# Marginalized Particle Flow Filter

- 10 Downloads

## Abstract

As an alternative to the Kalman filter and the particle filter, the particle flow filter has recently attracted interest for solving the curse of dimensionality of the particle filter. Compared with the particle filter, the particle flow filter can obtain a better performance in high-dimensional state spaces with fewer samples. However, for some unobservable state dimensions, the flow operation wastes computational resources. In this paper, we propose a marginalized particle flow filter to handle the unobservable sub-state estimation. In contrast to the standard particle flow filter, we only migrate those observable dimensions of each particle according to homotopy theory and estimate the unobservable dimensions using the Kalman filter. The proposed algorithm can enhance the estimation quality of the unobservable state space and reduce the runtime of the particle flow filter. We evaluate the performance of the proposed algorithm through a multi-target tracking simulation.

## Keywords

Nonlinear filter Particle filter Particle flow High-dimensional filtering## Notes

### Acknowledgements

We are grateful to the referees for their clarifying suggestions, which have improved the presentation of this material, and in articular to Jeremie Houssineau for his comments. This study was supported by the National Natural Science Foundation of China (NSFC, Grant No. 61305013).

## References

- 1.M.S. Arulampalam, S. Maskell, N. Gordon, T. Clapp, A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans. Signal Process.
**50**(2), 174–188 (2002)CrossRefGoogle Scholar - 2.T. Bengtsson, P. Bickel, B. Li et al., Curse-of-dimensionality revisited: collapse of the particle filter in very large scale systems, in
*Probability and Statistics: Essays in Honor of David A. Freedman*, ed. by D. Nolan, T. Speed (Institute of Mathematical Statistics, Beachwood, 2008), pp. 316–334CrossRefGoogle Scholar - 3.A. Beskos, D. Crisan, A. Jasra et al., On the stability of sequential Monte Carlo methods in high dimensions. Ann Appl Probab
**24**(4), 1396–1445 (2014)MathSciNetCrossRefGoogle Scholar - 4.F. Beutler, M.F. Huber, U.D. Hanebeck, Gaussian filtering using state decomposition methods, in
*12th International Conference on Information Fusion, 2009, FUSION’09*(IEEE, 2009), pp. 579–586Google Scholar - 5.P. Bickel, B. Li, T. Bengtsson et al., Sharp failure rates for the bootstrap particle filter in high dimensions. In
*Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh*(Institute of Mathematical Statistics, 2008), pp. 318–329Google Scholar - 6.P. Bunch, S. Godsill, Approximations of the optimal importance density using Gaussian particle flow importance sampling. J. Am. Stat. Assoc.
**111**(514), 748–762 (2016)MathSciNetCrossRefGoogle Scholar - 7.B. Chen, G. Hu, D.W.C. Ho, L. Yu, A new approach to linear/nonlinear distributed fusion estimation problem. IEEE Trans. Autom. Control (2018). https://doi.org/10.1109/TAC.2018.2849612
- 8.S. Choi, P. Willett, F. Daum, J. Huang, Discussion and application of the homotopy filter, in
*SPIE Defense, Security, and Sensing*(International Society for Optics and Photonics, 2011), p. 805021Google Scholar - 9.R. Costa, T.A. Wettergren, Computationally efficient angles-only tracking with particle flow filters, in
*SPIE Defense+ Security*(International Society for Optics and Photonics, 2015), p. 947404Google Scholar - 10.F. Daum, J. Huang, Nonlinear filters with log-homotopy, in
*Proc. SPIE*, vol. 6699, p. 669918- (2007)Google Scholar - 11.F. Daum, J. Huang, Particle flow for nonlinear filters with log-homotopy, in
*SPIE Defense and Security Symposium*(International Society for Optics and Photonics, 2008), p. 696918Google Scholar - 12.F. Daum, J. Huang, Generalized particle flow for nonlinear filters, in
*SPIE Defense, Security, and Sensing*(International Society for Optics and Photonics, 2010), p. 76980IGoogle Scholar - 13.F. Daum, J. Huang. Particle flow with non-zero diffusion for nonlinear filters, in
*Proceedings of SPIE: Signal processing, Sensor Fusion and Target Tracking XXII*(2013), p. 87450PGoogle Scholar - 14.F. Daum, J. Huang, A. Noushin, Exact particle flow for nonlinear filters, in
*SPIE Defense, Security, and Sensing*(International Society for Optics and Photonics, 2010), p. 769704Google Scholar - 15.F. Daum, J. Huang, A. Noushin, Generalized Gromov method for stochastic particle flow filters, in
*SPIE Defense+ Security*(International Society for Optics and Photonics, 2017), p. 102000IGoogle Scholar - 16.F. Daum, J. Huang, Nonlinear filters with particle flow induced by log-homotopy, in
*SPIE Defense, Security, and Sensing*(International Society for Optics and Photonics, 2009), p. 733603Google Scholar - 17.T. Ding, M. Coates, Implementation of the Daum–Huang exact-flow particle filter. 2012 IEEE Statistical Signal Processing Workshop (SSP) (2012), pp. 257–260Google Scholar
- 18.A. Doucet, N. De Freitas, N. Gordon,
*Sequential Monte Carlo Methods in Practice*(Springer, Berlin, 2001)CrossRefGoogle Scholar - 19.G. Hendeby, R. Karlsson, F. Gustafsson, The Rao-Blackwellized particle filter: a filter bank implementation. EURASIP J. Adv. Signal Process.
**2010**(1), 724087 (2010)CrossRefGoogle Scholar - 20.S.J. Julier, J.K. Uhlmann, Unscented filtering and nonlinear estimation. Proc. IEEE
**92**(3), 401–422 (2004)CrossRefGoogle Scholar - 21.R. Karlsson, T. Schon, F. Gustafsson,
*Complexity Analysis of the Marginalized Particle Filter*(IEEE Press, New York, 2005)CrossRefGoogle Scholar - 22.M.A. Khan, M. Ulmke. Improvements in the implementation of log-homotopy based particle flow filters, in
*2015 18th International Conference on Information Fusion (Fusion)*(IEEE, 2015), pp. 74–81Google Scholar - 23.Y. Li, M. Coates, Particle filtering with invertible particle flow. IEEE Trans. Signal Process.
**65**(15), 4102–4116 (2016)MathSciNetCrossRefGoogle Scholar - 24.S. Maskell, N. Gordon, A tutorial on particle filters for on-line nonlinear/non-Gaussian Bayesian tracking. Target Track. Algorithms Appl. (Ref. No. 2001/174),
**2**, 21–215 (2001)Google Scholar - 25.M. Morzfeld, D. Hodyss, C. Snyder, What the collapse of the ensemble Kalman filter tells us about particle filters. Tellus A Dyn. Meteorol. Oceanogr.
**69**(1), 1283809 (2017)CrossRefGoogle Scholar - 26.N. Moshtagh, J. Chan, M. Chan, Homotopy particle filter for ground-based tracking of satellites at GEO, in
*Advanced Maui Optical and Space Surveillance Technologies Conference*(2016)Google Scholar - 27.N. Moshtagh, M.W. Chan, Multisensor fusion using homotopy particle filter, in
*2015 18th International Conference on Information Fusion (Fusion)*(IEEE, 2015), pp. 1641–1648Google Scholar - 28.M.K. Pitt, N. Shephard, Filtering via simulation: auxiliary particle filters. J. Am. Stat. Assoc.
**94**(446), 590–599 (1999)MathSciNetCrossRefGoogle Scholar - 29.T. Schon, F. Gustafsson, P.J. Nordlund, Marginalized particle filters for mixed linear/nonlinear state-space models. IEEE Trans. Signal Process.
**53**(7), 2279–2289 (2005)MathSciNetCrossRefGoogle Scholar - 30.C. Snyder, T. Bengtsson, P. Bickel, J. Anderson, Obstacles to high-dimensional particle filtering. Mon. Weather Rev.
**136**(12), 4629–4640 (2008)CrossRefGoogle Scholar - 31.R. Van Der Merwe, A. Doucet, N. De Freitas, E.A. Wan, The unscented particle filter, in
*Advances in Neural Information Processing Systems*(2001), pp. 584–590Google Scholar