Optimal collapsing of mixture distributions in robust recursive estimation |
| |
Authors: | Daniel Peña Irwin Guttman |
| |
Institution: | 1. Universidad Politenica de Madrid , Jose Gutierrez Abaseal 2, Madrid, 28006, Spain;2. Department of Statistics , University of Toronto , Toronto, Ontario, M5S 1A1, Canada |
| |
Abstract: | Several authors have discussed Kalman filtering procedures using a mixture of normals as a model for the distributions of the noise in the observation and/or the state space equations. Under this model, resulting posteriors involve a mixture of normal distributions, and a “collapsing method” must be found in order to keep the recursive procedure simple. We prove that the Kullback-Leibler distance between the mixture posterior and that of a single normal distribution is minimized when we choose the mean and variance of the single normal distribution to be the mean and variance of the mixture posterior. Hence, “collapsing by moments” is optimal in this sense. We then develop the resulting optimal algorithm for “Kalman filtering” for this situation, and illustrate its performance with an example. |
| |
Keywords: | mixture noise distributions Kullback-Leibler distance robust Kalman filtering spurious observations posterior and predictive distributions |
|
|