scholarly journals Unscented Filtering from Delayed Observations with Correlated Noises

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
A. Hermoso-Carazo ◽  
J. Linares-Pérez
Keyword(s):  
Nonlinear System ◽  
Random Variables ◽  
Sampling Time ◽  
The State ◽  
Unscented Transformation ◽  
Filtering Algorithm ◽  
Bernoulli Random Variables ◽  
Noisy Measurements ◽  
Correlated Noises

A filtering algorithm based on the unscented transformation is proposed to estimate the state of a nonlinear system from noisy measurements which can be randomly delayed by one sampling time. The state and observation noises are perturbed by correlated nonadditive noises, and the delay is modeled by independent Bernoulli random variables.

scholarly journals A Robust Recursive Filter for Nonlinear Systems with Correlated Noises, Packet Losses, and Multiplicative Noises

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Hua-Ming Qian ◽  
Wei Huang ◽  
Biao Liu ◽  
Chen Shen
Keyword(s):  
Nonlinear Systems ◽  
Random Variables ◽  
Robust Filtering ◽  
Packet Losses ◽  
Recursive Filter ◽  
Bernoulli Random Variables ◽  
Multiplicative Noises ◽  
Measurement Noises ◽  
Correlated Noises ◽  
Filtering Problem

A robust filtering problem is formulated and investigated for a class of nonlinear systems with correlated noises, packet losses, and multiplicative noises. The packet losses are assumed to be independent Bernoulli random variables. The multiplicative noises are described as random variables with bounded variance. Different from the traditional robust filter based on the assumption that the process noises are uncorrelated with the measurement noises, the objective of the addressed robust filtering problem is to design a recursive filter such that, for packet losses and multiplicative noises, the state prediction and filtering covariance matrices have the optimized upper bounds in the case that there are correlated process and measurement noises. Two examples are used to illustrate the effectiveness of the proposed filter.

On improvements of the order of approximation in the Poisson limit theorem

1996 ◽  
Vol 33 (01) ◽  
pp. 146-155 ◽  
Author(s):  
K. Borovkov ◽  
D. Pfeifer
Keyword(s):  
Limit Theorem ◽  
Random Variables ◽  
Poisson Approximation ◽  
Order Of Approximation ◽  
Operator Semigroups ◽  
Bernoulli Random Variables ◽  
Usual Rate ◽  
Poisson Limit ◽  
Poisson Measures ◽  
Special Case

In this paper we consider improvements in the rate of approximation for the distribution of sums of independent Bernoulli random variables via convolutions of Poisson measures with signed measures of specific type. As a special case, the distribution of the number of records in an i.i.d. sequence of length n is investigated. For this particular example, it is shown that the usual rate of Poisson approximation of O(1/log n) can be lowered to O(1/n 2). The general case is discussed in terms of operator semigroups.

scholarly journals Distribution of Geometrically Weighted Sum of Bernoulli Random Variables

2011 ◽  
Vol 02 (11) ◽  
pp. 1382-1386 ◽  
Author(s):  
Deepesh Bhati ◽  
Phazamile Kgosi ◽  
Ranganath Narayanacharya Rattihalli
Keyword(s):  
Random Variables ◽  
Weighted Sum ◽  
Bernoulli Random Variables

Comparing sums of exchangeable Bernoulli random variables

1996 ◽  
Vol 33 (02) ◽  
pp. 285-310 ◽  
Author(s):  
Claude Lefèvre ◽  
Sergey Utev
Keyword(s):  
Iterative Procedure ◽  
First Passage Time ◽  
Random Variables ◽  
Passage Time ◽  
Partial Sums ◽  
First Passage ◽  
Sampling Schemes ◽  
Bernoulli Random Variables ◽  
Discrete Random Variables ◽  
Comparison Results

The paper is first concerned with a comparison of the partial sums associated with two sequences of n exchangeable Bernoulli random variables. It then considers a situation where such partial sums are obtained through an iterative procedure of branching type stopped at the first-passage time in a linearly decreasing upper barrier. These comparison results are illustrated with applications to certain urn models, sampling schemes and epidemic processes. A key tool is a non-standard hierarchical class of stochastic orderings between discrete random variables valued in {0, 1,· ··, n}.

Sign in / Sign up

Export Citation Format

Share Document