# Pearson chi^2-divergence Approach to Gaussian Mixture Reduction and its Application to Gaussian-sum Filter and Smoother

@article{Kitagawa2020PearsonCA, title={Pearson chi^2-divergence Approach to Gaussian Mixture Reduction and its Application to Gaussian-sum Filter and Smoother}, author={Genshiro Kitagawa}, journal={arXiv: Methodology}, year={2020} }

The Gaussian mixture distribution is important in various statistical problems. In particular it is used in the Gaussian-sum filter and smoother for linear state-space model with non-Gaussian noise inputs. However, for this method to be practical, an efficient method of reducing the number of Gaussian components is necessary. In this paper, we show that a closed form expression of Pearson chi^2-divergence can be obtained and it can apply to the determination of the pair of two Gaussian… Expand

#### Figures and Tables from this paper

#### References

SHOWING 1-10 OF 13 REFERENCES

The two-filter formula for smoothing and an implementation of the Gaussian-sum smoother

- Mathematics
- 1994

A Gaussian-sum smoother is developed based on the two filter formula for smoothing. This facilitates the application of non-Gaussian state space modeling to diverse problems in time series analysis.… Expand

Nonlinear Bayesian estimation using Gaussian sum approximations

- Mathematics
- 1972

Knowledge of the probability density function of the state conditioned on all available measurement data provides the most complete possible description of the state, and from this density any of the… Expand

Recursive bayesian estimation using gaussian sums

- Mathematics
- 1971

The Bayesian recursion relations which describe the behavior of the a posteriori probability density function of the state of a time-discrete stochastic system conditioned on available measurement… Expand

A look at Gaussian mixture reduction algorithms

- Computer Science, Mathematics
- 14th International Conference on Information Fusion
- 2011

A brute-force approach to mixture reduction that can be used as a basis for comparison against other algorithms on small problems is derived and used in a number of different domains. Expand

Kullback-Leibler Approach to Gaussian Mixture Reduction

- Engineering
- IEEE Transactions on Aerospace and Electronic Systems
- 2007

A common problem in multi-target tracking is to approximate a Gaussian mixture by one containing fewer components; similar problems can arise in integrated navigation. A common approach is… Expand

Mixture reduction algorithms for target tracking in clutter

- Mathematics, Computer Science
- 1990

In this paper, two new algorithms for reducing Gaussian mixture distributions are presented, which preserve the mean and covariance of the mixture, and the fmal approximation is itself aGaussian mixture. Expand

Mixture reduction algorithms for target tracking in clutter

- Engineering, Computer Science
- Defense + Commercial Sensing
- 1990

The performance of the most economical of these algorithms has been compared with that of the PDAF for the problem of tracking a single target which moves in a plane according to a second order model. Expand

Non-Gaussian seasonal adjustment

- Mathematics
- 1989

Abstract A non-Gaussian state space modeling of time series with trend and seasonality is shown. An observed time series is decomposed into trend, seasonal and observational noise. Each component is… Expand

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

- Mathematics
- 1996

Abstract A new algorithm for the prediction, filtering, and smoothing of non-Gaussian nonlinear state space models is shown. The algorithm is based on a Monte Carlo method in which successive… Expand

Cost-function-based gaussian mixture reduction for target tracking

- Computer Science
- Sixth International Conference of Information Fusion, 2003. Proceedings of the
- 2003

A structured cost-function- based approach to the hypothesis control problem is proposed, utilising the newly defined Integral Square Difference (ISD) cost measure, and it is shown that the ISD algorithm outperforms the joining filter remark- ably, yielding an average track life more than double that achievable using the joiningfilter. Expand