Posterior Linearization Filter: Principles and Implementation Using Sigma Points
This paper is concerned with Gaussian approximations to the posterior probability density function (PDF) in the update step of Bayesian filtering with nonlinear measurements. In this setting, sigma-point approximations to the Kalman filter (KF) recursion are widely used due to their ease of implemen...
| Main Authors: | , , , |
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| Format: | Journal Article |
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IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
2015
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| Online Access: | https://research.chalmers.se/publication/224518 http://hdl.handle.net/20.500.11937/5634 |
| _version_ | 1848744851557842944 |
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| author | Garcia-Fernandez, Angel Svensson, Lennart Morelande, M. Sarkka, S. |
| author_facet | Garcia-Fernandez, Angel Svensson, Lennart Morelande, M. Sarkka, S. |
| author_sort | Garcia-Fernandez, Angel |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper is concerned with Gaussian approximations to the posterior probability density function (PDF) in the update step of Bayesian filtering with nonlinear measurements. In this setting, sigma-point approximations to the Kalman filter (KF) recursion are widely used due to their ease of implementation and relatively good performance. In the update step, these sigma-point KFs are equivalent to linearizing the nonlinear measurement function by statistical linear regression (SLR) with respect to the prior PDF. In this paper, we argue that the measurement function should be linearized using SLR with respect to the posterior rather than the prior to take into account the information provided by the measurement. The resulting filter is referred to as the posterior linearization filter (PLF). In practice, the exact PLF update is intractable but can be approximated by the iterated PLF (IPLF), which carries out iterated SLRs with respect to the best available approximation to the posterior. The IPLF can be seen as an approximate recursive Kullback-Leibler divergence minimization procedure. We demonstrate the high performance of the IPLF in relation to other Gaussian filters in two numerical examples. |
| first_indexed | 2025-11-14T06:08:02Z |
| format | Journal Article |
| id | curtin-20.500.11937-5634 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T06:08:02Z |
| publishDate | 2015 |
| publisher | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-56342022-09-01T06:07:15Z Posterior Linearization Filter: Principles and Implementation Using Sigma Points Garcia-Fernandez, Angel Svensson, Lennart Morelande, M. Sarkka, S. This paper is concerned with Gaussian approximations to the posterior probability density function (PDF) in the update step of Bayesian filtering with nonlinear measurements. In this setting, sigma-point approximations to the Kalman filter (KF) recursion are widely used due to their ease of implementation and relatively good performance. In the update step, these sigma-point KFs are equivalent to linearizing the nonlinear measurement function by statistical linear regression (SLR) with respect to the prior PDF. In this paper, we argue that the measurement function should be linearized using SLR with respect to the posterior rather than the prior to take into account the information provided by the measurement. The resulting filter is referred to as the posterior linearization filter (PLF). In practice, the exact PLF update is intractable but can be approximated by the iterated PLF (IPLF), which carries out iterated SLRs with respect to the best available approximation to the posterior. The IPLF can be seen as an approximate recursive Kullback-Leibler divergence minimization procedure. We demonstrate the high performance of the IPLF in relation to other Gaussian filters in two numerical examples. 2015 Journal Article http://hdl.handle.net/20.500.11937/5634 10.1109/TSP.2015.2454485 https://research.chalmers.se/publication/224518 http://purl.org/au-research/grants/arc/DP130104404 IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC unknown |
| spellingShingle | Garcia-Fernandez, Angel Svensson, Lennart Morelande, M. Sarkka, S. Posterior Linearization Filter: Principles and Implementation Using Sigma Points |
| title | Posterior Linearization Filter: Principles and Implementation Using Sigma Points |
| title_full | Posterior Linearization Filter: Principles and Implementation Using Sigma Points |
| title_fullStr | Posterior Linearization Filter: Principles and Implementation Using Sigma Points |
| title_full_unstemmed | Posterior Linearization Filter: Principles and Implementation Using Sigma Points |
| title_short | Posterior Linearization Filter: Principles and Implementation Using Sigma Points |
| title_sort | posterior linearization filter: principles and implementation using sigma points |
| url | https://research.chalmers.se/publication/224518 https://research.chalmers.se/publication/224518 http://hdl.handle.net/20.500.11937/5634 |