Degeneracy-Free Particle Filter: Ensemble Kalman Smoother Multiple Distribution Estimation Filter

• Published in: IEEE transactions on automatic control Vol. 67; no. 12; pp. 6956 - 6961
• Main Authors: Murata, Masaya, Kawano, Isao, Inoue, Koichi
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Benchmark testing; Ensemble Kalman smoother (EnKS); Estimation; extended or unscented Kalman multiple distribution estimation filter (EnKS-EKMDEF or EnKS-UKMDEF); Kalman filters; Mathematical analysis; Mathematical models; multiple distribution estimation filter (MDEF); nonlinear growth model; particle filter (PF); Probability density function; Probability density functions; satellite reentry; Smoothing methods; State estimation
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2022.3185007

We propose the ensemble Kalman smoother multiple distribution estimation filter (EnKS-MDEF) for nonlinear state estimation problems. The EnKS-MDEF is an example of the multiple distribution estimation filter (MDEF), which is a particle filter (PF) that estimates the filtered state probability density function (pdf) using multiple conditional state pdfs. The one step behind (OSB) smoothed state pdf used for calculating the filtered state pdf of the MDEF is approximated by the ensemble Kalman smoother (EnKS). Then, the particle weights for the EnKS-MDEF remain equal during the filter execution, which indicates that the EnKS-MDEF is a degeneracy-free PF. Since, the MDEF and the EnKS-MDEF, both estimate the OSB smoothed state pdf prior to calculating the filtered state pdf, these filters provide a simultaneous estimation of filtered and OSB smoothed states. The examples of the EnKS-MDEF are the EnKS-extended and unscented Kalman multiple distribution estimation filters, and their filtering and OSB smoothing performances are evaluated and compared with those for the representative filters and smoothers using a benchmark simulation problems.