# Use of the Kalman filter for inference in state-space models with unknown noise distributions

@article{Maryak2004UseOT, title={Use of the Kalman filter for inference in state-space models with unknown noise distributions}, author={John L. Maryak and James C. Spall and Bryan D. Heydon}, journal={IEEE Transactions on Automatic Control}, year={2004}, volume={49}, pages={87-90} }

The Kalman filter is frequently used for state estimation in state-space models when the standard Gaussian noise assumption does not apply. A problem arises, however, in that inference based on the incorrect Gaussian assumption can lead to misleading or erroneous conclusions about the relationship of the Kalman filter estimate to the true (unknown) state. This note shows how inequalities from probability theory associated with the probabilities of convex sets have potential for characterizing…

## Figures from this paper

## 43 Citations

Kalman-like filtering with intermittent observations and non-Gaussian noise

- Computer ScienceIFAC-PapersOnLine
- 2019

Bayesian Inference for Linear Dynamic Models With Dirichlet Process Mixtures

- Computer ScienceIEEE Transactions on Signal Processing
- 2008

A flexible Bayesian nonparametric noise model based on Dirichlet process mixtures is introduced and efficient Markov chain Monte Carlo and sequential Monte Carlo methods are developed to perform optimal batch and sequential estimation in linear Gaussian state-space models.

Filtering of systems with nonlinear measurements with an application to target tracking

- Computer Science, MathematicsInternational Journal of Robust and Nonlinear Control
- 2019

This work provides two sufficient conditions for the application of the virtual measurement approach and shows its effectiveness in the case of the maneuvering target tracking problem.

Adaptive High-degree Cubature Kalman Filter with Unknown Noise Statistics ?

- Engineering
- 2014

This paper is concerned with the state estimation problem for nonlinear systems with unknown covariance of process noise. The advantages of recently developed High-degree Cubature Kalman Filter…

Bayesian Inference for Dynamic Models with Dirichlet Process Mixtures

- Computer Science, Mathematics2006 9th International Conference on Information Fusion
- 2006

A flexible Bayesian nonparametric noise model based on mixture of Dirichlet processes is introduced and efficient Markov chain Monte Carlo and sequential Monte Carlo methods are developed to perform optimal estimation in linear Gaussian state-space models.

Reduced-Order Quadratic Kalman-Like Filtering of Non-Gaussian Systems

- Computer Science, MathematicsIEEE Transactions on Automatic Control
- 2013

This paper derives the suboptimal quadratic estimate of the state by means of a recursive algorithm, obtained by applying the Kalman filter to a suitably augmented system, which is fully observable.

A Modified Kalman Filter for Non-gaussian Measurement Noise

- Mathematics
- 2011

A novel modification is proposed to the Kalman filter for the case of non-Gaussian measurement noise that provides satisfactory results and a significant improvement in mean square error with the proposed scheme.

Confidence Analysis of Linear Unbiased Estimates under Uncertain Unimodal Noise Distributions

- MathematicsJournal of Computer and Systems Sciences International
- 2019

The estimation problem for a linear parametric function in a linear regression model with uncertain symmetric unimodal noise distributions and given noise covariances is solved. The quality of…

Worst-Case Prediction Performance Analysis of the Kalman Filter

- Computer ScienceIEEE Transactions on Automatic Control
- 2018

This paper studies the prediction performance of the Kalman filter in a worst case minimax setting and proves worst-case bounds on the cumulative squared prediction errors using a priori knowledge about the complexity of reference predictor sequence.

## References

SHOWING 1-10 OF 32 REFERENCES

Use of the Kalman filter for inference in state-space models with unknown noise distributions

- MathematicsProceedings of the 1997 American Control Conference (Cat. No.97CH36041)
- 1997

The Kalman filter is frequently used for state estimation in state-space models when the standard Gaussian noise assumption does not apply. A problem arises, however, in that inference based on the…

Use of the Kalman Filterfor Inference in State-Space Models with Unknown Noise Distributions

- Mathematics
- 1996

The Kantorovich inequality for error analysis of the Kalman filter with unknown noise distributions

- MathematicsAutom.
- 1995

Evaluation of convergence rate in the central limit theorem for the Kalman filter

- MathematicsIEEE Trans. Autom. Control.
- 1999

In this study, some convergence rates in the central limit theorem are given and are used for the development of a nonparametric test of the validity of the model.

Bayesian State Estimation for Tracking and Guidance Using the Bootstrap Filter

- Engineering
- 1995

A Monte Carlo simulation example of a bearings-only tracking problem is presented, and the performance of the bootstrap filter is compared with a standard Cartesian extended Kalman filter (EKF), a modified gain EKF, and a hybrid filter.

Uncertainties for recursive estimators in nonlinear state-space models, with applications to epidemiology

- Mathematics, Computer ScienceAutom.
- 1995

Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models

- Computer Science
- 1996

A new algorithm based on a Monte Carlo method that can be applied to a broad class of nonlinear non-Gaussian higher dimensional state space models on the provision that the dimensions of the system noise and the observation noise are relatively low.

A three-state Kalman tracker using position and rate measurements

- Physics
- 1993

A three-state Kalman tracker is described for tracking a moving target, such as an aircraft, making use of the position and rate measurements obtained by a track-white-scan radar sensor which employs…

On Gibbs sampling for state space models

- Computer Science
- 1994

SUMMARY We show how to use the Gibbs sampler to carry out Bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time. Our…

A Monte Carlo Approach to Nonnormal and Nonlinear State-Space Modeling

- Mathematics
- 1992

Abstract A solution to multivariate state-space modeling, forecasting, and smoothing is discussed. We allow for the possibilities of nonnormal errors and nonlinear functionals in the state equation,…