# Novel approach to nonlinear/non-Gaussian Bayesian state estimation

@inproceedings{Gordon1993NovelAT, title={Novel approach to nonlinear/non-Gaussian Bayesian state estimation}, author={Neil J. Gordon and David Salmond and Adrian F. M. Smith}, year={1993} }

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, which are updated and propagated by the algorithm. The method is not restricted by assumptions of linear- ity or Gaussian noise: it may be applied to any state transition or measurement model. A simula- tion example of the bearings only tracking problem is presented. This simulation includes schemes for improving the…

## 8,170 Citations

### Development and numerical investigation of new non-linear Kalman filter variants

- Engineering, Mathematics
- 2011

This study deals with recursive state estimation for non-linear systems. A new set of σ-points for the unscented Kalman filter is proposed as well as a way to substitute a non-linear output with a…

### The Kalman Laplace filter: A new deterministic algorithm for nonlinear Bayesian filtering

- Computer Science2015 18th International Conference on Information Fusion (Fusion)
- 2015

A new recursive algorithm for nonlinear Bayesian filtering, where the prediction step is performed like in the extended Kalman filter, and the update step is done thanks to the Laplace method for integral approximation, called the Kalman Laplace filter (KLF).

### Fundamental Filtering Limitations in Linear Non-Gaussian Systems

- Engineering
- 2004

The Kalman filter is known to be the optimal linear filter for linear non-Gaussian systems. However, nonlinear filters such as Kalman filter banks and more recent numerical methods such as the…

### Comparison of standard and modified recursive state estimation techniques for nonlinear systems

- Engineering2009 17th Mediterranean Conference on Control and Automation
- 2009

A new set of σ-points for the Unscented Kalman Filter is proposed as well as a way to substitute a nonlinear output with a linear one and the results show that the modifications proposed in some cases lead to considerable reduction in estimation error.

### Gaussian particle filtering

- Computer Science, EngineeringProceedings of the 11th IEEE Signal Processing Workshop on Statistical Signal Processing (Cat. No.01TH8563)
- 2001

The Gaussian particle filter (GPF) is introduced, where densities are approximated as a single Gaussian, an assumption which is also made in the extended Kalman filter (EKF), and analytically shown that it minimizes the mean square error of the estimates asymptotically.

### Bayesian state estimation using generalized coordinates

- EngineeringDefense + Commercial Sensing
- 2011

A pedagogical review of the theoretical formulation of the continuous-discrete Bayesian nonlinear state estimation problem is presented, with an emphasis on concepts that are not as widely known in the filtering literature.

### Bayesian Filtering Techniques: Kalman and Extended

- Computer Science
- 2009

Bayesian filters provide a statistical tool for deal- ing with measurement uncertainty by representing the state by random variable and in each time step probability distribution over random variable rep- resents the uncertainty.

### Bayesian filtering techniques: Kalman and extended Kalman filter basics

- Computer Science2009 19th International Conference Radioelektronika
- 2009

Bayesian filters provide a statistical tool for dealing with measurement uncertainty by representing the state by random variable and in each time step probability distribution over random variable represents the uncertainty.

### Sequential Bayesian Inference for Dynamic State Space Model Parameters

- Computer Science
- 2013

Simulation studies show that the method provides a good trade off between computation speed and accuracy, relative to the integrated nested Laplace approximation and a particle filter, in examples of both non-linear and non-Gaussian models.

## 17 References

### Approximate non-Gaussian filtering with linear state and observation relations

- Engineering
- 1975

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…

### A Bayesian approach to problems in stochastic estimation and control

- Mathematics
- 1964

In this paper, a general class of stochastic estimation and control problems is formulated from the Bayesian Decision-Theoretic viewpoint. A discussion as to how these problems can be solved step by…

### Nonlinear Bayesian estimation using Gaussian sum approximations

- Computer Science
- 1972

In this paper an approximation that permits the explicit calculation of the a posteriori density from the Bayesian recursion relations is discussed and applied to the solution of the nonlinear filtering problem.

### 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,…

### Dynamic Generalized Linear Models and Bayesian Forecasting

- Computer Science, Mathematics
- 1985

The structure of the models depends on the time evolution of underlying state variables, and the feedback of observational information to these variables is achieved using linear Bayesian prediction methods.

### Utilization of modified polar coordinates for bearings-only tracking

- Engineering
- 1983

Previous studies have shown that the Cartesian coordinate extended Kalman filter exhibits unstable behavior characteristics when utilized for bearings-only target motion analysis (TMA). In contrast,…

### Stochastic Processes and Filtering Theory

- Mathematics
- 1970

This book presents a unified treatment of linear and nonlinear filtering theory for engineers, with sufficient emphasis on applications to enable the reader to use the theory. The need for this book…

### Bayesian statistics without tears: A sampling-resampling perspective

- Physics
- 1992

A straightforward sampling-resampling perspective on Bayesian inference is offered, which has both pedagogic appeal and suggests easily implemented calculation strategies.

### Density Estimation for Statistics and Data Analysis

- Computer Science
- 1986

The Kernel Method for Multivariate Data: Three Important Methods and Density Estimation in Action.