Robust Adaptive Gaussian Mixture Sigma Point Particle Filter (original) (raw)

Bridging the ensemble Kalman filter and particle filters: the adaptive Gaussian mixture filter

Computational Geosciences, 2011

The nonlinear filtering problem occurs in many scientific areas. Sequential Monte Carlo solutions with the correct asymptotic behavior such as particle filters exist, but they are computationally too expensive when working with high-dimensional systems. The ensemble Kalman filter (EnKF) is a more robust method that has shown promising results with a small sample size, but the samples are not guaranteed to come from the true posterior distribution. By approximating the model error with a Gaussian distribution, one may represent the posterior distribution as a sum of Gaussian kernels. The resulting Gaussian mixture filter has the advantage of both a local Kalman type correction and the weighting/resampling step of a particle filter. The Gaussian mixture approximation relies on a bandwidth parameter which often has to be kept quite large in order to avoid a weight collapse in high dimensions. As a result, the Kalman correction is too large to capture highly non-Gaussian posterior distributions. In this paper, we have extended the Gaussian mixture filter (Hoteit et al., Mon Weather Rev 136:317-334, 2008) and also made the connection to particle filters more transparent. In particular, we introduce a tuning parameter for the importance weights. In the last part of the paper, we have performed a simulation experiment with the Lorenz40 model where our method has been A. S. Stordal (B) · G. Naevdal · B. Vallès IRIS, compared to the EnKF and a full implementation of a particle filter. The results clearly indicate that the new method has advantages compared to the standard EnKF.

Sigma-point particle filter for parameter estimation in a multiplicative noise environment

Journal of Advances in Modeling Earth Systems, 2011

A prerequisite for the ''optimal estimate'' by the ensemble-based Kalman filter (EnKF) is the Gaussian assumption for background and observation errors, which is often violated when the errors are multiplicative, even for a linear system. This study first explores the challenge of the multiplicative noise to the current EnKF schemes. Then, a Sigma Point Kalman Filter based Particle Filter (SPPF) is presented as an alternative to solve the issues associated with multiplicative noise. The classic Lorenz '63 model and a higher dimensional Lorenz '96 model are used as test beds for the data assimilation experiments. Performance of the SPPF algorithm is compared against a standard EnKF as well as an advanced square-root Sigma-Point Kalman Filters (SPKF). The results show that the SPPF outperforms the EnKF and the square-root SPKF in the presence of multiplicative noise. The super ensemble structure of the SPPF makes it computationally attractive compared to the standard Particle Filter (PF).

Particle Kalman Filtering: A Nonlinear Bayesian Framework for Ensemble Kalman Filters

2011

Abstract: This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter, but is different from it in that, the standard weight-type correction in the particle filter is complemented by the Kalman-type correction with the associated covariance matrices in the Gaussian mixture.

Robust Adaptive Unscented Particle Filter

International Journal of Intelligent Mechatronics and Robotics, 2013

This paper presents a new robust adaptive unscented particle filtering algorithm by adopting the concept of robust adaptive filtering to the unscented particle filter. In order to prevent particles from degeneracy, this algorithm adaptively determines the equivalent weight function according to robust estimation and adaptively adjusts the adaptive factor constructed from predicted residuals to resist the disturbances of singular observations and the kinematic model noise. It also uses the unscented transformation to improve the accuracy of particle filtering, thus providing the reliable state estimation for improving the performance of robust adaptive filtering. Experiments and comparison analysis demonstrate that the proposed filtering algorithm can effectively resist disturbances due to system state noise and observation noise, leading to the improved filtering accuracy.

NONLINEAR BAYESIAN FILTERING IN THE GAUSSIAN SCALE MIXTURE CONTEXT

2012

In many real-life Bayesian estimation problems, it is appropriate to consider non-Gaussian noise distributions to model possible outliers or impulsive behaviors in the measurements. In this paper, we considered a nonlinear Bayesian filtering problem with a Gaussian process noise and a Gaussian scale mixture (GSM) distributed measurement noise. Both processes' statistics parameters are assumed unknown. Within this framework, we present a filtering method based on a sigma-point core that exploits GSM's product property and accounts for such heavier distribution tail and parameter uncertainty. Numerical results exhibit enhanced robustness against both outliers and a weak knowledge of the system with respect to state-of-the-art nonlinear Bayesian filters based on the Gaussian assumption, requiring much less computational load than standard Sequential Monte-Carlo methods and approaching theoretical bounds of performance.

Innovative and Additive Outlier Robust Kalman Filtering With a Robust Particle Filter

IEEE Transactions on Signal Processing, 2021

In this paper, we propose CE-BASS, a particle mixture Kalman filter which is robust to both innovative and additive outliers, and able to fully capture multi-modality in the distribution of the hidden state. Furthermore, the particle sampling approach re-samples past states, which enables CE-BASS to handle innovative outliers which are not immediately visible in the observations, such as trend changes. The filter is computationally efficient as we derive new, accurate approximations to the optimal proposal distributions for the particles. The proposed algorithm is shown to compare well with existing approaches and is applied to both machine temperature and server data.

A Note on the Particle Filter with Posterior Gaussian Resampling

Tellus A, 2006

A B S T R A C T Particle filter (PF) is a fully non-linear filter with Bayesian conditional probability estimation, compared here with the well-known ensemble Kalman filter (EnKF). A Gaussian resampling (GR) method is proposed to generate the posterior analysis ensemble in an effective and efficient way. The Lorenz model is used to test the proposed method. The PF with Gaussian resampling (PFGR) can approximate more accurately the Bayesian analysis. The present work demonstrates that the proposed PFGR possesses good stability and accuracy and is potentially applicable to large-scale data assimilation problems.

Sigma-point multiple particle filtering

Signal Processing, 2019

In this paper, we introduce two new particle filtering algorithms for high-dimensional state spaces in the multiple particle filtering approach. In multiple particle filtering, the state space is partitioned and a different particle filter is used for each component of the partition. At each time step, all particle filters share information about their marginal densities so that they can adequately approximate the filtering recursion. In this paper, we propose a second order approximation to the involved densities based on sigma-point integration methods. We then introduce two different particle filters that make use of this strategy. Finally, we demonstrate their remarkable performance through simulations of a multiple target tracking scenario with a sensor network.

Robust Adaptive Central Difference Particle Filter

International Journal of Robotics Applications and Technologies, 2014

This paper presents a new robust adaptive central difference particle filtering method for nonlinear systems by combining the concept of robust adaptive estimation with the central difference particle filter. This method obtains system state estimate and covariances using the principle of robust estimation. Subsequently, the importance density is obtained by adjusting the state estimate and covariances through the equivalent weight function and adaptive factor constructed from predicted residuals to control the contributions to the new state estimation from measurement and kinematic model. The proposed method can not only minimize the variance of the importance density distribution to resist the disturbances of systematic noises, but it also fully takes advantage of present measurement information to avoid particle degeneration. Experiments and comparison analysis with the existing methods demonstrate the improved filtering accuracy of the proposed method.

Constrained particle filtering using gaussian sum approximations

In many filtering problems, there are hard constraints in the state vector that can be a valuable source of information in the estimation process. In this contribution a method to incorporate hard state constraints in particle filters is proposed. The derived approach is based on Gaussian mixture model representation of probability distributions within the particle filter framework and a projection approach to generate constrained samples from these truncated distributions. The developed particle filters show significant improved state estimation performance and robustness against filter divergence compared to their unconstrained counterparts.