Name
Title | ||
|---|---|---|
A State-Space Calculus for Rational Probability Density Functions and Applications to Non-Gaussian Filtering |
Abstract | ||
|---|---|---|
We propose what we believe to be a novel approach to performing calculations for rational density functions using state-space representations of the densities. By standard results from realization theory, a rational probability density function is considered to be the transfer function of a linear system with generally complex entries. The stable part of this system is positive-real, which we call the density summand. The existence of moments is investigated using the Markov parameters of the density summand. Moreover, explicit formulae are given for the existing moments in terms of these Markov parameters. Some of the main contributions of the paper are explicit state-space descriptions for products and convolutions of rational densities.As an application which is of interest in its own right, the filtering problem is investigated for a linear time-varying system whose noise inputs have rational probability density functions. In particular, state-space formulations are derived for the calculation of the prediction and update equations. The case of Cauchy noise is treated as an illustrative example. |
Year | DOI | Venue |
|---|---|---|
2001 | 10.1137/S036301299731610X | SIAM J. Control and Optimization |
Keywords | Field | DocType |
markov parameter,rational density,non-gaussian filtering,rational probability density function,state-space calculus,state-space representation,state-space formulation,explicit state-space description,linear system,rational density function,density summand,rational probability density functions,linear time-varying system,probability density function,linear algebra,state space,rational functions,state space representation,probability theory,transfer function | Elliptic rational functions,Mathematical optimization,Linear system,Mathematical analysis,Markov chain,Filtering problem,Cauchy distribution,Probability theory,Rational function,Probability density function,Mathematics | Journal |
Volume | Issue | ISSN |
40 | 3 | 0363-0129 |
Citations | PageRank | References |
1 | 0.37 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bernard Hanzon | 1 | 49 | 9.54 |
| Raimund J Ober | 2 | 46 | 22.05 |