Abstract
Two approaches to the non-Gaussian filtering problem are presented. The proposed filters retain the computationally attractive recursive structure of the Kalman filter and they approximate well the exact minimum variance filter in cases where either 1) the state noise is Gaussian or its variance small in comparison to the observation noise variance, or 2) the observation noise is Gaussian and the system is one step observable. In both cases, the state estimate is formed as a linear prediction corrected by a nonlinear function of past and present observations. Some simulation results are presented.
Keywords
Kalman filterGaussianGaussian noiseNoise (video)MathematicsNonlinear filterVariance (accounting)Gaussian filterEnsemble Kalman filterState (computer science)AlgorithmFilter (signal processing)Invariant extended Kalman filterControl theory (sociology)Linear filterGaussian random fieldExtended Kalman filterObservableFiltering problemApplied mathematicsGaussian functionComputer scienceStatisticsFilter designArtificial intelligencePhysics
Affiliated Institutions
Related Publications
Novel approach to nonlinear/non-Gaussian Bayesian state estimation
An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples, ...
Gaussian mixture sigma-point particle filters for sequential probabilistic inference in dynamic state-space models
For sequential probabilistic inference in nonlinear non-Gaussian systems, approximate solutions must be used. We present a novel recursive Bayesian estimation algorithm that com...
Distributed Kalman Filter with Embedded Consensus Filters
The problem of distributed Kalman filtering (DKF) for sensor networks is one of the most fundamental distributed estimation problems for scalable sensor fusion. This paper addre...
A comparison of several nonlinear filters for reentry vehicle tracking
This paper compares the performance of several non-linear filters for the real-time estimation of the trajectory of a reentry vehicle from its radar observations. In particular,...
New extension of the Kalman filter to nonlinear systems
The Kalman Filter (KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. However, the applicatio...
Publication Info
- Year
- 1975
- Type
- article
- Volume
- 20
- Issue
- 1
- Pages
- 107-110
- Citations
- 368
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
368
OpenAlex
Cite This
C. Johan Masreliez
(1975).
Approximate non-Gaussian filtering with linear state and observation relations.
IEEE Transactions on Automatic Control
, 20
(1)
, 107-110.
https://doi.org/10.1109/tac.1975.1100882
Identifiers
- DOI
- 10.1109/tac.1975.1100882