DH filters now exist, and the purpose of this paper is to attempt to provide some perspective on them. We stress that this paper discusses the efforts of the first two authors to learn about and to explain in their own terms these these filters that others might benefit from that. The latter pair of authors - these are the developers of the DH filter family - have been instrumental in this effort. But it must be noted that they continue to develop their algorithms, and that this paper represents a snapshot of a rapidly changing landscape.

[1]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[2]  Fred Daum,et al.  Particle flow for nonlinear filters with log-homotopy , 2008, SPIE Defense + Commercial Sensing.

[3]  Yakov Bar-Shalom,et al.  Multitarget-Multisensor Tracking: Principles and Techniques , 1995 .

[4]  Fred Daum,et al.  Nonlinear filters with particle flow , 2009, Optical Engineering + Applications.

[5]  Fred Daum,et al.  Nonlinear filters with particle flow induced by log-homotopy , 2009, Defense + Commercial Sensing.

[6]  Fred Daum,et al.  Generalized particle flow for nonlinear filters , 2010, Defense + Commercial Sensing.

[7]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[8]  Fred Daum,et al.  Seventeen dubious methods to approximate the gradient for nonlinear filters with particle flow , 2009, Optical Engineering + Applications.

[9]  Fred Daum,et al.  Exact particle flow for nonlinear filters , 2010, Defense + Commercial Sensing.

[10]  Rudolph van der Merwe,et al.  The Unscented Kalman Filter , 2002 .

[11]  Jim Huang,et al.  Gradient estimation for particle flow induced by log-homotopy for nonlinear filters , 2009, Defense + Commercial Sensing.

[12]  Fred Daum,et al.  Nonlinear filters with log-homotopy , 2007, SPIE Optical Engineering + Applications.

[13]  Fred Daum,et al.  Numerical experiments for nonlinear filters with exact particle flow induced by log-homotopy , 2010, Defense + Commercial Sensing.